David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1 | /* |
| 2 | * QEMU float support |
| 3 | * |
| 4 | * Derived from SoftFloat. |
| 5 | */ |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6 | |
| 7 | /*============================================================================ |
| 8 | |
| 9 | This C source file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic |
| 10 | Package, Release 2b. |
| 11 | |
| 12 | Written by John R. Hauser. This work was made possible in part by the |
| 13 | International Computer Science Institute, located at Suite 600, 1947 Center |
| 14 | Street, Berkeley, California 94704. Funding was partially provided by the |
| 15 | National Science Foundation under grant MIP-9311980. The original version |
| 16 | of this code was written as part of a project to build a fixed-point vector |
| 17 | processor in collaboration with the University of California at Berkeley, |
| 18 | overseen by Profs. Nelson Morgan and John Wawrzynek. More information |
| 19 | is available through the Web page `http://www.cs.berkeley.edu/~jhauser/ |
| 20 | arithmetic/SoftFloat.html'. |
| 21 | |
| 22 | THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has |
| 23 | been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES |
| 24 | RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS |
| 25 | AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES, |
| 26 | COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE |
| 27 | EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE |
| 28 | INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR |
| 29 | OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE. |
| 30 | |
| 31 | Derivative works are acceptable, even for commercial purposes, so long as |
| 32 | (1) the source code for the derivative work includes prominent notice that |
| 33 | the work is derivative, and (2) the source code includes prominent notice with |
| 34 | these four paragraphs for those parts of this code that are retained. |
| 35 | |
| 36 | =============================================================================*/ |
| 37 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 38 | /* softfloat (and in particular the code in softfloat-specialize.h) is |
| 39 | * target-dependent and needs the TARGET_* macros. |
| 40 | */ |
| 41 | #include "config.h" |
| 42 | |
David 'Digit' Turner | 5425d40 | 2013-12-15 00:28:46 +0100 | [diff] [blame] | 43 | #include "fpu/softfloat.h" |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 44 | |
| 45 | /*---------------------------------------------------------------------------- |
| 46 | | Primitive arithmetic functions, including multi-word arithmetic, and |
| 47 | | division and square root approximations. (Can be specialized to target if |
| 48 | | desired.) |
| 49 | *----------------------------------------------------------------------------*/ |
| 50 | #include "softfloat-macros.h" |
| 51 | |
| 52 | /*---------------------------------------------------------------------------- |
| 53 | | Functions and definitions to determine: (1) whether tininess for underflow |
| 54 | | is detected before or after rounding by default, (2) what (if anything) |
| 55 | | happens when exceptions are raised, (3) how signaling NaNs are distinguished |
| 56 | | from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs |
| 57 | | are propagated from function inputs to output. These details are target- |
| 58 | | specific. |
| 59 | *----------------------------------------------------------------------------*/ |
| 60 | #include "softfloat-specialize.h" |
| 61 | |
| 62 | void set_float_rounding_mode(int val STATUS_PARAM) |
| 63 | { |
| 64 | STATUS(float_rounding_mode) = val; |
| 65 | } |
| 66 | |
| 67 | void set_float_exception_flags(int val STATUS_PARAM) |
| 68 | { |
| 69 | STATUS(float_exception_flags) = val; |
| 70 | } |
| 71 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 72 | void set_floatx80_rounding_precision(int val STATUS_PARAM) |
| 73 | { |
| 74 | STATUS(floatx80_rounding_precision) = val; |
| 75 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 76 | |
| 77 | /*---------------------------------------------------------------------------- |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 78 | | Returns the fraction bits of the half-precision floating-point value `a'. |
| 79 | *----------------------------------------------------------------------------*/ |
| 80 | |
| 81 | INLINE uint32_t extractFloat16Frac(float16 a) |
| 82 | { |
| 83 | return float16_val(a) & 0x3ff; |
| 84 | } |
| 85 | |
| 86 | /*---------------------------------------------------------------------------- |
| 87 | | Returns the exponent bits of the half-precision floating-point value `a'. |
| 88 | *----------------------------------------------------------------------------*/ |
| 89 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 90 | INLINE int_fast16_t extractFloat16Exp(float16 a) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 91 | { |
| 92 | return (float16_val(a) >> 10) & 0x1f; |
| 93 | } |
| 94 | |
| 95 | /*---------------------------------------------------------------------------- |
| 96 | | Returns the sign bit of the single-precision floating-point value `a'. |
| 97 | *----------------------------------------------------------------------------*/ |
| 98 | |
| 99 | INLINE flag extractFloat16Sign(float16 a) |
| 100 | { |
| 101 | return float16_val(a)>>15; |
| 102 | } |
| 103 | |
| 104 | /*---------------------------------------------------------------------------- |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 105 | | Takes a 64-bit fixed-point value `absZ' with binary point between bits 6 |
| 106 | | and 7, and returns the properly rounded 32-bit integer corresponding to the |
| 107 | | input. If `zSign' is 1, the input is negated before being converted to an |
| 108 | | integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input |
| 109 | | is simply rounded to an integer, with the inexact exception raised if the |
| 110 | | input cannot be represented exactly as an integer. However, if the fixed- |
| 111 | | point input is too large, the invalid exception is raised and the largest |
| 112 | | positive or negative integer is returned. |
| 113 | *----------------------------------------------------------------------------*/ |
| 114 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 115 | static int32 roundAndPackInt32( flag zSign, uint64_t absZ STATUS_PARAM) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 116 | { |
| 117 | int8 roundingMode; |
| 118 | flag roundNearestEven; |
| 119 | int8 roundIncrement, roundBits; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 120 | int32_t z; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 121 | |
| 122 | roundingMode = STATUS(float_rounding_mode); |
| 123 | roundNearestEven = ( roundingMode == float_round_nearest_even ); |
| 124 | roundIncrement = 0x40; |
| 125 | if ( ! roundNearestEven ) { |
| 126 | if ( roundingMode == float_round_to_zero ) { |
| 127 | roundIncrement = 0; |
| 128 | } |
| 129 | else { |
| 130 | roundIncrement = 0x7F; |
| 131 | if ( zSign ) { |
| 132 | if ( roundingMode == float_round_up ) roundIncrement = 0; |
| 133 | } |
| 134 | else { |
| 135 | if ( roundingMode == float_round_down ) roundIncrement = 0; |
| 136 | } |
| 137 | } |
| 138 | } |
| 139 | roundBits = absZ & 0x7F; |
| 140 | absZ = ( absZ + roundIncrement )>>7; |
| 141 | absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); |
| 142 | z = absZ; |
| 143 | if ( zSign ) z = - z; |
| 144 | if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) { |
| 145 | float_raise( float_flag_invalid STATUS_VAR); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 146 | return zSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 147 | } |
| 148 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 149 | return z; |
| 150 | |
| 151 | } |
| 152 | |
| 153 | /*---------------------------------------------------------------------------- |
| 154 | | Takes the 128-bit fixed-point value formed by concatenating `absZ0' and |
| 155 | | `absZ1', with binary point between bits 63 and 64 (between the input words), |
| 156 | | and returns the properly rounded 64-bit integer corresponding to the input. |
| 157 | | If `zSign' is 1, the input is negated before being converted to an integer. |
| 158 | | Ordinarily, the fixed-point input is simply rounded to an integer, with |
| 159 | | the inexact exception raised if the input cannot be represented exactly as |
| 160 | | an integer. However, if the fixed-point input is too large, the invalid |
| 161 | | exception is raised and the largest positive or negative integer is |
| 162 | | returned. |
| 163 | *----------------------------------------------------------------------------*/ |
| 164 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 165 | static int64 roundAndPackInt64( flag zSign, uint64_t absZ0, uint64_t absZ1 STATUS_PARAM) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 166 | { |
| 167 | int8 roundingMode; |
| 168 | flag roundNearestEven, increment; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 169 | int64_t z; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 170 | |
| 171 | roundingMode = STATUS(float_rounding_mode); |
| 172 | roundNearestEven = ( roundingMode == float_round_nearest_even ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 173 | increment = ( (int64_t) absZ1 < 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 174 | if ( ! roundNearestEven ) { |
| 175 | if ( roundingMode == float_round_to_zero ) { |
| 176 | increment = 0; |
| 177 | } |
| 178 | else { |
| 179 | if ( zSign ) { |
| 180 | increment = ( roundingMode == float_round_down ) && absZ1; |
| 181 | } |
| 182 | else { |
| 183 | increment = ( roundingMode == float_round_up ) && absZ1; |
| 184 | } |
| 185 | } |
| 186 | } |
| 187 | if ( increment ) { |
| 188 | ++absZ0; |
| 189 | if ( absZ0 == 0 ) goto overflow; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 190 | absZ0 &= ~ ( ( (uint64_t) ( absZ1<<1 ) == 0 ) & roundNearestEven ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 191 | } |
| 192 | z = absZ0; |
| 193 | if ( zSign ) z = - z; |
| 194 | if ( z && ( ( z < 0 ) ^ zSign ) ) { |
| 195 | overflow: |
| 196 | float_raise( float_flag_invalid STATUS_VAR); |
| 197 | return |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 198 | zSign ? (int64_t) LIT64( 0x8000000000000000 ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 199 | : LIT64( 0x7FFFFFFFFFFFFFFF ); |
| 200 | } |
| 201 | if ( absZ1 ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 202 | return z; |
| 203 | |
| 204 | } |
| 205 | |
| 206 | /*---------------------------------------------------------------------------- |
| 207 | | Returns the fraction bits of the single-precision floating-point value `a'. |
| 208 | *----------------------------------------------------------------------------*/ |
| 209 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 210 | INLINE uint32_t extractFloat32Frac( float32 a ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 211 | { |
| 212 | |
| 213 | return float32_val(a) & 0x007FFFFF; |
| 214 | |
| 215 | } |
| 216 | |
| 217 | /*---------------------------------------------------------------------------- |
| 218 | | Returns the exponent bits of the single-precision floating-point value `a'. |
| 219 | *----------------------------------------------------------------------------*/ |
| 220 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 221 | INLINE int_fast16_t extractFloat32Exp(float32 a) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 222 | { |
| 223 | |
| 224 | return ( float32_val(a)>>23 ) & 0xFF; |
| 225 | |
| 226 | } |
| 227 | |
| 228 | /*---------------------------------------------------------------------------- |
| 229 | | Returns the sign bit of the single-precision floating-point value `a'. |
| 230 | *----------------------------------------------------------------------------*/ |
| 231 | |
| 232 | INLINE flag extractFloat32Sign( float32 a ) |
| 233 | { |
| 234 | |
| 235 | return float32_val(a)>>31; |
| 236 | |
| 237 | } |
| 238 | |
| 239 | /*---------------------------------------------------------------------------- |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 240 | | If `a' is denormal and we are in flush-to-zero mode then set the |
| 241 | | input-denormal exception and return zero. Otherwise just return the value. |
| 242 | *----------------------------------------------------------------------------*/ |
| 243 | static float32 float32_squash_input_denormal(float32 a STATUS_PARAM) |
| 244 | { |
| 245 | if (STATUS(flush_inputs_to_zero)) { |
| 246 | if (extractFloat32Exp(a) == 0 && extractFloat32Frac(a) != 0) { |
| 247 | float_raise(float_flag_input_denormal STATUS_VAR); |
| 248 | return make_float32(float32_val(a) & 0x80000000); |
| 249 | } |
| 250 | } |
| 251 | return a; |
| 252 | } |
| 253 | |
| 254 | /*---------------------------------------------------------------------------- |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 255 | | Normalizes the subnormal single-precision floating-point value represented |
| 256 | | by the denormalized significand `aSig'. The normalized exponent and |
| 257 | | significand are stored at the locations pointed to by `zExpPtr' and |
| 258 | | `zSigPtr', respectively. |
| 259 | *----------------------------------------------------------------------------*/ |
| 260 | |
| 261 | static void |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 262 | normalizeFloat32Subnormal(uint32_t aSig, int_fast16_t *zExpPtr, uint32_t *zSigPtr) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 263 | { |
| 264 | int8 shiftCount; |
| 265 | |
| 266 | shiftCount = countLeadingZeros32( aSig ) - 8; |
| 267 | *zSigPtr = aSig<<shiftCount; |
| 268 | *zExpPtr = 1 - shiftCount; |
| 269 | |
| 270 | } |
| 271 | |
| 272 | /*---------------------------------------------------------------------------- |
| 273 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a |
| 274 | | single-precision floating-point value, returning the result. After being |
| 275 | | shifted into the proper positions, the three fields are simply added |
| 276 | | together to form the result. This means that any integer portion of `zSig' |
| 277 | | will be added into the exponent. Since a properly normalized significand |
| 278 | | will have an integer portion equal to 1, the `zExp' input should be 1 less |
| 279 | | than the desired result exponent whenever `zSig' is a complete, normalized |
| 280 | | significand. |
| 281 | *----------------------------------------------------------------------------*/ |
| 282 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 283 | INLINE float32 packFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 284 | { |
| 285 | |
| 286 | return make_float32( |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 287 | ( ( (uint32_t) zSign )<<31 ) + ( ( (uint32_t) zExp )<<23 ) + zSig); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 288 | |
| 289 | } |
| 290 | |
| 291 | /*---------------------------------------------------------------------------- |
| 292 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', |
| 293 | | and significand `zSig', and returns the proper single-precision floating- |
| 294 | | point value corresponding to the abstract input. Ordinarily, the abstract |
| 295 | | value is simply rounded and packed into the single-precision format, with |
| 296 | | the inexact exception raised if the abstract input cannot be represented |
| 297 | | exactly. However, if the abstract value is too large, the overflow and |
| 298 | | inexact exceptions are raised and an infinity or maximal finite value is |
| 299 | | returned. If the abstract value is too small, the input value is rounded to |
| 300 | | a subnormal number, and the underflow and inexact exceptions are raised if |
| 301 | | the abstract input cannot be represented exactly as a subnormal single- |
| 302 | | precision floating-point number. |
| 303 | | The input significand `zSig' has its binary point between bits 30 |
| 304 | | and 29, which is 7 bits to the left of the usual location. This shifted |
| 305 | | significand must be normalized or smaller. If `zSig' is not normalized, |
| 306 | | `zExp' must be 0; in that case, the result returned is a subnormal number, |
| 307 | | and it must not require rounding. In the usual case that `zSig' is |
| 308 | | normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. |
| 309 | | The handling of underflow and overflow follows the IEC/IEEE Standard for |
| 310 | | Binary Floating-Point Arithmetic. |
| 311 | *----------------------------------------------------------------------------*/ |
| 312 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 313 | static float32 roundAndPackFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig STATUS_PARAM) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 314 | { |
| 315 | int8 roundingMode; |
| 316 | flag roundNearestEven; |
| 317 | int8 roundIncrement, roundBits; |
| 318 | flag isTiny; |
| 319 | |
| 320 | roundingMode = STATUS(float_rounding_mode); |
| 321 | roundNearestEven = ( roundingMode == float_round_nearest_even ); |
| 322 | roundIncrement = 0x40; |
| 323 | if ( ! roundNearestEven ) { |
| 324 | if ( roundingMode == float_round_to_zero ) { |
| 325 | roundIncrement = 0; |
| 326 | } |
| 327 | else { |
| 328 | roundIncrement = 0x7F; |
| 329 | if ( zSign ) { |
| 330 | if ( roundingMode == float_round_up ) roundIncrement = 0; |
| 331 | } |
| 332 | else { |
| 333 | if ( roundingMode == float_round_down ) roundIncrement = 0; |
| 334 | } |
| 335 | } |
| 336 | } |
| 337 | roundBits = zSig & 0x7F; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 338 | if ( 0xFD <= (uint16_t) zExp ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 339 | if ( ( 0xFD < zExp ) |
| 340 | || ( ( zExp == 0xFD ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 341 | && ( (int32_t) ( zSig + roundIncrement ) < 0 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 342 | ) { |
| 343 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
| 344 | return packFloat32( zSign, 0xFF, - ( roundIncrement == 0 )); |
| 345 | } |
| 346 | if ( zExp < 0 ) { |
David 'Digit' Turner | 5285864 | 2011-06-03 13:41:05 +0200 | [diff] [blame] | 347 | if (STATUS(flush_to_zero)) { |
| 348 | float_raise(float_flag_output_denormal STATUS_VAR); |
| 349 | return packFloat32(zSign, 0, 0); |
| 350 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 351 | isTiny = |
| 352 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
| 353 | || ( zExp < -1 ) |
| 354 | || ( zSig + roundIncrement < 0x80000000 ); |
| 355 | shift32RightJamming( zSig, - zExp, &zSig ); |
| 356 | zExp = 0; |
| 357 | roundBits = zSig & 0x7F; |
| 358 | if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); |
| 359 | } |
| 360 | } |
| 361 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 362 | zSig = ( zSig + roundIncrement )>>7; |
| 363 | zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); |
| 364 | if ( zSig == 0 ) zExp = 0; |
| 365 | return packFloat32( zSign, zExp, zSig ); |
| 366 | |
| 367 | } |
| 368 | |
| 369 | /*---------------------------------------------------------------------------- |
| 370 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', |
| 371 | | and significand `zSig', and returns the proper single-precision floating- |
| 372 | | point value corresponding to the abstract input. This routine is just like |
| 373 | | `roundAndPackFloat32' except that `zSig' does not have to be normalized. |
| 374 | | Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true'' |
| 375 | | floating-point exponent. |
| 376 | *----------------------------------------------------------------------------*/ |
| 377 | |
| 378 | static float32 |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 379 | normalizeRoundAndPackFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig STATUS_PARAM) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 380 | { |
| 381 | int8 shiftCount; |
| 382 | |
| 383 | shiftCount = countLeadingZeros32( zSig ) - 1; |
| 384 | return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR); |
| 385 | |
| 386 | } |
| 387 | |
| 388 | /*---------------------------------------------------------------------------- |
| 389 | | Returns the fraction bits of the double-precision floating-point value `a'. |
| 390 | *----------------------------------------------------------------------------*/ |
| 391 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 392 | INLINE uint64_t extractFloat64Frac( float64 a ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 393 | { |
| 394 | |
| 395 | return float64_val(a) & LIT64( 0x000FFFFFFFFFFFFF ); |
| 396 | |
| 397 | } |
| 398 | |
| 399 | /*---------------------------------------------------------------------------- |
| 400 | | Returns the exponent bits of the double-precision floating-point value `a'. |
| 401 | *----------------------------------------------------------------------------*/ |
| 402 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 403 | INLINE int_fast16_t extractFloat64Exp(float64 a) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 404 | { |
| 405 | |
| 406 | return ( float64_val(a)>>52 ) & 0x7FF; |
| 407 | |
| 408 | } |
| 409 | |
| 410 | /*---------------------------------------------------------------------------- |
| 411 | | Returns the sign bit of the double-precision floating-point value `a'. |
| 412 | *----------------------------------------------------------------------------*/ |
| 413 | |
| 414 | INLINE flag extractFloat64Sign( float64 a ) |
| 415 | { |
| 416 | |
| 417 | return float64_val(a)>>63; |
| 418 | |
| 419 | } |
| 420 | |
| 421 | /*---------------------------------------------------------------------------- |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 422 | | If `a' is denormal and we are in flush-to-zero mode then set the |
| 423 | | input-denormal exception and return zero. Otherwise just return the value. |
| 424 | *----------------------------------------------------------------------------*/ |
| 425 | static float64 float64_squash_input_denormal(float64 a STATUS_PARAM) |
| 426 | { |
| 427 | if (STATUS(flush_inputs_to_zero)) { |
| 428 | if (extractFloat64Exp(a) == 0 && extractFloat64Frac(a) != 0) { |
| 429 | float_raise(float_flag_input_denormal STATUS_VAR); |
| 430 | return make_float64(float64_val(a) & (1ULL << 63)); |
| 431 | } |
| 432 | } |
| 433 | return a; |
| 434 | } |
| 435 | |
| 436 | /*---------------------------------------------------------------------------- |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 437 | | Normalizes the subnormal double-precision floating-point value represented |
| 438 | | by the denormalized significand `aSig'. The normalized exponent and |
| 439 | | significand are stored at the locations pointed to by `zExpPtr' and |
| 440 | | `zSigPtr', respectively. |
| 441 | *----------------------------------------------------------------------------*/ |
| 442 | |
| 443 | static void |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 444 | normalizeFloat64Subnormal(uint64_t aSig, int_fast16_t *zExpPtr, uint64_t *zSigPtr) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 445 | { |
| 446 | int8 shiftCount; |
| 447 | |
| 448 | shiftCount = countLeadingZeros64( aSig ) - 11; |
| 449 | *zSigPtr = aSig<<shiftCount; |
| 450 | *zExpPtr = 1 - shiftCount; |
| 451 | |
| 452 | } |
| 453 | |
| 454 | /*---------------------------------------------------------------------------- |
| 455 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a |
| 456 | | double-precision floating-point value, returning the result. After being |
| 457 | | shifted into the proper positions, the three fields are simply added |
| 458 | | together to form the result. This means that any integer portion of `zSig' |
| 459 | | will be added into the exponent. Since a properly normalized significand |
| 460 | | will have an integer portion equal to 1, the `zExp' input should be 1 less |
| 461 | | than the desired result exponent whenever `zSig' is a complete, normalized |
| 462 | | significand. |
| 463 | *----------------------------------------------------------------------------*/ |
| 464 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 465 | INLINE float64 packFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 466 | { |
| 467 | |
| 468 | return make_float64( |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 469 | ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<52 ) + zSig); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 470 | |
| 471 | } |
| 472 | |
| 473 | /*---------------------------------------------------------------------------- |
| 474 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', |
| 475 | | and significand `zSig', and returns the proper double-precision floating- |
| 476 | | point value corresponding to the abstract input. Ordinarily, the abstract |
| 477 | | value is simply rounded and packed into the double-precision format, with |
| 478 | | the inexact exception raised if the abstract input cannot be represented |
| 479 | | exactly. However, if the abstract value is too large, the overflow and |
| 480 | | inexact exceptions are raised and an infinity or maximal finite value is |
| 481 | | returned. If the abstract value is too small, the input value is rounded |
| 482 | | to a subnormal number, and the underflow and inexact exceptions are raised |
| 483 | | if the abstract input cannot be represented exactly as a subnormal double- |
| 484 | | precision floating-point number. |
| 485 | | The input significand `zSig' has its binary point between bits 62 |
| 486 | | and 61, which is 10 bits to the left of the usual location. This shifted |
| 487 | | significand must be normalized or smaller. If `zSig' is not normalized, |
| 488 | | `zExp' must be 0; in that case, the result returned is a subnormal number, |
| 489 | | and it must not require rounding. In the usual case that `zSig' is |
| 490 | | normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. |
| 491 | | The handling of underflow and overflow follows the IEC/IEEE Standard for |
| 492 | | Binary Floating-Point Arithmetic. |
| 493 | *----------------------------------------------------------------------------*/ |
| 494 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 495 | static float64 roundAndPackFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig STATUS_PARAM) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 496 | { |
| 497 | int8 roundingMode; |
| 498 | flag roundNearestEven; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 499 | int_fast16_t roundIncrement, roundBits; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 500 | flag isTiny; |
| 501 | |
| 502 | roundingMode = STATUS(float_rounding_mode); |
| 503 | roundNearestEven = ( roundingMode == float_round_nearest_even ); |
| 504 | roundIncrement = 0x200; |
| 505 | if ( ! roundNearestEven ) { |
| 506 | if ( roundingMode == float_round_to_zero ) { |
| 507 | roundIncrement = 0; |
| 508 | } |
| 509 | else { |
| 510 | roundIncrement = 0x3FF; |
| 511 | if ( zSign ) { |
| 512 | if ( roundingMode == float_round_up ) roundIncrement = 0; |
| 513 | } |
| 514 | else { |
| 515 | if ( roundingMode == float_round_down ) roundIncrement = 0; |
| 516 | } |
| 517 | } |
| 518 | } |
| 519 | roundBits = zSig & 0x3FF; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 520 | if ( 0x7FD <= (uint16_t) zExp ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 521 | if ( ( 0x7FD < zExp ) |
| 522 | || ( ( zExp == 0x7FD ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 523 | && ( (int64_t) ( zSig + roundIncrement ) < 0 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 524 | ) { |
| 525 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
| 526 | return packFloat64( zSign, 0x7FF, - ( roundIncrement == 0 )); |
| 527 | } |
| 528 | if ( zExp < 0 ) { |
David 'Digit' Turner | 5285864 | 2011-06-03 13:41:05 +0200 | [diff] [blame] | 529 | if (STATUS(flush_to_zero)) { |
| 530 | float_raise(float_flag_output_denormal STATUS_VAR); |
| 531 | return packFloat64(zSign, 0, 0); |
| 532 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 533 | isTiny = |
| 534 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
| 535 | || ( zExp < -1 ) |
| 536 | || ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) ); |
| 537 | shift64RightJamming( zSig, - zExp, &zSig ); |
| 538 | zExp = 0; |
| 539 | roundBits = zSig & 0x3FF; |
| 540 | if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); |
| 541 | } |
| 542 | } |
| 543 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 544 | zSig = ( zSig + roundIncrement )>>10; |
| 545 | zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven ); |
| 546 | if ( zSig == 0 ) zExp = 0; |
| 547 | return packFloat64( zSign, zExp, zSig ); |
| 548 | |
| 549 | } |
| 550 | |
| 551 | /*---------------------------------------------------------------------------- |
| 552 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', |
| 553 | | and significand `zSig', and returns the proper double-precision floating- |
| 554 | | point value corresponding to the abstract input. This routine is just like |
| 555 | | `roundAndPackFloat64' except that `zSig' does not have to be normalized. |
| 556 | | Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true'' |
| 557 | | floating-point exponent. |
| 558 | *----------------------------------------------------------------------------*/ |
| 559 | |
| 560 | static float64 |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 561 | normalizeRoundAndPackFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig STATUS_PARAM) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 562 | { |
| 563 | int8 shiftCount; |
| 564 | |
| 565 | shiftCount = countLeadingZeros64( zSig ) - 1; |
| 566 | return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR); |
| 567 | |
| 568 | } |
| 569 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 570 | /*---------------------------------------------------------------------------- |
| 571 | | Returns the fraction bits of the extended double-precision floating-point |
| 572 | | value `a'. |
| 573 | *----------------------------------------------------------------------------*/ |
| 574 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 575 | INLINE uint64_t extractFloatx80Frac( floatx80 a ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 576 | { |
| 577 | |
| 578 | return a.low; |
| 579 | |
| 580 | } |
| 581 | |
| 582 | /*---------------------------------------------------------------------------- |
| 583 | | Returns the exponent bits of the extended double-precision floating-point |
| 584 | | value `a'. |
| 585 | *----------------------------------------------------------------------------*/ |
| 586 | |
| 587 | INLINE int32 extractFloatx80Exp( floatx80 a ) |
| 588 | { |
| 589 | |
| 590 | return a.high & 0x7FFF; |
| 591 | |
| 592 | } |
| 593 | |
| 594 | /*---------------------------------------------------------------------------- |
| 595 | | Returns the sign bit of the extended double-precision floating-point value |
| 596 | | `a'. |
| 597 | *----------------------------------------------------------------------------*/ |
| 598 | |
| 599 | INLINE flag extractFloatx80Sign( floatx80 a ) |
| 600 | { |
| 601 | |
| 602 | return a.high>>15; |
| 603 | |
| 604 | } |
| 605 | |
| 606 | /*---------------------------------------------------------------------------- |
| 607 | | Normalizes the subnormal extended double-precision floating-point value |
| 608 | | represented by the denormalized significand `aSig'. The normalized exponent |
| 609 | | and significand are stored at the locations pointed to by `zExpPtr' and |
| 610 | | `zSigPtr', respectively. |
| 611 | *----------------------------------------------------------------------------*/ |
| 612 | |
| 613 | static void |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 614 | normalizeFloatx80Subnormal( uint64_t aSig, int32 *zExpPtr, uint64_t *zSigPtr ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 615 | { |
| 616 | int8 shiftCount; |
| 617 | |
| 618 | shiftCount = countLeadingZeros64( aSig ); |
| 619 | *zSigPtr = aSig<<shiftCount; |
| 620 | *zExpPtr = 1 - shiftCount; |
| 621 | |
| 622 | } |
| 623 | |
| 624 | /*---------------------------------------------------------------------------- |
| 625 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into an |
| 626 | | extended double-precision floating-point value, returning the result. |
| 627 | *----------------------------------------------------------------------------*/ |
| 628 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 629 | INLINE floatx80 packFloatx80( flag zSign, int32 zExp, uint64_t zSig ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 630 | { |
| 631 | floatx80 z; |
| 632 | |
| 633 | z.low = zSig; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 634 | z.high = ( ( (uint16_t) zSign )<<15 ) + zExp; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 635 | return z; |
| 636 | |
| 637 | } |
| 638 | |
| 639 | /*---------------------------------------------------------------------------- |
| 640 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', |
| 641 | | and extended significand formed by the concatenation of `zSig0' and `zSig1', |
| 642 | | and returns the proper extended double-precision floating-point value |
| 643 | | corresponding to the abstract input. Ordinarily, the abstract value is |
| 644 | | rounded and packed into the extended double-precision format, with the |
| 645 | | inexact exception raised if the abstract input cannot be represented |
| 646 | | exactly. However, if the abstract value is too large, the overflow and |
| 647 | | inexact exceptions are raised and an infinity or maximal finite value is |
| 648 | | returned. If the abstract value is too small, the input value is rounded to |
| 649 | | a subnormal number, and the underflow and inexact exceptions are raised if |
| 650 | | the abstract input cannot be represented exactly as a subnormal extended |
| 651 | | double-precision floating-point number. |
| 652 | | If `roundingPrecision' is 32 or 64, the result is rounded to the same |
| 653 | | number of bits as single or double precision, respectively. Otherwise, the |
| 654 | | result is rounded to the full precision of the extended double-precision |
| 655 | | format. |
| 656 | | The input significand must be normalized or smaller. If the input |
| 657 | | significand is not normalized, `zExp' must be 0; in that case, the result |
| 658 | | returned is a subnormal number, and it must not require rounding. The |
| 659 | | handling of underflow and overflow follows the IEC/IEEE Standard for Binary |
| 660 | | Floating-Point Arithmetic. |
| 661 | *----------------------------------------------------------------------------*/ |
| 662 | |
| 663 | static floatx80 |
| 664 | roundAndPackFloatx80( |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 665 | int8 roundingPrecision, flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 666 | STATUS_PARAM) |
| 667 | { |
| 668 | int8 roundingMode; |
| 669 | flag roundNearestEven, increment, isTiny; |
| 670 | int64 roundIncrement, roundMask, roundBits; |
| 671 | |
| 672 | roundingMode = STATUS(float_rounding_mode); |
| 673 | roundNearestEven = ( roundingMode == float_round_nearest_even ); |
| 674 | if ( roundingPrecision == 80 ) goto precision80; |
| 675 | if ( roundingPrecision == 64 ) { |
| 676 | roundIncrement = LIT64( 0x0000000000000400 ); |
| 677 | roundMask = LIT64( 0x00000000000007FF ); |
| 678 | } |
| 679 | else if ( roundingPrecision == 32 ) { |
| 680 | roundIncrement = LIT64( 0x0000008000000000 ); |
| 681 | roundMask = LIT64( 0x000000FFFFFFFFFF ); |
| 682 | } |
| 683 | else { |
| 684 | goto precision80; |
| 685 | } |
| 686 | zSig0 |= ( zSig1 != 0 ); |
| 687 | if ( ! roundNearestEven ) { |
| 688 | if ( roundingMode == float_round_to_zero ) { |
| 689 | roundIncrement = 0; |
| 690 | } |
| 691 | else { |
| 692 | roundIncrement = roundMask; |
| 693 | if ( zSign ) { |
| 694 | if ( roundingMode == float_round_up ) roundIncrement = 0; |
| 695 | } |
| 696 | else { |
| 697 | if ( roundingMode == float_round_down ) roundIncrement = 0; |
| 698 | } |
| 699 | } |
| 700 | } |
| 701 | roundBits = zSig0 & roundMask; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 702 | if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 703 | if ( ( 0x7FFE < zExp ) |
| 704 | || ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) ) |
| 705 | ) { |
| 706 | goto overflow; |
| 707 | } |
| 708 | if ( zExp <= 0 ) { |
David 'Digit' Turner | 5285864 | 2011-06-03 13:41:05 +0200 | [diff] [blame] | 709 | if (STATUS(flush_to_zero)) { |
| 710 | float_raise(float_flag_output_denormal STATUS_VAR); |
| 711 | return packFloatx80(zSign, 0, 0); |
| 712 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 713 | isTiny = |
| 714 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
| 715 | || ( zExp < 0 ) |
| 716 | || ( zSig0 <= zSig0 + roundIncrement ); |
| 717 | shift64RightJamming( zSig0, 1 - zExp, &zSig0 ); |
| 718 | zExp = 0; |
| 719 | roundBits = zSig0 & roundMask; |
| 720 | if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); |
| 721 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 722 | zSig0 += roundIncrement; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 723 | if ( (int64_t) zSig0 < 0 ) zExp = 1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 724 | roundIncrement = roundMask + 1; |
| 725 | if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { |
| 726 | roundMask |= roundIncrement; |
| 727 | } |
| 728 | zSig0 &= ~ roundMask; |
| 729 | return packFloatx80( zSign, zExp, zSig0 ); |
| 730 | } |
| 731 | } |
| 732 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 733 | zSig0 += roundIncrement; |
| 734 | if ( zSig0 < roundIncrement ) { |
| 735 | ++zExp; |
| 736 | zSig0 = LIT64( 0x8000000000000000 ); |
| 737 | } |
| 738 | roundIncrement = roundMask + 1; |
| 739 | if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { |
| 740 | roundMask |= roundIncrement; |
| 741 | } |
| 742 | zSig0 &= ~ roundMask; |
| 743 | if ( zSig0 == 0 ) zExp = 0; |
| 744 | return packFloatx80( zSign, zExp, zSig0 ); |
| 745 | precision80: |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 746 | increment = ( (int64_t) zSig1 < 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 747 | if ( ! roundNearestEven ) { |
| 748 | if ( roundingMode == float_round_to_zero ) { |
| 749 | increment = 0; |
| 750 | } |
| 751 | else { |
| 752 | if ( zSign ) { |
| 753 | increment = ( roundingMode == float_round_down ) && zSig1; |
| 754 | } |
| 755 | else { |
| 756 | increment = ( roundingMode == float_round_up ) && zSig1; |
| 757 | } |
| 758 | } |
| 759 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 760 | if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 761 | if ( ( 0x7FFE < zExp ) |
| 762 | || ( ( zExp == 0x7FFE ) |
| 763 | && ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) ) |
| 764 | && increment |
| 765 | ) |
| 766 | ) { |
| 767 | roundMask = 0; |
| 768 | overflow: |
| 769 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
| 770 | if ( ( roundingMode == float_round_to_zero ) |
| 771 | || ( zSign && ( roundingMode == float_round_up ) ) |
