sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 1 | |
sewardj | 07e0962 | 2004-09-06 20:39:20 +0000 | [diff] [blame] | 2 | #ifndef USED_AS_INCLUDE |
| 3 | |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 4 | #include "../pub/libvex_basictypes.h" |
| 5 | #include <stdio.h> |
| 6 | #include <malloc.h> |
| 7 | #include <stdlib.h> |
| 8 | #include <string.h> |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 9 | #include <assert.h> |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 10 | |
| 11 | |
| 12 | /* Test program for developing code for conversions between |
| 13 | x87 64-bit and 80-bit floats. |
| 14 | |
| 15 | 80-bit format exists only for x86/x86-64, and so the routines |
| 16 | hardwire it as little-endian. The 64-bit format (IEEE double) |
| 17 | could exist on any platform, little or big-endian and so we |
| 18 | have to take that into account. IOW, these routines have to |
| 19 | work correctly when compiled on both big- and little-endian |
| 20 | targets, but the 80-bit images only ever have to exist in |
| 21 | little-endian format. |
| 22 | */ |
sewardj | b298562 | 2004-11-16 02:06:09 +0000 | [diff] [blame] | 23 | static void show_f80 ( UChar* ); |
| 24 | static void show_f64 ( UChar* ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 25 | |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 26 | static inline |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 27 | UInt read_bit_array ( UChar* arr, UInt n ) |
| 28 | { |
| 29 | UChar c = arr[n >> 3]; |
| 30 | c >>= (n&7); |
| 31 | return c & 1; |
| 32 | } |
| 33 | |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 34 | static inline |
| 35 | void write_bit_array ( UChar* arr, UInt n, UInt b ) |
| 36 | { |
| 37 | UChar c = arr[n >> 3]; |
| 38 | c &= ~(1 << (n&7)); |
| 39 | c |= ((b&1) << (n&7)); |
| 40 | arr[n >> 3] = c; |
| 41 | } |
| 42 | |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 43 | |
| 44 | static void convert_f80le_to_f64le_HW ( /*IN*/UChar* f80, /*OUT*/UChar* f64 ) |
| 45 | { |
| 46 | asm volatile ("ffree %%st(7); fldt (%0); fstpl (%1)" |
| 47 | : |
| 48 | : "r" (&f80[0]), "r" (&f64[0]) |
| 49 | : "memory" ); |
| 50 | } |
| 51 | |
| 52 | static void convert_f64le_to_f80le_HW ( /*IN*/UChar* f64, /*OUT*/UChar* f80 ) |
| 53 | { |
| 54 | asm volatile ("ffree %%st(7); fldl (%0); fstpt (%1)" |
| 55 | : |
| 56 | : "r" (&f64[0]), "r" (&f80[0]) |
| 57 | : "memory" ); |
| 58 | } |
| 59 | |
sewardj | 07e0962 | 2004-09-06 20:39:20 +0000 | [diff] [blame] | 60 | #endif /* ndef USED_AS_INCLUDE */ |
| 61 | |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 62 | |
| 63 | |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 64 | /* 80 and 64-bit floating point formats: |
| 65 | |
| 66 | 80-bit: |
| 67 | |
| 68 | S 0 0-------0 zero |
| 69 | S 0 0X------X denormals |
| 70 | S 1-7FFE 1X------X normals (all normals have leading 1) |
| 71 | S 7FFF 10------0 infinity |
| 72 | S 7FFF 10X-----X snan |
| 73 | S 7FFF 11X-----X qnan |
| 74 | |
| 75 | S is the sign bit. For runs X----X, at least one of the Xs must be |
| 76 | nonzero. Exponent is 15 bits, fractional part is 63 bits, and |
| 77 | there is an explicitly represented leading 1, and a sign bit, |
| 78 | giving 80 in total. |
| 79 | |
| 80 | 64-bit avoids the confusion of an explicitly represented leading 1 |
| 81 | and so is simpler: |
| 82 | |
| 83 | S 0 0------0 zero |
| 84 | S 0 X------X denormals |
| 85 | S 1-7FE any normals |
| 86 | S 7FF 0------0 infinity |
| 87 | S 7FF 0X-----X snan |
| 88 | S 7FF 1X-----X qnan |
| 89 | |
| 90 | Exponent is 11 bits, fractional part is 52 bits, and there is a |
| 91 | sign bit, giving 64 in total. |
| 92 | */ |
| 93 | |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 94 | /* Convert a IEEE754 double (64-bit) into an x87 extended double |
| 95 | (80-bit), mimicing the hardware fairly closely. Both numbers are |
| 96 | stored little-endian. Limitations, all of which could be fixed, |
| 97 | given some level of hassle: |
| 98 | |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 99 | * Identity of NaNs is not preserved. |
| 100 | |
| 101 | See comments in the code for more details. |
| 102 | */ |
| 103 | static void convert_f64le_to_f80le ( /*IN*/UChar* f64, /*OUT*/UChar* f80 ) |
| 104 | { |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 105 | Bool mantissaIsZero; |
| 106 | Int bexp, i, j, shift; |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 107 | UChar sign; |
| 108 | |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 109 | sign = toUChar( (f64[7] >> 7) & 1 ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 110 | bexp = (f64[7] << 4) | ((f64[6] >> 4) & 0x0F); |
| 111 | bexp &= 0x7FF; |
| 112 | |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 113 | mantissaIsZero = False; |
| 114 | if (bexp == 0 || bexp == 0x7FF) { |
| 115 | /* We'll need to know whether or not the mantissa (bits 51:0) is |
| 116 | all zeroes in order to handle these cases. So figure it |
| 117 | out. */ |
| 118 | mantissaIsZero |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 119 | = toBool( |
| 120 | (f64[6] & 0x0F) == 0 |
| 121 | && f64[5] == 0 && f64[4] == 0 && f64[3] == 0 |
| 122 | && f64[2] == 0 && f64[1] == 0 && f64[0] == 0 |
| 123 | ); |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 124 | } |
| 125 | |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 126 | /* If the exponent is zero, either we have a zero or a denormal. |
| 127 | Produce a zero. This is a hack in that it forces denormals to |
| 128 | zero. Could do better. */ |
| 129 | if (bexp == 0) { |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 130 | f80[9] = toUChar( sign << 7 ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 131 | f80[8] = f80[7] = f80[6] = f80[5] = f80[4] |
| 132 | = f80[3] = f80[2] = f80[1] = f80[0] = 0; |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 133 | |
| 134 | if (mantissaIsZero) |
| 135 | /* It really is zero, so that's all we can do. */ |
| 136 | return; |
| 137 | |
| 138 | /* There is at least one 1-bit in the mantissa. So it's a |
| 139 | potentially denormalised double -- but we can produce a |
| 140 | normalised long double. Count the leading zeroes in the |
| 141 | mantissa so as to decide how much to bump the exponent down |
| 142 | by. Note, this is SLOW. */ |
| 143 | shift = 0; |
| 144 | for (i = 51; i >= 0; i--) { |
| 145 | if (read_bit_array(f64, i)) |
| 146 | break; |
| 147 | shift++; |
| 148 | } |
| 149 | |
| 150 | /* and copy into place as many bits as we can get our hands on. */ |
| 151 | j = 63; |
| 152 | for (i = 51 - shift; i >= 0; i--) { |
| 153 | write_bit_array( f80, j, |
| 154 | read_bit_array( f64, i ) ); |
| 155 | j--; |
| 156 | } |
| 157 | |
| 158 | /* Set the exponent appropriately, and we're done. */ |