| 772 | || ( ! zSign && ( roundingMode == float_round_down ) ) |
| 773 | ) { |
| 774 | return packFloatx80( zSign, 0x7FFE, ~ roundMask ); |
| 775 | } |
| 776 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
| 777 | } |
| 778 | if ( zExp <= 0 ) { |
| 779 | isTiny = |
| 780 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
| 781 | || ( zExp < 0 ) |
| 782 | || ! increment |
| 783 | || ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) ); |
| 784 | shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 ); |
| 785 | zExp = 0; |
| 786 | if ( isTiny && zSig1 ) float_raise( float_flag_underflow STATUS_VAR); |
| 787 | if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 788 | if ( roundNearestEven ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 789 | increment = ( (int64_t) zSig1 < 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 790 | } |
| 791 | else { |
| 792 | if ( zSign ) { |
| 793 | increment = ( roundingMode == float_round_down ) && zSig1; |
| 794 | } |
| 795 | else { |
| 796 | increment = ( roundingMode == float_round_up ) && zSig1; |
| 797 | } |
| 798 | } |
| 799 | if ( increment ) { |
| 800 | ++zSig0; |
| 801 | zSig0 &= |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 802 | ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven ); |
| 803 | if ( (int64_t) zSig0 < 0 ) zExp = 1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 804 | } |
| 805 | return packFloatx80( zSign, zExp, zSig0 ); |
| 806 | } |
| 807 | } |
| 808 | if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 809 | if ( increment ) { |
| 810 | ++zSig0; |
| 811 | if ( zSig0 == 0 ) { |
| 812 | ++zExp; |
| 813 | zSig0 = LIT64( 0x8000000000000000 ); |
| 814 | } |
| 815 | else { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 816 | zSig0 &= ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 817 | } |
| 818 | } |
| 819 | else { |
| 820 | if ( zSig0 == 0 ) zExp = 0; |
| 821 | } |
| 822 | return packFloatx80( zSign, zExp, zSig0 ); |
| 823 | |
| 824 | } |
| 825 | |
| 826 | /*---------------------------------------------------------------------------- |
| 827 | | Takes an abstract floating-point value having sign `zSign', exponent |
| 828 | | `zExp', and significand formed by the concatenation of `zSig0' and `zSig1', |
| 829 | | and returns the proper extended double-precision floating-point value |
| 830 | | corresponding to the abstract input. This routine is just like |
| 831 | | `roundAndPackFloatx80' except that the input significand does not have to be |
| 832 | | normalized. |
| 833 | *----------------------------------------------------------------------------*/ |
| 834 | |
| 835 | static floatx80 |
| 836 | normalizeRoundAndPackFloatx80( |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 837 | int8 roundingPrecision, flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 838 | STATUS_PARAM) |
| 839 | { |
| 840 | int8 shiftCount; |
| 841 | |
| 842 | if ( zSig0 == 0 ) { |
| 843 | zSig0 = zSig1; |
| 844 | zSig1 = 0; |
| 845 | zExp -= 64; |
| 846 | } |
| 847 | shiftCount = countLeadingZeros64( zSig0 ); |
| 848 | shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); |
| 849 | zExp -= shiftCount; |
| 850 | return |
| 851 | roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 STATUS_VAR); |
| 852 | |
| 853 | } |
| 854 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 855 | /*---------------------------------------------------------------------------- |
| 856 | | Returns the least-significant 64 fraction bits of the quadruple-precision |
| 857 | | floating-point value `a'. |
| 858 | *----------------------------------------------------------------------------*/ |
| 859 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 860 | INLINE uint64_t extractFloat128Frac1( float128 a ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 861 | { |
| 862 | |
| 863 | return a.low; |
| 864 | |
| 865 | } |
| 866 | |
| 867 | /*---------------------------------------------------------------------------- |
| 868 | | Returns the most-significant 48 fraction bits of the quadruple-precision |
| 869 | | floating-point value `a'. |
| 870 | *----------------------------------------------------------------------------*/ |
| 871 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 872 | INLINE uint64_t extractFloat128Frac0( float128 a ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 873 | { |
| 874 | |
| 875 | return a.high & LIT64( 0x0000FFFFFFFFFFFF ); |
| 876 | |
| 877 | } |
| 878 | |
| 879 | /*---------------------------------------------------------------------------- |
| 880 | | Returns the exponent bits of the quadruple-precision floating-point value |
| 881 | | `a'. |
| 882 | *----------------------------------------------------------------------------*/ |
| 883 | |
| 884 | INLINE int32 extractFloat128Exp( float128 a ) |
| 885 | { |
| 886 | |
| 887 | return ( a.high>>48 ) & 0x7FFF; |
| 888 | |
| 889 | } |
| 890 | |
| 891 | /*---------------------------------------------------------------------------- |
| 892 | | Returns the sign bit of the quadruple-precision floating-point value `a'. |
| 893 | *----------------------------------------------------------------------------*/ |
| 894 | |
| 895 | INLINE flag extractFloat128Sign( float128 a ) |
| 896 | { |
| 897 | |
| 898 | return a.high>>63; |
| 899 | |
| 900 | } |
| 901 | |
| 902 | /*---------------------------------------------------------------------------- |
| 903 | | Normalizes the subnormal quadruple-precision floating-point value |
| 904 | | represented by the denormalized significand formed by the concatenation of |
| 905 | | `aSig0' and `aSig1'. The normalized exponent is stored at the location |
| 906 | | pointed to by `zExpPtr'. The most significant 49 bits of the normalized |
| 907 | | significand are stored at the location pointed to by `zSig0Ptr', and the |
| 908 | | least significant 64 bits of the normalized significand are stored at the |
| 909 | | location pointed to by `zSig1Ptr'. |
| 910 | *----------------------------------------------------------------------------*/ |
| 911 | |
| 912 | static void |
| 913 | normalizeFloat128Subnormal( |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 914 | uint64_t aSig0, |
| 915 | uint64_t aSig1, |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 916 | int32 *zExpPtr, |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 917 | uint64_t *zSig0Ptr, |
| 918 | uint64_t *zSig1Ptr |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 919 | ) |
| 920 | { |
| 921 | int8 shiftCount; |
| 922 | |
| 923 | if ( aSig0 == 0 ) { |
| 924 | shiftCount = countLeadingZeros64( aSig1 ) - 15; |
| 925 | if ( shiftCount < 0 ) { |
| 926 | *zSig0Ptr = aSig1>>( - shiftCount ); |
| 927 | *zSig1Ptr = aSig1<<( shiftCount & 63 ); |
| 928 | } |
| 929 | else { |
| 930 | *zSig0Ptr = aSig1<<shiftCount; |
| 931 | *zSig1Ptr = 0; |
| 932 | } |
| 933 | *zExpPtr = - shiftCount - 63; |
| 934 | } |
| 935 | else { |
| 936 | shiftCount = countLeadingZeros64( aSig0 ) - 15; |
| 937 | shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr ); |
| 938 | *zExpPtr = 1 - shiftCount; |
| 939 | } |
| 940 | |
| 941 | } |
| 942 | |
| 943 | /*---------------------------------------------------------------------------- |
| 944 | | Packs the sign `zSign', the exponent `zExp', and the significand formed |
| 945 | | by the concatenation of `zSig0' and `zSig1' into a quadruple-precision |
| 946 | | floating-point value, returning the result. After being shifted into the |
| 947 | | proper positions, the three fields `zSign', `zExp', and `zSig0' are simply |
| 948 | | added together to form the most significant 32 bits of the result. This |
| 949 | | means that any integer portion of `zSig0' will be added into the exponent. |
| 950 | | Since a properly normalized significand will have an integer portion equal |
| 951 | | to 1, the `zExp' input should be 1 less than the desired result exponent |
| 952 | | whenever `zSig0' and `zSig1' concatenated form a complete, normalized |
| 953 | | significand. |
| 954 | *----------------------------------------------------------------------------*/ |
| 955 | |
| 956 | INLINE float128 |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 957 | packFloat128( flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 958 | { |
| 959 | float128 z; |
| 960 | |
| 961 | z.low = zSig1; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 962 | z.high = ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<48 ) + zSig0; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 963 | return z; |
| 964 | |
| 965 | } |
| 966 | |
| 967 | /*---------------------------------------------------------------------------- |
| 968 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', |
| 969 | | and extended significand formed by the concatenation of `zSig0', `zSig1', |
| 970 | | and `zSig2', and returns the proper quadruple-precision floating-point value |
| 971 | | corresponding to the abstract input. Ordinarily, the abstract value is |
| 972 | | simply rounded and packed into the quadruple-precision format, with the |
| 973 | | inexact exception raised if the abstract input cannot be represented |
| 974 | | exactly. However, if the abstract value is too large, the overflow and |
| 975 | | inexact exceptions are raised and an infinity or maximal finite value is |
| 976 | | returned. If the abstract value is too small, the input value is rounded to |
| 977 | | a subnormal number, and the underflow and inexact exceptions are raised if |
| 978 | | the abstract input cannot be represented exactly as a subnormal quadruple- |
| 979 | | precision floating-point number. |
| 980 | | The input significand must be normalized or smaller. If the input |
| 981 | | significand is not normalized, `zExp' must be 0; in that case, the result |
| 982 | | returned is a subnormal number, and it must not require rounding. In the |
| 983 | | usual case that the input significand is normalized, `zExp' must be 1 less |
| 984 | | than the ``true'' floating-point exponent. The handling of underflow and |
| 985 | | overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 986 | *----------------------------------------------------------------------------*/ |
| 987 | |
| 988 | static float128 |
| 989 | roundAndPackFloat128( |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 990 | flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1, uint64_t zSig2 STATUS_PARAM) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 991 | { |
| 992 | int8 roundingMode; |
| 993 | flag roundNearestEven, increment, isTiny; |
| 994 | |
| 995 | roundingMode = STATUS(float_rounding_mode); |
| 996 | roundNearestEven = ( roundingMode == float_round_nearest_even ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 997 | increment = ( (int64_t) zSig2 < 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 998 | if ( ! roundNearestEven ) { |
| 999 | if ( roundingMode == float_round_to_zero ) { |
| 1000 | increment = 0; |
| 1001 | } |
| 1002 | else { |
| 1003 | if ( zSign ) { |
| 1004 | increment = ( roundingMode == float_round_down ) && zSig2; |
| 1005 | } |
| 1006 | else { |
| 1007 | increment = ( roundingMode == float_round_up ) && zSig2; |
| 1008 | } |
| 1009 | } |
| 1010 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1011 | if ( 0x7FFD <= (uint32_t) zExp ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1012 | if ( ( 0x7FFD < zExp ) |
| 1013 | || ( ( zExp == 0x7FFD ) |
| 1014 | && eq128( |
| 1015 | LIT64( 0x0001FFFFFFFFFFFF ), |
| 1016 | LIT64( 0xFFFFFFFFFFFFFFFF ), |
| 1017 | zSig0, |
| 1018 | zSig1 |
| 1019 | ) |
| 1020 | && increment |
| 1021 | ) |
| 1022 | ) { |
| 1023 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
| 1024 | if ( ( roundingMode == float_round_to_zero ) |
| 1025 | || ( zSign && ( roundingMode == float_round_up ) ) |
| 1026 | || ( ! zSign && ( roundingMode == float_round_down ) ) |
| 1027 | ) { |
| 1028 | return |
| 1029 | packFloat128( |
| 1030 | zSign, |
| 1031 | 0x7FFE, |
| 1032 | LIT64( 0x0000FFFFFFFFFFFF ), |
| 1033 | LIT64( 0xFFFFFFFFFFFFFFFF ) |
| 1034 | ); |
| 1035 | } |
| 1036 | return packFloat128( zSign, 0x7FFF, 0, 0 ); |
| 1037 | } |
| 1038 | if ( zExp < 0 ) { |
David 'Digit' Turner | 5285864 | 2011-06-03 13:41:05 +0200 | [diff] [blame] | 1039 | if (STATUS(flush_to_zero)) { |
| 1040 | float_raise(float_flag_output_denormal STATUS_VAR); |
| 1041 | return packFloat128(zSign, 0, 0, 0); |
| 1042 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1043 | isTiny = |
| 1044 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
| 1045 | || ( zExp < -1 ) |
| 1046 | || ! increment |
| 1047 | || lt128( |
| 1048 | zSig0, |
| 1049 | zSig1, |
| 1050 | LIT64( 0x0001FFFFFFFFFFFF ), |
| 1051 | LIT64( 0xFFFFFFFFFFFFFFFF ) |
| 1052 | ); |
| 1053 | shift128ExtraRightJamming( |
| 1054 | zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 ); |
| 1055 | zExp = 0; |
| 1056 | if ( isTiny && zSig2 ) float_raise( float_flag_underflow STATUS_VAR); |
| 1057 | if ( roundNearestEven ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1058 | increment = ( (int64_t) zSig2 < 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1059 | } |
| 1060 | else { |
| 1061 | if ( zSign ) { |
| 1062 | increment = ( roundingMode == float_round_down ) && zSig2; |
| 1063 | } |
| 1064 | else { |
| 1065 | increment = ( roundingMode == float_round_up ) && zSig2; |
| 1066 | } |
| 1067 | } |
| 1068 | } |
| 1069 | } |
| 1070 | if ( zSig2 ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 1071 | if ( increment ) { |
| 1072 | add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 ); |
| 1073 | zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven ); |
| 1074 | } |
| 1075 | else { |
| 1076 | if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0; |
| 1077 | } |
| 1078 | return packFloat128( zSign, zExp, zSig0, zSig1 ); |
| 1079 | |
| 1080 | } |
| 1081 | |
| 1082 | /*---------------------------------------------------------------------------- |
| 1083 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', |
| 1084 | | and significand formed by the concatenation of `zSig0' and `zSig1', and |
| 1085 | | returns the proper quadruple-precision floating-point value corresponding |
| 1086 | | to the abstract input. This routine is just like `roundAndPackFloat128' |
| 1087 | | except that the input significand has fewer bits and does not have to be |
| 1088 | | normalized. In all cases, `zExp' must be 1 less than the ``true'' floating- |
| 1089 | | point exponent. |
| 1090 | *----------------------------------------------------------------------------*/ |
| 1091 | |
| 1092 | static float128 |
| 1093 | normalizeRoundAndPackFloat128( |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1094 | flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 STATUS_PARAM) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1095 | { |
| 1096 | int8 shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1097 | uint64_t zSig2; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1098 | |
| 1099 | if ( zSig0 == 0 ) { |
| 1100 | zSig0 = zSig1; |
| 1101 | zSig1 = 0; |
| 1102 | zExp -= 64; |
| 1103 | } |
| 1104 | shiftCount = countLeadingZeros64( zSig0 ) - 15; |
| 1105 | if ( 0 <= shiftCount ) { |
| 1106 | zSig2 = 0; |
| 1107 | shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); |
| 1108 | } |
| 1109 | else { |
| 1110 | shift128ExtraRightJamming( |
| 1111 | zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 ); |
| 1112 | } |
| 1113 | zExp -= shiftCount; |
| 1114 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR); |
| 1115 | |
| 1116 | } |
| 1117 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1118 | /*---------------------------------------------------------------------------- |
| 1119 | | Returns the result of converting the 32-bit two's complement integer `a' |
| 1120 | | to the single-precision floating-point format. The conversion is performed |
| 1121 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 1122 | *----------------------------------------------------------------------------*/ |
| 1123 | |
| 1124 | float32 int32_to_float32( int32 a STATUS_PARAM ) |
| 1125 | { |
| 1126 | flag zSign; |
| 1127 | |
| 1128 | if ( a == 0 ) return float32_zero; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1129 | if ( a == (int32_t) 0x80000000 ) return packFloat32( 1, 0x9E, 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1130 | zSign = ( a < 0 ); |
| 1131 | return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a STATUS_VAR ); |
| 1132 | |
| 1133 | } |
| 1134 | |
| 1135 | /*---------------------------------------------------------------------------- |
| 1136 | | Returns the result of converting the 32-bit two's complement integer `a' |
| 1137 | | to the double-precision floating-point format. The conversion is performed |
| 1138 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 1139 | *----------------------------------------------------------------------------*/ |
| 1140 | |
| 1141 | float64 int32_to_float64( int32 a STATUS_PARAM ) |
| 1142 | { |
| 1143 | flag zSign; |
| 1144 | uint32 absA; |
| 1145 | int8 shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1146 | uint64_t zSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1147 | |
| 1148 | if ( a == 0 ) return float64_zero; |
| 1149 | zSign = ( a < 0 ); |
| 1150 | absA = zSign ? - a : a; |
| 1151 | shiftCount = countLeadingZeros32( absA ) + 21; |
| 1152 | zSig = absA; |
| 1153 | return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount ); |
| 1154 | |
| 1155 | } |
| 1156 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1157 | /*---------------------------------------------------------------------------- |
| 1158 | | Returns the result of converting the 32-bit two's complement integer `a' |
| 1159 | | to the extended double-precision floating-point format. The conversion |
| 1160 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 1161 | | Arithmetic. |
| 1162 | *----------------------------------------------------------------------------*/ |
| 1163 | |
| 1164 | floatx80 int32_to_floatx80( int32 a STATUS_PARAM ) |
| 1165 | { |
| 1166 | flag zSign; |
| 1167 | uint32 absA; |
| 1168 | int8 shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1169 | uint64_t zSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1170 | |
| 1171 | if ( a == 0 ) return packFloatx80( 0, 0, 0 ); |
| 1172 | zSign = ( a < 0 ); |
| 1173 | absA = zSign ? - a : a; |
| 1174 | shiftCount = countLeadingZeros32( absA ) + 32; |
| 1175 | zSig = absA; |
| 1176 | return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount ); |
| 1177 | |
| 1178 | } |
| 1179 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1180 | /*---------------------------------------------------------------------------- |
| 1181 | | Returns the result of converting the 32-bit two's complement integer `a' to |
| 1182 | | the quadruple-precision floating-point format. The conversion is performed |
| 1183 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 1184 | *----------------------------------------------------------------------------*/ |
| 1185 | |
| 1186 | float128 int32_to_float128( int32 a STATUS_PARAM ) |
| 1187 | { |
| 1188 | flag zSign; |
| 1189 | uint32 absA; |
| 1190 | int8 shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1191 | uint64_t zSig0; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1192 | |
| 1193 | if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); |
| 1194 | zSign = ( a < 0 ); |
| 1195 | absA = zSign ? - a : a; |
| 1196 | shiftCount = countLeadingZeros32( absA ) + 17; |
| 1197 | zSig0 = absA; |
| 1198 | return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 ); |
| 1199 | |
| 1200 | } |
| 1201 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1202 | /*---------------------------------------------------------------------------- |
| 1203 | | Returns the result of converting the 64-bit two's complement integer `a' |
| 1204 | | to the single-precision floating-point format. The conversion is performed |
| 1205 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 1206 | *----------------------------------------------------------------------------*/ |
| 1207 | |
| 1208 | float32 int64_to_float32( int64 a STATUS_PARAM ) |
| 1209 | { |
| 1210 | flag zSign; |
| 1211 | uint64 absA; |
| 1212 | int8 shiftCount; |
| 1213 | |
| 1214 | if ( a == 0 ) return float32_zero; |
| 1215 | zSign = ( a < 0 ); |
| 1216 | absA = zSign ? - a : a; |
| 1217 | shiftCount = countLeadingZeros64( absA ) - 40; |
| 1218 | if ( 0 <= shiftCount ) { |
| 1219 | return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount ); |
| 1220 | } |
| 1221 | else { |
| 1222 | shiftCount += 7; |
| 1223 | if ( shiftCount < 0 ) { |
| 1224 | shift64RightJamming( absA, - shiftCount, &absA ); |
| 1225 | } |
| 1226 | else { |
| 1227 | absA <<= shiftCount; |
| 1228 | } |
| 1229 | return roundAndPackFloat32( zSign, 0x9C - shiftCount, absA STATUS_VAR ); |
| 1230 | } |
| 1231 | |
| 1232 | } |
| 1233 | |
| 1234 | float32 uint64_to_float32( uint64 a STATUS_PARAM ) |
| 1235 | { |
| 1236 | int8 shiftCount; |
| 1237 | |
| 1238 | if ( a == 0 ) return float32_zero; |
| 1239 | shiftCount = countLeadingZeros64( a ) - 40; |
| 1240 | if ( 0 <= shiftCount ) { |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1241 | return packFloat32(0, 0x95 - shiftCount, a<<shiftCount); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1242 | } |
| 1243 | else { |
| 1244 | shiftCount += 7; |
| 1245 | if ( shiftCount < 0 ) { |
| 1246 | shift64RightJamming( a, - shiftCount, &a ); |
| 1247 | } |
| 1248 | else { |
| 1249 | a <<= shiftCount; |
| 1250 | } |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1251 | return roundAndPackFloat32(0, 0x9C - shiftCount, a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1252 | } |
| 1253 | } |
| 1254 | |
| 1255 | /*---------------------------------------------------------------------------- |
| 1256 | | Returns the result of converting the 64-bit two's complement integer `a' |
| 1257 | | to the double-precision floating-point format. The conversion is performed |
| 1258 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 1259 | *----------------------------------------------------------------------------*/ |
| 1260 | |
| 1261 | float64 int64_to_float64( int64 a STATUS_PARAM ) |
| 1262 | { |
| 1263 | flag zSign; |
| 1264 | |
| 1265 | if ( a == 0 ) return float64_zero; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1266 | if ( a == (int64_t) LIT64( 0x8000000000000000 ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1267 | return packFloat64( 1, 0x43E, 0 ); |
| 1268 | } |
| 1269 | zSign = ( a < 0 ); |
| 1270 | return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a STATUS_VAR ); |
| 1271 | |
| 1272 | } |
| 1273 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1274 | float64 uint64_to_float64(uint64 a STATUS_PARAM) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1275 | { |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1276 | int exp = 0x43C; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1277 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1278 | if (a == 0) { |
| 1279 | return float64_zero; |
| 1280 | } |
| 1281 | if ((int64_t)a < 0) { |
| 1282 | shift64RightJamming(a, 1, &a); |
| 1283 | exp += 1; |
| 1284 | } |
| 1285 | return normalizeRoundAndPackFloat64(0, exp, a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1286 | } |
| 1287 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1288 | /*---------------------------------------------------------------------------- |
| 1289 | | Returns the result of converting the 64-bit two's complement integer `a' |
| 1290 | | to the extended double-precision floating-point format. The conversion |
| 1291 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 1292 | | Arithmetic. |
| 1293 | *----------------------------------------------------------------------------*/ |
| 1294 | |
| 1295 | floatx80 int64_to_floatx80( int64 a STATUS_PARAM ) |
| 1296 | { |
| 1297 | flag zSign; |
| 1298 | uint64 absA; |
| 1299 | int8 shiftCount; |
| 1300 | |
| 1301 | if ( a == 0 ) return packFloatx80( 0, 0, 0 ); |
| 1302 | zSign = ( a < 0 ); |
| 1303 | absA = zSign ? - a : a; |
| 1304 | shiftCount = countLeadingZeros64( absA ); |
| 1305 | return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount ); |
| 1306 | |
| 1307 | } |
| 1308 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1309 | /*---------------------------------------------------------------------------- |
| 1310 | | Returns the result of converting the 64-bit two's complement integer `a' to |
| 1311 | | the quadruple-precision floating-point format. The conversion is performed |
| 1312 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 1313 | *----------------------------------------------------------------------------*/ |
| 1314 | |
| 1315 | float128 int64_to_float128( int64 a STATUS_PARAM ) |
| 1316 | { |
| 1317 | flag zSign; |
| 1318 | uint64 absA; |
| 1319 | int8 shiftCount; |
| 1320 | int32 zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1321 | uint64_t zSig0, zSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1322 | |
| 1323 | if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); |
| 1324 | zSign = ( a < 0 ); |
| 1325 | absA = zSign ? - a : a; |
| 1326 | shiftCount = countLeadingZeros64( absA ) + 49; |
| 1327 | zExp = 0x406E - shiftCount; |
| 1328 | if ( 64 <= shiftCount ) { |
| 1329 | zSig1 = 0; |
| 1330 | zSig0 = absA; |
| 1331 | shiftCount -= 64; |
| 1332 | } |
| 1333 | else { |
| 1334 | zSig1 = absA; |
| 1335 | zSig0 = 0; |
| 1336 | } |
| 1337 | shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); |
| 1338 | return packFloat128( zSign, zExp, zSig0, zSig1 ); |
| 1339 | |
| 1340 | } |
| 1341 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1342 | float128 uint64_to_float128(uint64 a STATUS_PARAM) |
| 1343 | { |
| 1344 | if (a == 0) { |
| 1345 | return float128_zero; |
| 1346 | } |
| 1347 | return normalizeRoundAndPackFloat128(0, 0x406E, a, 0 STATUS_VAR); |
| 1348 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1349 | |
| 1350 | /*---------------------------------------------------------------------------- |
| 1351 | | Returns the result of converting the single-precision floating-point value |
| 1352 | | `a' to the 32-bit two's complement integer format. The conversion is |
| 1353 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 1354 | | Arithmetic---which means in particular that the conversion is rounded |
| 1355 | | according to the current rounding mode. If `a' is a NaN, the largest |
| 1356 | | positive integer is returned. Otherwise, if the conversion overflows, the |
| 1357 | | largest integer with the same sign as `a' is returned. |
| 1358 | *----------------------------------------------------------------------------*/ |
| 1359 | |
| 1360 | int32 float32_to_int32( float32 a STATUS_PARAM ) |
| 1361 | { |
| 1362 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1363 | int_fast16_t aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1364 | uint32_t aSig; |
| 1365 | uint64_t aSig64; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1366 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1367 | a = float32_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1368 | aSig = extractFloat32Frac( a ); |
| 1369 | aExp = extractFloat32Exp( a ); |
| 1370 | aSign = extractFloat32Sign( a ); |
| 1371 | if ( ( aExp == 0xFF ) && aSig ) aSign = 0; |
| 1372 | if ( aExp ) aSig |= 0x00800000; |
| 1373 | shiftCount = 0xAF - aExp; |
| 1374 | aSig64 = aSig; |
| 1375 | aSig64 <<= 32; |
| 1376 | if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 ); |
| 1377 | return roundAndPackInt32( aSign, aSig64 STATUS_VAR ); |
| 1378 | |
| 1379 | } |
| 1380 | |
| 1381 | /*---------------------------------------------------------------------------- |
| 1382 | | Returns the result of converting the single-precision floating-point value |
| 1383 | | `a' to the 32-bit two's complement integer format. The conversion is |
| 1384 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 1385 | | Arithmetic, except that the conversion is always rounded toward zero. |
| 1386 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if |
| 1387 | | the conversion overflows, the largest integer with the same sign as `a' is |
| 1388 | | returned. |
| 1389 | *----------------------------------------------------------------------------*/ |
| 1390 | |
| 1391 | int32 float32_to_int32_round_to_zero( float32 a STATUS_PARAM ) |
| 1392 | { |
| 1393 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1394 | int_fast16_t aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1395 | uint32_t aSig; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1396 | int32_t z; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1397 | a = float32_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1398 | |
| 1399 | aSig = extractFloat32Frac( a ); |
| 1400 | aExp = extractFloat32Exp( a ); |
| 1401 | aSign = extractFloat32Sign( a ); |
| 1402 | shiftCount = aExp - 0x9E; |
| 1403 | if ( 0 <= shiftCount ) { |
| 1404 | if ( float32_val(a) != 0xCF000000 ) { |
| 1405 | float_raise( float_flag_invalid STATUS_VAR); |
| 1406 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; |
| 1407 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1408 | return (int32_t) 0x80000000; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1409 | } |
| 1410 | else if ( aExp <= 0x7E ) { |
| 1411 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 1412 | return 0; |
| 1413 | } |
| 1414 | aSig = ( aSig | 0x00800000 )<<8; |
| 1415 | z = aSig>>( - shiftCount ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1416 | if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1417 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 1418 | } |
| 1419 | if ( aSign ) z = - z; |
| 1420 | return z; |
| 1421 | |
| 1422 | } |
| 1423 | |
| 1424 | /*---------------------------------------------------------------------------- |
| 1425 | | Returns the result of converting the single-precision floating-point value |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1426 | | `a' to the 16-bit two's complement integer format. The conversion is |
| 1427 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 1428 | | Arithmetic, except that the conversion is always rounded toward zero. |
| 1429 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if |
| 1430 | | the conversion overflows, the largest integer with the same sign as `a' is |
| 1431 | | returned. |
| 1432 | *----------------------------------------------------------------------------*/ |
| 1433 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1434 | int_fast16_t float32_to_int16_round_to_zero(float32 a STATUS_PARAM) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1435 | { |
| 1436 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1437 | int_fast16_t aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1438 | uint32_t aSig; |
| 1439 | int32 z; |
| 1440 | |
| 1441 | aSig = extractFloat32Frac( a ); |
| 1442 | aExp = extractFloat32Exp( a ); |
| 1443 | aSign = extractFloat32Sign( a ); |
| 1444 | shiftCount = aExp - 0x8E; |
| 1445 | if ( 0 <= shiftCount ) { |
| 1446 | if ( float32_val(a) != 0xC7000000 ) { |
| 1447 | float_raise( float_flag_invalid STATUS_VAR); |
| 1448 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { |
| 1449 | return 0x7FFF; |
| 1450 | } |
| 1451 | } |
| 1452 | return (int32_t) 0xffff8000; |
| 1453 | } |
| 1454 | else if ( aExp <= 0x7E ) { |
| 1455 | if ( aExp | aSig ) { |
| 1456 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 1457 | } |
| 1458 | return 0; |
| 1459 | } |
| 1460 | shiftCount -= 0x10; |
| 1461 | aSig = ( aSig | 0x00800000 )<<8; |
| 1462 | z = aSig>>( - shiftCount ); |
| 1463 | if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) { |
| 1464 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 1465 | } |
| 1466 | if ( aSign ) { |
| 1467 | z = - z; |
| 1468 | } |
| 1469 | return z; |
| 1470 | |
| 1471 | } |
| 1472 | |
| 1473 | /*---------------------------------------------------------------------------- |
| 1474 | | Returns the result of converting the single-precision floating-point value |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1475 | | `a' to the 64-bit two's complement integer format. The conversion is |
| 1476 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 1477 | | Arithmetic---which means in particular that the conversion is rounded |
| 1478 | | according to the current rounding mode. If `a' is a NaN, the largest |
| 1479 | | positive integer is returned. Otherwise, if the conversion overflows, the |
| 1480 | | largest integer with the same sign as `a' is returned. |
| 1481 | *----------------------------------------------------------------------------*/ |
| 1482 | |
| 1483 | int64 float32_to_int64( float32 a STATUS_PARAM ) |
| 1484 | { |
| 1485 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1486 | int_fast16_t aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1487 | uint32_t aSig; |
| 1488 | uint64_t aSig64, aSigExtra; |
| 1489 | a = float32_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1490 | |
| 1491 | aSig = extractFloat32Frac( a ); |
| 1492 | aExp = extractFloat32Exp( a ); |
| 1493 | aSign = extractFloat32Sign( a ); |
| 1494 | shiftCount = 0xBE - aExp; |
| 1495 | if ( shiftCount < 0 ) { |
| 1496 | float_raise( float_flag_invalid STATUS_VAR); |
| 1497 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { |
| 1498 | return LIT64( 0x7FFFFFFFFFFFFFFF ); |
| 1499 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1500 | return (int64_t) LIT64( 0x8000000000000000 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1501 | } |
| 1502 | if ( aExp ) aSig |= 0x00800000; |
| 1503 | aSig64 = aSig; |
| 1504 | aSig64 <<= 40; |
| 1505 | shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra ); |
| 1506 | return roundAndPackInt64( aSign, aSig64, aSigExtra STATUS_VAR ); |
| 1507 | |
| 1508 | } |
| 1509 | |
| 1510 | /*---------------------------------------------------------------------------- |
| 1511 | | Returns the result of converting the single-precision floating-point value |
| 1512 | | `a' to the 64-bit two's complement integer format. The conversion is |
| 1513 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 1514 | | Arithmetic, except that the conversion is always rounded toward zero. If |
| 1515 | | `a' is a NaN, the largest positive integer is returned. Otherwise, if the |
| 1516 | | conversion overflows, the largest integer with the same sign as `a' is |
| 1517 | | returned. |
| 1518 | *----------------------------------------------------------------------------*/ |
| 1519 | |
| 1520 | int64 float32_to_int64_round_to_zero( float32 a STATUS_PARAM ) |
| 1521 | { |
| 1522 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1523 | int_fast16_t aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1524 | uint32_t aSig; |
| 1525 | uint64_t aSig64; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1526 | int64 z; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1527 | a = float32_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1528 | |
| 1529 | aSig = extractFloat32Frac( a ); |
| 1530 | aExp = extractFloat32Exp( a ); |
| 1531 | aSign = extractFloat32Sign( a ); |
| 1532 | shiftCount = aExp - 0xBE; |
| 1533 | if ( 0 <= shiftCount ) { |
| 1534 | if ( float32_val(a) != 0xDF000000 ) { |
| 1535 | float_raise( float_flag_invalid STATUS_VAR); |
| 1536 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { |
| 1537 | return LIT64( 0x7FFFFFFFFFFFFFFF ); |
| 1538 | } |
| 1539 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1540 | return (int64_t) LIT64( 0x8000000000000000 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1541 | } |
| 1542 | else if ( aExp <= 0x7E ) { |
| 1543 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 1544 | return 0; |
| 1545 | } |
| 1546 | aSig64 = aSig | 0x00800000; |
| 1547 | aSig64 <<= 40; |
| 1548 | z = aSig64>>( - shiftCount ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1549 | if ( (uint64_t) ( aSig64<<( shiftCount & 63 ) ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1550 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 1551 | } |
| 1552 | if ( aSign ) z = - z; |
| 1553 | return z; |
| 1554 | |
| 1555 | } |
| 1556 | |
| 1557 | /*---------------------------------------------------------------------------- |
| 1558 | | Returns the result of converting the single-precision floating-point value |
| 1559 | | `a' to the double-precision floating-point format. The conversion is |
| 1560 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 1561 | | Arithmetic. |
| 1562 | *----------------------------------------------------------------------------*/ |
| 1563 | |
| 1564 | float64 float32_to_float64( float32 a STATUS_PARAM ) |
| 1565 | { |
| 1566 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1567 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1568 | uint32_t aSig; |
| 1569 | a = float32_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1570 | |
| 1571 | aSig = extractFloat32Frac( a ); |
| 1572 | aExp = extractFloat32Exp( a ); |
| 1573 | aSign = extractFloat32Sign( a ); |
| 1574 | if ( aExp == 0xFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1575 | if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1576 | return packFloat64( aSign, 0x7FF, 0 ); |
| 1577 | } |
| 1578 | if ( aExp == 0 ) { |
| 1579 | if ( aSig == 0 ) return packFloat64( aSign, 0, 0 ); |
| 1580 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
| 1581 | --aExp; |
| 1582 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1583 | return packFloat64( aSign, aExp + 0x380, ( (uint64_t) aSig )<<29 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1584 | |
| 1585 | } |
| 1586 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1587 | /*---------------------------------------------------------------------------- |
| 1588 | | Returns the result of converting the single-precision floating-point value |
| 1589 | | `a' to the extended double-precision floating-point format. The conversion |
| 1590 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 1591 | | Arithmetic. |
| 1592 | *----------------------------------------------------------------------------*/ |
| 1593 | |
| 1594 | floatx80 float32_to_floatx80( float32 a STATUS_PARAM ) |
| 1595 | { |
| 1596 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1597 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1598 | uint32_t aSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1599 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1600 | a = float32_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1601 | aSig = extractFloat32Frac( a ); |
| 1602 | aExp = extractFloat32Exp( a ); |
| 1603 | aSign = extractFloat32Sign( a ); |
| 1604 | if ( aExp == 0xFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1605 | if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1606 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
| 1607 | } |
| 1608 | if ( aExp == 0 ) { |
| 1609 | if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); |
| 1610 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
| 1611 | } |
| 1612 | aSig |= 0x00800000; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1613 | return packFloatx80( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<40 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1614 | |