| 159 | bexp -= shift; |
| 160 | bexp += (16383 - 1023); |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 161 | f80[9] = toUChar( (sign << 7) | ((bexp >> 8) & 0xFF) ); |
| 162 | f80[8] = toUChar( bexp & 0xFF ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 163 | return; |
| 164 | } |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 165 | |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 166 | /* If the exponent is 7FF, this is either an Infinity, a SNaN or |
| 167 | QNaN, as determined by examining bits 51:0, thus: |
| 168 | 0 ... 0 Inf |
| 169 | 0X ... X SNaN |
| 170 | 1X ... X QNaN |
| 171 | where at least one of the Xs is not zero. |
| 172 | */ |
| 173 | if (bexp == 0x7FF) { |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 174 | if (mantissaIsZero) { |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 175 | /* Produce an appropriately signed infinity: |
| 176 | S 1--1 (15) 1 0--0 (63) |
| 177 | */ |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 178 | f80[9] = toUChar( (sign << 7) | 0x7F ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 179 | f80[8] = 0xFF; |
| 180 | f80[7] = 0x80; |
| 181 | f80[6] = f80[5] = f80[4] = f80[3] |
| 182 | = f80[2] = f80[1] = f80[0] = 0; |
| 183 | return; |
| 184 | } |
| 185 | /* So it's either a QNaN or SNaN. Distinguish by considering |
| 186 | bit 51. Note, this destroys all the trailing bits |
| 187 | (identity?) of the NaN. IEEE754 doesn't require preserving |
| 188 | these (it only requires that there be one QNaN value and one |
| 189 | SNaN value), but x87 does seem to have some ability to |
| 190 | preserve them. Anyway, here, the NaN's identity is |
| 191 | destroyed. Could be improved. */ |
| 192 | if (f64[6] & 8) { |
| 193 | /* QNaN. Make a QNaN: |
| 194 | S 1--1 (15) 1 1--1 (63) |
| 195 | */ |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 196 | f80[9] = toUChar( (sign << 7) | 0x7F ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 197 | f80[8] = 0xFF; |
| 198 | f80[7] = 0xFF; |
| 199 | f80[6] = f80[5] = f80[4] = f80[3] |
| 200 | = f80[2] = f80[1] = f80[0] = 0xFF; |
| 201 | } else { |
| 202 | /* SNaN. Make a SNaN: |
| 203 | S 1--1 (15) 0 1--1 (63) |
| 204 | */ |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 205 | f80[9] = toUChar( (sign << 7) | 0x7F ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 206 | f80[8] = 0xFF; |
| 207 | f80[7] = 0x7F; |
| 208 | f80[6] = f80[5] = f80[4] = f80[3] |
| 209 | = f80[2] = f80[1] = f80[0] = 0xFF; |
| 210 | } |
| 211 | return; |
| 212 | } |
| 213 | |
| 214 | /* It's not a zero, denormal, infinity or nan. So it must be a |
| 215 | normalised number. Rebias the exponent and build the new |
| 216 | number. */ |
| 217 | bexp += (16383 - 1023); |
| 218 | |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 219 | f80[9] = toUChar( (sign << 7) | ((bexp >> 8) & 0xFF) ); |
| 220 | f80[8] = toUChar( bexp & 0xFF ); |
| 221 | f80[7] = toUChar( (1 << 7) | ((f64[6] << 3) & 0x78) |
| 222 | | ((f64[5] >> 5) & 7) ); |
| 223 | f80[6] = toUChar( ((f64[5] << 3) & 0xF8) | ((f64[4] >> 5) & 7) ); |
| 224 | f80[5] = toUChar( ((f64[4] << 3) & 0xF8) | ((f64[3] >> 5) & 7) ); |
| 225 | f80[4] = toUChar( ((f64[3] << 3) & 0xF8) | ((f64[2] >> 5) & 7) ); |
| 226 | f80[3] = toUChar( ((f64[2] << 3) & 0xF8) | ((f64[1] >> 5) & 7) ); |
| 227 | f80[2] = toUChar( ((f64[1] << 3) & 0xF8) | ((f64[0] >> 5) & 7) ); |
| 228 | f80[1] = toUChar( ((f64[0] << 3) & 0xF8) ); |
| 229 | f80[0] = toUChar( 0 ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 230 | } |
| 231 | |
| 232 | |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 233 | /* Convert a x87 extended double (80-bit) into an IEEE 754 double |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 234 | (64-bit), mimicking the hardware fairly closely. Both numbers are |
| 235 | stored little-endian. Limitations, both of which could be fixed, |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 236 | given some level of hassle: |
| 237 | |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 238 | * Rounding following truncation could be a bit better. |
| 239 | |
| 240 | * Identity of NaNs is not preserved. |
| 241 | |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 242 | See comments in the code for more details. |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 243 | */ |
| 244 | static void convert_f80le_to_f64le ( /*IN*/UChar* f80, /*OUT*/UChar* f64 ) |
| 245 | { |
| 246 | Bool isInf; |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 247 | Int bexp, i, j; |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 248 | UChar sign; |
| 249 | |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 250 | sign = toUChar((f80[9] >> 7) & 1); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 251 | bexp = (((UInt)f80[9]) << 8) | (UInt)f80[8]; |
| 252 | bexp &= 0x7FFF; |
| 253 | |
| 254 | /* If the exponent is zero, either we have a zero or a denormal. |
| 255 | But an extended precision denormal becomes a double precision |
| 256 | zero, so in either case, just produce the appropriately signed |
| 257 | zero. */ |
| 258 | if (bexp == 0) { |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 259 | f64[7] = toUChar(sign << 7); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 260 | f64[6] = f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; |
| 261 | return; |
| 262 | } |
| 263 | |
| 264 | /* If the exponent is 7FFF, this is either an Infinity, a SNaN or |
| 265 | QNaN, as determined by examining bits 62:0, thus: |
| 266 | 0 ... 0 Inf |
| 267 | 0X ... X SNaN |
| 268 | 1X ... X QNaN |
| 269 | where at least one of the Xs is not zero. |
| 270 | */ |
| 271 | if (bexp == 0x7FFF) { |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 272 | isInf = toBool( |
| 273 | (f80[7] & 0x7F) == 0 |
| 274 | && f80[6] == 0 && f80[5] == 0 && f80[4] == 0 |
| 275 | && f80[3] == 0 && f80[2] == 0 && f80[1] == 0 |
| 276 | && f80[0] == 0 |
| 277 | ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 278 | if (isInf) { |
| 279 | if (0 == (f80[7] & 0x80)) |
| 280 | goto wierd_NaN; |
| 281 | /* Produce an appropriately signed infinity: |
| 282 | S 1--1 (11) 0--0 (52) |
| 283 | */ |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 284 | f64[7] = toUChar((sign << 7) | 0x7F); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 285 | f64[6] = 0xF0; |
| 286 | f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; |
| 287 | return; |
| 288 | } |
| 289 | /* So it's either a QNaN or SNaN. Distinguish by considering |
| 290 | bit 62. Note, this destroys all the trailing bits |
| 291 | (identity?) of the NaN. IEEE754 doesn't require preserving |
| 292 | these (it only requires that there be one QNaN value and one |