| 1615 | } |
| 1616 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1617 | /*---------------------------------------------------------------------------- |
| 1618 | | Returns the result of converting the single-precision floating-point value |
| 1619 | | `a' to the double-precision floating-point format. The conversion is |
| 1620 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 1621 | | Arithmetic. |
| 1622 | *----------------------------------------------------------------------------*/ |
| 1623 | |
| 1624 | float128 float32_to_float128( float32 a STATUS_PARAM ) |
| 1625 | { |
| 1626 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1627 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1628 | uint32_t aSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1629 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1630 | a = float32_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1631 | aSig = extractFloat32Frac( a ); |
| 1632 | aExp = extractFloat32Exp( a ); |
| 1633 | aSign = extractFloat32Sign( a ); |
| 1634 | if ( aExp == 0xFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1635 | if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1636 | return packFloat128( aSign, 0x7FFF, 0, 0 ); |
| 1637 | } |
| 1638 | if ( aExp == 0 ) { |
| 1639 | if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); |
| 1640 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
| 1641 | --aExp; |
| 1642 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1643 | return packFloat128( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<25, 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1644 | |
| 1645 | } |
| 1646 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1647 | /*---------------------------------------------------------------------------- |
| 1648 | | Rounds the single-precision floating-point value `a' to an integer, and |
| 1649 | | returns the result as a single-precision floating-point value. The |
| 1650 | | operation is performed according to the IEC/IEEE Standard for Binary |
| 1651 | | Floating-Point Arithmetic. |
| 1652 | *----------------------------------------------------------------------------*/ |
| 1653 | |
| 1654 | float32 float32_round_to_int( float32 a STATUS_PARAM) |
| 1655 | { |
| 1656 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1657 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1658 | uint32_t lastBitMask, roundBitsMask; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1659 | int8 roundingMode; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1660 | uint32_t z; |
| 1661 | a = float32_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1662 | |
| 1663 | aExp = extractFloat32Exp( a ); |
| 1664 | if ( 0x96 <= aExp ) { |
| 1665 | if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) { |
| 1666 | return propagateFloat32NaN( a, a STATUS_VAR ); |
| 1667 | } |
| 1668 | return a; |
| 1669 | } |
| 1670 | if ( aExp <= 0x7E ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1671 | if ( (uint32_t) ( float32_val(a)<<1 ) == 0 ) return a; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1672 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 1673 | aSign = extractFloat32Sign( a ); |
| 1674 | switch ( STATUS(float_rounding_mode) ) { |
| 1675 | case float_round_nearest_even: |
| 1676 | if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) { |
| 1677 | return packFloat32( aSign, 0x7F, 0 ); |
| 1678 | } |
| 1679 | break; |
| 1680 | case float_round_down: |
| 1681 | return make_float32(aSign ? 0xBF800000 : 0); |
| 1682 | case float_round_up: |
| 1683 | return make_float32(aSign ? 0x80000000 : 0x3F800000); |
| 1684 | } |
| 1685 | return packFloat32( aSign, 0, 0 ); |
| 1686 | } |
| 1687 | lastBitMask = 1; |
| 1688 | lastBitMask <<= 0x96 - aExp; |
| 1689 | roundBitsMask = lastBitMask - 1; |
| 1690 | z = float32_val(a); |
| 1691 | roundingMode = STATUS(float_rounding_mode); |
| 1692 | if ( roundingMode == float_round_nearest_even ) { |
| 1693 | z += lastBitMask>>1; |
| 1694 | if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; |
| 1695 | } |
| 1696 | else if ( roundingMode != float_round_to_zero ) { |
| 1697 | if ( extractFloat32Sign( make_float32(z) ) ^ ( roundingMode == float_round_up ) ) { |
| 1698 | z += roundBitsMask; |
| 1699 | } |
| 1700 | } |
| 1701 | z &= ~ roundBitsMask; |
| 1702 | if ( z != float32_val(a) ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 1703 | return make_float32(z); |
| 1704 | |
| 1705 | } |
| 1706 | |
| 1707 | /*---------------------------------------------------------------------------- |
| 1708 | | Returns the result of adding the absolute values of the single-precision |
| 1709 | | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated |
| 1710 | | before being returned. `zSign' is ignored if the result is a NaN. |
| 1711 | | The addition is performed according to the IEC/IEEE Standard for Binary |
| 1712 | | Floating-Point Arithmetic. |
| 1713 | *----------------------------------------------------------------------------*/ |
| 1714 | |
| 1715 | static float32 addFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM) |
| 1716 | { |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1717 | int_fast16_t aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1718 | uint32_t aSig, bSig, zSig; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1719 | int_fast16_t expDiff; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1720 | |
| 1721 | aSig = extractFloat32Frac( a ); |
| 1722 | aExp = extractFloat32Exp( a ); |
| 1723 | bSig = extractFloat32Frac( b ); |
| 1724 | bExp = extractFloat32Exp( b ); |
| 1725 | expDiff = aExp - bExp; |
| 1726 | aSig <<= 6; |
| 1727 | bSig <<= 6; |
| 1728 | if ( 0 < expDiff ) { |
| 1729 | if ( aExp == 0xFF ) { |
| 1730 | if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 1731 | return a; |
| 1732 | } |
| 1733 | if ( bExp == 0 ) { |
| 1734 | --expDiff; |
| 1735 | } |
| 1736 | else { |
| 1737 | bSig |= 0x20000000; |
| 1738 | } |
| 1739 | shift32RightJamming( bSig, expDiff, &bSig ); |
| 1740 | zExp = aExp; |
| 1741 | } |
| 1742 | else if ( expDiff < 0 ) { |
| 1743 | if ( bExp == 0xFF ) { |
| 1744 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 1745 | return packFloat32( zSign, 0xFF, 0 ); |
| 1746 | } |
| 1747 | if ( aExp == 0 ) { |
| 1748 | ++expDiff; |
| 1749 | } |
| 1750 | else { |
| 1751 | aSig |= 0x20000000; |
| 1752 | } |
| 1753 | shift32RightJamming( aSig, - expDiff, &aSig ); |
| 1754 | zExp = bExp; |
| 1755 | } |
| 1756 | else { |
| 1757 | if ( aExp == 0xFF ) { |
| 1758 | if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 1759 | return a; |
| 1760 | } |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 1761 | if ( aExp == 0 ) { |
David 'Digit' Turner | 5285864 | 2011-06-03 13:41:05 +0200 | [diff] [blame] | 1762 | if (STATUS(flush_to_zero)) { |
| 1763 | if (aSig | bSig) { |
| 1764 | float_raise(float_flag_output_denormal STATUS_VAR); |
| 1765 | } |
| 1766 | return packFloat32(zSign, 0, 0); |
| 1767 | } |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 1768 | return packFloat32( zSign, 0, ( aSig + bSig )>>6 ); |
| 1769 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1770 | zSig = 0x40000000 + aSig + bSig; |
| 1771 | zExp = aExp; |
| 1772 | goto roundAndPack; |
| 1773 | } |
| 1774 | aSig |= 0x20000000; |
| 1775 | zSig = ( aSig + bSig )<<1; |
| 1776 | --zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1777 | if ( (int32_t) zSig < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1778 | zSig = aSig + bSig; |
| 1779 | ++zExp; |
| 1780 | } |
| 1781 | roundAndPack: |
| 1782 | return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); |
| 1783 | |
| 1784 | } |
| 1785 | |
| 1786 | /*---------------------------------------------------------------------------- |
| 1787 | | Returns the result of subtracting the absolute values of the single- |
| 1788 | | precision floating-point values `a' and `b'. If `zSign' is 1, the |
| 1789 | | difference is negated before being returned. `zSign' is ignored if the |
| 1790 | | result is a NaN. The subtraction is performed according to the IEC/IEEE |
| 1791 | | Standard for Binary Floating-Point Arithmetic. |
| 1792 | *----------------------------------------------------------------------------*/ |
| 1793 | |
| 1794 | static float32 subFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM) |
| 1795 | { |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1796 | int_fast16_t aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1797 | uint32_t aSig, bSig, zSig; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1798 | int_fast16_t expDiff; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1799 | |
| 1800 | aSig = extractFloat32Frac( a ); |
| 1801 | aExp = extractFloat32Exp( a ); |
| 1802 | bSig = extractFloat32Frac( b ); |
| 1803 | bExp = extractFloat32Exp( b ); |
| 1804 | expDiff = aExp - bExp; |
| 1805 | aSig <<= 7; |
| 1806 | bSig <<= 7; |
| 1807 | if ( 0 < expDiff ) goto aExpBigger; |
| 1808 | if ( expDiff < 0 ) goto bExpBigger; |
| 1809 | if ( aExp == 0xFF ) { |
| 1810 | if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 1811 | float_raise( float_flag_invalid STATUS_VAR); |
| 1812 | return float32_default_nan; |
| 1813 | } |
| 1814 | if ( aExp == 0 ) { |
| 1815 | aExp = 1; |
| 1816 | bExp = 1; |
| 1817 | } |
| 1818 | if ( bSig < aSig ) goto aBigger; |
| 1819 | if ( aSig < bSig ) goto bBigger; |
| 1820 | return packFloat32( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); |
| 1821 | bExpBigger: |
| 1822 | if ( bExp == 0xFF ) { |
| 1823 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 1824 | return packFloat32( zSign ^ 1, 0xFF, 0 ); |
| 1825 | } |
| 1826 | if ( aExp == 0 ) { |
| 1827 | ++expDiff; |
| 1828 | } |
| 1829 | else { |
| 1830 | aSig |= 0x40000000; |
| 1831 | } |
| 1832 | shift32RightJamming( aSig, - expDiff, &aSig ); |
| 1833 | bSig |= 0x40000000; |
| 1834 | bBigger: |
| 1835 | zSig = bSig - aSig; |
| 1836 | zExp = bExp; |
| 1837 | zSign ^= 1; |
| 1838 | goto normalizeRoundAndPack; |
| 1839 | aExpBigger: |
| 1840 | if ( aExp == 0xFF ) { |
| 1841 | if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 1842 | return a; |
| 1843 | } |
| 1844 | if ( bExp == 0 ) { |
| 1845 | --expDiff; |
| 1846 | } |
| 1847 | else { |
| 1848 | bSig |= 0x40000000; |
| 1849 | } |
| 1850 | shift32RightJamming( bSig, expDiff, &bSig ); |
| 1851 | aSig |= 0x40000000; |
| 1852 | aBigger: |
| 1853 | zSig = aSig - bSig; |
| 1854 | zExp = aExp; |
| 1855 | normalizeRoundAndPack: |
| 1856 | --zExp; |
| 1857 | return normalizeRoundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); |
| 1858 | |
| 1859 | } |
| 1860 | |
| 1861 | /*---------------------------------------------------------------------------- |
| 1862 | | Returns the result of adding the single-precision floating-point values `a' |
| 1863 | | and `b'. The operation is performed according to the IEC/IEEE Standard for |
| 1864 | | Binary Floating-Point Arithmetic. |
| 1865 | *----------------------------------------------------------------------------*/ |
| 1866 | |
| 1867 | float32 float32_add( float32 a, float32 b STATUS_PARAM ) |
| 1868 | { |
| 1869 | flag aSign, bSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1870 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 1871 | b = float32_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1872 | |
| 1873 | aSign = extractFloat32Sign( a ); |
| 1874 | bSign = extractFloat32Sign( b ); |
| 1875 | if ( aSign == bSign ) { |
| 1876 | return addFloat32Sigs( a, b, aSign STATUS_VAR); |
| 1877 | } |
| 1878 | else { |
| 1879 | return subFloat32Sigs( a, b, aSign STATUS_VAR ); |
| 1880 | } |
| 1881 | |
| 1882 | } |
| 1883 | |
| 1884 | /*---------------------------------------------------------------------------- |
| 1885 | | Returns the result of subtracting the single-precision floating-point values |
| 1886 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard |
| 1887 | | for Binary Floating-Point Arithmetic. |
| 1888 | *----------------------------------------------------------------------------*/ |
| 1889 | |
| 1890 | float32 float32_sub( float32 a, float32 b STATUS_PARAM ) |
| 1891 | { |
| 1892 | flag aSign, bSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1893 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 1894 | b = float32_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1895 | |
| 1896 | aSign = extractFloat32Sign( a ); |
| 1897 | bSign = extractFloat32Sign( b ); |
| 1898 | if ( aSign == bSign ) { |
| 1899 | return subFloat32Sigs( a, b, aSign STATUS_VAR ); |
| 1900 | } |
| 1901 | else { |
| 1902 | return addFloat32Sigs( a, b, aSign STATUS_VAR ); |
| 1903 | } |
| 1904 | |
| 1905 | } |
| 1906 | |
| 1907 | /*---------------------------------------------------------------------------- |
| 1908 | | Returns the result of multiplying the single-precision floating-point values |
| 1909 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard |
| 1910 | | for Binary Floating-Point Arithmetic. |
| 1911 | *----------------------------------------------------------------------------*/ |
| 1912 | |
| 1913 | float32 float32_mul( float32 a, float32 b STATUS_PARAM ) |
| 1914 | { |
| 1915 | flag aSign, bSign, zSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1916 | int_fast16_t aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1917 | uint32_t aSig, bSig; |
| 1918 | uint64_t zSig64; |
| 1919 | uint32_t zSig; |
| 1920 | |
| 1921 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 1922 | b = float32_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1923 | |
| 1924 | aSig = extractFloat32Frac( a ); |
| 1925 | aExp = extractFloat32Exp( a ); |
| 1926 | aSign = extractFloat32Sign( a ); |
| 1927 | bSig = extractFloat32Frac( b ); |
| 1928 | bExp = extractFloat32Exp( b ); |
| 1929 | bSign = extractFloat32Sign( b ); |
| 1930 | zSign = aSign ^ bSign; |
| 1931 | if ( aExp == 0xFF ) { |
| 1932 | if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { |
| 1933 | return propagateFloat32NaN( a, b STATUS_VAR ); |
| 1934 | } |
| 1935 | if ( ( bExp | bSig ) == 0 ) { |
| 1936 | float_raise( float_flag_invalid STATUS_VAR); |
| 1937 | return float32_default_nan; |
| 1938 | } |
| 1939 | return packFloat32( zSign, 0xFF, 0 ); |
| 1940 | } |
| 1941 | if ( bExp == 0xFF ) { |
| 1942 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 1943 | if ( ( aExp | aSig ) == 0 ) { |
| 1944 | float_raise( float_flag_invalid STATUS_VAR); |
| 1945 | return float32_default_nan; |
| 1946 | } |
| 1947 | return packFloat32( zSign, 0xFF, 0 ); |
| 1948 | } |
| 1949 | if ( aExp == 0 ) { |
| 1950 | if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); |
| 1951 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
| 1952 | } |
| 1953 | if ( bExp == 0 ) { |
| 1954 | if ( bSig == 0 ) return packFloat32( zSign, 0, 0 ); |
| 1955 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); |
| 1956 | } |
| 1957 | zExp = aExp + bExp - 0x7F; |
| 1958 | aSig = ( aSig | 0x00800000 )<<7; |
| 1959 | bSig = ( bSig | 0x00800000 )<<8; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1960 | shift64RightJamming( ( (uint64_t) aSig ) * bSig, 32, &zSig64 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1961 | zSig = zSig64; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1962 | if ( 0 <= (int32_t) ( zSig<<1 ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1963 | zSig <<= 1; |
| 1964 | --zExp; |
| 1965 | } |
| 1966 | return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); |
| 1967 | |
| 1968 | } |
| 1969 | |
| 1970 | /*---------------------------------------------------------------------------- |
| 1971 | | Returns the result of dividing the single-precision floating-point value `a' |
| 1972 | | by the corresponding value `b'. The operation is performed according to the |
| 1973 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 1974 | *----------------------------------------------------------------------------*/ |
| 1975 | |
| 1976 | float32 float32_div( float32 a, float32 b STATUS_PARAM ) |
| 1977 | { |
| 1978 | flag aSign, bSign, zSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 1979 | int_fast16_t aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 1980 | uint32_t aSig, bSig, zSig; |
| 1981 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 1982 | b = float32_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 1983 | |
| 1984 | aSig = extractFloat32Frac( a ); |
| 1985 | aExp = extractFloat32Exp( a ); |
| 1986 | aSign = extractFloat32Sign( a ); |
| 1987 | bSig = extractFloat32Frac( b ); |
| 1988 | bExp = extractFloat32Exp( b ); |
| 1989 | bSign = extractFloat32Sign( b ); |
| 1990 | zSign = aSign ^ bSign; |
| 1991 | if ( aExp == 0xFF ) { |
| 1992 | if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 1993 | if ( bExp == 0xFF ) { |
| 1994 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 1995 | float_raise( float_flag_invalid STATUS_VAR); |
| 1996 | return float32_default_nan; |
| 1997 | } |
| 1998 | return packFloat32( zSign, 0xFF, 0 ); |
| 1999 | } |
| 2000 | if ( bExp == 0xFF ) { |
| 2001 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 2002 | return packFloat32( zSign, 0, 0 ); |
| 2003 | } |
| 2004 | if ( bExp == 0 ) { |
| 2005 | if ( bSig == 0 ) { |
| 2006 | if ( ( aExp | aSig ) == 0 ) { |
| 2007 | float_raise( float_flag_invalid STATUS_VAR); |
| 2008 | return float32_default_nan; |
| 2009 | } |
| 2010 | float_raise( float_flag_divbyzero STATUS_VAR); |
| 2011 | return packFloat32( zSign, 0xFF, 0 ); |
| 2012 | } |
| 2013 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); |
| 2014 | } |
| 2015 | if ( aExp == 0 ) { |
| 2016 | if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); |
| 2017 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
| 2018 | } |
| 2019 | zExp = aExp - bExp + 0x7D; |
| 2020 | aSig = ( aSig | 0x00800000 )<<7; |
| 2021 | bSig = ( bSig | 0x00800000 )<<8; |
| 2022 | if ( bSig <= ( aSig + aSig ) ) { |
| 2023 | aSig >>= 1; |
| 2024 | ++zExp; |
| 2025 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2026 | zSig = ( ( (uint64_t) aSig )<<32 ) / bSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2027 | if ( ( zSig & 0x3F ) == 0 ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2028 | zSig |= ( (uint64_t) bSig * zSig != ( (uint64_t) aSig )<<32 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2029 | } |
| 2030 | return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); |
| 2031 | |
| 2032 | } |
| 2033 | |
| 2034 | /*---------------------------------------------------------------------------- |
| 2035 | | Returns the remainder of the single-precision floating-point value `a' |
| 2036 | | with respect to the corresponding value `b'. The operation is performed |
| 2037 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 2038 | *----------------------------------------------------------------------------*/ |
| 2039 | |
| 2040 | float32 float32_rem( float32 a, float32 b STATUS_PARAM ) |
| 2041 | { |
David Turner | 2738c26 | 2010-09-09 17:41:26 +0200 | [diff] [blame] | 2042 | flag aSign, zSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2043 | int_fast16_t aExp, bExp, expDiff; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2044 | uint32_t aSig, bSig; |
| 2045 | uint32_t q; |
| 2046 | uint64_t aSig64, bSig64, q64; |
| 2047 | uint32_t alternateASig; |
| 2048 | int32_t sigMean; |
| 2049 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 2050 | b = float32_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2051 | |
| 2052 | aSig = extractFloat32Frac( a ); |
| 2053 | aExp = extractFloat32Exp( a ); |
| 2054 | aSign = extractFloat32Sign( a ); |
| 2055 | bSig = extractFloat32Frac( b ); |
| 2056 | bExp = extractFloat32Exp( b ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2057 | if ( aExp == 0xFF ) { |
| 2058 | if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { |
| 2059 | return propagateFloat32NaN( a, b STATUS_VAR ); |
| 2060 | } |
| 2061 | float_raise( float_flag_invalid STATUS_VAR); |
| 2062 | return float32_default_nan; |
| 2063 | } |
| 2064 | if ( bExp == 0xFF ) { |
| 2065 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
| 2066 | return a; |
| 2067 | } |
| 2068 | if ( bExp == 0 ) { |
| 2069 | if ( bSig == 0 ) { |
| 2070 | float_raise( float_flag_invalid STATUS_VAR); |
| 2071 | return float32_default_nan; |
| 2072 | } |
| 2073 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); |
| 2074 | } |
| 2075 | if ( aExp == 0 ) { |
| 2076 | if ( aSig == 0 ) return a; |
| 2077 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
| 2078 | } |
| 2079 | expDiff = aExp - bExp; |
| 2080 | aSig |= 0x00800000; |
| 2081 | bSig |= 0x00800000; |
| 2082 | if ( expDiff < 32 ) { |
| 2083 | aSig <<= 8; |
| 2084 | bSig <<= 8; |
| 2085 | if ( expDiff < 0 ) { |
| 2086 | if ( expDiff < -1 ) return a; |
| 2087 | aSig >>= 1; |
| 2088 | } |
| 2089 | q = ( bSig <= aSig ); |
| 2090 | if ( q ) aSig -= bSig; |
| 2091 | if ( 0 < expDiff ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2092 | q = ( ( (uint64_t) aSig )<<32 ) / bSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2093 | q >>= 32 - expDiff; |
| 2094 | bSig >>= 2; |
| 2095 | aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; |
| 2096 | } |
| 2097 | else { |
| 2098 | aSig >>= 2; |
| 2099 | bSig >>= 2; |
| 2100 | } |
| 2101 | } |
| 2102 | else { |
| 2103 | if ( bSig <= aSig ) aSig -= bSig; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2104 | aSig64 = ( (uint64_t) aSig )<<40; |
| 2105 | bSig64 = ( (uint64_t) bSig )<<40; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2106 | expDiff -= 64; |
| 2107 | while ( 0 < expDiff ) { |
| 2108 | q64 = estimateDiv128To64( aSig64, 0, bSig64 ); |
| 2109 | q64 = ( 2 < q64 ) ? q64 - 2 : 0; |
| 2110 | aSig64 = - ( ( bSig * q64 )<<38 ); |
| 2111 | expDiff -= 62; |
| 2112 | } |
| 2113 | expDiff += 64; |
| 2114 | q64 = estimateDiv128To64( aSig64, 0, bSig64 ); |
| 2115 | q64 = ( 2 < q64 ) ? q64 - 2 : 0; |
| 2116 | q = q64>>( 64 - expDiff ); |
| 2117 | bSig <<= 6; |
| 2118 | aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q; |
| 2119 | } |
| 2120 | do { |
| 2121 | alternateASig = aSig; |
| 2122 | ++q; |
| 2123 | aSig -= bSig; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2124 | } while ( 0 <= (int32_t) aSig ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2125 | sigMean = aSig + alternateASig; |
| 2126 | if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { |
| 2127 | aSig = alternateASig; |
| 2128 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2129 | zSign = ( (int32_t) aSig < 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2130 | if ( zSign ) aSig = - aSig; |
| 2131 | return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig STATUS_VAR ); |
| 2132 | |
| 2133 | } |
| 2134 | |
| 2135 | /*---------------------------------------------------------------------------- |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2136 | | Returns the result of multiplying the single-precision floating-point values |
| 2137 | | `a' and `b' then adding 'c', with no intermediate rounding step after the |
| 2138 | | multiplication. The operation is performed according to the IEC/IEEE |
| 2139 | | Standard for Binary Floating-Point Arithmetic 754-2008. |
| 2140 | | The flags argument allows the caller to select negation of the |
| 2141 | | addend, the intermediate product, or the final result. (The difference |
| 2142 | | between this and having the caller do a separate negation is that negating |
| 2143 | | externally will flip the sign bit on NaNs.) |
| 2144 | *----------------------------------------------------------------------------*/ |
| 2145 | |
| 2146 | float32 float32_muladd(float32 a, float32 b, float32 c, int flags STATUS_PARAM) |
| 2147 | { |
| 2148 | flag aSign, bSign, cSign, zSign; |
| 2149 | int_fast16_t aExp, bExp, cExp, pExp, zExp, expDiff; |
| 2150 | uint32_t aSig, bSig, cSig; |
| 2151 | flag pInf, pZero, pSign; |
| 2152 | uint64_t pSig64, cSig64, zSig64; |
| 2153 | uint32_t pSig; |
| 2154 | int shiftcount; |
| 2155 | flag signflip, infzero; |
| 2156 | |
| 2157 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 2158 | b = float32_squash_input_denormal(b STATUS_VAR); |
| 2159 | c = float32_squash_input_denormal(c STATUS_VAR); |
| 2160 | aSig = extractFloat32Frac(a); |
| 2161 | aExp = extractFloat32Exp(a); |
| 2162 | aSign = extractFloat32Sign(a); |
| 2163 | bSig = extractFloat32Frac(b); |
| 2164 | bExp = extractFloat32Exp(b); |
| 2165 | bSign = extractFloat32Sign(b); |
| 2166 | cSig = extractFloat32Frac(c); |
| 2167 | cExp = extractFloat32Exp(c); |
| 2168 | cSign = extractFloat32Sign(c); |
| 2169 | |
| 2170 | infzero = ((aExp == 0 && aSig == 0 && bExp == 0xff && bSig == 0) || |
| 2171 | (aExp == 0xff && aSig == 0 && bExp == 0 && bSig == 0)); |
| 2172 | |
| 2173 | /* It is implementation-defined whether the cases of (0,inf,qnan) |
| 2174 | * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN |
| 2175 | * they return if they do), so we have to hand this information |
| 2176 | * off to the target-specific pick-a-NaN routine. |
| 2177 | */ |
| 2178 | if (((aExp == 0xff) && aSig) || |
| 2179 | ((bExp == 0xff) && bSig) || |
| 2180 | ((cExp == 0xff) && cSig)) { |
| 2181 | return propagateFloat32MulAddNaN(a, b, c, infzero STATUS_VAR); |
| 2182 | } |
| 2183 | |
| 2184 | if (infzero) { |
| 2185 | float_raise(float_flag_invalid STATUS_VAR); |
| 2186 | return float32_default_nan; |
| 2187 | } |
| 2188 | |
| 2189 | if (flags & float_muladd_negate_c) { |
| 2190 | cSign ^= 1; |
| 2191 | } |
| 2192 | |
| 2193 | signflip = (flags & float_muladd_negate_result) ? 1 : 0; |
| 2194 | |
| 2195 | /* Work out the sign and type of the product */ |
| 2196 | pSign = aSign ^ bSign; |
| 2197 | if (flags & float_muladd_negate_product) { |
| 2198 | pSign ^= 1; |
| 2199 | } |
| 2200 | pInf = (aExp == 0xff) || (bExp == 0xff); |
| 2201 | pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0); |
| 2202 | |
| 2203 | if (cExp == 0xff) { |
| 2204 | if (pInf && (pSign ^ cSign)) { |
| 2205 | /* addition of opposite-signed infinities => InvalidOperation */ |
| 2206 | float_raise(float_flag_invalid STATUS_VAR); |
| 2207 | return float32_default_nan; |
| 2208 | } |
| 2209 | /* Otherwise generate an infinity of the same sign */ |
| 2210 | return packFloat32(cSign ^ signflip, 0xff, 0); |
| 2211 | } |
| 2212 | |
| 2213 | if (pInf) { |
| 2214 | return packFloat32(pSign ^ signflip, 0xff, 0); |
| 2215 | } |
| 2216 | |
| 2217 | if (pZero) { |
| 2218 | if (cExp == 0) { |
| 2219 | if (cSig == 0) { |
| 2220 | /* Adding two exact zeroes */ |
| 2221 | if (pSign == cSign) { |
| 2222 | zSign = pSign; |
| 2223 | } else if (STATUS(float_rounding_mode) == float_round_down) { |
| 2224 | zSign = 1; |
| 2225 | } else { |
| 2226 | zSign = 0; |
| 2227 | } |
| 2228 | return packFloat32(zSign ^ signflip, 0, 0); |
| 2229 | } |
| 2230 | /* Exact zero plus a denorm */ |
| 2231 | if (STATUS(flush_to_zero)) { |
| 2232 | float_raise(float_flag_output_denormal STATUS_VAR); |
| 2233 | return packFloat32(cSign ^ signflip, 0, 0); |
| 2234 | } |
| 2235 | } |
| 2236 | /* Zero plus something non-zero : just return the something */ |
| 2237 | return packFloat32(cSign ^ signflip, cExp, cSig); |
| 2238 | } |
| 2239 | |
| 2240 | if (aExp == 0) { |
| 2241 | normalizeFloat32Subnormal(aSig, &aExp, &aSig); |
| 2242 | } |
| 2243 | if (bExp == 0) { |
| 2244 | normalizeFloat32Subnormal(bSig, &bExp, &bSig); |
| 2245 | } |
| 2246 | |
| 2247 | /* Calculate the actual result a * b + c */ |
| 2248 | |
| 2249 | /* Multiply first; this is easy. */ |
| 2250 | /* NB: we subtract 0x7e where float32_mul() subtracts 0x7f |
| 2251 | * because we want the true exponent, not the "one-less-than" |
| 2252 | * flavour that roundAndPackFloat32() takes. |
| 2253 | */ |
| 2254 | pExp = aExp + bExp - 0x7e; |
| 2255 | aSig = (aSig | 0x00800000) << 7; |
| 2256 | bSig = (bSig | 0x00800000) << 8; |
| 2257 | pSig64 = (uint64_t)aSig * bSig; |
| 2258 | if ((int64_t)(pSig64 << 1) >= 0) { |
| 2259 | pSig64 <<= 1; |
| 2260 | pExp--; |
| 2261 | } |
| 2262 | |
| 2263 | zSign = pSign ^ signflip; |
| 2264 | |
| 2265 | /* Now pSig64 is the significand of the multiply, with the explicit bit in |
| 2266 | * position 62. |
| 2267 | */ |
| 2268 | if (cExp == 0) { |
| 2269 | if (!cSig) { |
| 2270 | /* Throw out the special case of c being an exact zero now */ |
| 2271 | shift64RightJamming(pSig64, 32, &pSig64); |
| 2272 | pSig = pSig64; |
| 2273 | return roundAndPackFloat32(zSign, pExp - 1, |
| 2274 | pSig STATUS_VAR); |
| 2275 | } |
| 2276 | normalizeFloat32Subnormal(cSig, &cExp, &cSig); |
| 2277 | } |
| 2278 | |
| 2279 | cSig64 = (uint64_t)cSig << (62 - 23); |
| 2280 | cSig64 |= LIT64(0x4000000000000000); |
| 2281 | expDiff = pExp - cExp; |
| 2282 | |
| 2283 | if (pSign == cSign) { |
| 2284 | /* Addition */ |
| 2285 | if (expDiff > 0) { |
| 2286 | /* scale c to match p */ |
| 2287 | shift64RightJamming(cSig64, expDiff, &cSig64); |
| 2288 | zExp = pExp; |
| 2289 | } else if (expDiff < 0) { |
| 2290 | /* scale p to match c */ |
| 2291 | shift64RightJamming(pSig64, -expDiff, &pSig64); |
| 2292 | zExp = cExp; |
| 2293 | } else { |
| 2294 | /* no scaling needed */ |
| 2295 | zExp = cExp; |
| 2296 | } |
| 2297 | /* Add significands and make sure explicit bit ends up in posn 62 */ |
| 2298 | zSig64 = pSig64 + cSig64; |
| 2299 | if ((int64_t)zSig64 < 0) { |
| 2300 | shift64RightJamming(zSig64, 1, &zSig64); |
| 2301 | } else { |
| 2302 | zExp--; |
| 2303 | } |
| 2304 | } else { |
| 2305 | /* Subtraction */ |
| 2306 | if (expDiff > 0) { |
| 2307 | shift64RightJamming(cSig64, expDiff, &cSig64); |
| 2308 | zSig64 = pSig64 - cSig64; |
| 2309 | zExp = pExp; |
| 2310 | } else if (expDiff < 0) { |
| 2311 | shift64RightJamming(pSig64, -expDiff, &pSig64); |
| 2312 | zSig64 = cSig64 - pSig64; |
| 2313 | zExp = cExp; |
| 2314 | zSign ^= 1; |
| 2315 | } else { |
| 2316 | zExp = pExp; |
| 2317 | if (cSig64 < pSig64) { |
| 2318 | zSig64 = pSig64 - cSig64; |
| 2319 | } else if (pSig64 < cSig64) { |
| 2320 | zSig64 = cSig64 - pSig64; |
| 2321 | zSign ^= 1; |
| 2322 | } else { |
| 2323 | /* Exact zero */ |
| 2324 | zSign = signflip; |
| 2325 | if (STATUS(float_rounding_mode) == float_round_down) { |
| 2326 | zSign ^= 1; |
| 2327 | } |
| 2328 | return packFloat32(zSign, 0, 0); |
| 2329 | } |
| 2330 | } |
| 2331 | --zExp; |
| 2332 | /* Normalize to put the explicit bit back into bit 62. */ |
| 2333 | shiftcount = countLeadingZeros64(zSig64) - 1; |
| 2334 | zSig64 <<= shiftcount; |
| 2335 | zExp -= shiftcount; |
| 2336 | } |
| 2337 | shift64RightJamming(zSig64, 32, &zSig64); |
| 2338 | return roundAndPackFloat32(zSign, zExp, zSig64 STATUS_VAR); |
| 2339 | } |
| 2340 | |
| 2341 | |
| 2342 | /*---------------------------------------------------------------------------- |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2343 | | Returns the square root of the single-precision floating-point value `a'. |
| 2344 | | The operation is performed according to the IEC/IEEE Standard for Binary |
| 2345 | | Floating-Point Arithmetic. |
| 2346 | *----------------------------------------------------------------------------*/ |
| 2347 | |
| 2348 | float32 float32_sqrt( float32 a STATUS_PARAM ) |
| 2349 | { |
| 2350 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2351 | int_fast16_t aExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2352 | uint32_t aSig, zSig; |
| 2353 | uint64_t rem, term; |
| 2354 | a = float32_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2355 | |
| 2356 | aSig = extractFloat32Frac( a ); |
| 2357 | aExp = extractFloat32Exp( a ); |
| 2358 | aSign = extractFloat32Sign( a ); |
| 2359 | if ( aExp == 0xFF ) { |
| 2360 | if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); |
| 2361 | if ( ! aSign ) return a; |
| 2362 | float_raise( float_flag_invalid STATUS_VAR); |
| 2363 | return float32_default_nan; |
| 2364 | } |
| 2365 | if ( aSign ) { |
| 2366 | if ( ( aExp | aSig ) == 0 ) return a; |
| 2367 | float_raise( float_flag_invalid STATUS_VAR); |
| 2368 | return float32_default_nan; |
| 2369 | } |
| 2370 | if ( aExp == 0 ) { |
| 2371 | if ( aSig == 0 ) return float32_zero; |
| 2372 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
| 2373 | } |
| 2374 | zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E; |
| 2375 | aSig = ( aSig | 0x00800000 )<<8; |
| 2376 | zSig = estimateSqrt32( aExp, aSig ) + 2; |
| 2377 | if ( ( zSig & 0x7F ) <= 5 ) { |
| 2378 | if ( zSig < 2 ) { |
| 2379 | zSig = 0x7FFFFFFF; |
| 2380 | goto roundAndPack; |
| 2381 | } |
| 2382 | aSig >>= aExp & 1; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2383 | term = ( (uint64_t) zSig ) * zSig; |
| 2384 | rem = ( ( (uint64_t) aSig )<<32 ) - term; |
| 2385 | while ( (int64_t) rem < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2386 | --zSig; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2387 | rem += ( ( (uint64_t) zSig )<<1 ) | 1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2388 | } |
| 2389 | zSig |= ( rem != 0 ); |
| 2390 | } |
| 2391 | shift32RightJamming( zSig, 1, &zSig ); |
| 2392 | roundAndPack: |
| 2393 | return roundAndPackFloat32( 0, zExp, zSig STATUS_VAR ); |
| 2394 | |
| 2395 | } |
| 2396 | |
| 2397 | /*---------------------------------------------------------------------------- |
David Turner | 2738c26 | 2010-09-09 17:41:26 +0200 | [diff] [blame] | 2398 | | Returns the binary exponential of the single-precision floating-point value |
| 2399 | | `a'. The operation is performed according to the IEC/IEEE Standard for |
| 2400 | | Binary Floating-Point Arithmetic. |
| 2401 | | |
| 2402 | | Uses the following identities: |
| 2403 | | |
| 2404 | | 1. ------------------------------------------------------------------------- |
| 2405 | | x x*ln(2) |
| 2406 | | 2 = e |
| 2407 | | |
| 2408 | | 2. ------------------------------------------------------------------------- |
| 2409 | | 2 3 4 5 n |
| 2410 | | x x x x x x x |
| 2411 | | e = 1 + --- + --- + --- + --- + --- + ... + --- + ... |
| 2412 | | 1! 2! 3! 4! 5! n! |
| 2413 | *----------------------------------------------------------------------------*/ |
| 2414 | |
| 2415 | static const float64 float32_exp2_coefficients[15] = |
| 2416 | { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2417 | const_float64( 0x3ff0000000000000ll ), /* 1 */ |
| 2418 | const_float64( 0x3fe0000000000000ll ), /* 2 */ |
| 2419 | const_float64( 0x3fc5555555555555ll ), /* 3 */ |
| 2420 | const_float64( 0x3fa5555555555555ll ), /* 4 */ |
| 2421 | const_float64( 0x3f81111111111111ll ), /* 5 */ |
| 2422 | const_float64( 0x3f56c16c16c16c17ll ), /* 6 */ |
| 2423 | const_float64( 0x3f2a01a01a01a01all ), /* 7 */ |
| 2424 | const_float64( 0x3efa01a01a01a01all ), /* 8 */ |
| 2425 | const_float64( 0x3ec71de3a556c734ll ), /* 9 */ |
| 2426 | const_float64( 0x3e927e4fb7789f5cll ), /* 10 */ |
| 2427 | const_float64( 0x3e5ae64567f544e4ll ), /* 11 */ |
| 2428 | const_float64( 0x3e21eed8eff8d898ll ), /* 12 */ |
| 2429 | const_float64( 0x3de6124613a86d09ll ), /* 13 */ |
| 2430 | const_float64( 0x3da93974a8c07c9dll ), /* 14 */ |
| 2431 | const_float64( 0x3d6ae7f3e733b81fll ), /* 15 */ |
David Turner | 2738c26 | 2010-09-09 17:41:26 +0200 | [diff] [blame] | 2432 | }; |
| 2433 | |
| 2434 | float32 float32_exp2( float32 a STATUS_PARAM ) |
| 2435 | { |
| 2436 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2437 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2438 | uint32_t aSig; |
David Turner | 2738c26 | 2010-09-09 17:41:26 +0200 | [diff] [blame] | 2439 | float64 r, x, xn; |
| 2440 | int i; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2441 | a = float32_squash_input_denormal(a STATUS_VAR); |
David Turner | 2738c26 | 2010-09-09 17:41:26 +0200 | [diff] [blame] | 2442 | |
| 2443 | aSig = extractFloat32Frac( a ); |
| 2444 | aExp = extractFloat32Exp( a ); |
| 2445 | aSign = extractFloat32Sign( a ); |
| 2446 | |
| 2447 | if ( aExp == 0xFF) { |
| 2448 | if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); |
| 2449 | return (aSign) ? float32_zero : a; |
| 2450 | } |
| 2451 | if (aExp == 0) { |
| 2452 | if (aSig == 0) return float32_one; |
| 2453 | } |
| 2454 | |
| 2455 | float_raise( float_flag_inexact STATUS_VAR); |
| 2456 | |
| 2457 | /* ******************************* */ |
| 2458 | /* using float64 for approximation */ |
| 2459 | /* ******************************* */ |
| 2460 | x = float32_to_float64(a STATUS_VAR); |
| 2461 | x = float64_mul(x, float64_ln2 STATUS_VAR); |
| 2462 | |
| 2463 | xn = x; |
| 2464 | r = float64_one; |
| 2465 | for (i = 0 ; i < 15 ; i++) { |
| 2466 | float64 f; |
| 2467 | |
| 2468 | f = float64_mul(xn, float32_exp2_coefficients[i] STATUS_VAR); |
| 2469 | r = float64_add(r, f STATUS_VAR); |
| 2470 | |
| 2471 | xn = float64_mul(xn, x STATUS_VAR); |
| 2472 | } |
| 2473 | |
| 2474 | return float64_to_float32(r, status); |
| 2475 | } |
| 2476 | |
| 2477 | /*---------------------------------------------------------------------------- |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 2478 | | Returns the binary log of the single-precision floating-point value `a'. |
| 2479 | | The operation is performed according to the IEC/IEEE Standard for Binary |
| 2480 | | Floating-Point Arithmetic. |
| 2481 | *----------------------------------------------------------------------------*/ |
| 2482 | float32 float32_log2( float32 a STATUS_PARAM ) |
| 2483 | { |
| 2484 | flag aSign, zSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2485 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2486 | uint32_t aSig, zSig, i; |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 2487 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2488 | a = float32_squash_input_denormal(a STATUS_VAR); |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 2489 | aSig = extractFloat32Frac( a ); |
| 2490 | aExp = extractFloat32Exp( a ); |
| 2491 | aSign = extractFloat32Sign( a ); |
| 2492 | |
| 2493 | if ( aExp == 0 ) { |
| 2494 | if ( aSig == 0 ) return packFloat32( 1, 0xFF, 0 ); |
| 2495 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
| 2496 | } |
| 2497 | if ( aSign ) { |
| 2498 | float_raise( float_flag_invalid STATUS_VAR); |
| 2499 | return float32_default_nan; |
| 2500 | } |
| 2501 | if ( aExp == 0xFF ) { |
| 2502 | if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); |
| 2503 | return a; |
| 2504 | } |
| 2505 | |
| 2506 | aExp -= 0x7F; |
| 2507 | aSig |= 0x00800000; |
| 2508 | zSign = aExp < 0; |
| 2509 | zSig = aExp << 23; |
| 2510 | |
| 2511 | for (i = 1 << 22; i > 0; i >>= 1) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2512 | aSig = ( (uint64_t)aSig * aSig ) >> 23; |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 2513 | if ( aSig & 0x01000000 ) { |
| 2514 | aSig >>= 1; |
| 2515 | zSig |= i; |
| 2516 | } |
| 2517 | } |
| 2518 | |
| 2519 | if ( zSign ) |
| 2520 | zSig = -zSig; |
| 2521 | |
| 2522 | return normalizeRoundAndPackFloat32( zSign, 0x85, zSig STATUS_VAR ); |
| 2523 | } |
| 2524 | |
| 2525 | /*---------------------------------------------------------------------------- |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2526 | | Returns 1 if the single-precision floating-point value `a' is equal to |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2527 | | the corresponding value `b', and 0 otherwise. The invalid exception is |