| 293 | SNaN value), but x87 does seem to have some ability to |
| 294 | preserve them. Anyway, here, the NaN's identity is |
| 295 | destroyed. Could be improved. */ |
| 296 | if (f80[8] & 0x40) { |
| 297 | /* QNaN. Make a QNaN: |
| 298 | S 1--1 (11) 1 1--1 (51) |
| 299 | */ |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 300 | f64[7] = toUChar((sign << 7) | 0x7F); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 301 | f64[6] = 0xFF; |
| 302 | f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0xFF; |
| 303 | } else { |
| 304 | /* SNaN. Make a SNaN: |
| 305 | S 1--1 (11) 0 1--1 (51) |
| 306 | */ |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 307 | f64[7] = toUChar((sign << 7) | 0x7F); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 308 | f64[6] = 0xF7; |
| 309 | f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0xFF; |
| 310 | } |
| 311 | return; |
| 312 | } |
| 313 | |
| 314 | /* If it's not a Zero, NaN or Inf, and the integer part (bit 62) is |
| 315 | zero, the x87 FPU appears to consider the number denormalised |
| 316 | and converts it to a QNaN. */ |
| 317 | if (0 == (f80[7] & 0x80)) { |
| 318 | wierd_NaN: |
| 319 | /* Strange hardware QNaN: |
| 320 | S 1--1 (11) 1 0--0 (51) |
| 321 | */ |
| 322 | /* On a PIII, these QNaNs always appear with sign==1. I have |
| 323 | no idea why. */ |
| 324 | f64[7] = (1 /*sign*/ << 7) | 0x7F; |
| 325 | f64[6] = 0xF8; |
| 326 | f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; |
| 327 | return; |
| 328 | } |
| 329 | |
| 330 | /* It's not a zero, denormal, infinity or nan. So it must be a |
| 331 | normalised number. Rebias the exponent and consider. */ |
| 332 | bexp -= (16383 - 1023); |
| 333 | if (bexp >= 0x7FF) { |
| 334 | /* It's too big for a double. Construct an infinity. */ |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 335 | f64[7] = toUChar((sign << 7) | 0x7F); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 336 | f64[6] = 0xF0; |
| 337 | f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; |
| 338 | return; |
| 339 | } |
| 340 | |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 341 | if (bexp <= 0) { |
| 342 | /* It's too small for a normalised double. First construct a |
| 343 | zero and then see if it can be improved into a denormal. */ |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 344 | f64[7] = toUChar(sign << 7); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 345 | f64[6] = f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0; |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 346 | |
| 347 | if (bexp < -52) |
| 348 | /* Too small even for a denormal. */ |
| 349 | return; |
| 350 | |
| 351 | /* Ok, let's make a denormal. Note, this is SLOW. */ |
| 352 | /* Copy bits 63, 62, 61, etc of the src mantissa into the dst, |
| 353 | indexes 52+bexp, 51+bexp, etc, until k+bexp < 0. */ |
| 354 | /* bexp is in range -52 .. 0 inclusive */ |
| 355 | for (i = 63; i >= 0; i--) { |
| 356 | j = i - 12 + bexp; |
| 357 | if (j < 0) break; |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 358 | /* We shouldn't really call vassert from generated code. */ |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 359 | assert(j >= 0 && j < 52); |
| 360 | write_bit_array ( f64, |
| 361 | j, |
| 362 | read_bit_array ( f80, i ) ); |
| 363 | } |
| 364 | /* and now we might have to round ... */ |
| 365 | if (read_bit_array(f80, 10+1 - bexp) == 1) |