| 2528 | | raised if either operand is a NaN. Otherwise, the comparison is performed |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2529 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 2530 | *----------------------------------------------------------------------------*/ |
| 2531 | |
| 2532 | int float32_eq( float32 a, float32 b STATUS_PARAM ) |
| 2533 | { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2534 | uint32_t av, bv; |
| 2535 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 2536 | b = float32_squash_input_denormal(b STATUS_VAR); |
| 2537 | |
| 2538 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
| 2539 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) |
| 2540 | ) { |
| 2541 | float_raise( float_flag_invalid STATUS_VAR); |
| 2542 | return 0; |
| 2543 | } |
| 2544 | av = float32_val(a); |
| 2545 | bv = float32_val(b); |
| 2546 | return ( av == bv ) || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); |
| 2547 | } |
| 2548 | |
| 2549 | /*---------------------------------------------------------------------------- |
| 2550 | | Returns 1 if the single-precision floating-point value `a' is less than |
| 2551 | | or equal to the corresponding value `b', and 0 otherwise. The invalid |
| 2552 | | exception is raised if either operand is a NaN. The comparison is performed |
| 2553 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 2554 | *----------------------------------------------------------------------------*/ |
| 2555 | |
| 2556 | int float32_le( float32 a, float32 b STATUS_PARAM ) |
| 2557 | { |
| 2558 | flag aSign, bSign; |
| 2559 | uint32_t av, bv; |
| 2560 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 2561 | b = float32_squash_input_denormal(b STATUS_VAR); |
| 2562 | |
| 2563 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
| 2564 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) |
| 2565 | ) { |
| 2566 | float_raise( float_flag_invalid STATUS_VAR); |
| 2567 | return 0; |
| 2568 | } |
| 2569 | aSign = extractFloat32Sign( a ); |
| 2570 | bSign = extractFloat32Sign( b ); |
| 2571 | av = float32_val(a); |
| 2572 | bv = float32_val(b); |
| 2573 | if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); |
| 2574 | return ( av == bv ) || ( aSign ^ ( av < bv ) ); |
| 2575 | |
| 2576 | } |
| 2577 | |
| 2578 | /*---------------------------------------------------------------------------- |
| 2579 | | Returns 1 if the single-precision floating-point value `a' is less than |
| 2580 | | the corresponding value `b', and 0 otherwise. The invalid exception is |
| 2581 | | raised if either operand is a NaN. The comparison is performed according |
| 2582 | | to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 2583 | *----------------------------------------------------------------------------*/ |
| 2584 | |
| 2585 | int float32_lt( float32 a, float32 b STATUS_PARAM ) |
| 2586 | { |
| 2587 | flag aSign, bSign; |
| 2588 | uint32_t av, bv; |
| 2589 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 2590 | b = float32_squash_input_denormal(b STATUS_VAR); |
| 2591 | |
| 2592 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
| 2593 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) |
| 2594 | ) { |
| 2595 | float_raise( float_flag_invalid STATUS_VAR); |
| 2596 | return 0; |
| 2597 | } |
| 2598 | aSign = extractFloat32Sign( a ); |
| 2599 | bSign = extractFloat32Sign( b ); |
| 2600 | av = float32_val(a); |
| 2601 | bv = float32_val(b); |
| 2602 | if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 ); |
| 2603 | return ( av != bv ) && ( aSign ^ ( av < bv ) ); |
| 2604 | |
| 2605 | } |
| 2606 | |
| 2607 | /*---------------------------------------------------------------------------- |
| 2608 | | Returns 1 if the single-precision floating-point values `a' and `b' cannot |
| 2609 | | be compared, and 0 otherwise. The invalid exception is raised if either |
| 2610 | | operand is a NaN. The comparison is performed according to the IEC/IEEE |
| 2611 | | Standard for Binary Floating-Point Arithmetic. |
| 2612 | *----------------------------------------------------------------------------*/ |
| 2613 | |
| 2614 | int float32_unordered( float32 a, float32 b STATUS_PARAM ) |
| 2615 | { |
| 2616 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 2617 | b = float32_squash_input_denormal(b STATUS_VAR); |
| 2618 | |
| 2619 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
| 2620 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) |
| 2621 | ) { |
| 2622 | float_raise( float_flag_invalid STATUS_VAR); |
| 2623 | return 1; |
| 2624 | } |
| 2625 | return 0; |
| 2626 | } |
| 2627 | |
| 2628 | /*---------------------------------------------------------------------------- |
| 2629 | | Returns 1 if the single-precision floating-point value `a' is equal to |
| 2630 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an |
| 2631 | | exception. The comparison is performed according to the IEC/IEEE Standard |
| 2632 | | for Binary Floating-Point Arithmetic. |
| 2633 | *----------------------------------------------------------------------------*/ |
| 2634 | |
| 2635 | int float32_eq_quiet( float32 a, float32 b STATUS_PARAM ) |
| 2636 | { |
| 2637 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 2638 | b = float32_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2639 | |
| 2640 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
| 2641 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) |
| 2642 | ) { |
| 2643 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { |
| 2644 | float_raise( float_flag_invalid STATUS_VAR); |
| 2645 | } |
| 2646 | return 0; |
| 2647 | } |
| 2648 | return ( float32_val(a) == float32_val(b) ) || |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2649 | ( (uint32_t) ( ( float32_val(a) | float32_val(b) )<<1 ) == 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2650 | } |
| 2651 | |
| 2652 | /*---------------------------------------------------------------------------- |
| 2653 | | Returns 1 if the single-precision floating-point value `a' is less than or |
| 2654 | | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not |
| 2655 | | cause an exception. Otherwise, the comparison is performed according to the |
| 2656 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 2657 | *----------------------------------------------------------------------------*/ |
| 2658 | |
| 2659 | int float32_le_quiet( float32 a, float32 b STATUS_PARAM ) |
| 2660 | { |
| 2661 | flag aSign, bSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2662 | uint32_t av, bv; |
| 2663 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 2664 | b = float32_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2665 | |
| 2666 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
| 2667 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) |
| 2668 | ) { |
| 2669 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { |
| 2670 | float_raise( float_flag_invalid STATUS_VAR); |
| 2671 | } |
| 2672 | return 0; |
| 2673 | } |
| 2674 | aSign = extractFloat32Sign( a ); |
| 2675 | bSign = extractFloat32Sign( b ); |
| 2676 | av = float32_val(a); |
| 2677 | bv = float32_val(b); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2678 | if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2679 | return ( av == bv ) || ( aSign ^ ( av < bv ) ); |
| 2680 | |
| 2681 | } |
| 2682 | |
| 2683 | /*---------------------------------------------------------------------------- |
| 2684 | | Returns 1 if the single-precision floating-point value `a' is less than |
| 2685 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an |
| 2686 | | exception. Otherwise, the comparison is performed according to the IEC/IEEE |
| 2687 | | Standard for Binary Floating-Point Arithmetic. |
| 2688 | *----------------------------------------------------------------------------*/ |
| 2689 | |
| 2690 | int float32_lt_quiet( float32 a, float32 b STATUS_PARAM ) |
| 2691 | { |
| 2692 | flag aSign, bSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2693 | uint32_t av, bv; |
| 2694 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 2695 | b = float32_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2696 | |
| 2697 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
| 2698 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) |
| 2699 | ) { |
| 2700 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { |
| 2701 | float_raise( float_flag_invalid STATUS_VAR); |
| 2702 | } |
| 2703 | return 0; |
| 2704 | } |
| 2705 | aSign = extractFloat32Sign( a ); |
| 2706 | bSign = extractFloat32Sign( b ); |
| 2707 | av = float32_val(a); |
| 2708 | bv = float32_val(b); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2709 | if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2710 | return ( av != bv ) && ( aSign ^ ( av < bv ) ); |
| 2711 | |
| 2712 | } |
| 2713 | |
| 2714 | /*---------------------------------------------------------------------------- |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2715 | | Returns 1 if the single-precision floating-point values `a' and `b' cannot |
| 2716 | | be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The |
| 2717 | | comparison is performed according to the IEC/IEEE Standard for Binary |
| 2718 | | Floating-Point Arithmetic. |
| 2719 | *----------------------------------------------------------------------------*/ |
| 2720 | |
| 2721 | int float32_unordered_quiet( float32 a, float32 b STATUS_PARAM ) |
| 2722 | { |
| 2723 | a = float32_squash_input_denormal(a STATUS_VAR); |
| 2724 | b = float32_squash_input_denormal(b STATUS_VAR); |
| 2725 | |
| 2726 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
| 2727 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) |
| 2728 | ) { |
| 2729 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { |
| 2730 | float_raise( float_flag_invalid STATUS_VAR); |
| 2731 | } |
| 2732 | return 1; |
| 2733 | } |
| 2734 | return 0; |
| 2735 | } |
| 2736 | |
| 2737 | /*---------------------------------------------------------------------------- |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2738 | | Returns the result of converting the double-precision floating-point value |
| 2739 | | `a' to the 32-bit two's complement integer format. The conversion is |
| 2740 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 2741 | | Arithmetic---which means in particular that the conversion is rounded |
| 2742 | | according to the current rounding mode. If `a' is a NaN, the largest |
| 2743 | | positive integer is returned. Otherwise, if the conversion overflows, the |
| 2744 | | largest integer with the same sign as `a' is returned. |
| 2745 | *----------------------------------------------------------------------------*/ |
| 2746 | |
| 2747 | int32 float64_to_int32( float64 a STATUS_PARAM ) |
| 2748 | { |
| 2749 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2750 | int_fast16_t aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2751 | uint64_t aSig; |
| 2752 | a = float64_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2753 | |
| 2754 | aSig = extractFloat64Frac( a ); |
| 2755 | aExp = extractFloat64Exp( a ); |
| 2756 | aSign = extractFloat64Sign( a ); |
| 2757 | if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; |
| 2758 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); |
| 2759 | shiftCount = 0x42C - aExp; |
| 2760 | if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig ); |
| 2761 | return roundAndPackInt32( aSign, aSig STATUS_VAR ); |
| 2762 | |
| 2763 | } |
| 2764 | |
| 2765 | /*---------------------------------------------------------------------------- |
| 2766 | | Returns the result of converting the double-precision floating-point value |
| 2767 | | `a' to the 32-bit two's complement integer format. The conversion is |
| 2768 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 2769 | | Arithmetic, except that the conversion is always rounded toward zero. |
| 2770 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if |
| 2771 | | the conversion overflows, the largest integer with the same sign as `a' is |
| 2772 | | returned. |
| 2773 | *----------------------------------------------------------------------------*/ |
| 2774 | |
| 2775 | int32 float64_to_int32_round_to_zero( float64 a STATUS_PARAM ) |
| 2776 | { |
| 2777 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2778 | int_fast16_t aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2779 | uint64_t aSig, savedASig; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2780 | int32_t z; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2781 | a = float64_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2782 | |
| 2783 | aSig = extractFloat64Frac( a ); |
| 2784 | aExp = extractFloat64Exp( a ); |
| 2785 | aSign = extractFloat64Sign( a ); |
| 2786 | if ( 0x41E < aExp ) { |
| 2787 | if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; |
| 2788 | goto invalid; |
| 2789 | } |
| 2790 | else if ( aExp < 0x3FF ) { |
| 2791 | if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 2792 | return 0; |
| 2793 | } |
| 2794 | aSig |= LIT64( 0x0010000000000000 ); |
| 2795 | shiftCount = 0x433 - aExp; |
| 2796 | savedASig = aSig; |
| 2797 | aSig >>= shiftCount; |
| 2798 | z = aSig; |
| 2799 | if ( aSign ) z = - z; |
| 2800 | if ( ( z < 0 ) ^ aSign ) { |
| 2801 | invalid: |
| 2802 | float_raise( float_flag_invalid STATUS_VAR); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2803 | return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2804 | } |
| 2805 | if ( ( aSig<<shiftCount ) != savedASig ) { |
| 2806 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 2807 | } |
| 2808 | return z; |
| 2809 | |
| 2810 | } |
| 2811 | |
| 2812 | /*---------------------------------------------------------------------------- |
| 2813 | | Returns the result of converting the double-precision floating-point value |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2814 | | `a' to the 16-bit two's complement integer format. The conversion is |
| 2815 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 2816 | | Arithmetic, except that the conversion is always rounded toward zero. |
| 2817 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if |
| 2818 | | the conversion overflows, the largest integer with the same sign as `a' is |
| 2819 | | returned. |
| 2820 | *----------------------------------------------------------------------------*/ |
| 2821 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2822 | int_fast16_t float64_to_int16_round_to_zero(float64 a STATUS_PARAM) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2823 | { |
| 2824 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2825 | int_fast16_t aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2826 | uint64_t aSig, savedASig; |
| 2827 | int32 z; |
| 2828 | |
| 2829 | aSig = extractFloat64Frac( a ); |
| 2830 | aExp = extractFloat64Exp( a ); |
| 2831 | aSign = extractFloat64Sign( a ); |
| 2832 | if ( 0x40E < aExp ) { |
| 2833 | if ( ( aExp == 0x7FF ) && aSig ) { |
| 2834 | aSign = 0; |
| 2835 | } |
| 2836 | goto invalid; |
| 2837 | } |
| 2838 | else if ( aExp < 0x3FF ) { |
| 2839 | if ( aExp || aSig ) { |
| 2840 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 2841 | } |
| 2842 | return 0; |
| 2843 | } |
| 2844 | aSig |= LIT64( 0x0010000000000000 ); |
| 2845 | shiftCount = 0x433 - aExp; |
| 2846 | savedASig = aSig; |
| 2847 | aSig >>= shiftCount; |
| 2848 | z = aSig; |
| 2849 | if ( aSign ) { |
| 2850 | z = - z; |
| 2851 | } |
| 2852 | if ( ( (int16_t)z < 0 ) ^ aSign ) { |
| 2853 | invalid: |
| 2854 | float_raise( float_flag_invalid STATUS_VAR); |
| 2855 | return aSign ? (int32_t) 0xffff8000 : 0x7FFF; |
| 2856 | } |
| 2857 | if ( ( aSig<<shiftCount ) != savedASig ) { |
| 2858 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 2859 | } |
| 2860 | return z; |
| 2861 | } |
| 2862 | |
| 2863 | /*---------------------------------------------------------------------------- |
| 2864 | | Returns the result of converting the double-precision floating-point value |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2865 | | `a' to the 64-bit two's complement integer format. The conversion is |
| 2866 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 2867 | | Arithmetic---which means in particular that the conversion is rounded |
| 2868 | | according to the current rounding mode. If `a' is a NaN, the largest |
| 2869 | | positive integer is returned. Otherwise, if the conversion overflows, the |
| 2870 | | largest integer with the same sign as `a' is returned. |
| 2871 | *----------------------------------------------------------------------------*/ |
| 2872 | |
| 2873 | int64 float64_to_int64( float64 a STATUS_PARAM ) |
| 2874 | { |
| 2875 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2876 | int_fast16_t aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2877 | uint64_t aSig, aSigExtra; |
| 2878 | a = float64_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2879 | |
| 2880 | aSig = extractFloat64Frac( a ); |
| 2881 | aExp = extractFloat64Exp( a ); |
| 2882 | aSign = extractFloat64Sign( a ); |
| 2883 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); |
| 2884 | shiftCount = 0x433 - aExp; |
| 2885 | if ( shiftCount <= 0 ) { |
| 2886 | if ( 0x43E < aExp ) { |
| 2887 | float_raise( float_flag_invalid STATUS_VAR); |
| 2888 | if ( ! aSign |
| 2889 | || ( ( aExp == 0x7FF ) |
| 2890 | && ( aSig != LIT64( 0x0010000000000000 ) ) ) |
| 2891 | ) { |
| 2892 | return LIT64( 0x7FFFFFFFFFFFFFFF ); |
| 2893 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2894 | return (int64_t) LIT64( 0x8000000000000000 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2895 | } |
| 2896 | aSigExtra = 0; |
| 2897 | aSig <<= - shiftCount; |
| 2898 | } |
| 2899 | else { |
| 2900 | shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); |
| 2901 | } |
| 2902 | return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR ); |
| 2903 | |
| 2904 | } |
| 2905 | |
| 2906 | /*---------------------------------------------------------------------------- |
| 2907 | | Returns the result of converting the double-precision floating-point value |
| 2908 | | `a' to the 64-bit two's complement integer format. The conversion is |
| 2909 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 2910 | | Arithmetic, except that the conversion is always rounded toward zero. |
| 2911 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if |
| 2912 | | the conversion overflows, the largest integer with the same sign as `a' is |
| 2913 | | returned. |
| 2914 | *----------------------------------------------------------------------------*/ |
| 2915 | |
| 2916 | int64 float64_to_int64_round_to_zero( float64 a STATUS_PARAM ) |
| 2917 | { |
| 2918 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2919 | int_fast16_t aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2920 | uint64_t aSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2921 | int64 z; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2922 | a = float64_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2923 | |
| 2924 | aSig = extractFloat64Frac( a ); |
| 2925 | aExp = extractFloat64Exp( a ); |
| 2926 | aSign = extractFloat64Sign( a ); |
| 2927 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); |
| 2928 | shiftCount = aExp - 0x433; |
| 2929 | if ( 0 <= shiftCount ) { |
| 2930 | if ( 0x43E <= aExp ) { |
| 2931 | if ( float64_val(a) != LIT64( 0xC3E0000000000000 ) ) { |
| 2932 | float_raise( float_flag_invalid STATUS_VAR); |
| 2933 | if ( ! aSign |
| 2934 | || ( ( aExp == 0x7FF ) |
| 2935 | && ( aSig != LIT64( 0x0010000000000000 ) ) ) |
| 2936 | ) { |
| 2937 | return LIT64( 0x7FFFFFFFFFFFFFFF ); |
| 2938 | } |
| 2939 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2940 | return (int64_t) LIT64( 0x8000000000000000 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2941 | } |
| 2942 | z = aSig<<shiftCount; |
| 2943 | } |
| 2944 | else { |
| 2945 | if ( aExp < 0x3FE ) { |
| 2946 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 2947 | return 0; |
| 2948 | } |
| 2949 | z = aSig>>( - shiftCount ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2950 | if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2951 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 2952 | } |
| 2953 | } |
| 2954 | if ( aSign ) z = - z; |
| 2955 | return z; |
| 2956 | |
| 2957 | } |
| 2958 | |
| 2959 | /*---------------------------------------------------------------------------- |
| 2960 | | Returns the result of converting the double-precision floating-point value |
| 2961 | | `a' to the single-precision floating-point format. The conversion is |
| 2962 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 2963 | | Arithmetic. |
| 2964 | *----------------------------------------------------------------------------*/ |
| 2965 | |
| 2966 | float32 float64_to_float32( float64 a STATUS_PARAM ) |
| 2967 | { |
| 2968 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 2969 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2970 | uint64_t aSig; |
| 2971 | uint32_t zSig; |
| 2972 | a = float64_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2973 | |
| 2974 | aSig = extractFloat64Frac( a ); |
| 2975 | aExp = extractFloat64Exp( a ); |
| 2976 | aSign = extractFloat64Sign( a ); |
| 2977 | if ( aExp == 0x7FF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 2978 | if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 2979 | return packFloat32( aSign, 0xFF, 0 ); |
| 2980 | } |
| 2981 | shift64RightJamming( aSig, 22, &aSig ); |
| 2982 | zSig = aSig; |
| 2983 | if ( aExp || zSig ) { |
| 2984 | zSig |= 0x40000000; |
| 2985 | aExp -= 0x381; |
| 2986 | } |
| 2987 | return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR ); |
| 2988 | |
| 2989 | } |
| 2990 | |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 2991 | |
| 2992 | /*---------------------------------------------------------------------------- |
| 2993 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a |
| 2994 | | half-precision floating-point value, returning the result. After being |
| 2995 | | shifted into the proper positions, the three fields are simply added |
| 2996 | | together to form the result. This means that any integer portion of `zSig' |
| 2997 | | will be added into the exponent. Since a properly normalized significand |
| 2998 | | will have an integer portion equal to 1, the `zExp' input should be 1 less |
| 2999 | | than the desired result exponent whenever `zSig' is a complete, normalized |
| 3000 | | significand. |
| 3001 | *----------------------------------------------------------------------------*/ |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3002 | static float16 packFloat16(flag zSign, int_fast16_t zExp, uint16_t zSig) |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3003 | { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3004 | return make_float16( |
| 3005 | (((uint32_t)zSign) << 15) + (((uint32_t)zExp) << 10) + zSig); |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3006 | } |
| 3007 | |
| 3008 | /* Half precision floats come in two formats: standard IEEE and "ARM" format. |
| 3009 | The latter gains extra exponent range by omitting the NaN/Inf encodings. */ |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3010 | |
| 3011 | float32 float16_to_float32(float16 a, flag ieee STATUS_PARAM) |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3012 | { |
| 3013 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3014 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3015 | uint32_t aSig; |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3016 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3017 | aSign = extractFloat16Sign(a); |
| 3018 | aExp = extractFloat16Exp(a); |
| 3019 | aSig = extractFloat16Frac(a); |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3020 | |
| 3021 | if (aExp == 0x1f && ieee) { |
| 3022 | if (aSig) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3023 | return commonNaNToFloat32(float16ToCommonNaN(a STATUS_VAR) STATUS_VAR); |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3024 | } |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3025 | return packFloat32(aSign, 0xff, 0); |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3026 | } |
| 3027 | if (aExp == 0) { |
| 3028 | int8 shiftCount; |
| 3029 | |
| 3030 | if (aSig == 0) { |
| 3031 | return packFloat32(aSign, 0, 0); |
| 3032 | } |
| 3033 | |
| 3034 | shiftCount = countLeadingZeros32( aSig ) - 21; |
| 3035 | aSig = aSig << shiftCount; |
| 3036 | aExp = -shiftCount; |
| 3037 | } |
| 3038 | return packFloat32( aSign, aExp + 0x70, aSig << 13); |
| 3039 | } |
| 3040 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3041 | float16 float32_to_float16(float32 a, flag ieee STATUS_PARAM) |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3042 | { |
| 3043 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3044 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3045 | uint32_t aSig; |
| 3046 | uint32_t mask; |
| 3047 | uint32_t increment; |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3048 | int8 roundingMode; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3049 | a = float32_squash_input_denormal(a STATUS_VAR); |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3050 | |
| 3051 | aSig = extractFloat32Frac( a ); |
| 3052 | aExp = extractFloat32Exp( a ); |
| 3053 | aSign = extractFloat32Sign( a ); |
| 3054 | if ( aExp == 0xFF ) { |
| 3055 | if (aSig) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3056 | /* Input is a NaN */ |
| 3057 | float16 r = commonNaNToFloat16( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
| 3058 | if (!ieee) { |
| 3059 | return packFloat16(aSign, 0, 0); |
| 3060 | } |
| 3061 | return r; |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3062 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3063 | /* Infinity */ |
| 3064 | if (!ieee) { |
| 3065 | float_raise(float_flag_invalid STATUS_VAR); |
| 3066 | return packFloat16(aSign, 0x1f, 0x3ff); |
| 3067 | } |
| 3068 | return packFloat16(aSign, 0x1f, 0); |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3069 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3070 | if (aExp == 0 && aSig == 0) { |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3071 | return packFloat16(aSign, 0, 0); |
| 3072 | } |
| 3073 | /* Decimal point between bits 22 and 23. */ |
| 3074 | aSig |= 0x00800000; |
| 3075 | aExp -= 0x7f; |
| 3076 | if (aExp < -14) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3077 | mask = 0x00ffffff; |
| 3078 | if (aExp >= -24) { |
| 3079 | mask >>= 25 + aExp; |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3080 | } |
| 3081 | } else { |
| 3082 | mask = 0x00001fff; |
| 3083 | } |
| 3084 | if (aSig & mask) { |
| 3085 | float_raise( float_flag_underflow STATUS_VAR ); |
| 3086 | roundingMode = STATUS(float_rounding_mode); |
| 3087 | switch (roundingMode) { |
| 3088 | case float_round_nearest_even: |
| 3089 | increment = (mask + 1) >> 1; |
| 3090 | if ((aSig & mask) == increment) { |
| 3091 | increment = aSig & (increment << 1); |
| 3092 | } |
| 3093 | break; |
| 3094 | case float_round_up: |
| 3095 | increment = aSign ? 0 : mask; |
| 3096 | break; |
| 3097 | case float_round_down: |
| 3098 | increment = aSign ? mask : 0; |
| 3099 | break; |
| 3100 | default: /* round_to_zero */ |
| 3101 | increment = 0; |
| 3102 | break; |
| 3103 | } |
| 3104 | aSig += increment; |
| 3105 | if (aSig >= 0x01000000) { |
| 3106 | aSig >>= 1; |
| 3107 | aExp++; |
| 3108 | } |
| 3109 | } else if (aExp < -14 |
| 3110 | && STATUS(float_detect_tininess) == float_tininess_before_rounding) { |
| 3111 | float_raise( float_flag_underflow STATUS_VAR); |
| 3112 | } |
| 3113 | |
| 3114 | if (ieee) { |
| 3115 | if (aExp > 15) { |
| 3116 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
| 3117 | return packFloat16(aSign, 0x1f, 0); |
| 3118 | } |
| 3119 | } else { |
| 3120 | if (aExp > 16) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3121 | float_raise(float_flag_invalid | float_flag_inexact STATUS_VAR); |
David 'Digit' Turner | 2c538c8 | 2010-05-10 16:48:20 -0700 | [diff] [blame] | 3122 | return packFloat16(aSign, 0x1f, 0x3ff); |
| 3123 | } |
| 3124 | } |
| 3125 | if (aExp < -24) { |
| 3126 | return packFloat16(aSign, 0, 0); |
| 3127 | } |
| 3128 | if (aExp < -14) { |
| 3129 | aSig >>= -14 - aExp; |
| 3130 | aExp = -14; |
| 3131 | } |
| 3132 | return packFloat16(aSign, aExp + 14, aSig >> 13); |
| 3133 | } |
| 3134 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3135 | /*---------------------------------------------------------------------------- |
| 3136 | | Returns the result of converting the double-precision floating-point value |
| 3137 | | `a' to the extended double-precision floating-point format. The conversion |
| 3138 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 3139 | | Arithmetic. |
| 3140 | *----------------------------------------------------------------------------*/ |
| 3141 | |
| 3142 | floatx80 float64_to_floatx80( float64 a STATUS_PARAM ) |
| 3143 | { |
| 3144 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3145 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3146 | uint64_t aSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3147 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3148 | a = float64_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3149 | aSig = extractFloat64Frac( a ); |
| 3150 | aExp = extractFloat64Exp( a ); |
| 3151 | aSign = extractFloat64Sign( a ); |
| 3152 | if ( aExp == 0x7FF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3153 | if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3154 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
| 3155 | } |
| 3156 | if ( aExp == 0 ) { |
| 3157 | if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); |
| 3158 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
| 3159 | } |
| 3160 | return |
| 3161 | packFloatx80( |
| 3162 | aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 ); |
| 3163 | |
| 3164 | } |
| 3165 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3166 | /*---------------------------------------------------------------------------- |
| 3167 | | Returns the result of converting the double-precision floating-point value |
| 3168 | | `a' to the quadruple-precision floating-point format. The conversion is |
| 3169 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 3170 | | Arithmetic. |
| 3171 | *----------------------------------------------------------------------------*/ |
| 3172 | |
| 3173 | float128 float64_to_float128( float64 a STATUS_PARAM ) |
| 3174 | { |
| 3175 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3176 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3177 | uint64_t aSig, zSig0, zSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3178 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3179 | a = float64_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3180 | aSig = extractFloat64Frac( a ); |
| 3181 | aExp = extractFloat64Exp( a ); |
| 3182 | aSign = extractFloat64Sign( a ); |
| 3183 | if ( aExp == 0x7FF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3184 | if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3185 | return packFloat128( aSign, 0x7FFF, 0, 0 ); |
| 3186 | } |
| 3187 | if ( aExp == 0 ) { |
| 3188 | if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); |
| 3189 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
| 3190 | --aExp; |
| 3191 | } |
| 3192 | shift128Right( aSig, 0, 4, &zSig0, &zSig1 ); |
| 3193 | return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 ); |
| 3194 | |
| 3195 | } |
| 3196 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3197 | /*---------------------------------------------------------------------------- |
| 3198 | | Rounds the double-precision floating-point value `a' to an integer, and |
| 3199 | | returns the result as a double-precision floating-point value. The |
| 3200 | | operation is performed according to the IEC/IEEE Standard for Binary |
| 3201 | | Floating-Point Arithmetic. |
| 3202 | *----------------------------------------------------------------------------*/ |
| 3203 | |
| 3204 | float64 float64_round_to_int( float64 a STATUS_PARAM ) |
| 3205 | { |
| 3206 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3207 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3208 | uint64_t lastBitMask, roundBitsMask; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3209 | int8 roundingMode; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3210 | uint64_t z; |
| 3211 | a = float64_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3212 | |
| 3213 | aExp = extractFloat64Exp( a ); |
| 3214 | if ( 0x433 <= aExp ) { |
| 3215 | if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) { |
| 3216 | return propagateFloat64NaN( a, a STATUS_VAR ); |
| 3217 | } |
| 3218 | return a; |
| 3219 | } |
| 3220 | if ( aExp < 0x3FF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3221 | if ( (uint64_t) ( float64_val(a)<<1 ) == 0 ) return a; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3222 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 3223 | aSign = extractFloat64Sign( a ); |
| 3224 | switch ( STATUS(float_rounding_mode) ) { |
| 3225 | case float_round_nearest_even: |
| 3226 | if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) { |
| 3227 | return packFloat64( aSign, 0x3FF, 0 ); |
| 3228 | } |
| 3229 | break; |
| 3230 | case float_round_down: |
| 3231 | return make_float64(aSign ? LIT64( 0xBFF0000000000000 ) : 0); |
| 3232 | case float_round_up: |
| 3233 | return make_float64( |
| 3234 | aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 )); |
| 3235 | } |
| 3236 | return packFloat64( aSign, 0, 0 ); |
| 3237 | } |
| 3238 | lastBitMask = 1; |
| 3239 | lastBitMask <<= 0x433 - aExp; |
| 3240 | roundBitsMask = lastBitMask - 1; |
| 3241 | z = float64_val(a); |
| 3242 | roundingMode = STATUS(float_rounding_mode); |
| 3243 | if ( roundingMode == float_round_nearest_even ) { |
| 3244 | z += lastBitMask>>1; |
| 3245 | if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; |
| 3246 | } |
| 3247 | else if ( roundingMode != float_round_to_zero ) { |
| 3248 | if ( extractFloat64Sign( make_float64(z) ) ^ ( roundingMode == float_round_up ) ) { |
| 3249 | z += roundBitsMask; |
| 3250 | } |
| 3251 | } |
| 3252 | z &= ~ roundBitsMask; |
| 3253 | if ( z != float64_val(a) ) |
| 3254 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 3255 | return make_float64(z); |
| 3256 | |
| 3257 | } |
| 3258 | |
| 3259 | float64 float64_trunc_to_int( float64 a STATUS_PARAM) |
| 3260 | { |
| 3261 | int oldmode; |
| 3262 | float64 res; |
| 3263 | oldmode = STATUS(float_rounding_mode); |
| 3264 | STATUS(float_rounding_mode) = float_round_to_zero; |
| 3265 | res = float64_round_to_int(a STATUS_VAR); |
| 3266 | STATUS(float_rounding_mode) = oldmode; |
| 3267 | return res; |
| 3268 | } |
| 3269 | |
| 3270 | /*---------------------------------------------------------------------------- |
| 3271 | | Returns the result of adding the absolute values of the double-precision |
| 3272 | | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated |
| 3273 | | before being returned. `zSign' is ignored if the result is a NaN. |
| 3274 | | The addition is performed according to the IEC/IEEE Standard for Binary |
| 3275 | | Floating-Point Arithmetic. |
| 3276 | *----------------------------------------------------------------------------*/ |
| 3277 | |
| 3278 | static float64 addFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM ) |
| 3279 | { |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3280 | int_fast16_t aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3281 | uint64_t aSig, bSig, zSig; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3282 | int_fast16_t expDiff; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3283 | |
| 3284 | aSig = extractFloat64Frac( a ); |
| 3285 | aExp = extractFloat64Exp( a ); |
| 3286 | bSig = extractFloat64Frac( b ); |
| 3287 | bExp = extractFloat64Exp( b ); |
| 3288 | expDiff = aExp - bExp; |
| 3289 | aSig <<= 9; |
| 3290 | bSig <<= 9; |
| 3291 | if ( 0 < expDiff ) { |
| 3292 | if ( aExp == 0x7FF ) { |
| 3293 | if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3294 | return a; |
| 3295 | } |
| 3296 | if ( bExp == 0 ) { |
| 3297 | --expDiff; |
| 3298 | } |
| 3299 | else { |
| 3300 | bSig |= LIT64( 0x2000000000000000 ); |
| 3301 | } |
| 3302 | shift64RightJamming( bSig, expDiff, &bSig ); |
| 3303 | zExp = aExp; |
| 3304 | } |
| 3305 | else if ( expDiff < 0 ) { |
| 3306 | if ( bExp == 0x7FF ) { |
| 3307 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3308 | return packFloat64( zSign, 0x7FF, 0 ); |
| 3309 | } |
| 3310 | if ( aExp == 0 ) { |
| 3311 | ++expDiff; |
| 3312 | } |
| 3313 | else { |
| 3314 | aSig |= LIT64( 0x2000000000000000 ); |
| 3315 | } |
| 3316 | shift64RightJamming( aSig, - expDiff, &aSig ); |
| 3317 | zExp = bExp; |
| 3318 | } |
| 3319 | else { |
| 3320 | if ( aExp == 0x7FF ) { |
| 3321 | if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3322 | return a; |
| 3323 | } |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 3324 | if ( aExp == 0 ) { |
David 'Digit' Turner | 5285864 | 2011-06-03 13:41:05 +0200 | [diff] [blame] | 3325 | if (STATUS(flush_to_zero)) { |
| 3326 | if (aSig | bSig) { |
| 3327 | float_raise(float_flag_output_denormal STATUS_VAR); |
| 3328 | } |
| 3329 | return packFloat64(zSign, 0, 0); |
| 3330 | } |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 3331 | return packFloat64( zSign, 0, ( aSig + bSig )>>9 ); |
| 3332 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3333 | zSig = LIT64( 0x4000000000000000 ) + aSig + bSig; |
| 3334 | zExp = aExp; |
| 3335 | goto roundAndPack; |
| 3336 | } |
| 3337 | aSig |= LIT64( 0x2000000000000000 ); |
| 3338 | zSig = ( aSig + bSig )<<1; |
| 3339 | --zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3340 | if ( (int64_t) zSig < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3341 | zSig = aSig + bSig; |
| 3342 | ++zExp; |
| 3343 | } |
| 3344 | roundAndPack: |
| 3345 | return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); |
| 3346 | |
| 3347 | } |
| 3348 | |
| 3349 | /*---------------------------------------------------------------------------- |
| 3350 | | Returns the result of subtracting the absolute values of the double- |
| 3351 | | precision floating-point values `a' and `b'. If `zSign' is 1, the |
| 3352 | | difference is negated before being returned. `zSign' is ignored if the |
| 3353 | | result is a NaN. The subtraction is performed according to the IEC/IEEE |
| 3354 | | Standard for Binary Floating-Point Arithmetic. |
| 3355 | *----------------------------------------------------------------------------*/ |
| 3356 | |
| 3357 | static float64 subFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM ) |
| 3358 | { |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3359 | int_fast16_t aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3360 | uint64_t aSig, bSig, zSig; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3361 | int_fast16_t expDiff; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3362 | |
| 3363 | aSig = extractFloat64Frac( a ); |
| 3364 | aExp = extractFloat64Exp( a ); |
| 3365 | bSig = extractFloat64Frac( b ); |
| 3366 | bExp = extractFloat64Exp( b ); |
| 3367 | expDiff = aExp - bExp; |
| 3368 | aSig <<= 10; |
| 3369 | bSig <<= 10; |
| 3370 | if ( 0 < expDiff ) goto aExpBigger; |
| 3371 | if ( expDiff < 0 ) goto bExpBigger; |
| 3372 | if ( aExp == 0x7FF ) { |
| 3373 | if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3374 | float_raise( float_flag_invalid STATUS_VAR); |
| 3375 | return float64_default_nan; |
| 3376 | } |
| 3377 | if ( aExp == 0 ) { |
| 3378 | aExp = 1; |
| 3379 | bExp = 1; |
| 3380 | } |
| 3381 | if ( bSig < aSig ) goto aBigger; |
| 3382 | if ( aSig < bSig ) goto bBigger; |
| 3383 | return packFloat64( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); |
| 3384 | bExpBigger: |
| 3385 | if ( bExp == 0x7FF ) { |
| 3386 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3387 | return packFloat64( zSign ^ 1, 0x7FF, 0 ); |
| 3388 | } |
| 3389 | if ( aExp == 0 ) { |
| 3390 | ++expDiff; |
| 3391 | } |
| 3392 | else { |
| 3393 | aSig |= LIT64( 0x4000000000000000 ); |
| 3394 | } |
| 3395 | shift64RightJamming( aSig, - expDiff, &aSig ); |
| 3396 | bSig |= LIT64( 0x4000000000000000 ); |
| 3397 | bBigger: |
| 3398 | zSig = bSig - aSig; |
| 3399 | zExp = bExp; |
| 3400 | zSign ^= 1; |
| 3401 | goto normalizeRoundAndPack; |
| 3402 | aExpBigger: |
| 3403 | if ( aExp == 0x7FF ) { |
| 3404 | if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3405 | return a; |
| 3406 | } |
| 3407 | if ( bExp == 0 ) { |
| 3408 | --expDiff; |
| 3409 | } |
| 3410 | else { |
| 3411 | bSig |= LIT64( 0x4000000000000000 ); |
| 3412 | } |
| 3413 | shift64RightJamming( bSig, expDiff, &bSig ); |
| 3414 | aSig |= LIT64( 0x4000000000000000 ); |
| 3415 | aBigger: |
| 3416 | zSig = aSig - bSig; |
| 3417 | zExp = aExp; |
| 3418 | normalizeRoundAndPack: |
| 3419 | --zExp; |
| 3420 | return normalizeRoundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); |
| 3421 | |
| 3422 | } |
| 3423 | |
| 3424 | /*---------------------------------------------------------------------------- |
| 3425 | | Returns the result of adding the double-precision floating-point values `a' |
| 3426 | | and `b'. The operation is performed according to the IEC/IEEE Standard for |
| 3427 | | Binary Floating-Point Arithmetic. |
| 3428 | *----------------------------------------------------------------------------*/ |
| 3429 | |
| 3430 | float64 float64_add( float64 a, float64 b STATUS_PARAM ) |
| 3431 | { |
| 3432 | flag aSign, bSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3433 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 3434 | b = float64_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3435 | |
| 3436 | aSign = extractFloat64Sign( a ); |
| 3437 | bSign = extractFloat64Sign( b ); |
| 3438 | if ( aSign == bSign ) { |
| 3439 | return addFloat64Sigs( a, b, aSign STATUS_VAR ); |
| 3440 | } |
| 3441 | else { |
| 3442 | return subFloat64Sigs( a, b, aSign STATUS_VAR ); |
| 3443 | } |
| 3444 | |
| 3445 | } |
| 3446 | |
| 3447 | /*---------------------------------------------------------------------------- |
| 3448 | | Returns the result of subtracting the double-precision floating-point values |
| 3449 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard |
| 3450 | | for Binary Floating-Point Arithmetic. |
| 3451 | *----------------------------------------------------------------------------*/ |
| 3452 | |
| 3453 | float64 float64_sub( float64 a, float64 b STATUS_PARAM ) |
| 3454 | { |
| 3455 | flag aSign, bSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3456 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 3457 | b = float64_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3458 | |
| 3459 | aSign = extractFloat64Sign( a ); |
| 3460 | bSign = extractFloat64Sign( b ); |
| 3461 | if ( aSign == bSign ) { |
| 3462 | return subFloat64Sigs( a, b, aSign STATUS_VAR ); |
| 3463 | } |
| 3464 | else { |
| 3465 | return addFloat64Sigs( a, b, aSign STATUS_VAR ); |
| 3466 | } |
| 3467 | |
| 3468 | } |
| 3469 | |
| 3470 | /*---------------------------------------------------------------------------- |
| 3471 | | Returns the result of multiplying the double-precision floating-point values |
| 3472 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard |
| 3473 | | for Binary Floating-Point Arithmetic. |
| 3474 | *----------------------------------------------------------------------------*/ |
| 3475 | |
| 3476 | float64 float64_mul( float64 a, float64 b STATUS_PARAM ) |
| 3477 | { |
| 3478 | flag aSign, bSign, zSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3479 | int_fast16_t aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3480 | uint64_t aSig, bSig, zSig0, zSig1; |
| 3481 | |
| 3482 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 3483 | b = float64_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3484 | |
| 3485 | aSig = extractFloat64Frac( a ); |
| 3486 | aExp = extractFloat64Exp( a ); |
| 3487 | aSign = extractFloat64Sign( a ); |
| 3488 | bSig = extractFloat64Frac( b ); |
| 3489 | bExp = extractFloat64Exp( b ); |
| 3490 | bSign = extractFloat64Sign( b ); |
| 3491 | zSign = aSign ^ bSign; |
| 3492 | if ( aExp == 0x7FF ) { |
| 3493 | if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { |
| 3494 | return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3495 | } |
| 3496 | if ( ( bExp | bSig ) == 0 ) { |
| 3497 | float_raise( float_flag_invalid STATUS_VAR); |
| 3498 | return float64_default_nan; |
| 3499 | } |
| 3500 | return packFloat64( zSign, 0x7FF, 0 ); |
| 3501 | } |
| 3502 | if ( bExp == 0x7FF ) { |
| 3503 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3504 | if ( ( aExp | aSig ) == 0 ) { |
| 3505 | float_raise( float_flag_invalid STATUS_VAR); |
| 3506 | return float64_default_nan; |
| 3507 | } |
| 3508 | return packFloat64( zSign, 0x7FF, 0 ); |
| 3509 | } |
| 3510 | if ( aExp == 0 ) { |
| 3511 | if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); |
| 3512 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
| 3513 | } |
| 3514 | if ( bExp == 0 ) { |
| 3515 | if ( bSig == 0 ) return packFloat64( zSign, 0, 0 ); |
| 3516 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); |
| 3517 | } |
| 3518 | zExp = aExp + bExp - 0x3FF; |
| 3519 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; |
| 3520 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; |
| 3521 | mul64To128( aSig, bSig, &zSig0, &zSig1 ); |
| 3522 | zSig0 |= ( zSig1 != 0 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3523 | if ( 0 <= (int64_t) ( zSig0<<1 ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3524 | zSig0 <<= 1; |
| 3525 | --zExp; |
| 3526 | } |
| 3527 | return roundAndPackFloat64( zSign, zExp, zSig0 STATUS_VAR ); |
| 3528 | |
| 3529 | } |
| 3530 | |
| 3531 | /*---------------------------------------------------------------------------- |
| 3532 | | Returns the result of dividing the double-precision floating-point value `a' |
| 3533 | | by the corresponding value `b'. The operation is performed according to |
| 3534 | | the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 3535 | *----------------------------------------------------------------------------*/ |
| 3536 | |
| 3537 | float64 float64_div( float64 a, float64 b STATUS_PARAM ) |
| 3538 | { |
| 3539 | flag aSign, bSign, zSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3540 | int_fast16_t aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3541 | uint64_t aSig, bSig, zSig; |
| 3542 | uint64_t rem0, rem1; |
| 3543 | uint64_t term0, term1; |
| 3544 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 3545 | b = float64_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3546 | |
| 3547 | aSig = extractFloat64Frac( a ); |
| 3548 | aExp = extractFloat64Exp( a ); |
| 3549 | aSign = extractFloat64Sign( a ); |
| 3550 | bSig = extractFloat64Frac( b ); |
| 3551 | bExp = extractFloat64Exp( b ); |
| 3552 | bSign = extractFloat64Sign( b ); |
| 3553 | zSign = aSign ^ bSign; |
| 3554 | if ( aExp == 0x7FF ) { |
| 3555 | if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3556 | if ( bExp == 0x7FF ) { |
| 3557 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3558 | float_raise( float_flag_invalid STATUS_VAR); |
| 3559 | return float64_default_nan; |
| 3560 | } |
| 3561 | return packFloat64( zSign, 0x7FF, 0 ); |
| 3562 | } |
| 3563 | if ( bExp == 0x7FF ) { |
| 3564 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3565 | return packFloat64( zSign, 0, 0 ); |
| 3566 | } |
| 3567 | if ( bExp == 0 ) { |
| 3568 | if ( bSig == 0 ) { |
| 3569 | if ( ( aExp | aSig ) == 0 ) { |
| 3570 | float_raise( float_flag_invalid STATUS_VAR); |
| 3571 | return float64_default_nan; |
| 3572 | } |
| 3573 | float_raise( float_flag_divbyzero STATUS_VAR); |
| 3574 | return packFloat64( zSign, 0x7FF, 0 ); |
| 3575 | } |
| 3576 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); |
| 3577 | } |
| 3578 | if ( aExp == 0 ) { |
| 3579 | if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); |
| 3580 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
| 3581 | } |
| 3582 | zExp = aExp - bExp + 0x3FD; |
| 3583 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; |
| 3584 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; |
| 3585 | if ( bSig <= ( aSig + aSig ) ) { |
| 3586 | aSig >>= 1; |
| 3587 | ++zExp; |
| 3588 | } |
| 3589 | zSig = estimateDiv128To64( aSig, 0, bSig ); |
| 3590 | if ( ( zSig & 0x1FF ) <= 2 ) { |
| 3591 | mul64To128( bSig, zSig, &term0, &term1 ); |
| 3592 | sub128( aSig, 0, term0, term1, &rem0, &rem1 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3593 | while ( (int64_t) rem0 < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3594 | --zSig; |
| 3595 | add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); |
| 3596 | } |
| 3597 | zSig |= ( rem1 != 0 ); |
| 3598 | } |
| 3599 | return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); |
| 3600 | |
| 3601 | } |
| 3602 | |
| 3603 | /*---------------------------------------------------------------------------- |
| 3604 | | Returns the remainder of the double-precision floating-point value `a' |
| 3605 | | with respect to the corresponding value `b'. The operation is performed |
| 3606 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 3607 | *----------------------------------------------------------------------------*/ |
| 3608 | |
| 3609 | float64 float64_rem( float64 a, float64 b STATUS_PARAM ) |
| 3610 | { |
David Turner | 2738c26 | 2010-09-09 17:41:26 +0200 | [diff] [blame] | 3611 | flag aSign, zSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3612 | int_fast16_t aExp, bExp, expDiff; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3613 | uint64_t aSig, bSig; |
| 3614 | uint64_t q, alternateASig; |
| 3615 | int64_t sigMean; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3616 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3617 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 3618 | b = float64_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3619 | aSig = extractFloat64Frac( a ); |
| 3620 | aExp = extractFloat64Exp( a ); |
| 3621 | aSign = extractFloat64Sign( a ); |
| 3622 | bSig = extractFloat64Frac( b ); |
| 3623 | bExp = extractFloat64Exp( b ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3624 | if ( aExp == 0x7FF ) { |
| 3625 | if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { |
| 3626 | return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3627 | } |
| 3628 | float_raise( float_flag_invalid STATUS_VAR); |
| 3629 | return float64_default_nan; |
| 3630 | } |
| 3631 | if ( bExp == 0x7FF ) { |
| 3632 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
| 3633 | return a; |
| 3634 | } |
| 3635 | if ( bExp == 0 ) { |
| 3636 | if ( bSig == 0 ) { |
| 3637 | float_raise( float_flag_invalid STATUS_VAR); |
| 3638 | return float64_default_nan; |
| 3639 | } |
| 3640 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); |
| 3641 | } |
| 3642 | if ( aExp == 0 ) { |
| 3643 | if ( aSig == 0 ) return a; |
| 3644 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
| 3645 | } |
| 3646 | expDiff = aExp - bExp; |
| 3647 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11; |
| 3648 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; |
| 3649 | if ( expDiff < 0 ) { |
| 3650 | if ( expDiff < -1 ) return a; |
| 3651 | aSig >>= 1; |
| 3652 | } |
| 3653 | q = ( bSig <= aSig ); |
| 3654 | if ( q ) aSig -= bSig; |
| 3655 | expDiff -= 64; |
| 3656 | while ( 0 < expDiff ) { |
| 3657 | q = estimateDiv128To64( aSig, 0, bSig ); |
| 3658 | q = ( 2 < q ) ? q - 2 : 0; |
| 3659 | aSig = - ( ( bSig>>2 ) * q ); |
| 3660 | expDiff -= 62; |
| 3661 | } |
| 3662 | expDiff += 64; |
| 3663 | if ( 0 < expDiff ) { |
| 3664 | q = estimateDiv128To64( aSig, 0, bSig ); |
| 3665 | q = ( 2 < q ) ? q - 2 : 0; |
| 3666 | q >>= 64 - expDiff; |
| 3667 | bSig >>= 2; |
| 3668 | aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; |
| 3669 | } |
| 3670 | else { |
| 3671 | aSig >>= 2; |
| 3672 | bSig >>= 2; |
| 3673 | } |
| 3674 | do { |
| 3675 | alternateASig = aSig; |
| 3676 | ++q; |
| 3677 | aSig -= bSig; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3678 | } while ( 0 <= (int64_t) aSig ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3679 | sigMean = aSig + alternateASig; |
| 3680 | if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { |
| 3681 | aSig = alternateASig; |
| 3682 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3683 | zSign = ( (int64_t) aSig < 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3684 | if ( zSign ) aSig = - aSig; |
| 3685 | return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig STATUS_VAR ); |
| 3686 | |
| 3687 | } |
| 3688 | |
| 3689 | /*---------------------------------------------------------------------------- |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3690 | | Returns the result of multiplying the double-precision floating-point values |
| 3691 | | `a' and `b' then adding 'c', with no intermediate rounding step after the |
| 3692 | | multiplication. The operation is performed according to the IEC/IEEE |
| 3693 | | Standard for Binary Floating-Point Arithmetic 754-2008. |
| 3694 | | The flags argument allows the caller to select negation of the |
| 3695 | | addend, the intermediate product, or the final result. (The difference |
| 3696 | | between this and having the caller do a separate negation is that negating |
| 3697 | | externally will flip the sign bit on NaNs.) |
| 3698 | *----------------------------------------------------------------------------*/ |
| 3699 | |
| 3700 | float64 float64_muladd(float64 a, float64 b, float64 c, int flags STATUS_PARAM) |
| 3701 | { |
| 3702 | flag aSign, bSign, cSign, zSign; |
| 3703 | int_fast16_t aExp, bExp, cExp, pExp, zExp, expDiff; |
| 3704 | uint64_t aSig, bSig, cSig; |
| 3705 | flag pInf, pZero, pSign; |
| 3706 | uint64_t pSig0, pSig1, cSig0, cSig1, zSig0, zSig1; |
| 3707 | int shiftcount; |
| 3708 | flag signflip, infzero; |
| 3709 | |
| 3710 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 3711 | b = float64_squash_input_denormal(b STATUS_VAR); |
| 3712 | c = float64_squash_input_denormal(c STATUS_VAR); |
| 3713 | aSig = extractFloat64Frac(a); |
| 3714 | aExp = extractFloat64Exp(a); |
| 3715 | aSign = extractFloat64Sign(a); |
| 3716 | bSig = extractFloat64Frac(b); |
| 3717 | bExp = extractFloat64Exp(b); |
| 3718 | bSign = extractFloat64Sign(b); |
| 3719 | cSig = extractFloat64Frac(c); |
| 3720 | cExp = extractFloat64Exp(c); |
| 3721 | cSign = extractFloat64Sign(c); |
| 3722 | |
| 3723 | infzero = ((aExp == 0 && aSig == 0 && bExp == 0x7ff && bSig == 0) || |
| 3724 | (aExp == 0x7ff && aSig == 0 && bExp == 0 && bSig == 0)); |
| 3725 | |
| 3726 | /* It is implementation-defined whether the cases of (0,inf,qnan) |
| 3727 | * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN |
| 3728 | * they return if they do), so we have to hand this information |
| 3729 | * off to the target-specific pick-a-NaN routine. |
| 3730 | */ |
| 3731 | if (((aExp == 0x7ff) && aSig) || |
| 3732 | ((bExp == 0x7ff) && bSig) || |
| 3733 | ((cExp == 0x7ff) && cSig)) { |
| 3734 | return propagateFloat64MulAddNaN(a, b, c, infzero STATUS_VAR); |
| 3735 | } |
| 3736 | |
| 3737 | if (infzero) { |
| 3738 | float_raise(float_flag_invalid STATUS_VAR); |
| 3739 | return float64_default_nan; |
| 3740 | } |
| 3741 | |
| 3742 | if (flags & float_muladd_negate_c) { |
| 3743 | cSign ^= 1; |
| 3744 | } |
| 3745 | |
| 3746 | signflip = (flags & float_muladd_negate_result) ? 1 : 0; |
| 3747 | |
| 3748 | /* Work out the sign and type of the product */ |
| 3749 | pSign = aSign ^ bSign; |
| 3750 | if (flags & float_muladd_negate_product) { |
| 3751 | pSign ^= 1; |
| 3752 | } |
| 3753 | pInf = (aExp == 0x7ff) || (bExp == 0x7ff); |
| 3754 | pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0); |
| 3755 | |
| 3756 | if (cExp == 0x7ff) { |
| 3757 | if (pInf && (pSign ^ cSign)) { |
| 3758 | /* addition of opposite-signed infinities => InvalidOperation */ |
| 3759 | float_raise(float_flag_invalid STATUS_VAR); |
| 3760 | return float64_default_nan; |
| 3761 | } |
| 3762 | /* Otherwise generate an infinity of the same sign */ |
| 3763 | return packFloat64(cSign ^ signflip, 0x7ff, 0); |
| 3764 | } |
| 3765 | |
| 3766 | if (pInf) { |
| 3767 | return packFloat64(pSign ^ signflip, 0x7ff, 0); |
| 3768 | } |
| 3769 | |
| 3770 | if (pZero) { |
| 3771 | if (cExp == 0) { |
| 3772 | if (cSig == 0) { |
| 3773 | /* Adding two exact zeroes */ |
| 3774 | if (pSign == cSign) { |
| 3775 | zSign = pSign; |
| 3776 | } else if (STATUS(float_rounding_mode) == float_round_down) { |
| 3777 | zSign = 1; |
| 3778 | } else { |
| 3779 | zSign = 0; |
| 3780 | } |
| 3781 | return packFloat64(zSign ^ signflip, 0, 0); |
| 3782 | } |
| 3783 | /* Exact zero plus a denorm */ |
| 3784 | if (STATUS(flush_to_zero)) { |
| 3785 | float_raise(float_flag_output_denormal STATUS_VAR); |
| 3786 | return packFloat64(cSign ^ signflip, 0, 0); |
| 3787 | } |
| 3788 | } |
| 3789 | /* Zero plus something non-zero : just return the something */ |
| 3790 | return packFloat64(cSign ^ signflip, cExp, cSig); |
| 3791 | } |
| 3792 | |
| 3793 | if (aExp == 0) { |
| 3794 | normalizeFloat64Subnormal(aSig, &aExp, &aSig); |
| 3795 | } |
| 3796 | if (bExp == 0) { |
| 3797 | normalizeFloat64Subnormal(bSig, &bExp, &bSig); |
| 3798 | } |
| 3799 | |
| 3800 | /* Calculate the actual result a * b + c */ |
| 3801 | |
| 3802 | /* Multiply first; this is easy. */ |
| 3803 | /* NB: we subtract 0x3fe where float64_mul() subtracts 0x3ff |
| 3804 | * because we want the true exponent, not the "one-less-than" |
| 3805 | * flavour that roundAndPackFloat64() takes. |
| 3806 | */ |
| 3807 | pExp = aExp + bExp - 0x3fe; |
| 3808 | aSig = (aSig | LIT64(0x0010000000000000))<<10; |
| 3809 | bSig = (bSig | LIT64(0x0010000000000000))<<11; |
| 3810 | mul64To128(aSig, bSig, &pSig0, &pSig1); |
| 3811 | if ((int64_t)(pSig0 << 1) >= 0) { |
| 3812 | shortShift128Left(pSig0, pSig1, 1, &pSig0, &pSig1); |
| 3813 | pExp--; |
| 3814 | } |
| 3815 | |
| 3816 | zSign = pSign ^ signflip; |
| 3817 | |
| 3818 | /* Now [pSig0:pSig1] is the significand of the multiply, with the explicit |
| 3819 | * bit in position 126. |
| 3820 | */ |
| 3821 | if (cExp == 0) { |
| 3822 | if (!cSig) { |
| 3823 | /* Throw out the special case of c being an exact zero now */ |
| 3824 | shift128RightJamming(pSig0, pSig1, 64, &pSig0, &pSig1); |
| 3825 | return roundAndPackFloat64(zSign, pExp - 1, |
| 3826 | pSig1 STATUS_VAR); |
| 3827 | } |
| 3828 | normalizeFloat64Subnormal(cSig, &cExp, &cSig); |
| 3829 | } |
| 3830 | |
| 3831 | /* Shift cSig and add the explicit bit so [cSig0:cSig1] is the |
| 3832 | * significand of the addend, with the explicit bit in position 126. |
| 3833 | */ |
| 3834 | cSig0 = cSig << (126 - 64 - 52); |
| 3835 | cSig1 = 0; |
| 3836 | cSig0 |= LIT64(0x4000000000000000); |
| 3837 | expDiff = pExp - cExp; |
| 3838 | |
| 3839 | if (pSign == cSign) { |
| 3840 | /* Addition */ |
| 3841 | if (expDiff > 0) { |
| 3842 | /* scale c to match p */ |
| 3843 | shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1); |
| 3844 | zExp = pExp; |
| 3845 | } else if (expDiff < 0) { |
| 3846 | /* scale p to match c */ |
| 3847 | shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1); |
| 3848 | zExp = cExp; |
| 3849 | } else { |
| 3850 | /* no scaling needed */ |
| 3851 | zExp = cExp; |
| 3852 | } |
| 3853 | /* Add significands and make sure explicit bit ends up in posn 126 */ |
| 3854 | add128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); |
| 3855 | if ((int64_t)zSig0 < 0) { |
| 3856 | shift128RightJamming(zSig0, zSig1, 1, &zSig0, &zSig1); |
| 3857 | } else { |
| 3858 | zExp--; |
| 3859 | } |
| 3860 | shift128RightJamming(zSig0, zSig1, 64, &zSig0, &zSig1); |
| 3861 | return roundAndPackFloat64(zSign, zExp, zSig1 STATUS_VAR); |
| 3862 | } else { |
| 3863 | /* Subtraction */ |
| 3864 | if (expDiff > 0) { |
| 3865 | shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1); |
| 3866 | sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); |
| 3867 | zExp = pExp; |
| 3868 | } else if (expDiff < 0) { |
| 3869 | shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1); |
| 3870 | sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1); |
| 3871 | zExp = cExp; |
| 3872 | zSign ^= 1; |
| 3873 | } else { |
| 3874 | zExp = pExp; |
| 3875 | if (lt128(cSig0, cSig1, pSig0, pSig1)) { |
| 3876 | sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); |
| 3877 | } else if (lt128(pSig0, pSig1, cSig0, cSig1)) { |
| 3878 | sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1); |
| 3879 | zSign ^= 1; |
| 3880 | } else { |
| 3881 | /* Exact zero */ |
| 3882 | zSign = signflip; |
| 3883 | if (STATUS(float_rounding_mode) == float_round_down) { |
| 3884 | zSign ^= 1; |
| 3885 | } |
| 3886 | return packFloat64(zSign, 0, 0); |
| 3887 | } |
| 3888 | } |
| 3889 | --zExp; |
| 3890 | /* Do the equivalent of normalizeRoundAndPackFloat64() but |
| 3891 | * starting with the significand in a pair of uint64_t. |
| 3892 | */ |
| 3893 | if (zSig0) { |
| 3894 | shiftcount = countLeadingZeros64(zSig0) - 1; |
| 3895 | shortShift128Left(zSig0, zSig1, shiftcount, &zSig0, &zSig1); |
| 3896 | if (zSig1) { |
| 3897 | zSig0 |= 1; |
| 3898 | } |
| 3899 | zExp -= shiftcount; |
| 3900 | } else { |
| 3901 | shiftcount = countLeadingZeros64(zSig1); |
| 3902 | if (shiftcount == 0) { |
| 3903 | zSig0 = (zSig1 >> 1) | (zSig1 & 1); |
| 3904 | zExp -= 63; |
| 3905 | } else { |
| 3906 | shiftcount--; |
| 3907 | zSig0 = zSig1 << shiftcount; |
| 3908 | zExp -= (shiftcount + 64); |
| 3909 | } |
| 3910 | } |
| 3911 | return roundAndPackFloat64(zSign, zExp, zSig0 STATUS_VAR); |
| 3912 | } |
| 3913 | } |
| 3914 | |
| 3915 | /*---------------------------------------------------------------------------- |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3916 | | Returns the square root of the double-precision floating-point value `a'. |
| 3917 | | The operation is performed according to the IEC/IEEE Standard for Binary |
| 3918 | | Floating-Point Arithmetic. |
| 3919 | *----------------------------------------------------------------------------*/ |
| 3920 | |
| 3921 | float64 float64_sqrt( float64 a STATUS_PARAM ) |
| 3922 | { |
| 3923 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3924 | int_fast16_t aExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3925 | uint64_t aSig, zSig, doubleZSig; |
| 3926 | uint64_t rem0, rem1, term0, term1; |
| 3927 | a = float64_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3928 | |
| 3929 | aSig = extractFloat64Frac( a ); |
| 3930 | aExp = extractFloat64Exp( a ); |
| 3931 | aSign = extractFloat64Sign( a ); |
| 3932 | if ( aExp == 0x7FF ) { |
| 3933 | if ( aSig ) return propagateFloat64NaN( a, a STATUS_VAR ); |
| 3934 | if ( ! aSign ) return a; |
| 3935 | float_raise( float_flag_invalid STATUS_VAR); |
| 3936 | return float64_default_nan; |
| 3937 | } |
| 3938 | if ( aSign ) { |
| 3939 | if ( ( aExp | aSig ) == 0 ) return a; |
| 3940 | float_raise( float_flag_invalid STATUS_VAR); |
| 3941 | return float64_default_nan; |
| 3942 | } |
| 3943 | if ( aExp == 0 ) { |
| 3944 | if ( aSig == 0 ) return float64_zero; |
| 3945 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
| 3946 | } |
| 3947 | zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE; |
| 3948 | aSig |= LIT64( 0x0010000000000000 ); |
| 3949 | zSig = estimateSqrt32( aExp, aSig>>21 ); |
| 3950 | aSig <<= 9 - ( aExp & 1 ); |
| 3951 | zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 ); |
| 3952 | if ( ( zSig & 0x1FF ) <= 5 ) { |
| 3953 | doubleZSig = zSig<<1; |
| 3954 | mul64To128( zSig, zSig, &term0, &term1 ); |
| 3955 | sub128( aSig, 0, term0, term1, &rem0, &rem1 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3956 | while ( (int64_t) rem0 < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 3957 | --zSig; |
| 3958 | doubleZSig -= 2; |
| 3959 | add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 ); |
| 3960 | } |
| 3961 | zSig |= ( ( rem0 | rem1 ) != 0 ); |
| 3962 | } |
| 3963 | return roundAndPackFloat64( 0, zExp, zSig STATUS_VAR ); |
| 3964 | |
| 3965 | } |
| 3966 | |
| 3967 | /*---------------------------------------------------------------------------- |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 3968 | | Returns the binary log of the double-precision floating-point value `a'. |
| 3969 | | The operation is performed according to the IEC/IEEE Standard for Binary |
| 3970 | | Floating-Point Arithmetic. |
| 3971 | *----------------------------------------------------------------------------*/ |
| 3972 | float64 float64_log2( float64 a STATUS_PARAM ) |
| 3973 | { |
| 3974 | flag aSign, zSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 3975 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3976 | uint64_t aSig, aSig0, aSig1, zSig, i; |
| 3977 | a = float64_squash_input_denormal(a STATUS_VAR); |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 3978 | |
| 3979 | aSig = extractFloat64Frac( a ); |
| 3980 | aExp = extractFloat64Exp( a ); |
| 3981 | aSign = extractFloat64Sign( a ); |
| 3982 | |
| 3983 | if ( aExp == 0 ) { |
| 3984 | if ( aSig == 0 ) return packFloat64( 1, 0x7FF, 0 ); |
| 3985 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
| 3986 | } |
| 3987 | if ( aSign ) { |
| 3988 | float_raise( float_flag_invalid STATUS_VAR); |
| 3989 | return float64_default_nan; |
| 3990 | } |
| 3991 | if ( aExp == 0x7FF ) { |
| 3992 | if ( aSig ) return propagateFloat64NaN( a, float64_zero STATUS_VAR ); |
| 3993 | return a; |
| 3994 | } |
| 3995 | |
| 3996 | aExp -= 0x3FF; |
| 3997 | aSig |= LIT64( 0x0010000000000000 ); |
| 3998 | zSign = aExp < 0; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 3999 | zSig = (uint64_t)aExp << 52; |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 4000 | for (i = 1LL << 51; i > 0; i >>= 1) { |
| 4001 | mul64To128( aSig, aSig, &aSig0, &aSig1 ); |
| 4002 | aSig = ( aSig0 << 12 ) | ( aSig1 >> 52 ); |
| 4003 | if ( aSig & LIT64( 0x0020000000000000 ) ) { |
| 4004 | aSig >>= 1; |
| 4005 | zSig |= i; |
| 4006 | } |
| 4007 | } |
| 4008 | |
| 4009 | if ( zSign ) |
| 4010 | zSig = -zSig; |
| 4011 | return normalizeRoundAndPackFloat64( zSign, 0x408, zSig STATUS_VAR ); |
| 4012 | } |
| 4013 | |
| 4014 | /*---------------------------------------------------------------------------- |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4015 | | Returns 1 if the double-precision floating-point value `a' is equal to the |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4016 | | corresponding value `b', and 0 otherwise. The invalid exception is raised |
| 4017 | | if either operand is a NaN. Otherwise, the comparison is performed |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4018 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 4019 | *----------------------------------------------------------------------------*/ |
| 4020 | |
| 4021 | int float64_eq( float64 a, float64 b STATUS_PARAM ) |
| 4022 | { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4023 | uint64_t av, bv; |
| 4024 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 4025 | b = float64_squash_input_denormal(b STATUS_VAR); |
| 4026 | |
| 4027 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
| 4028 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) |
| 4029 | ) { |
| 4030 | float_raise( float_flag_invalid STATUS_VAR); |
| 4031 | return 0; |
| 4032 | } |
| 4033 | av = float64_val(a); |
| 4034 | bv = float64_val(b); |
| 4035 | return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
| 4036 | |
| 4037 | } |
| 4038 | |
| 4039 | /*---------------------------------------------------------------------------- |
| 4040 | | Returns 1 if the double-precision floating-point value `a' is less than or |
| 4041 | | equal to the corresponding value `b', and 0 otherwise. The invalid |
| 4042 | | exception is raised if either operand is a NaN. The comparison is performed |
| 4043 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 4044 | *----------------------------------------------------------------------------*/ |
| 4045 | |
| 4046 | int float64_le( float64 a, float64 b STATUS_PARAM ) |
| 4047 | { |
| 4048 | flag aSign, bSign; |
| 4049 | uint64_t av, bv; |
| 4050 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 4051 | b = float64_squash_input_denormal(b STATUS_VAR); |
| 4052 | |
| 4053 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
| 4054 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) |
| 4055 | ) { |
| 4056 | float_raise( float_flag_invalid STATUS_VAR); |
| 4057 | return 0; |
| 4058 | } |
| 4059 | aSign = extractFloat64Sign( a ); |
| 4060 | bSign = extractFloat64Sign( b ); |
| 4061 | av = float64_val(a); |
| 4062 | bv = float64_val(b); |
| 4063 | if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
| 4064 | return ( av == bv ) || ( aSign ^ ( av < bv ) ); |
| 4065 | |
| 4066 | } |
| 4067 | |
| 4068 | /*---------------------------------------------------------------------------- |
| 4069 | | Returns 1 if the double-precision floating-point value `a' is less than |
| 4070 | | the corresponding value `b', and 0 otherwise. The invalid exception is |
| 4071 | | raised if either operand is a NaN. The comparison is performed according |
| 4072 | | to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 4073 | *----------------------------------------------------------------------------*/ |
| 4074 | |
| 4075 | int float64_lt( float64 a, float64 b STATUS_PARAM ) |
| 4076 | { |
| 4077 | flag aSign, bSign; |
| 4078 | uint64_t av, bv; |
| 4079 | |
| 4080 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 4081 | b = float64_squash_input_denormal(b STATUS_VAR); |
| 4082 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
| 4083 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) |
| 4084 | ) { |
| 4085 | float_raise( float_flag_invalid STATUS_VAR); |
| 4086 | return 0; |
| 4087 | } |
| 4088 | aSign = extractFloat64Sign( a ); |
| 4089 | bSign = extractFloat64Sign( b ); |
| 4090 | av = float64_val(a); |
| 4091 | bv = float64_val(b); |
| 4092 | if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 ); |
| 4093 | return ( av != bv ) && ( aSign ^ ( av < bv ) ); |
| 4094 | |
| 4095 | } |
| 4096 | |
| 4097 | /*---------------------------------------------------------------------------- |
| 4098 | | Returns 1 if the double-precision floating-point values `a' and `b' cannot |
| 4099 | | be compared, and 0 otherwise. The invalid exception is raised if either |
| 4100 | | operand is a NaN. The comparison is performed according to the IEC/IEEE |
| 4101 | | Standard for Binary Floating-Point Arithmetic. |
| 4102 | *----------------------------------------------------------------------------*/ |
| 4103 | |
| 4104 | int float64_unordered( float64 a, float64 b STATUS_PARAM ) |
| 4105 | { |
| 4106 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 4107 | b = float64_squash_input_denormal(b STATUS_VAR); |
| 4108 | |
| 4109 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
| 4110 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) |
| 4111 | ) { |
| 4112 | float_raise( float_flag_invalid STATUS_VAR); |
| 4113 | return 1; |
| 4114 | } |
| 4115 | return 0; |
| 4116 | } |
| 4117 | |
| 4118 | /*---------------------------------------------------------------------------- |
| 4119 | | Returns 1 if the double-precision floating-point value `a' is equal to the |
| 4120 | | corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an |
| 4121 | | exception.The comparison is performed according to the IEC/IEEE Standard |
| 4122 | | for Binary Floating-Point Arithmetic. |
| 4123 | *----------------------------------------------------------------------------*/ |
| 4124 | |
| 4125 | int float64_eq_quiet( float64 a, float64 b STATUS_PARAM ) |
| 4126 | { |
| 4127 | uint64_t av, bv; |
| 4128 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 4129 | b = float64_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4130 | |
| 4131 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
| 4132 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) |
| 4133 | ) { |
| 4134 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { |
| 4135 | float_raise( float_flag_invalid STATUS_VAR); |
| 4136 | } |
| 4137 | return 0; |
| 4138 | } |
| 4139 | av = float64_val(a); |
| 4140 | bv = float64_val(b); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4141 | return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4142 | |
| 4143 | } |
| 4144 | |
| 4145 | /*---------------------------------------------------------------------------- |
| 4146 | | Returns 1 if the double-precision floating-point value `a' is less than or |
| 4147 | | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not |
| 4148 | | cause an exception. Otherwise, the comparison is performed according to the |
| 4149 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 4150 | *----------------------------------------------------------------------------*/ |
| 4151 | |
| 4152 | int float64_le_quiet( float64 a, float64 b STATUS_PARAM ) |
| 4153 | { |
| 4154 | flag aSign, bSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4155 | uint64_t av, bv; |
| 4156 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 4157 | b = float64_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4158 | |
| 4159 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
| 4160 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) |
| 4161 | ) { |
| 4162 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { |
| 4163 | float_raise( float_flag_invalid STATUS_VAR); |
| 4164 | } |
| 4165 | return 0; |
| 4166 | } |
| 4167 | aSign = extractFloat64Sign( a ); |
| 4168 | bSign = extractFloat64Sign( b ); |
| 4169 | av = float64_val(a); |
| 4170 | bv = float64_val(b); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4171 | if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4172 | return ( av == bv ) || ( aSign ^ ( av < bv ) ); |
| 4173 | |
| 4174 | } |
| 4175 | |
| 4176 | /*---------------------------------------------------------------------------- |
| 4177 | | Returns 1 if the double-precision floating-point value `a' is less than |
| 4178 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an |
| 4179 | | exception. Otherwise, the comparison is performed according to the IEC/IEEE |
| 4180 | | Standard for Binary Floating-Point Arithmetic. |
| 4181 | *----------------------------------------------------------------------------*/ |
| 4182 | |
| 4183 | int float64_lt_quiet( float64 a, float64 b STATUS_PARAM ) |
| 4184 | { |
| 4185 | flag aSign, bSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4186 | uint64_t av, bv; |
| 4187 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 4188 | b = float64_squash_input_denormal(b STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4189 | |
| 4190 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
| 4191 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) |
| 4192 | ) { |
| 4193 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { |
| 4194 | float_raise( float_flag_invalid STATUS_VAR); |
| 4195 | } |
| 4196 | return 0; |
| 4197 | } |
| 4198 | aSign = extractFloat64Sign( a ); |
| 4199 | bSign = extractFloat64Sign( b ); |
| 4200 | av = float64_val(a); |
| 4201 | bv = float64_val(b); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4202 | if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4203 | return ( av != bv ) && ( aSign ^ ( av < bv ) ); |
| 4204 | |
| 4205 | } |
| 4206 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4207 | /*---------------------------------------------------------------------------- |
| 4208 | | Returns 1 if the double-precision floating-point values `a' and `b' cannot |
| 4209 | | be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The |
| 4210 | | comparison is performed according to the IEC/IEEE Standard for Binary |
| 4211 | | Floating-Point Arithmetic. |
| 4212 | *----------------------------------------------------------------------------*/ |
| 4213 | |
| 4214 | int float64_unordered_quiet( float64 a, float64 b STATUS_PARAM ) |
| 4215 | { |
| 4216 | a = float64_squash_input_denormal(a STATUS_VAR); |
| 4217 | b = float64_squash_input_denormal(b STATUS_VAR); |
| 4218 | |
| 4219 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
| 4220 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) |
| 4221 | ) { |
| 4222 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { |
| 4223 | float_raise( float_flag_invalid STATUS_VAR); |
| 4224 | } |
| 4225 | return 1; |
| 4226 | } |
| 4227 | return 0; |
| 4228 | } |
| 4229 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4230 | /*---------------------------------------------------------------------------- |
| 4231 | | Returns the result of converting the extended double-precision floating- |
| 4232 | | point value `a' to the 32-bit two's complement integer format. The |
| 4233 | | conversion is performed according to the IEC/IEEE Standard for Binary |
| 4234 | | Floating-Point Arithmetic---which means in particular that the conversion |
| 4235 | | is rounded according to the current rounding mode. If `a' is a NaN, the |
| 4236 | | largest positive integer is returned. Otherwise, if the conversion |
| 4237 | | overflows, the largest integer with the same sign as `a' is returned. |
| 4238 | *----------------------------------------------------------------------------*/ |
| 4239 | |
| 4240 | int32 floatx80_to_int32( floatx80 a STATUS_PARAM ) |
| 4241 | { |
| 4242 | flag aSign; |
| 4243 | int32 aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4244 | uint64_t aSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4245 | |
| 4246 | aSig = extractFloatx80Frac( a ); |
| 4247 | aExp = extractFloatx80Exp( a ); |
| 4248 | aSign = extractFloatx80Sign( a ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4249 | if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4250 | shiftCount = 0x4037 - aExp; |
| 4251 | if ( shiftCount <= 0 ) shiftCount = 1; |
| 4252 | shift64RightJamming( aSig, shiftCount, &aSig ); |
| 4253 | return roundAndPackInt32( aSign, aSig STATUS_VAR ); |
| 4254 | |
| 4255 | } |
| 4256 | |
| 4257 | /*---------------------------------------------------------------------------- |
| 4258 | | Returns the result of converting the extended double-precision floating- |
| 4259 | | point value `a' to the 32-bit two's complement integer format. The |