| 366 | goto do_rounding; |
| 367 | |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 368 | return; |
| 369 | } |
| 370 | |
| 371 | /* Ok, it's a normalised number which is representable as a double. |
| 372 | Copy the exponent and mantissa into place. */ |
| 373 | /* |
| 374 | for (i = 0; i < 52; i++) |
| 375 | write_bit_array ( f64, |
| 376 | i, |
| 377 | read_bit_array ( f80, i+11 ) ); |
| 378 | */ |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 379 | f64[0] = toUChar( (f80[1] >> 3) | (f80[2] << 5) ); |
| 380 | f64[1] = toUChar( (f80[2] >> 3) | (f80[3] << 5) ); |
| 381 | f64[2] = toUChar( (f80[3] >> 3) | (f80[4] << 5) ); |
| 382 | f64[3] = toUChar( (f80[4] >> 3) | (f80[5] << 5) ); |
| 383 | f64[4] = toUChar( (f80[5] >> 3) | (f80[6] << 5) ); |
| 384 | f64[5] = toUChar( (f80[6] >> 3) | (f80[7] << 5) ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 385 | |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 386 | f64[6] = toUChar( ((bexp << 4) & 0xF0) | ((f80[7] >> 3) & 0x0F) ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 387 | |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 388 | f64[7] = toUChar( (sign << 7) | ((bexp >> 4) & 0x7F) ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 389 | |
| 390 | /* Now consider any rounding that needs to happen as a result of |
| 391 | truncating the mantissa. */ |
| 392 | if (f80[1] & 4) /* read_bit_array(f80, 10) == 1) */ { |
sewardj | b298562 | 2004-11-16 02:06:09 +0000 | [diff] [blame] | 393 | |
| 394 | /* If the bottom bits of f80 are "100 0000 0000", then the |
| 395 | infinitely precise value is deemed to be mid-way between the |
| 396 | two closest representable values. Since we're doing |
| 397 | round-to-nearest (the default mode), in that case it is the |
| 398 | bit immediately above which indicates whether we should round |
| 399 | upwards or not -- if 0, we don't. All that is encapsulated |
| 400 | in the following simple test. */ |
| 401 | if ((f80[1] & 0xF) == 4/*0100b*/ && f80[0] == 0) |
| 402 | return; |
| 403 | |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 404 | do_rounding: |
sewardj | b298562 | 2004-11-16 02:06:09 +0000 | [diff] [blame] | 405 | /* Round upwards. This is a kludge. Once in every 2^24 |
| 406 | roundings (statistically) the bottom three bytes are all 0xFF |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 407 | and so we don't round at all. Could be improved. */ |
| 408 | if (f64[0] != 0xFF) { |
| 409 | f64[0]++; |
| 410 | } |
| 411 | else |
| 412 | if (f64[0] == 0xFF && f64[1] != 0xFF) { |
| 413 | f64[0] = 0; |
| 414 | f64[1]++; |
| 415 | } |
sewardj | b298562 | 2004-11-16 02:06:09 +0000 | [diff] [blame] | 416 | else |
| 417 | if (f64[0] == 0xFF && f64[1] == 0xFF && f64[2] != 0xFF) { |
| 418 | f64[0] = 0; |
| 419 | f64[1] = 0; |
| 420 | f64[2]++; |
| 421 | } |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 422 | /* else we don't round, but we should. */ |
| 423 | } |
| 424 | } |
| 425 | |
sewardj | 20f6129 | 2005-03-25 20:29:35 +0000 | [diff] [blame] | 426 | |
sewardj | 07e0962 | 2004-09-06 20:39:20 +0000 | [diff] [blame] | 427 | #ifndef USED_AS_INCLUDE |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 428 | |
| 429 | ////////////// |
| 430 | |
| 431 | static void show_f80 ( UChar* f80 ) |
| 432 | { |
| 433 | Int i; |
| 434 | printf("%d ", read_bit_array(f80, 79)); |