| 4260 | | conversion is performed according to the IEC/IEEE Standard for Binary |
| 4261 | | Floating-Point Arithmetic, except that the conversion is always rounded |
| 4262 | | toward zero. If `a' is a NaN, the largest positive integer is returned. |
| 4263 | | Otherwise, if the conversion overflows, the largest integer with the same |
| 4264 | | sign as `a' is returned. |
| 4265 | *----------------------------------------------------------------------------*/ |
| 4266 | |
| 4267 | int32 floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM ) |
| 4268 | { |
| 4269 | flag aSign; |
| 4270 | int32 aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4271 | uint64_t aSig, savedASig; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 4272 | int32_t z; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4273 | |
| 4274 | aSig = extractFloatx80Frac( a ); |
| 4275 | aExp = extractFloatx80Exp( a ); |
| 4276 | aSign = extractFloatx80Sign( a ); |
| 4277 | if ( 0x401E < aExp ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4278 | if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4279 | goto invalid; |
| 4280 | } |
| 4281 | else if ( aExp < 0x3FFF ) { |
| 4282 | if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 4283 | return 0; |
| 4284 | } |
| 4285 | shiftCount = 0x403E - aExp; |
| 4286 | savedASig = aSig; |
| 4287 | aSig >>= shiftCount; |
| 4288 | z = aSig; |
| 4289 | if ( aSign ) z = - z; |
| 4290 | if ( ( z < 0 ) ^ aSign ) { |
| 4291 | invalid: |
| 4292 | float_raise( float_flag_invalid STATUS_VAR); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4293 | return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4294 | } |
| 4295 | if ( ( aSig<<shiftCount ) != savedASig ) { |
| 4296 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 4297 | } |
| 4298 | return z; |
| 4299 | |
| 4300 | } |
| 4301 | |
| 4302 | /*---------------------------------------------------------------------------- |
| 4303 | | Returns the result of converting the extended double-precision floating- |
| 4304 | | point value `a' to the 64-bit two's complement integer format. The |
| 4305 | | conversion is performed according to the IEC/IEEE Standard for Binary |
| 4306 | | Floating-Point Arithmetic---which means in particular that the conversion |
| 4307 | | is rounded according to the current rounding mode. If `a' is a NaN, |
| 4308 | | the largest positive integer is returned. Otherwise, if the conversion |
| 4309 | | overflows, the largest integer with the same sign as `a' is returned. |
| 4310 | *----------------------------------------------------------------------------*/ |
| 4311 | |
| 4312 | int64 floatx80_to_int64( floatx80 a STATUS_PARAM ) |
| 4313 | { |
| 4314 | flag aSign; |
| 4315 | int32 aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4316 | uint64_t aSig, aSigExtra; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4317 | |
| 4318 | aSig = extractFloatx80Frac( a ); |
| 4319 | aExp = extractFloatx80Exp( a ); |
| 4320 | aSign = extractFloatx80Sign( a ); |
| 4321 | shiftCount = 0x403E - aExp; |
| 4322 | if ( shiftCount <= 0 ) { |
| 4323 | if ( shiftCount ) { |
| 4324 | float_raise( float_flag_invalid STATUS_VAR); |
| 4325 | if ( ! aSign |
| 4326 | || ( ( aExp == 0x7FFF ) |
| 4327 | && ( aSig != LIT64( 0x8000000000000000 ) ) ) |
| 4328 | ) { |
| 4329 | return LIT64( 0x7FFFFFFFFFFFFFFF ); |
| 4330 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4331 | return (int64_t) LIT64( 0x8000000000000000 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4332 | } |
| 4333 | aSigExtra = 0; |
| 4334 | } |
| 4335 | else { |
| 4336 | shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); |
| 4337 | } |
| 4338 | return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR ); |
| 4339 | |
| 4340 | } |
| 4341 | |
| 4342 | /*---------------------------------------------------------------------------- |
| 4343 | | Returns the result of converting the extended double-precision floating- |
| 4344 | | point value `a' to the 64-bit two's complement integer format. The |
| 4345 | | conversion is performed according to the IEC/IEEE Standard for Binary |
| 4346 | | Floating-Point Arithmetic, except that the conversion is always rounded |
| 4347 | | toward zero. If `a' is a NaN, the largest positive integer is returned. |
| 4348 | | Otherwise, if the conversion overflows, the largest integer with the same |
| 4349 | | sign as `a' is returned. |
| 4350 | *----------------------------------------------------------------------------*/ |
| 4351 | |
| 4352 | int64 floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM ) |
| 4353 | { |
| 4354 | flag aSign; |
| 4355 | int32 aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4356 | uint64_t aSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4357 | int64 z; |
| 4358 | |
| 4359 | aSig = extractFloatx80Frac( a ); |
| 4360 | aExp = extractFloatx80Exp( a ); |
| 4361 | aSign = extractFloatx80Sign( a ); |
| 4362 | shiftCount = aExp - 0x403E; |
| 4363 | if ( 0 <= shiftCount ) { |
| 4364 | aSig &= LIT64( 0x7FFFFFFFFFFFFFFF ); |
| 4365 | if ( ( a.high != 0xC03E ) || aSig ) { |
| 4366 | float_raise( float_flag_invalid STATUS_VAR); |
| 4367 | if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) { |
| 4368 | return LIT64( 0x7FFFFFFFFFFFFFFF ); |
| 4369 | } |
| 4370 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4371 | return (int64_t) LIT64( 0x8000000000000000 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4372 | } |
| 4373 | else if ( aExp < 0x3FFF ) { |
| 4374 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 4375 | return 0; |
| 4376 | } |
| 4377 | z = aSig>>( - shiftCount ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4378 | if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4379 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 4380 | } |
| 4381 | if ( aSign ) z = - z; |
| 4382 | return z; |
| 4383 | |
| 4384 | } |
| 4385 | |
| 4386 | /*---------------------------------------------------------------------------- |
| 4387 | | Returns the result of converting the extended double-precision floating- |
| 4388 | | point value `a' to the single-precision floating-point format. The |
| 4389 | | conversion is performed according to the IEC/IEEE Standard for Binary |
| 4390 | | Floating-Point Arithmetic. |
| 4391 | *----------------------------------------------------------------------------*/ |
| 4392 | |
| 4393 | float32 floatx80_to_float32( floatx80 a STATUS_PARAM ) |
| 4394 | { |
| 4395 | flag aSign; |
| 4396 | int32 aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4397 | uint64_t aSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4398 | |
| 4399 | aSig = extractFloatx80Frac( a ); |
| 4400 | aExp = extractFloatx80Exp( a ); |
| 4401 | aSign = extractFloatx80Sign( a ); |
| 4402 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4403 | if ( (uint64_t) ( aSig<<1 ) ) { |
| 4404 | return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4405 | } |
| 4406 | return packFloat32( aSign, 0xFF, 0 ); |
| 4407 | } |
| 4408 | shift64RightJamming( aSig, 33, &aSig ); |
| 4409 | if ( aExp || aSig ) aExp -= 0x3F81; |
| 4410 | return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR ); |
| 4411 | |
| 4412 | } |
| 4413 | |
| 4414 | /*---------------------------------------------------------------------------- |
| 4415 | | Returns the result of converting the extended double-precision floating- |
| 4416 | | point value `a' to the double-precision floating-point format. The |
| 4417 | | conversion is performed according to the IEC/IEEE Standard for Binary |
| 4418 | | Floating-Point Arithmetic. |
| 4419 | *----------------------------------------------------------------------------*/ |
| 4420 | |
| 4421 | float64 floatx80_to_float64( floatx80 a STATUS_PARAM ) |
| 4422 | { |
| 4423 | flag aSign; |
| 4424 | int32 aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4425 | uint64_t aSig, zSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4426 | |
| 4427 | aSig = extractFloatx80Frac( a ); |
| 4428 | aExp = extractFloatx80Exp( a ); |
| 4429 | aSign = extractFloatx80Sign( a ); |
| 4430 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4431 | if ( (uint64_t) ( aSig<<1 ) ) { |
| 4432 | return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4433 | } |
| 4434 | return packFloat64( aSign, 0x7FF, 0 ); |
| 4435 | } |
| 4436 | shift64RightJamming( aSig, 1, &zSig ); |
| 4437 | if ( aExp || aSig ) aExp -= 0x3C01; |
| 4438 | return roundAndPackFloat64( aSign, aExp, zSig STATUS_VAR ); |
| 4439 | |
| 4440 | } |
| 4441 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4442 | /*---------------------------------------------------------------------------- |
| 4443 | | Returns the result of converting the extended double-precision floating- |
| 4444 | | point value `a' to the quadruple-precision floating-point format. The |
| 4445 | | conversion is performed according to the IEC/IEEE Standard for Binary |
| 4446 | | Floating-Point Arithmetic. |
| 4447 | *----------------------------------------------------------------------------*/ |
| 4448 | |
| 4449 | float128 floatx80_to_float128( floatx80 a STATUS_PARAM ) |
| 4450 | { |
| 4451 | flag aSign; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 4452 | int_fast16_t aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4453 | uint64_t aSig, zSig0, zSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4454 | |
| 4455 | aSig = extractFloatx80Frac( a ); |
| 4456 | aExp = extractFloatx80Exp( a ); |
| 4457 | aSign = extractFloatx80Sign( a ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4458 | if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) { |
| 4459 | return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4460 | } |
| 4461 | shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 ); |
| 4462 | return packFloat128( aSign, aExp, zSig0, zSig1 ); |
| 4463 | |
| 4464 | } |
| 4465 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4466 | /*---------------------------------------------------------------------------- |
| 4467 | | Rounds the extended double-precision floating-point value `a' to an integer, |
| 4468 | | and returns the result as an extended quadruple-precision floating-point |
| 4469 | | value. The operation is performed according to the IEC/IEEE Standard for |
| 4470 | | Binary Floating-Point Arithmetic. |
| 4471 | *----------------------------------------------------------------------------*/ |
| 4472 | |
| 4473 | floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM ) |
| 4474 | { |
| 4475 | flag aSign; |
| 4476 | int32 aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4477 | uint64_t lastBitMask, roundBitsMask; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4478 | int8 roundingMode; |
| 4479 | floatx80 z; |
| 4480 | |
| 4481 | aExp = extractFloatx80Exp( a ); |
| 4482 | if ( 0x403E <= aExp ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4483 | if ( ( aExp == 0x7FFF ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4484 | return propagateFloatx80NaN( a, a STATUS_VAR ); |
| 4485 | } |
| 4486 | return a; |
| 4487 | } |
| 4488 | if ( aExp < 0x3FFF ) { |
| 4489 | if ( ( aExp == 0 ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4490 | && ( (uint64_t) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4491 | return a; |
| 4492 | } |
| 4493 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 4494 | aSign = extractFloatx80Sign( a ); |
| 4495 | switch ( STATUS(float_rounding_mode) ) { |
| 4496 | case float_round_nearest_even: |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4497 | if ( ( aExp == 0x3FFE ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4498 | ) { |
| 4499 | return |
| 4500 | packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) ); |
| 4501 | } |
| 4502 | break; |
| 4503 | case float_round_down: |
| 4504 | return |
| 4505 | aSign ? |
| 4506 | packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) ) |
| 4507 | : packFloatx80( 0, 0, 0 ); |
| 4508 | case float_round_up: |
| 4509 | return |
| 4510 | aSign ? packFloatx80( 1, 0, 0 ) |
| 4511 | : packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) ); |
| 4512 | } |
| 4513 | return packFloatx80( aSign, 0, 0 ); |
| 4514 | } |
| 4515 | lastBitMask = 1; |
| 4516 | lastBitMask <<= 0x403E - aExp; |
| 4517 | roundBitsMask = lastBitMask - 1; |
| 4518 | z = a; |
| 4519 | roundingMode = STATUS(float_rounding_mode); |
| 4520 | if ( roundingMode == float_round_nearest_even ) { |
| 4521 | z.low += lastBitMask>>1; |
| 4522 | if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; |
| 4523 | } |
| 4524 | else if ( roundingMode != float_round_to_zero ) { |
| 4525 | if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) { |
| 4526 | z.low += roundBitsMask; |
| 4527 | } |
| 4528 | } |
| 4529 | z.low &= ~ roundBitsMask; |
| 4530 | if ( z.low == 0 ) { |
| 4531 | ++z.high; |
| 4532 | z.low = LIT64( 0x8000000000000000 ); |
| 4533 | } |
| 4534 | if ( z.low != a.low ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 4535 | return z; |
| 4536 | |
| 4537 | } |
| 4538 | |
| 4539 | /*---------------------------------------------------------------------------- |
| 4540 | | Returns the result of adding the absolute values of the extended double- |
| 4541 | | precision floating-point values `a' and `b'. If `zSign' is 1, the sum is |
| 4542 | | negated before being returned. `zSign' is ignored if the result is a NaN. |
| 4543 | | The addition is performed according to the IEC/IEEE Standard for Binary |
| 4544 | | Floating-Point Arithmetic. |
| 4545 | *----------------------------------------------------------------------------*/ |
| 4546 | |
| 4547 | static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM) |
| 4548 | { |
| 4549 | int32 aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4550 | uint64_t aSig, bSig, zSig0, zSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4551 | int32 expDiff; |
| 4552 | |
| 4553 | aSig = extractFloatx80Frac( a ); |
| 4554 | aExp = extractFloatx80Exp( a ); |
| 4555 | bSig = extractFloatx80Frac( b ); |
| 4556 | bExp = extractFloatx80Exp( b ); |
| 4557 | expDiff = aExp - bExp; |
| 4558 | if ( 0 < expDiff ) { |
| 4559 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4560 | if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4561 | return a; |
| 4562 | } |
| 4563 | if ( bExp == 0 ) --expDiff; |
| 4564 | shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); |
| 4565 | zExp = aExp; |
| 4566 | } |
| 4567 | else if ( expDiff < 0 ) { |
| 4568 | if ( bExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4569 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4570 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
| 4571 | } |
| 4572 | if ( aExp == 0 ) ++expDiff; |
| 4573 | shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); |
| 4574 | zExp = bExp; |
| 4575 | } |
| 4576 | else { |
| 4577 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4578 | if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4579 | return propagateFloatx80NaN( a, b STATUS_VAR ); |
| 4580 | } |
| 4581 | return a; |
| 4582 | } |
| 4583 | zSig1 = 0; |
| 4584 | zSig0 = aSig + bSig; |
| 4585 | if ( aExp == 0 ) { |
| 4586 | normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 ); |
| 4587 | goto roundAndPack; |
| 4588 | } |
| 4589 | zExp = aExp; |
| 4590 | goto shiftRight1; |
| 4591 | } |
| 4592 | zSig0 = aSig + bSig; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4593 | if ( (int64_t) zSig0 < 0 ) goto roundAndPack; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4594 | shiftRight1: |
| 4595 | shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 ); |
| 4596 | zSig0 |= LIT64( 0x8000000000000000 ); |
| 4597 | ++zExp; |
| 4598 | roundAndPack: |
| 4599 | return |
| 4600 | roundAndPackFloatx80( |
| 4601 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
| 4602 | |
| 4603 | } |
| 4604 | |
| 4605 | /*---------------------------------------------------------------------------- |
| 4606 | | Returns the result of subtracting the absolute values of the extended |
| 4607 | | double-precision floating-point values `a' and `b'. If `zSign' is 1, the |
| 4608 | | difference is negated before being returned. `zSign' is ignored if the |
| 4609 | | result is a NaN. The subtraction is performed according to the IEC/IEEE |
| 4610 | | Standard for Binary Floating-Point Arithmetic. |
| 4611 | *----------------------------------------------------------------------------*/ |
| 4612 | |
| 4613 | static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM ) |
| 4614 | { |
| 4615 | int32 aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4616 | uint64_t aSig, bSig, zSig0, zSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4617 | int32 expDiff; |
| 4618 | floatx80 z; |
| 4619 | |
| 4620 | aSig = extractFloatx80Frac( a ); |
| 4621 | aExp = extractFloatx80Exp( a ); |
| 4622 | bSig = extractFloatx80Frac( b ); |
| 4623 | bExp = extractFloatx80Exp( b ); |
| 4624 | expDiff = aExp - bExp; |
| 4625 | if ( 0 < expDiff ) goto aExpBigger; |
| 4626 | if ( expDiff < 0 ) goto bExpBigger; |
| 4627 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4628 | if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4629 | return propagateFloatx80NaN( a, b STATUS_VAR ); |
| 4630 | } |
| 4631 | float_raise( float_flag_invalid STATUS_VAR); |
| 4632 | z.low = floatx80_default_nan_low; |
| 4633 | z.high = floatx80_default_nan_high; |
| 4634 | return z; |
| 4635 | } |
| 4636 | if ( aExp == 0 ) { |
| 4637 | aExp = 1; |
| 4638 | bExp = 1; |
| 4639 | } |
| 4640 | zSig1 = 0; |
| 4641 | if ( bSig < aSig ) goto aBigger; |
| 4642 | if ( aSig < bSig ) goto bBigger; |
| 4643 | return packFloatx80( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); |
| 4644 | bExpBigger: |
| 4645 | if ( bExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4646 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4647 | return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
| 4648 | } |
| 4649 | if ( aExp == 0 ) ++expDiff; |
| 4650 | shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); |
| 4651 | bBigger: |
| 4652 | sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 ); |
| 4653 | zExp = bExp; |
| 4654 | zSign ^= 1; |
| 4655 | goto normalizeRoundAndPack; |
| 4656 | aExpBigger: |
| 4657 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4658 | if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4659 | return a; |
| 4660 | } |
| 4661 | if ( bExp == 0 ) --expDiff; |
| 4662 | shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); |
| 4663 | aBigger: |
| 4664 | sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 ); |
| 4665 | zExp = aExp; |
| 4666 | normalizeRoundAndPack: |
| 4667 | return |
| 4668 | normalizeRoundAndPackFloatx80( |
| 4669 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
| 4670 | |
| 4671 | } |
| 4672 | |
| 4673 | /*---------------------------------------------------------------------------- |
| 4674 | | Returns the result of adding the extended double-precision floating-point |
| 4675 | | values `a' and `b'. The operation is performed according to the IEC/IEEE |
| 4676 | | Standard for Binary Floating-Point Arithmetic. |
| 4677 | *----------------------------------------------------------------------------*/ |
| 4678 | |
| 4679 | floatx80 floatx80_add( floatx80 a, floatx80 b STATUS_PARAM ) |
| 4680 | { |
| 4681 | flag aSign, bSign; |
| 4682 | |
| 4683 | aSign = extractFloatx80Sign( a ); |
| 4684 | bSign = extractFloatx80Sign( b ); |
| 4685 | if ( aSign == bSign ) { |
| 4686 | return addFloatx80Sigs( a, b, aSign STATUS_VAR ); |
| 4687 | } |
| 4688 | else { |
| 4689 | return subFloatx80Sigs( a, b, aSign STATUS_VAR ); |
| 4690 | } |
| 4691 | |
| 4692 | } |
| 4693 | |
| 4694 | /*---------------------------------------------------------------------------- |
| 4695 | | Returns the result of subtracting the extended double-precision floating- |
| 4696 | | point values `a' and `b'. The operation is performed according to the |
| 4697 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 4698 | *----------------------------------------------------------------------------*/ |
| 4699 | |
| 4700 | floatx80 floatx80_sub( floatx80 a, floatx80 b STATUS_PARAM ) |
| 4701 | { |
| 4702 | flag aSign, bSign; |
| 4703 | |
| 4704 | aSign = extractFloatx80Sign( a ); |
| 4705 | bSign = extractFloatx80Sign( b ); |
| 4706 | if ( aSign == bSign ) { |
| 4707 | return subFloatx80Sigs( a, b, aSign STATUS_VAR ); |
| 4708 | } |
| 4709 | else { |
| 4710 | return addFloatx80Sigs( a, b, aSign STATUS_VAR ); |
| 4711 | } |
| 4712 | |
| 4713 | } |
| 4714 | |
| 4715 | /*---------------------------------------------------------------------------- |
| 4716 | | Returns the result of multiplying the extended double-precision floating- |
| 4717 | | point values `a' and `b'. The operation is performed according to the |
| 4718 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 4719 | *----------------------------------------------------------------------------*/ |
| 4720 | |
| 4721 | floatx80 floatx80_mul( floatx80 a, floatx80 b STATUS_PARAM ) |
| 4722 | { |
| 4723 | flag aSign, bSign, zSign; |
| 4724 | int32 aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4725 | uint64_t aSig, bSig, zSig0, zSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4726 | floatx80 z; |
| 4727 | |
| 4728 | aSig = extractFloatx80Frac( a ); |
| 4729 | aExp = extractFloatx80Exp( a ); |
| 4730 | aSign = extractFloatx80Sign( a ); |
| 4731 | bSig = extractFloatx80Frac( b ); |
| 4732 | bExp = extractFloatx80Exp( b ); |
| 4733 | bSign = extractFloatx80Sign( b ); |
| 4734 | zSign = aSign ^ bSign; |
| 4735 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4736 | if ( (uint64_t) ( aSig<<1 ) |
| 4737 | || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4738 | return propagateFloatx80NaN( a, b STATUS_VAR ); |
| 4739 | } |
| 4740 | if ( ( bExp | bSig ) == 0 ) goto invalid; |
| 4741 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
| 4742 | } |
| 4743 | if ( bExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4744 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4745 | if ( ( aExp | aSig ) == 0 ) { |
| 4746 | invalid: |
| 4747 | float_raise( float_flag_invalid STATUS_VAR); |
| 4748 | z.low = floatx80_default_nan_low; |
| 4749 | z.high = floatx80_default_nan_high; |
| 4750 | return z; |
| 4751 | } |
| 4752 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
| 4753 | } |
| 4754 | if ( aExp == 0 ) { |
| 4755 | if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); |
| 4756 | normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); |
| 4757 | } |
| 4758 | if ( bExp == 0 ) { |
| 4759 | if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); |
| 4760 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); |
| 4761 | } |
| 4762 | zExp = aExp + bExp - 0x3FFE; |
| 4763 | mul64To128( aSig, bSig, &zSig0, &zSig1 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4764 | if ( 0 < (int64_t) zSig0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4765 | shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 ); |
| 4766 | --zExp; |
| 4767 | } |
| 4768 | return |
| 4769 | roundAndPackFloatx80( |
| 4770 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
| 4771 | |
| 4772 | } |
| 4773 | |
| 4774 | /*---------------------------------------------------------------------------- |
| 4775 | | Returns the result of dividing the extended double-precision floating-point |
| 4776 | | value `a' by the corresponding value `b'. The operation is performed |
| 4777 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 4778 | *----------------------------------------------------------------------------*/ |
| 4779 | |
| 4780 | floatx80 floatx80_div( floatx80 a, floatx80 b STATUS_PARAM ) |
| 4781 | { |
| 4782 | flag aSign, bSign, zSign; |
| 4783 | int32 aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4784 | uint64_t aSig, bSig, zSig0, zSig1; |
| 4785 | uint64_t rem0, rem1, rem2, term0, term1, term2; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4786 | floatx80 z; |
| 4787 | |
| 4788 | aSig = extractFloatx80Frac( a ); |
| 4789 | aExp = extractFloatx80Exp( a ); |
| 4790 | aSign = extractFloatx80Sign( a ); |
| 4791 | bSig = extractFloatx80Frac( b ); |
| 4792 | bExp = extractFloatx80Exp( b ); |
| 4793 | bSign = extractFloatx80Sign( b ); |
| 4794 | zSign = aSign ^ bSign; |
| 4795 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4796 | if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4797 | if ( bExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4798 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4799 | goto invalid; |
| 4800 | } |
| 4801 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
| 4802 | } |
| 4803 | if ( bExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4804 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4805 | return packFloatx80( zSign, 0, 0 ); |
| 4806 | } |
| 4807 | if ( bExp == 0 ) { |
| 4808 | if ( bSig == 0 ) { |
| 4809 | if ( ( aExp | aSig ) == 0 ) { |
| 4810 | invalid: |
| 4811 | float_raise( float_flag_invalid STATUS_VAR); |
| 4812 | z.low = floatx80_default_nan_low; |
| 4813 | z.high = floatx80_default_nan_high; |
| 4814 | return z; |
| 4815 | } |
| 4816 | float_raise( float_flag_divbyzero STATUS_VAR); |
| 4817 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
| 4818 | } |
| 4819 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); |
| 4820 | } |
| 4821 | if ( aExp == 0 ) { |
| 4822 | if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); |
| 4823 | normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); |
| 4824 | } |
| 4825 | zExp = aExp - bExp + 0x3FFE; |
| 4826 | rem1 = 0; |
| 4827 | if ( bSig <= aSig ) { |
| 4828 | shift128Right( aSig, 0, 1, &aSig, &rem1 ); |
| 4829 | ++zExp; |
| 4830 | } |
| 4831 | zSig0 = estimateDiv128To64( aSig, rem1, bSig ); |
| 4832 | mul64To128( bSig, zSig0, &term0, &term1 ); |
| 4833 | sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4834 | while ( (int64_t) rem0 < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4835 | --zSig0; |
| 4836 | add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); |
| 4837 | } |
| 4838 | zSig1 = estimateDiv128To64( rem1, 0, bSig ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4839 | if ( (uint64_t) ( zSig1<<1 ) <= 8 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4840 | mul64To128( bSig, zSig1, &term1, &term2 ); |
| 4841 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4842 | while ( (int64_t) rem1 < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4843 | --zSig1; |
| 4844 | add128( rem1, rem2, 0, bSig, &rem1, &rem2 ); |
| 4845 | } |
| 4846 | zSig1 |= ( ( rem1 | rem2 ) != 0 ); |
| 4847 | } |
| 4848 | return |
| 4849 | roundAndPackFloatx80( |
| 4850 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
| 4851 | |
| 4852 | } |
| 4853 | |
| 4854 | /*---------------------------------------------------------------------------- |
| 4855 | | Returns the remainder of the extended double-precision floating-point value |
| 4856 | | `a' with respect to the corresponding value `b'. The operation is performed |
| 4857 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 4858 | *----------------------------------------------------------------------------*/ |
| 4859 | |
| 4860 | floatx80 floatx80_rem( floatx80 a, floatx80 b STATUS_PARAM ) |
| 4861 | { |
David Turner | 2738c26 | 2010-09-09 17:41:26 +0200 | [diff] [blame] | 4862 | flag aSign, zSign; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4863 | int32 aExp, bExp, expDiff; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4864 | uint64_t aSig0, aSig1, bSig; |
| 4865 | uint64_t q, term0, term1, alternateASig0, alternateASig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4866 | floatx80 z; |
| 4867 | |
| 4868 | aSig0 = extractFloatx80Frac( a ); |
| 4869 | aExp = extractFloatx80Exp( a ); |
| 4870 | aSign = extractFloatx80Sign( a ); |
| 4871 | bSig = extractFloatx80Frac( b ); |
| 4872 | bExp = extractFloatx80Exp( b ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4873 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4874 | if ( (uint64_t) ( aSig0<<1 ) |
| 4875 | || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4876 | return propagateFloatx80NaN( a, b STATUS_VAR ); |
| 4877 | } |
| 4878 | goto invalid; |
| 4879 | } |
| 4880 | if ( bExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4881 | if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4882 | return a; |
| 4883 | } |
| 4884 | if ( bExp == 0 ) { |
| 4885 | if ( bSig == 0 ) { |
| 4886 | invalid: |
| 4887 | float_raise( float_flag_invalid STATUS_VAR); |
| 4888 | z.low = floatx80_default_nan_low; |
| 4889 | z.high = floatx80_default_nan_high; |
| 4890 | return z; |
| 4891 | } |
| 4892 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); |
| 4893 | } |
| 4894 | if ( aExp == 0 ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4895 | if ( (uint64_t) ( aSig0<<1 ) == 0 ) return a; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4896 | normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); |
| 4897 | } |
| 4898 | bSig |= LIT64( 0x8000000000000000 ); |
| 4899 | zSign = aSign; |
| 4900 | expDiff = aExp - bExp; |
| 4901 | aSig1 = 0; |
| 4902 | if ( expDiff < 0 ) { |
| 4903 | if ( expDiff < -1 ) return a; |
| 4904 | shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); |
| 4905 | expDiff = 0; |
| 4906 | } |
| 4907 | q = ( bSig <= aSig0 ); |
| 4908 | if ( q ) aSig0 -= bSig; |
| 4909 | expDiff -= 64; |
| 4910 | while ( 0 < expDiff ) { |
| 4911 | q = estimateDiv128To64( aSig0, aSig1, bSig ); |
| 4912 | q = ( 2 < q ) ? q - 2 : 0; |
| 4913 | mul64To128( bSig, q, &term0, &term1 ); |
| 4914 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); |
| 4915 | shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 ); |
| 4916 | expDiff -= 62; |
| 4917 | } |
| 4918 | expDiff += 64; |
| 4919 | if ( 0 < expDiff ) { |
| 4920 | q = estimateDiv128To64( aSig0, aSig1, bSig ); |
| 4921 | q = ( 2 < q ) ? q - 2 : 0; |
| 4922 | q >>= 64 - expDiff; |
| 4923 | mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 ); |
| 4924 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); |
| 4925 | shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); |
| 4926 | while ( le128( term0, term1, aSig0, aSig1 ) ) { |
| 4927 | ++q; |
| 4928 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); |
| 4929 | } |
| 4930 | } |
| 4931 | else { |
| 4932 | term1 = 0; |
| 4933 | term0 = bSig; |
| 4934 | } |
| 4935 | sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); |
| 4936 | if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 ) |
| 4937 | || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) |
| 4938 | && ( q & 1 ) ) |
| 4939 | ) { |
| 4940 | aSig0 = alternateASig0; |
| 4941 | aSig1 = alternateASig1; |
| 4942 | zSign = ! zSign; |
| 4943 | } |
| 4944 | return |
| 4945 | normalizeRoundAndPackFloatx80( |
| 4946 | 80, zSign, bExp + expDiff, aSig0, aSig1 STATUS_VAR ); |
| 4947 | |
| 4948 | } |
| 4949 | |
| 4950 | /*---------------------------------------------------------------------------- |
| 4951 | | Returns the square root of the extended double-precision floating-point |
| 4952 | | value `a'. The operation is performed according to the IEC/IEEE Standard |
| 4953 | | for Binary Floating-Point Arithmetic. |
| 4954 | *----------------------------------------------------------------------------*/ |
| 4955 | |
| 4956 | floatx80 floatx80_sqrt( floatx80 a STATUS_PARAM ) |
| 4957 | { |
| 4958 | flag aSign; |
| 4959 | int32 aExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4960 | uint64_t aSig0, aSig1, zSig0, zSig1, doubleZSig0; |
| 4961 | uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4962 | floatx80 z; |
| 4963 | |
| 4964 | aSig0 = extractFloatx80Frac( a ); |
| 4965 | aExp = extractFloatx80Exp( a ); |
| 4966 | aSign = extractFloatx80Sign( a ); |
| 4967 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4968 | if ( (uint64_t) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4969 | if ( ! aSign ) return a; |
| 4970 | goto invalid; |
| 4971 | } |
| 4972 | if ( aSign ) { |
| 4973 | if ( ( aExp | aSig0 ) == 0 ) return a; |
| 4974 | invalid: |
| 4975 | float_raise( float_flag_invalid STATUS_VAR); |
| 4976 | z.low = floatx80_default_nan_low; |
| 4977 | z.high = floatx80_default_nan_high; |
| 4978 | return z; |
| 4979 | } |
| 4980 | if ( aExp == 0 ) { |
| 4981 | if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 ); |
| 4982 | normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); |
| 4983 | } |
| 4984 | zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF; |
| 4985 | zSig0 = estimateSqrt32( aExp, aSig0>>32 ); |
| 4986 | shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 ); |
| 4987 | zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); |
| 4988 | doubleZSig0 = zSig0<<1; |
| 4989 | mul64To128( zSig0, zSig0, &term0, &term1 ); |
| 4990 | sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 4991 | while ( (int64_t) rem0 < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 4992 | --zSig0; |
| 4993 | doubleZSig0 -= 2; |
| 4994 | add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); |
| 4995 | } |
| 4996 | zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); |
| 4997 | if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) { |
| 4998 | if ( zSig1 == 0 ) zSig1 = 1; |
| 4999 | mul64To128( doubleZSig0, zSig1, &term1, &term2 ); |
| 5000 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); |
| 5001 | mul64To128( zSig1, zSig1, &term2, &term3 ); |
| 5002 | sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5003 | while ( (int64_t) rem1 < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5004 | --zSig1; |
| 5005 | shortShift128Left( 0, zSig1, 1, &term2, &term3 ); |
| 5006 | term3 |= 1; |
| 5007 | term2 |= doubleZSig0; |
| 5008 | add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); |
| 5009 | } |
| 5010 | zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); |
| 5011 | } |
| 5012 | shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 ); |
| 5013 | zSig0 |= doubleZSig0; |
| 5014 | return |
| 5015 | roundAndPackFloatx80( |
| 5016 | STATUS(floatx80_rounding_precision), 0, zExp, zSig0, zSig1 STATUS_VAR ); |
| 5017 | |
| 5018 | } |
| 5019 | |
| 5020 | /*---------------------------------------------------------------------------- |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5021 | | Returns 1 if the extended double-precision floating-point value `a' is equal |
| 5022 | | to the corresponding value `b', and 0 otherwise. The invalid exception is |
| 5023 | | raised if either operand is a NaN. Otherwise, the comparison is performed |
| 5024 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5025 | *----------------------------------------------------------------------------*/ |
| 5026 | |
| 5027 | int floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM ) |
| 5028 | { |
| 5029 | |
| 5030 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5031 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5032 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5033 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
| 5034 | ) { |
| 5035 | float_raise( float_flag_invalid STATUS_VAR); |
| 5036 | return 0; |
| 5037 | } |
| 5038 | return |
| 5039 | ( a.low == b.low ) |
| 5040 | && ( ( a.high == b.high ) |
| 5041 | || ( ( a.low == 0 ) |
| 5042 | && ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
| 5043 | ); |
| 5044 | |
| 5045 | } |
| 5046 | |
| 5047 | /*---------------------------------------------------------------------------- |
| 5048 | | Returns 1 if the extended double-precision floating-point value `a' is |
| 5049 | | less than or equal to the corresponding value `b', and 0 otherwise. The |
| 5050 | | invalid exception is raised if either operand is a NaN. The comparison is |
| 5051 | | performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 5052 | | Arithmetic. |
| 5053 | *----------------------------------------------------------------------------*/ |
| 5054 | |
| 5055 | int floatx80_le( floatx80 a, floatx80 b STATUS_PARAM ) |
| 5056 | { |
| 5057 | flag aSign, bSign; |
| 5058 | |
| 5059 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
| 5060 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
| 5061 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
| 5062 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
| 5063 | ) { |
| 5064 | float_raise( float_flag_invalid STATUS_VAR); |
| 5065 | return 0; |
| 5066 | } |
| 5067 | aSign = extractFloatx80Sign( a ); |
| 5068 | bSign = extractFloatx80Sign( b ); |
| 5069 | if ( aSign != bSign ) { |
| 5070 | return |
| 5071 | aSign |
| 5072 | || ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
| 5073 | == 0 ); |
| 5074 | } |
| 5075 | return |
| 5076 | aSign ? le128( b.high, b.low, a.high, a.low ) |
| 5077 | : le128( a.high, a.low, b.high, b.low ); |
| 5078 | |
| 5079 | } |
| 5080 | |
| 5081 | /*---------------------------------------------------------------------------- |
| 5082 | | Returns 1 if the extended double-precision floating-point value `a' is |
| 5083 | | less than the corresponding value `b', and 0 otherwise. The invalid |
| 5084 | | exception is raised if either operand is a NaN. The comparison is performed |
| 5085 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 5086 | *----------------------------------------------------------------------------*/ |
| 5087 | |
| 5088 | int floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM ) |
| 5089 | { |
| 5090 | flag aSign, bSign; |
| 5091 | |
| 5092 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
| 5093 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
| 5094 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
| 5095 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
| 5096 | ) { |
| 5097 | float_raise( float_flag_invalid STATUS_VAR); |
| 5098 | return 0; |
| 5099 | } |
| 5100 | aSign = extractFloatx80Sign( a ); |
| 5101 | bSign = extractFloatx80Sign( b ); |
| 5102 | if ( aSign != bSign ) { |
| 5103 | return |
| 5104 | aSign |
| 5105 | && ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
| 5106 | != 0 ); |
| 5107 | } |
| 5108 | return |
| 5109 | aSign ? lt128( b.high, b.low, a.high, a.low ) |
| 5110 | : lt128( a.high, a.low, b.high, b.low ); |
| 5111 | |
| 5112 | } |
| 5113 | |
| 5114 | /*---------------------------------------------------------------------------- |
| 5115 | | Returns 1 if the extended double-precision floating-point values `a' and `b' |
| 5116 | | cannot be compared, and 0 otherwise. The invalid exception is raised if |
| 5117 | | either operand is a NaN. The comparison is performed according to the |
| 5118 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 5119 | *----------------------------------------------------------------------------*/ |
| 5120 | int floatx80_unordered( floatx80 a, floatx80 b STATUS_PARAM ) |
| 5121 | { |
| 5122 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
| 5123 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
| 5124 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
| 5125 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
| 5126 | ) { |
| 5127 | float_raise( float_flag_invalid STATUS_VAR); |
| 5128 | return 1; |
| 5129 | } |
| 5130 | return 0; |
| 5131 | } |
| 5132 | |
| 5133 | /*---------------------------------------------------------------------------- |