| 435 | |
| 436 | for (i = 78; i >= 64; i--) |
| 437 | printf("%d", read_bit_array(f80, i)); |
| 438 | |
| 439 | printf(" %d ", read_bit_array(f80, 63)); |
| 440 | |
| 441 | for (i = 62; i >= 0; i--) |
| 442 | printf("%d", read_bit_array(f80, i)); |
| 443 | } |
| 444 | |
| 445 | static void show_f64le ( UChar* f64 ) |
| 446 | { |
| 447 | Int i; |
| 448 | printf("%d ", read_bit_array(f64, 63)); |
| 449 | |
| 450 | for (i = 62; i >= 52; i--) |
| 451 | printf("%d", read_bit_array(f64, i)); |
| 452 | |
| 453 | printf(" "); |
| 454 | for (i = 51; i >= 0; i--) |
| 455 | printf("%d", read_bit_array(f64, i)); |
| 456 | } |
| 457 | |
| 458 | ////////////// |
| 459 | |
| 460 | |
| 461 | /* Convert f80 to a 64-bit IEEE double using both the hardware and the |
| 462 | soft version, and compare the results. If they differ, print |
| 463 | details and return 1. If they are identical, return 0. |
| 464 | */ |
| 465 | int do_80_to_64_test ( Int test_no, UChar* f80, UChar* f64h, UChar* f64s) |
| 466 | { |
| 467 | Char buf64s[100], buf64h[100]; |
| 468 | Bool same; |
| 469 | Int k; |
| 470 | convert_f80le_to_f64le_HW(f80, f64h); |
| 471 | convert_f80le_to_f64le(f80, f64s); |
| 472 | same = True; |
| 473 | for (k = 0; k < 8; k++) { |
| 474 | if (f64s[k] != f64h[k]) { |
| 475 | same = False; break; |
| 476 | } |
| 477 | } |
| 478 | /* bitwise identical */ |
| 479 | if (same) |
| 480 | return 0; |
| 481 | |
| 482 | sprintf(buf64s, "%.16e", *(double*)f64s); |
| 483 | sprintf(buf64h, "%.16e", *(double*)f64h); |
| 484 | |
| 485 | /* Not bitwise identical, but pretty darn close */ |
| 486 | if (0 == strcmp(buf64s, buf64h)) |
| 487 | return 0; |
| 488 | |
| 489 | printf("\n"); |
| 490 | printf("f80: "); show_f80(f80); printf("\n"); |
| 491 | printf("f64h: "); show_f64le(f64h); printf("\n"); |
| 492 | printf("f64s: "); show_f64le(f64s); printf("\n"); |
| 493 | |
| 494 | printf("[test %d] %.16Le -> (hw %s, sw %s)\n", |
| 495 | test_no, *(long double*)f80, |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 496 | buf64h, buf64s ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 497 | |
| 498 | return 1; |
| 499 | } |
| 500 | |
| 501 | |
| 502 | /* Convert an IEEE 64-bit double to a x87 extended double (80 bit) |
| 503 | using both the hardware and the soft version, and compare the |
| 504 | results. If they differ, print details and return 1. If they are |
| 505 | identical, return 0. |
| 506 | */ |
| 507 | int do_64_to_80_test ( Int test_no, UChar* f64, UChar* f80h, UChar* f80s) |
| 508 | { |
| 509 | Char buf80s[100], buf80h[100]; |
| 510 | Bool same; |
| 511 | Int k; |
| 512 | convert_f64le_to_f80le_HW(f64, f80h); |
| 513 | convert_f64le_to_f80le(f64, f80s); |
| 514 | same = True; |
| 515 | for (k = 0; k < 10; k++) { |
| 516 | if (f80s[k] != f80h[k]) { |
| 517 | same = False; break; |
| 518 | } |
| 519 | } |
| 520 | /* bitwise identical */ |
| 521 | if (same) |
| 522 | return 0; |
| 523 | |
| 524 | sprintf(buf80s, "%.20Le", *(long double*)f80s); |
| 525 | sprintf(buf80h, "%.20Le", *(long double*)f80h); |
| 526 | |
| 527 | /* Not bitwise identical, but pretty darn close */ |
| 528 | if (0 == strcmp(buf80s, buf80h)) |
| 529 | return 0; |
| 530 | |
| 531 | printf("\n"); |
| 532 | printf("f64: "); show_f64le(f64); printf("\n"); |
| 533 | printf("f80h: "); show_f80(f80h); printf("\n"); |
| 534 | printf("f80s: "); show_f80(f80s); printf("\n"); |