| 5134 | | Returns 1 if the extended double-precision floating-point value `a' is |
| 5135 | | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not |
| 5136 | | cause an exception. The comparison is performed according to the IEC/IEEE |
| 5137 | | Standard for Binary Floating-Point Arithmetic. |
| 5138 | *----------------------------------------------------------------------------*/ |
| 5139 | |
| 5140 | int floatx80_eq_quiet( floatx80 a, floatx80 b STATUS_PARAM ) |
| 5141 | { |
| 5142 | |
| 5143 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
| 5144 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
| 5145 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
| 5146 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5147 | ) { |
| 5148 | if ( floatx80_is_signaling_nan( a ) |
| 5149 | || floatx80_is_signaling_nan( b ) ) { |
| 5150 | float_raise( float_flag_invalid STATUS_VAR); |
| 5151 | } |
| 5152 | return 0; |
| 5153 | } |
| 5154 | return |
| 5155 | ( a.low == b.low ) |
| 5156 | && ( ( a.high == b.high ) |
| 5157 | || ( ( a.low == 0 ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5158 | && ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5159 | ); |
| 5160 | |
| 5161 | } |
| 5162 | |
| 5163 | /*---------------------------------------------------------------------------- |
| 5164 | | Returns 1 if the extended double-precision floating-point value `a' is less |
| 5165 | | than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs |
| 5166 | | do not cause an exception. Otherwise, the comparison is performed according |
| 5167 | | to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 5168 | *----------------------------------------------------------------------------*/ |
| 5169 | |
| 5170 | int floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM ) |
| 5171 | { |
| 5172 | flag aSign, bSign; |
| 5173 | |
| 5174 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5175 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5176 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5177 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5178 | ) { |
| 5179 | if ( floatx80_is_signaling_nan( a ) |
| 5180 | || floatx80_is_signaling_nan( b ) ) { |
| 5181 | float_raise( float_flag_invalid STATUS_VAR); |
| 5182 | } |
| 5183 | return 0; |
| 5184 | } |
| 5185 | aSign = extractFloatx80Sign( a ); |
| 5186 | bSign = extractFloatx80Sign( b ); |
| 5187 | if ( aSign != bSign ) { |
| 5188 | return |
| 5189 | aSign |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5190 | || ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5191 | == 0 ); |
| 5192 | } |
| 5193 | return |
| 5194 | aSign ? le128( b.high, b.low, a.high, a.low ) |
| 5195 | : le128( a.high, a.low, b.high, b.low ); |
| 5196 | |
| 5197 | } |
| 5198 | |
| 5199 | /*---------------------------------------------------------------------------- |
| 5200 | | Returns 1 if the extended double-precision floating-point value `a' is less |
| 5201 | | than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause |
| 5202 | | an exception. Otherwise, the comparison is performed according to the |
| 5203 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 5204 | *----------------------------------------------------------------------------*/ |
| 5205 | |
| 5206 | int floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM ) |
| 5207 | { |
| 5208 | flag aSign, bSign; |
| 5209 | |
| 5210 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5211 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5212 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5213 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5214 | ) { |
| 5215 | if ( floatx80_is_signaling_nan( a ) |
| 5216 | || floatx80_is_signaling_nan( b ) ) { |
| 5217 | float_raise( float_flag_invalid STATUS_VAR); |
| 5218 | } |
| 5219 | return 0; |
| 5220 | } |
| 5221 | aSign = extractFloatx80Sign( a ); |
| 5222 | bSign = extractFloatx80Sign( b ); |
| 5223 | if ( aSign != bSign ) { |
| 5224 | return |
| 5225 | aSign |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5226 | && ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5227 | != 0 ); |
| 5228 | } |
| 5229 | return |
| 5230 | aSign ? lt128( b.high, b.low, a.high, a.low ) |
| 5231 | : lt128( a.high, a.low, b.high, b.low ); |
| 5232 | |
| 5233 | } |
| 5234 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5235 | /*---------------------------------------------------------------------------- |
| 5236 | | Returns 1 if the extended double-precision floating-point values `a' and `b' |
| 5237 | | cannot be compared, and 0 otherwise. Quiet NaNs do not cause an exception. |
| 5238 | | The comparison is performed according to the IEC/IEEE Standard for Binary |
| 5239 | | Floating-Point Arithmetic. |
| 5240 | *----------------------------------------------------------------------------*/ |
| 5241 | int floatx80_unordered_quiet( floatx80 a, floatx80 b STATUS_PARAM ) |
| 5242 | { |
| 5243 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
| 5244 | && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) |
| 5245 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) |
| 5246 | && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) |
| 5247 | ) { |
| 5248 | if ( floatx80_is_signaling_nan( a ) |
| 5249 | || floatx80_is_signaling_nan( b ) ) { |
| 5250 | float_raise( float_flag_invalid STATUS_VAR); |
| 5251 | } |
| 5252 | return 1; |
| 5253 | } |
| 5254 | return 0; |
| 5255 | } |
| 5256 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5257 | /*---------------------------------------------------------------------------- |
| 5258 | | Returns the result of converting the quadruple-precision floating-point |
| 5259 | | value `a' to the 32-bit two's complement integer format. The conversion |
| 5260 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 5261 | | Arithmetic---which means in particular that the conversion is rounded |
| 5262 | | according to the current rounding mode. If `a' is a NaN, the largest |
| 5263 | | positive integer is returned. Otherwise, if the conversion overflows, the |
| 5264 | | largest integer with the same sign as `a' is returned. |
| 5265 | *----------------------------------------------------------------------------*/ |
| 5266 | |
| 5267 | int32 float128_to_int32( float128 a STATUS_PARAM ) |
| 5268 | { |
| 5269 | flag aSign; |
| 5270 | int32 aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5271 | uint64_t aSig0, aSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5272 | |
| 5273 | aSig1 = extractFloat128Frac1( a ); |
| 5274 | aSig0 = extractFloat128Frac0( a ); |
| 5275 | aExp = extractFloat128Exp( a ); |
| 5276 | aSign = extractFloat128Sign( a ); |
| 5277 | if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0; |
| 5278 | if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); |
| 5279 | aSig0 |= ( aSig1 != 0 ); |
| 5280 | shiftCount = 0x4028 - aExp; |
| 5281 | if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 ); |
| 5282 | return roundAndPackInt32( aSign, aSig0 STATUS_VAR ); |
| 5283 | |
| 5284 | } |
| 5285 | |
| 5286 | /*---------------------------------------------------------------------------- |
| 5287 | | Returns the result of converting the quadruple-precision floating-point |
| 5288 | | value `a' to the 32-bit two's complement integer format. The conversion |
| 5289 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 5290 | | Arithmetic, except that the conversion is always rounded toward zero. If |
| 5291 | | `a' is a NaN, the largest positive integer is returned. Otherwise, if the |
| 5292 | | conversion overflows, the largest integer with the same sign as `a' is |
| 5293 | | returned. |
| 5294 | *----------------------------------------------------------------------------*/ |
| 5295 | |
| 5296 | int32 float128_to_int32_round_to_zero( float128 a STATUS_PARAM ) |
| 5297 | { |
| 5298 | flag aSign; |
| 5299 | int32 aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5300 | uint64_t aSig0, aSig1, savedASig; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 5301 | int32_t z; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5302 | |
| 5303 | aSig1 = extractFloat128Frac1( a ); |
| 5304 | aSig0 = extractFloat128Frac0( a ); |
| 5305 | aExp = extractFloat128Exp( a ); |
| 5306 | aSign = extractFloat128Sign( a ); |
| 5307 | aSig0 |= ( aSig1 != 0 ); |
| 5308 | if ( 0x401E < aExp ) { |
| 5309 | if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0; |
| 5310 | goto invalid; |
| 5311 | } |
| 5312 | else if ( aExp < 0x3FFF ) { |
| 5313 | if ( aExp || aSig0 ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 5314 | return 0; |
| 5315 | } |
| 5316 | aSig0 |= LIT64( 0x0001000000000000 ); |
| 5317 | shiftCount = 0x402F - aExp; |
| 5318 | savedASig = aSig0; |
| 5319 | aSig0 >>= shiftCount; |
| 5320 | z = aSig0; |
| 5321 | if ( aSign ) z = - z; |
| 5322 | if ( ( z < 0 ) ^ aSign ) { |
| 5323 | invalid: |
| 5324 | float_raise( float_flag_invalid STATUS_VAR); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5325 | return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5326 | } |
| 5327 | if ( ( aSig0<<shiftCount ) != savedASig ) { |
| 5328 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 5329 | } |
| 5330 | return z; |
| 5331 | |
| 5332 | } |
| 5333 | |
| 5334 | /*---------------------------------------------------------------------------- |
| 5335 | | Returns the result of converting the quadruple-precision floating-point |
| 5336 | | value `a' to the 64-bit two's complement integer format. The conversion |
| 5337 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 5338 | | Arithmetic---which means in particular that the conversion is rounded |
| 5339 | | according to the current rounding mode. If `a' is a NaN, the largest |
| 5340 | | positive integer is returned. Otherwise, if the conversion overflows, the |
| 5341 | | largest integer with the same sign as `a' is returned. |
| 5342 | *----------------------------------------------------------------------------*/ |
| 5343 | |
| 5344 | int64 float128_to_int64( float128 a STATUS_PARAM ) |
| 5345 | { |
| 5346 | flag aSign; |
| 5347 | int32 aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5348 | uint64_t aSig0, aSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5349 | |
| 5350 | aSig1 = extractFloat128Frac1( a ); |
| 5351 | aSig0 = extractFloat128Frac0( a ); |
| 5352 | aExp = extractFloat128Exp( a ); |
| 5353 | aSign = extractFloat128Sign( a ); |
| 5354 | if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); |
| 5355 | shiftCount = 0x402F - aExp; |
| 5356 | if ( shiftCount <= 0 ) { |
| 5357 | if ( 0x403E < aExp ) { |
| 5358 | float_raise( float_flag_invalid STATUS_VAR); |
| 5359 | if ( ! aSign |
| 5360 | || ( ( aExp == 0x7FFF ) |
| 5361 | && ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) ) |
| 5362 | ) |
| 5363 | ) { |
| 5364 | return LIT64( 0x7FFFFFFFFFFFFFFF ); |
| 5365 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5366 | return (int64_t) LIT64( 0x8000000000000000 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5367 | } |
| 5368 | shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 ); |
| 5369 | } |
| 5370 | else { |
| 5371 | shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 ); |
| 5372 | } |
| 5373 | return roundAndPackInt64( aSign, aSig0, aSig1 STATUS_VAR ); |
| 5374 | |
| 5375 | } |
| 5376 | |
| 5377 | /*---------------------------------------------------------------------------- |
| 5378 | | Returns the result of converting the quadruple-precision floating-point |
| 5379 | | value `a' to the 64-bit two's complement integer format. The conversion |
| 5380 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 5381 | | Arithmetic, except that the conversion is always rounded toward zero. |
| 5382 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if |
| 5383 | | the conversion overflows, the largest integer with the same sign as `a' is |
| 5384 | | returned. |
| 5385 | *----------------------------------------------------------------------------*/ |
| 5386 | |
| 5387 | int64 float128_to_int64_round_to_zero( float128 a STATUS_PARAM ) |
| 5388 | { |
| 5389 | flag aSign; |
| 5390 | int32 aExp, shiftCount; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5391 | uint64_t aSig0, aSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5392 | int64 z; |
| 5393 | |
| 5394 | aSig1 = extractFloat128Frac1( a ); |
| 5395 | aSig0 = extractFloat128Frac0( a ); |
| 5396 | aExp = extractFloat128Exp( a ); |
| 5397 | aSign = extractFloat128Sign( a ); |
| 5398 | if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); |
| 5399 | shiftCount = aExp - 0x402F; |
| 5400 | if ( 0 < shiftCount ) { |
| 5401 | if ( 0x403E <= aExp ) { |
| 5402 | aSig0 &= LIT64( 0x0000FFFFFFFFFFFF ); |
| 5403 | if ( ( a.high == LIT64( 0xC03E000000000000 ) ) |
| 5404 | && ( aSig1 < LIT64( 0x0002000000000000 ) ) ) { |
| 5405 | if ( aSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; |
| 5406 | } |
| 5407 | else { |
| 5408 | float_raise( float_flag_invalid STATUS_VAR); |
| 5409 | if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) { |
| 5410 | return LIT64( 0x7FFFFFFFFFFFFFFF ); |
| 5411 | } |
| 5412 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5413 | return (int64_t) LIT64( 0x8000000000000000 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5414 | } |
| 5415 | z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5416 | if ( (uint64_t) ( aSig1<<shiftCount ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5417 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 5418 | } |
| 5419 | } |
| 5420 | else { |
| 5421 | if ( aExp < 0x3FFF ) { |
| 5422 | if ( aExp | aSig0 | aSig1 ) { |
| 5423 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 5424 | } |
| 5425 | return 0; |
| 5426 | } |
| 5427 | z = aSig0>>( - shiftCount ); |
| 5428 | if ( aSig1 |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5429 | || ( shiftCount && (uint64_t) ( aSig0<<( shiftCount & 63 ) ) ) ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5430 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 5431 | } |
| 5432 | } |
| 5433 | if ( aSign ) z = - z; |
| 5434 | return z; |
| 5435 | |
| 5436 | } |
| 5437 | |
| 5438 | /*---------------------------------------------------------------------------- |
| 5439 | | Returns the result of converting the quadruple-precision floating-point |
| 5440 | | value `a' to the single-precision floating-point format. The conversion |
| 5441 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 5442 | | Arithmetic. |
| 5443 | *----------------------------------------------------------------------------*/ |
| 5444 | |
| 5445 | float32 float128_to_float32( float128 a STATUS_PARAM ) |
| 5446 | { |
| 5447 | flag aSign; |
| 5448 | int32 aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5449 | uint64_t aSig0, aSig1; |
| 5450 | uint32_t zSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5451 | |
| 5452 | aSig1 = extractFloat128Frac1( a ); |
| 5453 | aSig0 = extractFloat128Frac0( a ); |
| 5454 | aExp = extractFloat128Exp( a ); |
| 5455 | aSign = extractFloat128Sign( a ); |
| 5456 | if ( aExp == 0x7FFF ) { |
| 5457 | if ( aSig0 | aSig1 ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5458 | return commonNaNToFloat32( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5459 | } |
| 5460 | return packFloat32( aSign, 0xFF, 0 ); |
| 5461 | } |
| 5462 | aSig0 |= ( aSig1 != 0 ); |
| 5463 | shift64RightJamming( aSig0, 18, &aSig0 ); |
| 5464 | zSig = aSig0; |
| 5465 | if ( aExp || zSig ) { |
| 5466 | zSig |= 0x40000000; |
| 5467 | aExp -= 0x3F81; |
| 5468 | } |
| 5469 | return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR ); |
| 5470 | |
| 5471 | } |
| 5472 | |
| 5473 | /*---------------------------------------------------------------------------- |
| 5474 | | Returns the result of converting the quadruple-precision floating-point |
| 5475 | | value `a' to the double-precision floating-point format. The conversion |
| 5476 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point |
| 5477 | | Arithmetic. |
| 5478 | *----------------------------------------------------------------------------*/ |
| 5479 | |
| 5480 | float64 float128_to_float64( float128 a STATUS_PARAM ) |
| 5481 | { |
| 5482 | flag aSign; |
| 5483 | int32 aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5484 | uint64_t aSig0, aSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5485 | |
| 5486 | aSig1 = extractFloat128Frac1( a ); |
| 5487 | aSig0 = extractFloat128Frac0( a ); |
| 5488 | aExp = extractFloat128Exp( a ); |
| 5489 | aSign = extractFloat128Sign( a ); |
| 5490 | if ( aExp == 0x7FFF ) { |
| 5491 | if ( aSig0 | aSig1 ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5492 | return commonNaNToFloat64( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5493 | } |
| 5494 | return packFloat64( aSign, 0x7FF, 0 ); |
| 5495 | } |
| 5496 | shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); |
| 5497 | aSig0 |= ( aSig1 != 0 ); |
| 5498 | if ( aExp || aSig0 ) { |
| 5499 | aSig0 |= LIT64( 0x4000000000000000 ); |
| 5500 | aExp -= 0x3C01; |
| 5501 | } |
| 5502 | return roundAndPackFloat64( aSign, aExp, aSig0 STATUS_VAR ); |
| 5503 | |
| 5504 | } |
| 5505 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5506 | /*---------------------------------------------------------------------------- |
| 5507 | | Returns the result of converting the quadruple-precision floating-point |
| 5508 | | value `a' to the extended double-precision floating-point format. The |
| 5509 | | conversion is performed according to the IEC/IEEE Standard for Binary |
| 5510 | | Floating-Point Arithmetic. |
| 5511 | *----------------------------------------------------------------------------*/ |
| 5512 | |
| 5513 | floatx80 float128_to_floatx80( float128 a STATUS_PARAM ) |
| 5514 | { |
| 5515 | flag aSign; |
| 5516 | int32 aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5517 | uint64_t aSig0, aSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5518 | |
| 5519 | aSig1 = extractFloat128Frac1( a ); |
| 5520 | aSig0 = extractFloat128Frac0( a ); |
| 5521 | aExp = extractFloat128Exp( a ); |
| 5522 | aSign = extractFloat128Sign( a ); |
| 5523 | if ( aExp == 0x7FFF ) { |
| 5524 | if ( aSig0 | aSig1 ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5525 | return commonNaNToFloatx80( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5526 | } |
| 5527 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
| 5528 | } |
| 5529 | if ( aExp == 0 ) { |
| 5530 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 ); |
| 5531 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
| 5532 | } |
| 5533 | else { |
| 5534 | aSig0 |= LIT64( 0x0001000000000000 ); |
| 5535 | } |
| 5536 | shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 ); |
| 5537 | return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 STATUS_VAR ); |
| 5538 | |
| 5539 | } |
| 5540 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5541 | /*---------------------------------------------------------------------------- |
| 5542 | | Rounds the quadruple-precision floating-point value `a' to an integer, and |
| 5543 | | returns the result as a quadruple-precision floating-point value. The |
| 5544 | | operation is performed according to the IEC/IEEE Standard for Binary |
| 5545 | | Floating-Point Arithmetic. |
| 5546 | *----------------------------------------------------------------------------*/ |
| 5547 | |
| 5548 | float128 float128_round_to_int( float128 a STATUS_PARAM ) |
| 5549 | { |
| 5550 | flag aSign; |
| 5551 | int32 aExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5552 | uint64_t lastBitMask, roundBitsMask; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5553 | int8 roundingMode; |
| 5554 | float128 z; |
| 5555 | |
| 5556 | aExp = extractFloat128Exp( a ); |
| 5557 | if ( 0x402F <= aExp ) { |
| 5558 | if ( 0x406F <= aExp ) { |
| 5559 | if ( ( aExp == 0x7FFF ) |
| 5560 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) |
| 5561 | ) { |
| 5562 | return propagateFloat128NaN( a, a STATUS_VAR ); |
| 5563 | } |
| 5564 | return a; |
| 5565 | } |
| 5566 | lastBitMask = 1; |
| 5567 | lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1; |
| 5568 | roundBitsMask = lastBitMask - 1; |
| 5569 | z = a; |
| 5570 | roundingMode = STATUS(float_rounding_mode); |
| 5571 | if ( roundingMode == float_round_nearest_even ) { |
| 5572 | if ( lastBitMask ) { |
| 5573 | add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low ); |
| 5574 | if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; |
| 5575 | } |
| 5576 | else { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5577 | if ( (int64_t) z.low < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5578 | ++z.high; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5579 | if ( (uint64_t) ( z.low<<1 ) == 0 ) z.high &= ~1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5580 | } |
| 5581 | } |
| 5582 | } |
| 5583 | else if ( roundingMode != float_round_to_zero ) { |
| 5584 | if ( extractFloat128Sign( z ) |
| 5585 | ^ ( roundingMode == float_round_up ) ) { |
| 5586 | add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low ); |
| 5587 | } |
| 5588 | } |
| 5589 | z.low &= ~ roundBitsMask; |
| 5590 | } |
| 5591 | else { |
| 5592 | if ( aExp < 0x3FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5593 | if ( ( ( (uint64_t) ( a.high<<1 ) ) | a.low ) == 0 ) return a; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5594 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 5595 | aSign = extractFloat128Sign( a ); |
| 5596 | switch ( STATUS(float_rounding_mode) ) { |
| 5597 | case float_round_nearest_even: |
| 5598 | if ( ( aExp == 0x3FFE ) |
| 5599 | && ( extractFloat128Frac0( a ) |
| 5600 | | extractFloat128Frac1( a ) ) |
| 5601 | ) { |
| 5602 | return packFloat128( aSign, 0x3FFF, 0, 0 ); |
| 5603 | } |
| 5604 | break; |
| 5605 | case float_round_down: |
| 5606 | return |
| 5607 | aSign ? packFloat128( 1, 0x3FFF, 0, 0 ) |
| 5608 | : packFloat128( 0, 0, 0, 0 ); |
| 5609 | case float_round_up: |
| 5610 | return |
| 5611 | aSign ? packFloat128( 1, 0, 0, 0 ) |
| 5612 | : packFloat128( 0, 0x3FFF, 0, 0 ); |
| 5613 | } |
| 5614 | return packFloat128( aSign, 0, 0, 0 ); |
| 5615 | } |
| 5616 | lastBitMask = 1; |
| 5617 | lastBitMask <<= 0x402F - aExp; |
| 5618 | roundBitsMask = lastBitMask - 1; |
| 5619 | z.low = 0; |
| 5620 | z.high = a.high; |
| 5621 | roundingMode = STATUS(float_rounding_mode); |
| 5622 | if ( roundingMode == float_round_nearest_even ) { |
| 5623 | z.high += lastBitMask>>1; |
| 5624 | if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) { |
| 5625 | z.high &= ~ lastBitMask; |
| 5626 | } |
| 5627 | } |
| 5628 | else if ( roundingMode != float_round_to_zero ) { |
| 5629 | if ( extractFloat128Sign( z ) |
| 5630 | ^ ( roundingMode == float_round_up ) ) { |
| 5631 | z.high |= ( a.low != 0 ); |
| 5632 | z.high += roundBitsMask; |
| 5633 | } |
| 5634 | } |
| 5635 | z.high &= ~ roundBitsMask; |
| 5636 | } |
| 5637 | if ( ( z.low != a.low ) || ( z.high != a.high ) ) { |
| 5638 | STATUS(float_exception_flags) |= float_flag_inexact; |
| 5639 | } |
| 5640 | return z; |
| 5641 | |
| 5642 | } |
| 5643 | |
| 5644 | /*---------------------------------------------------------------------------- |
| 5645 | | Returns the result of adding the absolute values of the quadruple-precision |
| 5646 | | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated |
| 5647 | | before being returned. `zSign' is ignored if the result is a NaN. |
| 5648 | | The addition is performed according to the IEC/IEEE Standard for Binary |
| 5649 | | Floating-Point Arithmetic. |
| 5650 | *----------------------------------------------------------------------------*/ |
| 5651 | |
| 5652 | static float128 addFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM) |
| 5653 | { |
| 5654 | int32 aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5655 | uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5656 | int32 expDiff; |
| 5657 | |
| 5658 | aSig1 = extractFloat128Frac1( a ); |
| 5659 | aSig0 = extractFloat128Frac0( a ); |
| 5660 | aExp = extractFloat128Exp( a ); |
| 5661 | bSig1 = extractFloat128Frac1( b ); |
| 5662 | bSig0 = extractFloat128Frac0( b ); |
| 5663 | bExp = extractFloat128Exp( b ); |
| 5664 | expDiff = aExp - bExp; |
| 5665 | if ( 0 < expDiff ) { |
| 5666 | if ( aExp == 0x7FFF ) { |
| 5667 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5668 | return a; |
| 5669 | } |
| 5670 | if ( bExp == 0 ) { |
| 5671 | --expDiff; |
| 5672 | } |
| 5673 | else { |
| 5674 | bSig0 |= LIT64( 0x0001000000000000 ); |
| 5675 | } |
| 5676 | shift128ExtraRightJamming( |
| 5677 | bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 ); |
| 5678 | zExp = aExp; |
| 5679 | } |
| 5680 | else if ( expDiff < 0 ) { |
| 5681 | if ( bExp == 0x7FFF ) { |
| 5682 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5683 | return packFloat128( zSign, 0x7FFF, 0, 0 ); |
| 5684 | } |
| 5685 | if ( aExp == 0 ) { |
| 5686 | ++expDiff; |
| 5687 | } |
| 5688 | else { |
| 5689 | aSig0 |= LIT64( 0x0001000000000000 ); |
| 5690 | } |
| 5691 | shift128ExtraRightJamming( |
| 5692 | aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 ); |
| 5693 | zExp = bExp; |
| 5694 | } |
| 5695 | else { |
| 5696 | if ( aExp == 0x7FFF ) { |
| 5697 | if ( aSig0 | aSig1 | bSig0 | bSig1 ) { |
| 5698 | return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5699 | } |
| 5700 | return a; |
| 5701 | } |
| 5702 | add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 5703 | if ( aExp == 0 ) { |
David 'Digit' Turner | 5285864 | 2011-06-03 13:41:05 +0200 | [diff] [blame] | 5704 | if (STATUS(flush_to_zero)) { |
| 5705 | if (zSig0 | zSig1) { |
| 5706 | float_raise(float_flag_output_denormal STATUS_VAR); |
| 5707 | } |
| 5708 | return packFloat128(zSign, 0, 0, 0); |
| 5709 | } |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 5710 | return packFloat128( zSign, 0, zSig0, zSig1 ); |
| 5711 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5712 | zSig2 = 0; |
| 5713 | zSig0 |= LIT64( 0x0002000000000000 ); |
| 5714 | zExp = aExp; |
| 5715 | goto shiftRight1; |
| 5716 | } |
| 5717 | aSig0 |= LIT64( 0x0001000000000000 ); |
| 5718 | add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); |
| 5719 | --zExp; |
| 5720 | if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack; |
| 5721 | ++zExp; |
| 5722 | shiftRight1: |
| 5723 | shift128ExtraRightJamming( |
| 5724 | zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); |
| 5725 | roundAndPack: |
| 5726 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); |
| 5727 | |
| 5728 | } |
| 5729 | |
| 5730 | /*---------------------------------------------------------------------------- |
| 5731 | | Returns the result of subtracting the absolute values of the quadruple- |
| 5732 | | precision floating-point values `a' and `b'. If `zSign' is 1, the |
| 5733 | | difference is negated before being returned. `zSign' is ignored if the |
| 5734 | | result is a NaN. The subtraction is performed according to the IEC/IEEE |
| 5735 | | Standard for Binary Floating-Point Arithmetic. |
| 5736 | *----------------------------------------------------------------------------*/ |
| 5737 | |
| 5738 | static float128 subFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM) |
| 5739 | { |
| 5740 | int32 aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5741 | uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5742 | int32 expDiff; |
| 5743 | float128 z; |
| 5744 | |
| 5745 | aSig1 = extractFloat128Frac1( a ); |
| 5746 | aSig0 = extractFloat128Frac0( a ); |
| 5747 | aExp = extractFloat128Exp( a ); |
| 5748 | bSig1 = extractFloat128Frac1( b ); |
| 5749 | bSig0 = extractFloat128Frac0( b ); |
| 5750 | bExp = extractFloat128Exp( b ); |
| 5751 | expDiff = aExp - bExp; |
| 5752 | shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); |
| 5753 | shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 ); |
| 5754 | if ( 0 < expDiff ) goto aExpBigger; |
| 5755 | if ( expDiff < 0 ) goto bExpBigger; |
| 5756 | if ( aExp == 0x7FFF ) { |
| 5757 | if ( aSig0 | aSig1 | bSig0 | bSig1 ) { |
| 5758 | return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5759 | } |
| 5760 | float_raise( float_flag_invalid STATUS_VAR); |
| 5761 | z.low = float128_default_nan_low; |
| 5762 | z.high = float128_default_nan_high; |
| 5763 | return z; |
| 5764 | } |
| 5765 | if ( aExp == 0 ) { |
| 5766 | aExp = 1; |
| 5767 | bExp = 1; |
| 5768 | } |
| 5769 | if ( bSig0 < aSig0 ) goto aBigger; |
| 5770 | if ( aSig0 < bSig0 ) goto bBigger; |
| 5771 | if ( bSig1 < aSig1 ) goto aBigger; |
| 5772 | if ( aSig1 < bSig1 ) goto bBigger; |
| 5773 | return packFloat128( STATUS(float_rounding_mode) == float_round_down, 0, 0, 0 ); |
| 5774 | bExpBigger: |
| 5775 | if ( bExp == 0x7FFF ) { |
| 5776 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5777 | return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 ); |
| 5778 | } |
| 5779 | if ( aExp == 0 ) { |
| 5780 | ++expDiff; |
| 5781 | } |
| 5782 | else { |
| 5783 | aSig0 |= LIT64( 0x4000000000000000 ); |
| 5784 | } |
| 5785 | shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); |
| 5786 | bSig0 |= LIT64( 0x4000000000000000 ); |
| 5787 | bBigger: |
| 5788 | sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 ); |
| 5789 | zExp = bExp; |
| 5790 | zSign ^= 1; |
| 5791 | goto normalizeRoundAndPack; |
| 5792 | aExpBigger: |
| 5793 | if ( aExp == 0x7FFF ) { |
| 5794 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5795 | return a; |
| 5796 | } |
| 5797 | if ( bExp == 0 ) { |
| 5798 | --expDiff; |
| 5799 | } |
| 5800 | else { |
| 5801 | bSig0 |= LIT64( 0x4000000000000000 ); |
| 5802 | } |
| 5803 | shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 ); |
| 5804 | aSig0 |= LIT64( 0x4000000000000000 ); |
| 5805 | aBigger: |
| 5806 | sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); |
| 5807 | zExp = aExp; |
| 5808 | normalizeRoundAndPack: |
| 5809 | --zExp; |
| 5810 | return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 STATUS_VAR ); |
| 5811 | |
| 5812 | } |
| 5813 | |
| 5814 | /*---------------------------------------------------------------------------- |
| 5815 | | Returns the result of adding the quadruple-precision floating-point values |
| 5816 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard |
| 5817 | | for Binary Floating-Point Arithmetic. |
| 5818 | *----------------------------------------------------------------------------*/ |
| 5819 | |
| 5820 | float128 float128_add( float128 a, float128 b STATUS_PARAM ) |
| 5821 | { |
| 5822 | flag aSign, bSign; |
| 5823 | |
| 5824 | aSign = extractFloat128Sign( a ); |
| 5825 | bSign = extractFloat128Sign( b ); |
| 5826 | if ( aSign == bSign ) { |
| 5827 | return addFloat128Sigs( a, b, aSign STATUS_VAR ); |
| 5828 | } |
| 5829 | else { |
| 5830 | return subFloat128Sigs( a, b, aSign STATUS_VAR ); |
| 5831 | } |
| 5832 | |
| 5833 | } |
| 5834 | |
| 5835 | /*---------------------------------------------------------------------------- |
| 5836 | | Returns the result of subtracting the quadruple-precision floating-point |
| 5837 | | values `a' and `b'. The operation is performed according to the IEC/IEEE |
| 5838 | | Standard for Binary Floating-Point Arithmetic. |
| 5839 | *----------------------------------------------------------------------------*/ |
| 5840 | |
| 5841 | float128 float128_sub( float128 a, float128 b STATUS_PARAM ) |
| 5842 | { |
| 5843 | flag aSign, bSign; |
| 5844 | |
| 5845 | aSign = extractFloat128Sign( a ); |
| 5846 | bSign = extractFloat128Sign( b ); |
| 5847 | if ( aSign == bSign ) { |
| 5848 | return subFloat128Sigs( a, b, aSign STATUS_VAR ); |
| 5849 | } |
| 5850 | else { |
| 5851 | return addFloat128Sigs( a, b, aSign STATUS_VAR ); |
| 5852 | } |
| 5853 | |
| 5854 | } |
| 5855 | |
| 5856 | /*---------------------------------------------------------------------------- |
| 5857 | | Returns the result of multiplying the quadruple-precision floating-point |
| 5858 | | values `a' and `b'. The operation is performed according to the IEC/IEEE |
| 5859 | | Standard for Binary Floating-Point Arithmetic. |
| 5860 | *----------------------------------------------------------------------------*/ |
| 5861 | |
| 5862 | float128 float128_mul( float128 a, float128 b STATUS_PARAM ) |
| 5863 | { |
| 5864 | flag aSign, bSign, zSign; |
| 5865 | int32 aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5866 | uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5867 | float128 z; |
| 5868 | |
| 5869 | aSig1 = extractFloat128Frac1( a ); |
| 5870 | aSig0 = extractFloat128Frac0( a ); |
| 5871 | aExp = extractFloat128Exp( a ); |
| 5872 | aSign = extractFloat128Sign( a ); |
| 5873 | bSig1 = extractFloat128Frac1( b ); |
| 5874 | bSig0 = extractFloat128Frac0( b ); |
| 5875 | bExp = extractFloat128Exp( b ); |
| 5876 | bSign = extractFloat128Sign( b ); |
| 5877 | zSign = aSign ^ bSign; |
| 5878 | if ( aExp == 0x7FFF ) { |
| 5879 | if ( ( aSig0 | aSig1 ) |
| 5880 | || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { |
| 5881 | return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5882 | } |
| 5883 | if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid; |
| 5884 | return packFloat128( zSign, 0x7FFF, 0, 0 ); |
| 5885 | } |
| 5886 | if ( bExp == 0x7FFF ) { |
| 5887 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5888 | if ( ( aExp | aSig0 | aSig1 ) == 0 ) { |
| 5889 | invalid: |
| 5890 | float_raise( float_flag_invalid STATUS_VAR); |
| 5891 | z.low = float128_default_nan_low; |
| 5892 | z.high = float128_default_nan_high; |
| 5893 | return z; |
| 5894 | } |
| 5895 | return packFloat128( zSign, 0x7FFF, 0, 0 ); |
| 5896 | } |
| 5897 | if ( aExp == 0 ) { |
| 5898 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); |
| 5899 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
| 5900 | } |
| 5901 | if ( bExp == 0 ) { |
| 5902 | if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); |
| 5903 | normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); |
| 5904 | } |
| 5905 | zExp = aExp + bExp - 0x4000; |
| 5906 | aSig0 |= LIT64( 0x0001000000000000 ); |
| 5907 | shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 ); |
| 5908 | mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 ); |
| 5909 | add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 ); |
| 5910 | zSig2 |= ( zSig3 != 0 ); |
| 5911 | if ( LIT64( 0x0002000000000000 ) <= zSig0 ) { |
| 5912 | shift128ExtraRightJamming( |
| 5913 | zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); |
| 5914 | ++zExp; |
| 5915 | } |
| 5916 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); |
| 5917 | |
| 5918 | } |
| 5919 | |
| 5920 | /*---------------------------------------------------------------------------- |
| 5921 | | Returns the result of dividing the quadruple-precision floating-point value |
| 5922 | | `a' by the corresponding value `b'. The operation is performed according to |
| 5923 | | the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 5924 | *----------------------------------------------------------------------------*/ |
| 5925 | |
| 5926 | float128 float128_div( float128 a, float128 b STATUS_PARAM ) |
| 5927 | { |
| 5928 | flag aSign, bSign, zSign; |
| 5929 | int32 aExp, bExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5930 | uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; |
| 5931 | uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5932 | float128 z; |
| 5933 | |
| 5934 | aSig1 = extractFloat128Frac1( a ); |
| 5935 | aSig0 = extractFloat128Frac0( a ); |
| 5936 | aExp = extractFloat128Exp( a ); |
| 5937 | aSign = extractFloat128Sign( a ); |
| 5938 | bSig1 = extractFloat128Frac1( b ); |
| 5939 | bSig0 = extractFloat128Frac0( b ); |
| 5940 | bExp = extractFloat128Exp( b ); |
| 5941 | bSign = extractFloat128Sign( b ); |
| 5942 | zSign = aSign ^ bSign; |
| 5943 | if ( aExp == 0x7FFF ) { |
| 5944 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5945 | if ( bExp == 0x7FFF ) { |
| 5946 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5947 | goto invalid; |
| 5948 | } |
| 5949 | return packFloat128( zSign, 0x7FFF, 0, 0 ); |
| 5950 | } |
| 5951 | if ( bExp == 0x7FFF ) { |
| 5952 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
| 5953 | return packFloat128( zSign, 0, 0, 0 ); |
| 5954 | } |
| 5955 | if ( bExp == 0 ) { |
| 5956 | if ( ( bSig0 | bSig1 ) == 0 ) { |
| 5957 | if ( ( aExp | aSig0 | aSig1 ) == 0 ) { |
| 5958 | invalid: |
| 5959 | float_raise( float_flag_invalid STATUS_VAR); |
| 5960 | z.low = float128_default_nan_low; |
| 5961 | z.high = float128_default_nan_high; |
| 5962 | return z; |
| 5963 | } |
| 5964 | float_raise( float_flag_divbyzero STATUS_VAR); |
| 5965 | return packFloat128( zSign, 0x7FFF, 0, 0 ); |
| 5966 | } |
| 5967 | normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); |
| 5968 | } |
| 5969 | if ( aExp == 0 ) { |
| 5970 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); |
| 5971 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
| 5972 | } |
| 5973 | zExp = aExp - bExp + 0x3FFD; |
| 5974 | shortShift128Left( |
| 5975 | aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 ); |
| 5976 | shortShift128Left( |
| 5977 | bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); |
| 5978 | if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) { |
| 5979 | shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 ); |
| 5980 | ++zExp; |
| 5981 | } |
| 5982 | zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 ); |
| 5983 | mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 ); |
| 5984 | sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5985 | while ( (int64_t) rem0 < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5986 | --zSig0; |
| 5987 | add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 ); |
| 5988 | } |
| 5989 | zSig1 = estimateDiv128To64( rem1, rem2, bSig0 ); |
| 5990 | if ( ( zSig1 & 0x3FFF ) <= 4 ) { |
| 5991 | mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 ); |
| 5992 | sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 5993 | while ( (int64_t) rem1 < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 5994 | --zSig1; |
| 5995 | add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 ); |
| 5996 | } |
| 5997 | zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); |
| 5998 | } |
| 5999 | shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 ); |
| 6000 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); |
| 6001 | |
| 6002 | } |
| 6003 | |
| 6004 | /*---------------------------------------------------------------------------- |
| 6005 | | Returns the remainder of the quadruple-precision floating-point value `a' |
| 6006 | | with respect to the corresponding value `b'. The operation is performed |
| 6007 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 6008 | *----------------------------------------------------------------------------*/ |
| 6009 | |
| 6010 | float128 float128_rem( float128 a, float128 b STATUS_PARAM ) |
| 6011 | { |
David Turner | 2738c26 | 2010-09-09 17:41:26 +0200 | [diff] [blame] | 6012 | flag aSign, zSign; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6013 | int32 aExp, bExp, expDiff; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6014 | uint64_t aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2; |
| 6015 | uint64_t allZero, alternateASig0, alternateASig1, sigMean1; |