| 535 | |
| 536 | printf("[test %d] %.16e -> (hw %s, sw %s)\n", |
| 537 | test_no, *(double*)f64, |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 538 | buf80h, buf80s ); |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 539 | |
| 540 | return 1; |
| 541 | } |
| 542 | |
| 543 | |
| 544 | |
| 545 | void do_80_to_64_tests ( void ) |
| 546 | { |
| 547 | UInt b9,b8,b7,i, j; |
| 548 | Int fails=0, tests=0; |
| 549 | UChar* f64h = malloc(8); |
| 550 | UChar* f64s = malloc(8); |
| 551 | UChar* f80 = malloc(10); |
| 552 | int STEP = 1; |
| 553 | |
| 554 | srandom(4343); |
| 555 | |
| 556 | /* Ten million random bit patterns */ |
| 557 | for (i = 0; i < 10000000; i++) { |
| 558 | tests++; |
| 559 | for (j = 0; j < 10; j++) |
| 560 | f80[j] = (random() >> 7) & 255; |
| 561 | |
| 562 | fails += do_80_to_64_test(tests, f80, f64h, f64s); |
| 563 | } |
| 564 | |
| 565 | /* 2^24 numbers in which the first 24 bits are tested exhaustively |
| 566 | -- this covers the sign, exponent and leading part of the |
| 567 | mantissa. */ |
| 568 | for (b9 = 0; b9 < 256; b9 += STEP) { |
| 569 | for (b8 = 0; b8 < 256; b8 += STEP) { |
| 570 | for (b7 = 0; b7 < 256; b7 += STEP) { |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 571 | tests++; |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 572 | for (i = 0; i < 10; i++) |
| 573 | f80[i] = 0; |
| 574 | for (i = 0; i < 8; i++) |
| 575 | f64h[i] = f64s[i] = 0; |
| 576 | f80[9] = b9; |
| 577 | f80[8] = b8; |
| 578 | f80[7] = b7; |
| 579 | |
| 580 | fails += do_80_to_64_test(tests, f80, f64h, f64s); |
| 581 | }}} |
| 582 | |
| 583 | printf("\n80 -> 64: %d tests, %d fails\n\n", tests, fails); |
| 584 | } |
| 585 | |
| 586 | |
| 587 | void do_64_to_80_tests ( void ) |
| 588 | { |
| 589 | UInt b7,b6,b5,i, j; |
| 590 | Int fails=0, tests=0; |
| 591 | UChar* f80h = malloc(10); |
| 592 | UChar* f80s = malloc(10); |
| 593 | UChar* f64 = malloc(8); |
| 594 | int STEP = 1; |
| 595 | |
| 596 | srandom(2323); |
| 597 | |
| 598 | /* Ten million random bit patterns */ |
| 599 | for (i = 0; i < 10000000; i++) { |
| 600 | tests++; |
| 601 | for (j = 0; j < 8; j++) |
| 602 | f64[j] = (random() >> 13) & 255; |
| 603 | |
| 604 | fails += do_64_to_80_test(tests, f64, f80h, f80s); |
| 605 | } |
| 606 | |
| 607 | /* 2^24 numbers in which the first 24 bits are tested exhaustively |
| 608 | -- this covers the sign, exponent and leading part of the |
| 609 | mantissa. */ |
| 610 | for (b7 = 0; b7 < 256; b7 += STEP) { |
| 611 | for (b6 = 0; b6 < 256; b6 += STEP) { |
| 612 | for (b5 = 0; b5 < 256; b5 += STEP) { |
sewardj | aec3a1b | 2004-11-16 00:38:19 +0000 | [diff] [blame] | 613 | tests++; |
sewardj | cbe8efa | 2004-09-06 14:57:52 +0000 | [diff] [blame] | 614 | for (i = 0; i < 8; i++) |
| 615 | f64[i] = 0; |
| 616 | for (i = 0; i < 10; i++) |
| 617 | f80h[i] = f80s[i] = 0; |
| 618 | f64[7] = b7; |
| 619 | f64[6] = b6; |
| 620 | f64[5] = b5; |
| 621 | |
| 622 | fails += do_64_to_80_test(tests, f64, f80h, f80s); |
| 623 | }}} |
| 624 | |
| 625 | printf("\n64 -> 80: %d tests, %d fails\n\n", tests, fails); |
| 626 | } |
| 627 | |
| 628 | |
| 629 | int main ( void ) |
| 630 | { |
| 631 | do_80_to_64_tests(); |
| 632 | do_64_to_80_tests(); |
| 633 | return 0; |
| 634 | } |
| 635 | |
sewardj | 07e0962 | 2004-09-06 20:39:20 +0000 | [diff] [blame] | 636 | #endif /* ndef USED_AS_INCLUDE */ |