| 6016 | int64_t sigMean0; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6017 | float128 z; |
| 6018 | |
| 6019 | aSig1 = extractFloat128Frac1( a ); |
| 6020 | aSig0 = extractFloat128Frac0( a ); |
| 6021 | aExp = extractFloat128Exp( a ); |
| 6022 | aSign = extractFloat128Sign( a ); |
| 6023 | bSig1 = extractFloat128Frac1( b ); |
| 6024 | bSig0 = extractFloat128Frac0( b ); |
| 6025 | bExp = extractFloat128Exp( b ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6026 | if ( aExp == 0x7FFF ) { |
| 6027 | if ( ( aSig0 | aSig1 ) |
| 6028 | || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { |
| 6029 | return propagateFloat128NaN( a, b STATUS_VAR ); |
| 6030 | } |
| 6031 | goto invalid; |
| 6032 | } |
| 6033 | if ( bExp == 0x7FFF ) { |
| 6034 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
| 6035 | return a; |
| 6036 | } |
| 6037 | if ( bExp == 0 ) { |
| 6038 | if ( ( bSig0 | bSig1 ) == 0 ) { |
| 6039 | invalid: |
| 6040 | float_raise( float_flag_invalid STATUS_VAR); |
| 6041 | z.low = float128_default_nan_low; |
| 6042 | z.high = float128_default_nan_high; |
| 6043 | return z; |
| 6044 | } |
| 6045 | normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); |
| 6046 | } |
| 6047 | if ( aExp == 0 ) { |
| 6048 | if ( ( aSig0 | aSig1 ) == 0 ) return a; |
| 6049 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
| 6050 | } |
| 6051 | expDiff = aExp - bExp; |
| 6052 | if ( expDiff < -1 ) return a; |
| 6053 | shortShift128Left( |
| 6054 | aSig0 | LIT64( 0x0001000000000000 ), |
| 6055 | aSig1, |
| 6056 | 15 - ( expDiff < 0 ), |
| 6057 | &aSig0, |
| 6058 | &aSig1 |
| 6059 | ); |
| 6060 | shortShift128Left( |
| 6061 | bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); |
| 6062 | q = le128( bSig0, bSig1, aSig0, aSig1 ); |
| 6063 | if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); |
| 6064 | expDiff -= 64; |
| 6065 | while ( 0 < expDiff ) { |
| 6066 | q = estimateDiv128To64( aSig0, aSig1, bSig0 ); |
| 6067 | q = ( 4 < q ) ? q - 4 : 0; |
| 6068 | mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); |
| 6069 | shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero ); |
| 6070 | shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero ); |
| 6071 | sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 ); |
| 6072 | expDiff -= 61; |
| 6073 | } |
| 6074 | if ( -64 < expDiff ) { |
| 6075 | q = estimateDiv128To64( aSig0, aSig1, bSig0 ); |
| 6076 | q = ( 4 < q ) ? q - 4 : 0; |
| 6077 | q >>= - expDiff; |
| 6078 | shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); |
| 6079 | expDiff += 52; |
| 6080 | if ( expDiff < 0 ) { |
| 6081 | shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); |
| 6082 | } |
| 6083 | else { |
| 6084 | shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 ); |
| 6085 | } |
| 6086 | mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); |
| 6087 | sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 ); |
| 6088 | } |
| 6089 | else { |
| 6090 | shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 ); |
| 6091 | shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); |
| 6092 | } |
| 6093 | do { |
| 6094 | alternateASig0 = aSig0; |
| 6095 | alternateASig1 = aSig1; |
| 6096 | ++q; |
| 6097 | sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6098 | } while ( 0 <= (int64_t) aSig0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6099 | add128( |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6100 | aSig0, aSig1, alternateASig0, alternateASig1, (uint64_t *)&sigMean0, &sigMean1 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6101 | if ( ( sigMean0 < 0 ) |
| 6102 | || ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) { |
| 6103 | aSig0 = alternateASig0; |
| 6104 | aSig1 = alternateASig1; |
| 6105 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6106 | zSign = ( (int64_t) aSig0 < 0 ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6107 | if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 ); |
| 6108 | return |
| 6109 | normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 STATUS_VAR ); |
| 6110 | |
| 6111 | } |
| 6112 | |
| 6113 | /*---------------------------------------------------------------------------- |
| 6114 | | Returns the square root of the quadruple-precision floating-point value `a'. |
| 6115 | | The operation is performed according to the IEC/IEEE Standard for Binary |
| 6116 | | Floating-Point Arithmetic. |
| 6117 | *----------------------------------------------------------------------------*/ |
| 6118 | |
| 6119 | float128 float128_sqrt( float128 a STATUS_PARAM ) |
| 6120 | { |
| 6121 | flag aSign; |
| 6122 | int32 aExp, zExp; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6123 | uint64_t aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0; |
| 6124 | uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6125 | float128 z; |
| 6126 | |
| 6127 | aSig1 = extractFloat128Frac1( a ); |
| 6128 | aSig0 = extractFloat128Frac0( a ); |
| 6129 | aExp = extractFloat128Exp( a ); |
| 6130 | aSign = extractFloat128Sign( a ); |
| 6131 | if ( aExp == 0x7FFF ) { |
| 6132 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a STATUS_VAR ); |
| 6133 | if ( ! aSign ) return a; |
| 6134 | goto invalid; |
| 6135 | } |
| 6136 | if ( aSign ) { |
| 6137 | if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a; |
| 6138 | invalid: |
| 6139 | float_raise( float_flag_invalid STATUS_VAR); |
| 6140 | z.low = float128_default_nan_low; |
| 6141 | z.high = float128_default_nan_high; |
| 6142 | return z; |
| 6143 | } |
| 6144 | if ( aExp == 0 ) { |
| 6145 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 ); |
| 6146 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
| 6147 | } |
| 6148 | zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE; |
| 6149 | aSig0 |= LIT64( 0x0001000000000000 ); |
| 6150 | zSig0 = estimateSqrt32( aExp, aSig0>>17 ); |
| 6151 | shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 ); |
| 6152 | zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); |
| 6153 | doubleZSig0 = zSig0<<1; |
| 6154 | mul64To128( zSig0, zSig0, &term0, &term1 ); |
| 6155 | sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6156 | while ( (int64_t) rem0 < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6157 | --zSig0; |
| 6158 | doubleZSig0 -= 2; |
| 6159 | add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); |
| 6160 | } |
| 6161 | zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); |
| 6162 | if ( ( zSig1 & 0x1FFF ) <= 5 ) { |
| 6163 | if ( zSig1 == 0 ) zSig1 = 1; |
| 6164 | mul64To128( doubleZSig0, zSig1, &term1, &term2 ); |
| 6165 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); |
| 6166 | mul64To128( zSig1, zSig1, &term2, &term3 ); |
| 6167 | sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6168 | while ( (int64_t) rem1 < 0 ) { |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6169 | --zSig1; |
| 6170 | shortShift128Left( 0, zSig1, 1, &term2, &term3 ); |
| 6171 | term3 |= 1; |
| 6172 | term2 |= doubleZSig0; |
| 6173 | add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); |
| 6174 | } |
| 6175 | zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); |
| 6176 | } |
| 6177 | shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 ); |
| 6178 | return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); |
| 6179 | |
| 6180 | } |
| 6181 | |
| 6182 | /*---------------------------------------------------------------------------- |
| 6183 | | Returns 1 if the quadruple-precision floating-point value `a' is equal to |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6184 | | the corresponding value `b', and 0 otherwise. The invalid exception is |
| 6185 | | raised if either operand is a NaN. Otherwise, the comparison is performed |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6186 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 6187 | *----------------------------------------------------------------------------*/ |
| 6188 | |
| 6189 | int float128_eq( float128 a, float128 b STATUS_PARAM ) |
| 6190 | { |
| 6191 | |
| 6192 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
| 6193 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
| 6194 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) |
| 6195 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
| 6196 | ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6197 | float_raise( float_flag_invalid STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6198 | return 0; |
| 6199 | } |
| 6200 | return |
| 6201 | ( a.low == b.low ) |
| 6202 | && ( ( a.high == b.high ) |
| 6203 | || ( ( a.low == 0 ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6204 | && ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6205 | ); |
| 6206 | |
| 6207 | } |
| 6208 | |
| 6209 | /*---------------------------------------------------------------------------- |
| 6210 | | Returns 1 if the quadruple-precision floating-point value `a' is less than |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6211 | | or equal to the corresponding value `b', and 0 otherwise. The invalid |
| 6212 | | exception is raised if either operand is a NaN. The comparison is performed |
| 6213 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6214 | *----------------------------------------------------------------------------*/ |
| 6215 | |
| 6216 | int float128_le( float128 a, float128 b STATUS_PARAM ) |
| 6217 | { |
| 6218 | flag aSign, bSign; |
| 6219 | |
| 6220 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
| 6221 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
| 6222 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) |
| 6223 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
| 6224 | ) { |
| 6225 | float_raise( float_flag_invalid STATUS_VAR); |
| 6226 | return 0; |
| 6227 | } |
| 6228 | aSign = extractFloat128Sign( a ); |
| 6229 | bSign = extractFloat128Sign( b ); |
| 6230 | if ( aSign != bSign ) { |
| 6231 | return |
| 6232 | aSign |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6233 | || ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6234 | == 0 ); |
| 6235 | } |
| 6236 | return |
| 6237 | aSign ? le128( b.high, b.low, a.high, a.low ) |
| 6238 | : le128( a.high, a.low, b.high, b.low ); |
| 6239 | |
| 6240 | } |
| 6241 | |
| 6242 | /*---------------------------------------------------------------------------- |
| 6243 | | Returns 1 if the quadruple-precision floating-point value `a' is less than |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6244 | | the corresponding value `b', and 0 otherwise. The invalid exception is |
| 6245 | | raised if either operand is a NaN. The comparison is performed according |
| 6246 | | to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6247 | *----------------------------------------------------------------------------*/ |
| 6248 | |
| 6249 | int float128_lt( float128 a, float128 b STATUS_PARAM ) |
| 6250 | { |
| 6251 | flag aSign, bSign; |
| 6252 | |
| 6253 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
| 6254 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
| 6255 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) |
| 6256 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
| 6257 | ) { |
| 6258 | float_raise( float_flag_invalid STATUS_VAR); |
| 6259 | return 0; |
| 6260 | } |
| 6261 | aSign = extractFloat128Sign( a ); |
| 6262 | bSign = extractFloat128Sign( b ); |
| 6263 | if ( aSign != bSign ) { |
| 6264 | return |
| 6265 | aSign |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6266 | && ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6267 | != 0 ); |
| 6268 | } |
| 6269 | return |
| 6270 | aSign ? lt128( b.high, b.low, a.high, a.low ) |
| 6271 | : lt128( a.high, a.low, b.high, b.low ); |
| 6272 | |
| 6273 | } |
| 6274 | |
| 6275 | /*---------------------------------------------------------------------------- |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6276 | | Returns 1 if the quadruple-precision floating-point values `a' and `b' cannot |
| 6277 | | be compared, and 0 otherwise. The invalid exception is raised if either |
| 6278 | | operand is a NaN. The comparison is performed according to the IEC/IEEE |
| 6279 | | Standard for Binary Floating-Point Arithmetic. |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6280 | *----------------------------------------------------------------------------*/ |
| 6281 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6282 | int float128_unordered( float128 a, float128 b STATUS_PARAM ) |
| 6283 | { |
| 6284 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
| 6285 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
| 6286 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) |
| 6287 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
| 6288 | ) { |
| 6289 | float_raise( float_flag_invalid STATUS_VAR); |
| 6290 | return 1; |
| 6291 | } |
| 6292 | return 0; |
| 6293 | } |
| 6294 | |
| 6295 | /*---------------------------------------------------------------------------- |
| 6296 | | Returns 1 if the quadruple-precision floating-point value `a' is equal to |
| 6297 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an |
| 6298 | | exception. The comparison is performed according to the IEC/IEEE Standard |
| 6299 | | for Binary Floating-Point Arithmetic. |
| 6300 | *----------------------------------------------------------------------------*/ |
| 6301 | |
| 6302 | int float128_eq_quiet( float128 a, float128 b STATUS_PARAM ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6303 | { |
| 6304 | |
| 6305 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
| 6306 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
| 6307 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) |
| 6308 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
| 6309 | ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6310 | if ( float128_is_signaling_nan( a ) |
| 6311 | || float128_is_signaling_nan( b ) ) { |
| 6312 | float_raise( float_flag_invalid STATUS_VAR); |
| 6313 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6314 | return 0; |
| 6315 | } |
| 6316 | return |
| 6317 | ( a.low == b.low ) |
| 6318 | && ( ( a.high == b.high ) |
| 6319 | || ( ( a.low == 0 ) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6320 | && ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6321 | ); |
| 6322 | |
| 6323 | } |
| 6324 | |
| 6325 | /*---------------------------------------------------------------------------- |
| 6326 | | Returns 1 if the quadruple-precision floating-point value `a' is less than |
| 6327 | | or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not |
| 6328 | | cause an exception. Otherwise, the comparison is performed according to the |
| 6329 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. |
| 6330 | *----------------------------------------------------------------------------*/ |
| 6331 | |
| 6332 | int float128_le_quiet( float128 a, float128 b STATUS_PARAM ) |
| 6333 | { |
| 6334 | flag aSign, bSign; |
| 6335 | |
| 6336 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
| 6337 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
| 6338 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) |
| 6339 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
| 6340 | ) { |
| 6341 | if ( float128_is_signaling_nan( a ) |
| 6342 | || float128_is_signaling_nan( b ) ) { |
| 6343 | float_raise( float_flag_invalid STATUS_VAR); |
| 6344 | } |
| 6345 | return 0; |
| 6346 | } |
| 6347 | aSign = extractFloat128Sign( a ); |
| 6348 | bSign = extractFloat128Sign( b ); |
| 6349 | if ( aSign != bSign ) { |
| 6350 | return |
| 6351 | aSign |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6352 | || ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6353 | == 0 ); |
| 6354 | } |
| 6355 | return |
| 6356 | aSign ? le128( b.high, b.low, a.high, a.low ) |
| 6357 | : le128( a.high, a.low, b.high, b.low ); |
| 6358 | |
| 6359 | } |
| 6360 | |
| 6361 | /*---------------------------------------------------------------------------- |
| 6362 | | Returns 1 if the quadruple-precision floating-point value `a' is less than |
| 6363 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an |
| 6364 | | exception. Otherwise, the comparison is performed according to the IEC/IEEE |
| 6365 | | Standard for Binary Floating-Point Arithmetic. |
| 6366 | *----------------------------------------------------------------------------*/ |
| 6367 | |
| 6368 | int float128_lt_quiet( float128 a, float128 b STATUS_PARAM ) |
| 6369 | { |
| 6370 | flag aSign, bSign; |
| 6371 | |
| 6372 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
| 6373 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
| 6374 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) |
| 6375 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
| 6376 | ) { |
| 6377 | if ( float128_is_signaling_nan( a ) |
| 6378 | || float128_is_signaling_nan( b ) ) { |
| 6379 | float_raise( float_flag_invalid STATUS_VAR); |
| 6380 | } |
| 6381 | return 0; |
| 6382 | } |
| 6383 | aSign = extractFloat128Sign( a ); |
| 6384 | bSign = extractFloat128Sign( b ); |
| 6385 | if ( aSign != bSign ) { |
| 6386 | return |
| 6387 | aSign |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6388 | && ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6389 | != 0 ); |
| 6390 | } |
| 6391 | return |
| 6392 | aSign ? lt128( b.high, b.low, a.high, a.low ) |
| 6393 | : lt128( a.high, a.low, b.high, b.low ); |
| 6394 | |
| 6395 | } |
| 6396 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6397 | /*---------------------------------------------------------------------------- |
| 6398 | | Returns 1 if the quadruple-precision floating-point values `a' and `b' cannot |
| 6399 | | be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The |
| 6400 | | comparison is performed according to the IEC/IEEE Standard for Binary |
| 6401 | | Floating-Point Arithmetic. |
| 6402 | *----------------------------------------------------------------------------*/ |
| 6403 | |
| 6404 | int float128_unordered_quiet( float128 a, float128 b STATUS_PARAM ) |
| 6405 | { |
| 6406 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
| 6407 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
| 6408 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) |
| 6409 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
| 6410 | ) { |
| 6411 | if ( float128_is_signaling_nan( a ) |
| 6412 | || float128_is_signaling_nan( b ) ) { |
| 6413 | float_raise( float_flag_invalid STATUS_VAR); |
| 6414 | } |
| 6415 | return 1; |
| 6416 | } |
| 6417 | return 0; |
| 6418 | } |
| 6419 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6420 | /* misc functions */ |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6421 | float32 uint32_to_float32( uint32 a STATUS_PARAM ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6422 | { |
| 6423 | return int64_to_float32(a STATUS_VAR); |
| 6424 | } |
| 6425 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6426 | float64 uint32_to_float64( uint32 a STATUS_PARAM ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6427 | { |
| 6428 | return int64_to_float64(a STATUS_VAR); |
| 6429 | } |
| 6430 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6431 | uint32 float32_to_uint32( float32 a STATUS_PARAM ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6432 | { |
| 6433 | int64_t v; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6434 | uint32 res; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6435 | |
| 6436 | v = float32_to_int64(a STATUS_VAR); |
| 6437 | if (v < 0) { |
| 6438 | res = 0; |
| 6439 | float_raise( float_flag_invalid STATUS_VAR); |
| 6440 | } else if (v > 0xffffffff) { |
| 6441 | res = 0xffffffff; |
| 6442 | float_raise( float_flag_invalid STATUS_VAR); |
| 6443 | } else { |
| 6444 | res = v; |
| 6445 | } |
| 6446 | return res; |
| 6447 | } |
| 6448 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6449 | uint32 float32_to_uint32_round_to_zero( float32 a STATUS_PARAM ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6450 | { |
| 6451 | int64_t v; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6452 | uint32 res; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6453 | |
| 6454 | v = float32_to_int64_round_to_zero(a STATUS_VAR); |
| 6455 | if (v < 0) { |
| 6456 | res = 0; |
| 6457 | float_raise( float_flag_invalid STATUS_VAR); |
| 6458 | } else if (v > 0xffffffff) { |
| 6459 | res = 0xffffffff; |
| 6460 | float_raise( float_flag_invalid STATUS_VAR); |
| 6461 | } else { |
| 6462 | res = v; |
| 6463 | } |
| 6464 | return res; |
| 6465 | } |
| 6466 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6467 | uint_fast16_t float32_to_uint16_round_to_zero(float32 a STATUS_PARAM) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6468 | { |
| 6469 | int64_t v; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6470 | uint_fast16_t res; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6471 | |
| 6472 | v = float32_to_int64_round_to_zero(a STATUS_VAR); |
| 6473 | if (v < 0) { |
| 6474 | res = 0; |
| 6475 | float_raise( float_flag_invalid STATUS_VAR); |
| 6476 | } else if (v > 0xffff) { |
| 6477 | res = 0xffff; |
| 6478 | float_raise( float_flag_invalid STATUS_VAR); |
| 6479 | } else { |
| 6480 | res = v; |
| 6481 | } |
| 6482 | return res; |
| 6483 | } |
| 6484 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6485 | uint32 float64_to_uint32( float64 a STATUS_PARAM ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6486 | { |
| 6487 | int64_t v; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6488 | uint32 res; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6489 | |
| 6490 | v = float64_to_int64(a STATUS_VAR); |
| 6491 | if (v < 0) { |
| 6492 | res = 0; |
| 6493 | float_raise( float_flag_invalid STATUS_VAR); |
| 6494 | } else if (v > 0xffffffff) { |
| 6495 | res = 0xffffffff; |
| 6496 | float_raise( float_flag_invalid STATUS_VAR); |
| 6497 | } else { |
| 6498 | res = v; |
| 6499 | } |
| 6500 | return res; |
| 6501 | } |
| 6502 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6503 | uint32 float64_to_uint32_round_to_zero( float64 a STATUS_PARAM ) |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6504 | { |
| 6505 | int64_t v; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6506 | uint32 res; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6507 | |
| 6508 | v = float64_to_int64_round_to_zero(a STATUS_VAR); |
| 6509 | if (v < 0) { |
| 6510 | res = 0; |
| 6511 | float_raise( float_flag_invalid STATUS_VAR); |
| 6512 | } else if (v > 0xffffffff) { |
| 6513 | res = 0xffffffff; |
| 6514 | float_raise( float_flag_invalid STATUS_VAR); |
| 6515 | } else { |
| 6516 | res = v; |
| 6517 | } |
| 6518 | return res; |
| 6519 | } |
| 6520 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6521 | uint_fast16_t float64_to_uint16_round_to_zero(float64 a STATUS_PARAM) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6522 | { |
| 6523 | int64_t v; |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6524 | uint_fast16_t res; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6525 | |
| 6526 | v = float64_to_int64_round_to_zero(a STATUS_VAR); |
| 6527 | if (v < 0) { |
| 6528 | res = 0; |
| 6529 | float_raise( float_flag_invalid STATUS_VAR); |
| 6530 | } else if (v > 0xffff) { |
| 6531 | res = 0xffff; |
| 6532 | float_raise( float_flag_invalid STATUS_VAR); |
| 6533 | } else { |
| 6534 | res = v; |
| 6535 | } |
| 6536 | return res; |
| 6537 | } |
| 6538 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6539 | /* FIXME: This looks broken. */ |
| 6540 | uint64_t float64_to_uint64 (float64 a STATUS_PARAM) |
| 6541 | { |
| 6542 | int64_t v; |
| 6543 | |
| 6544 | v = float64_val(int64_to_float64(INT64_MIN STATUS_VAR)); |
| 6545 | v += float64_val(a); |
| 6546 | v = float64_to_int64(make_float64(v) STATUS_VAR); |
| 6547 | |
| 6548 | return v - INT64_MIN; |
| 6549 | } |
| 6550 | |
| 6551 | uint64_t float64_to_uint64_round_to_zero (float64 a STATUS_PARAM) |
| 6552 | { |
| 6553 | int64_t v; |
| 6554 | |
| 6555 | v = float64_val(int64_to_float64(INT64_MIN STATUS_VAR)); |
| 6556 | v += float64_val(a); |
| 6557 | v = float64_to_int64_round_to_zero(make_float64(v) STATUS_VAR); |
| 6558 | |
| 6559 | return v - INT64_MIN; |
| 6560 | } |
| 6561 | |
| 6562 | #define COMPARE(s, nan_exp) \ |
| 6563 | INLINE int float ## s ## _compare_internal( float ## s a, float ## s b, \ |
| 6564 | int is_quiet STATUS_PARAM ) \ |
| 6565 | { \ |
| 6566 | flag aSign, bSign; \ |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6567 | uint ## s ## _t av, bv; \ |
| 6568 | a = float ## s ## _squash_input_denormal(a STATUS_VAR); \ |
| 6569 | b = float ## s ## _squash_input_denormal(b STATUS_VAR); \ |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6570 | \ |
| 6571 | if (( ( extractFloat ## s ## Exp( a ) == nan_exp ) && \ |
| 6572 | extractFloat ## s ## Frac( a ) ) || \ |
| 6573 | ( ( extractFloat ## s ## Exp( b ) == nan_exp ) && \ |
| 6574 | extractFloat ## s ## Frac( b ) )) { \ |
| 6575 | if (!is_quiet || \ |
| 6576 | float ## s ## _is_signaling_nan( a ) || \ |
| 6577 | float ## s ## _is_signaling_nan( b ) ) { \ |
| 6578 | float_raise( float_flag_invalid STATUS_VAR); \ |
| 6579 | } \ |
| 6580 | return float_relation_unordered; \ |
| 6581 | } \ |
| 6582 | aSign = extractFloat ## s ## Sign( a ); \ |
| 6583 | bSign = extractFloat ## s ## Sign( b ); \ |
| 6584 | av = float ## s ## _val(a); \ |
| 6585 | bv = float ## s ## _val(b); \ |
| 6586 | if ( aSign != bSign ) { \ |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6587 | if ( (uint ## s ## _t) ( ( av | bv )<<1 ) == 0 ) { \ |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6588 | /* zero case */ \ |
| 6589 | return float_relation_equal; \ |
| 6590 | } else { \ |
| 6591 | return 1 - (2 * aSign); \ |
| 6592 | } \ |
| 6593 | } else { \ |
| 6594 | if (av == bv) { \ |
| 6595 | return float_relation_equal; \ |
| 6596 | } else { \ |
| 6597 | return 1 - 2 * (aSign ^ ( av < bv )); \ |
| 6598 | } \ |
| 6599 | } \ |
| 6600 | } \ |
| 6601 | \ |
| 6602 | int float ## s ## _compare( float ## s a, float ## s b STATUS_PARAM ) \ |
| 6603 | { \ |
| 6604 | return float ## s ## _compare_internal(a, b, 0 STATUS_VAR); \ |
| 6605 | } \ |
| 6606 | \ |
| 6607 | int float ## s ## _compare_quiet( float ## s a, float ## s b STATUS_PARAM ) \ |
| 6608 | { \ |
| 6609 | return float ## s ## _compare_internal(a, b, 1 STATUS_VAR); \ |
| 6610 | } |
| 6611 | |
| 6612 | COMPARE(32, 0xff) |
| 6613 | COMPARE(64, 0x7ff) |
| 6614 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6615 | INLINE int floatx80_compare_internal( floatx80 a, floatx80 b, |
| 6616 | int is_quiet STATUS_PARAM ) |
| 6617 | { |
| 6618 | flag aSign, bSign; |
| 6619 | |
| 6620 | if (( ( extractFloatx80Exp( a ) == 0x7fff ) && |
| 6621 | ( extractFloatx80Frac( a )<<1 ) ) || |
| 6622 | ( ( extractFloatx80Exp( b ) == 0x7fff ) && |
| 6623 | ( extractFloatx80Frac( b )<<1 ) )) { |
| 6624 | if (!is_quiet || |
| 6625 | floatx80_is_signaling_nan( a ) || |
| 6626 | floatx80_is_signaling_nan( b ) ) { |
| 6627 | float_raise( float_flag_invalid STATUS_VAR); |
| 6628 | } |
| 6629 | return float_relation_unordered; |
| 6630 | } |
| 6631 | aSign = extractFloatx80Sign( a ); |
| 6632 | bSign = extractFloatx80Sign( b ); |
| 6633 | if ( aSign != bSign ) { |
| 6634 | |
| 6635 | if ( ( ( (uint16_t) ( ( a.high | b.high ) << 1 ) ) == 0) && |
| 6636 | ( ( a.low | b.low ) == 0 ) ) { |
| 6637 | /* zero case */ |
| 6638 | return float_relation_equal; |
| 6639 | } else { |
| 6640 | return 1 - (2 * aSign); |
| 6641 | } |
| 6642 | } else { |
| 6643 | if (a.low == b.low && a.high == b.high) { |
| 6644 | return float_relation_equal; |
| 6645 | } else { |
| 6646 | return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) )); |
| 6647 | } |
| 6648 | } |
| 6649 | } |
| 6650 | |
| 6651 | int floatx80_compare( floatx80 a, floatx80 b STATUS_PARAM ) |
| 6652 | { |
| 6653 | return floatx80_compare_internal(a, b, 0 STATUS_VAR); |
| 6654 | } |
| 6655 | |
| 6656 | int floatx80_compare_quiet( floatx80 a, floatx80 b STATUS_PARAM ) |
| 6657 | { |
| 6658 | return floatx80_compare_internal(a, b, 1 STATUS_VAR); |
| 6659 | } |
| 6660 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6661 | INLINE int float128_compare_internal( float128 a, float128 b, |
| 6662 | int is_quiet STATUS_PARAM ) |
| 6663 | { |
| 6664 | flag aSign, bSign; |
| 6665 | |
| 6666 | if (( ( extractFloat128Exp( a ) == 0x7fff ) && |
| 6667 | ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) || |
| 6668 | ( ( extractFloat128Exp( b ) == 0x7fff ) && |
| 6669 | ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )) { |
| 6670 | if (!is_quiet || |
| 6671 | float128_is_signaling_nan( a ) || |
| 6672 | float128_is_signaling_nan( b ) ) { |
| 6673 | float_raise( float_flag_invalid STATUS_VAR); |
| 6674 | } |
| 6675 | return float_relation_unordered; |
| 6676 | } |
| 6677 | aSign = extractFloat128Sign( a ); |
| 6678 | bSign = extractFloat128Sign( b ); |
| 6679 | if ( aSign != bSign ) { |
| 6680 | if ( ( ( ( a.high | b.high )<<1 ) | a.low | b.low ) == 0 ) { |
| 6681 | /* zero case */ |
| 6682 | return float_relation_equal; |
| 6683 | } else { |
| 6684 | return 1 - (2 * aSign); |
| 6685 | } |
| 6686 | } else { |
| 6687 | if (a.low == b.low && a.high == b.high) { |
| 6688 | return float_relation_equal; |
| 6689 | } else { |
| 6690 | return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) )); |
| 6691 | } |
| 6692 | } |
| 6693 | } |
| 6694 | |
| 6695 | int float128_compare( float128 a, float128 b STATUS_PARAM ) |
| 6696 | { |
| 6697 | return float128_compare_internal(a, b, 0 STATUS_VAR); |
| 6698 | } |
| 6699 | |
| 6700 | int float128_compare_quiet( float128 a, float128 b STATUS_PARAM ) |
| 6701 | { |
| 6702 | return float128_compare_internal(a, b, 1 STATUS_VAR); |
| 6703 | } |
| 6704 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6705 | /* min() and max() functions. These can't be implemented as |
| 6706 | * 'compare and pick one input' because that would mishandle |
| 6707 | * NaNs and +0 vs -0. |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6708 | * |
| 6709 | * minnum() and maxnum() functions. These are similar to the min() |
| 6710 | * and max() functions but if one of the arguments is a QNaN and |
| 6711 | * the other is numerical then the numerical argument is returned. |
| 6712 | * minnum() and maxnum correspond to the IEEE 754-2008 minNum() |
| 6713 | * and maxNum() operations. min() and max() are the typical min/max |
| 6714 | * semantics provided by many CPUs which predate that specification. |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6715 | */ |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6716 | #define MINMAX(s) \ |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6717 | INLINE float ## s float ## s ## _minmax(float ## s a, float ## s b, \ |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6718 | int ismin, int isieee STATUS_PARAM) \ |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6719 | { \ |
| 6720 | flag aSign, bSign; \ |
| 6721 | uint ## s ## _t av, bv; \ |
| 6722 | a = float ## s ## _squash_input_denormal(a STATUS_VAR); \ |
| 6723 | b = float ## s ## _squash_input_denormal(b STATUS_VAR); \ |
| 6724 | if (float ## s ## _is_any_nan(a) || \ |
| 6725 | float ## s ## _is_any_nan(b)) { \ |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6726 | if (isieee) { \ |
| 6727 | if (float ## s ## _is_quiet_nan(a) && \ |
| 6728 | !float ## s ##_is_any_nan(b)) { \ |
| 6729 | return b; \ |
| 6730 | } else if (float ## s ## _is_quiet_nan(b) && \ |
| 6731 | !float ## s ## _is_any_nan(a)) { \ |
| 6732 | return a; \ |
| 6733 | } \ |
| 6734 | } \ |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6735 | return propagateFloat ## s ## NaN(a, b STATUS_VAR); \ |
| 6736 | } \ |
| 6737 | aSign = extractFloat ## s ## Sign(a); \ |
| 6738 | bSign = extractFloat ## s ## Sign(b); \ |
| 6739 | av = float ## s ## _val(a); \ |
| 6740 | bv = float ## s ## _val(b); \ |
| 6741 | if (aSign != bSign) { \ |
| 6742 | if (ismin) { \ |
| 6743 | return aSign ? a : b; \ |
| 6744 | } else { \ |
| 6745 | return aSign ? b : a; \ |
| 6746 | } \ |
| 6747 | } else { \ |
| 6748 | if (ismin) { \ |
| 6749 | return (aSign ^ (av < bv)) ? a : b; \ |
| 6750 | } else { \ |
| 6751 | return (aSign ^ (av < bv)) ? b : a; \ |
| 6752 | } \ |
| 6753 | } \ |
| 6754 | } \ |
| 6755 | \ |
| 6756 | float ## s float ## s ## _min(float ## s a, float ## s b STATUS_PARAM) \ |
| 6757 | { \ |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6758 | return float ## s ## _minmax(a, b, 1, 0 STATUS_VAR); \ |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6759 | } \ |
| 6760 | \ |
| 6761 | float ## s float ## s ## _max(float ## s a, float ## s b STATUS_PARAM) \ |
| 6762 | { \ |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6763 | return float ## s ## _minmax(a, b, 0, 0 STATUS_VAR); \ |
| 6764 | } \ |
| 6765 | \ |
| 6766 | float ## s float ## s ## _minnum(float ## s a, float ## s b STATUS_PARAM) \ |
| 6767 | { \ |
| 6768 | return float ## s ## _minmax(a, b, 1, 1 STATUS_VAR); \ |
| 6769 | } \ |
| 6770 | \ |
| 6771 | float ## s float ## s ## _maxnum(float ## s a, float ## s b STATUS_PARAM) \ |
| 6772 | { \ |
| 6773 | return float ## s ## _minmax(a, b, 0, 1 STATUS_VAR); \ |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6774 | } |
| 6775 | |
David 'Digit' Turner | e228840 | 2014-01-09 18:35:14 +0100 | [diff] [blame] | 6776 | MINMAX(32) |
| 6777 | MINMAX(64) |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6778 | |
| 6779 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6780 | /* Multiply A by 2 raised to the power N. */ |
| 6781 | float32 float32_scalbn( float32 a, int n STATUS_PARAM ) |
| 6782 | { |
| 6783 | flag aSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6784 | int16_t aExp; |
| 6785 | uint32_t aSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6786 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6787 | a = float32_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6788 | aSig = extractFloat32Frac( a ); |
| 6789 | aExp = extractFloat32Exp( a ); |
| 6790 | aSign = extractFloat32Sign( a ); |
| 6791 | |
| 6792 | if ( aExp == 0xFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6793 | if ( aSig ) { |
| 6794 | return propagateFloat32NaN( a, a STATUS_VAR ); |
| 6795 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6796 | return a; |
| 6797 | } |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 6798 | if ( aExp != 0 ) |
| 6799 | aSig |= 0x00800000; |
| 6800 | else if ( aSig == 0 ) |
| 6801 | return a; |
| 6802 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6803 | if (n > 0x200) { |
| 6804 | n = 0x200; |
| 6805 | } else if (n < -0x200) { |
| 6806 | n = -0x200; |
| 6807 | } |
| 6808 | |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 6809 | aExp += n - 1; |
| 6810 | aSig <<= 7; |
| 6811 | return normalizeRoundAndPackFloat32( aSign, aExp, aSig STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6812 | } |
| 6813 | |
| 6814 | float64 float64_scalbn( float64 a, int n STATUS_PARAM ) |
| 6815 | { |
| 6816 | flag aSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6817 | int16_t aExp; |
| 6818 | uint64_t aSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6819 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6820 | a = float64_squash_input_denormal(a STATUS_VAR); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6821 | aSig = extractFloat64Frac( a ); |
| 6822 | aExp = extractFloat64Exp( a ); |
| 6823 | aSign = extractFloat64Sign( a ); |
| 6824 | |
| 6825 | if ( aExp == 0x7FF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6826 | if ( aSig ) { |
| 6827 | return propagateFloat64NaN( a, a STATUS_VAR ); |
| 6828 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6829 | return a; |
| 6830 | } |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 6831 | if ( aExp != 0 ) |
| 6832 | aSig |= LIT64( 0x0010000000000000 ); |
| 6833 | else if ( aSig == 0 ) |
| 6834 | return a; |
| 6835 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6836 | if (n > 0x1000) { |
| 6837 | n = 0x1000; |
| 6838 | } else if (n < -0x1000) { |
| 6839 | n = -0x1000; |
| 6840 | } |
| 6841 | |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 6842 | aExp += n - 1; |
| 6843 | aSig <<= 10; |
| 6844 | return normalizeRoundAndPackFloat64( aSign, aExp, aSig STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6845 | } |
| 6846 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6847 | floatx80 floatx80_scalbn( floatx80 a, int n STATUS_PARAM ) |
| 6848 | { |
| 6849 | flag aSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6850 | int32_t aExp; |
| 6851 | uint64_t aSig; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6852 | |
| 6853 | aSig = extractFloatx80Frac( a ); |
| 6854 | aExp = extractFloatx80Exp( a ); |
| 6855 | aSign = extractFloatx80Sign( a ); |
| 6856 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6857 | if ( aExp == 0x7FFF ) { |
| 6858 | if ( aSig<<1 ) { |
| 6859 | return propagateFloatx80NaN( a, a STATUS_VAR ); |
| 6860 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6861 | return a; |
| 6862 | } |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6863 | |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 6864 | if (aExp == 0 && aSig == 0) |
| 6865 | return a; |
| 6866 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6867 | if (n > 0x10000) { |
| 6868 | n = 0x10000; |
| 6869 | } else if (n < -0x10000) { |
| 6870 | n = -0x10000; |
| 6871 | } |
| 6872 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6873 | aExp += n; |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 6874 | return normalizeRoundAndPackFloatx80( STATUS(floatx80_rounding_precision), |
| 6875 | aSign, aExp, aSig, 0 STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6876 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6877 | |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6878 | float128 float128_scalbn( float128 a, int n STATUS_PARAM ) |
| 6879 | { |
| 6880 | flag aSign; |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6881 | int32_t aExp; |
| 6882 | uint64_t aSig0, aSig1; |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6883 | |
| 6884 | aSig1 = extractFloat128Frac1( a ); |
| 6885 | aSig0 = extractFloat128Frac0( a ); |
| 6886 | aExp = extractFloat128Exp( a ); |
| 6887 | aSign = extractFloat128Sign( a ); |
| 6888 | if ( aExp == 0x7FFF ) { |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6889 | if ( aSig0 | aSig1 ) { |
| 6890 | return propagateFloat128NaN( a, a STATUS_VAR ); |
| 6891 | } |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6892 | return a; |
| 6893 | } |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 6894 | if ( aExp != 0 ) |
| 6895 | aSig0 |= LIT64( 0x0001000000000000 ); |
| 6896 | else if ( aSig0 == 0 && aSig1 == 0 ) |
| 6897 | return a; |
| 6898 | |
David 'Digit' Turner | bfec547 | 2011-05-10 12:59:13 +0200 | [diff] [blame] | 6899 | if (n > 0x10000) { |
| 6900 | n = 0x10000; |
| 6901 | } else if (n < -0x10000) { |
| 6902 | n = -0x10000; |
| 6903 | } |
| 6904 | |
David 'Digit' Turner | 5d8f37a | 2009-09-14 14:32:27 -0700 | [diff] [blame] | 6905 | aExp += n - 1; |
| 6906 | return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1 |
| 6907 | STATUS_VAR ); |
The Android Open Source Project | 8b23a6c | 2009-03-03 19:30:32 -0800 | [diff] [blame] | 6908 | |
| 6909 | } |