Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 1 | | |
| 2 | | setox.sa 3.1 12/10/90 |
| 3 | | |
| 4 | | The entry point setox computes the exponential of a value. |
| 5 | | setoxd does the same except the input value is a denormalized |
| 6 | | number. setoxm1 computes exp(X)-1, and setoxm1d computes |
| 7 | | exp(X)-1 for denormalized X. |
| 8 | | |
| 9 | | INPUT |
| 10 | | ----- |
| 11 | | Double-extended value in memory location pointed to by address |
| 12 | | register a0. |
| 13 | | |
| 14 | | OUTPUT |
| 15 | | ------ |
| 16 | | exp(X) or exp(X)-1 returned in floating-point register fp0. |
| 17 | | |
| 18 | | ACCURACY and MONOTONICITY |
| 19 | | ------------------------- |
| 20 | | The returned result is within 0.85 ulps in 64 significant bit, i.e. |
| 21 | | within 0.5001 ulp to 53 bits if the result is subsequently rounded |
| 22 | | to double precision. The result is provably monotonic in double |
| 23 | | precision. |
| 24 | | |
| 25 | | SPEED |
| 26 | | ----- |
| 27 | | Two timings are measured, both in the copy-back mode. The |
| 28 | | first one is measured when the function is invoked the first time |
| 29 | | (so the instructions and data are not in cache), and the |
| 30 | | second one is measured when the function is reinvoked at the same |
| 31 | | input argument. |
| 32 | | |
| 33 | | The program setox takes approximately 210/190 cycles for input |
| 34 | | argument X whose magnitude is less than 16380 log2, which |
| 35 | | is the usual situation. For the less common arguments, |
| 36 | | depending on their values, the program may run faster or slower -- |
| 37 | | but no worse than 10% slower even in the extreme cases. |
| 38 | | |
| 39 | | The program setoxm1 takes approximately ???/??? cycles for input |
| 40 | | argument X, 0.25 <= |X| < 70log2. For |X| < 0.25, it takes |
| 41 | | approximately ???/??? cycles. For the less common arguments, |
| 42 | | depending on their values, the program may run faster or slower -- |
| 43 | | but no worse than 10% slower even in the extreme cases. |
| 44 | | |
| 45 | | ALGORITHM and IMPLEMENTATION NOTES |
| 46 | | ---------------------------------- |
| 47 | | |
| 48 | | setoxd |
| 49 | | ------ |
| 50 | | Step 1. Set ans := 1.0 |
| 51 | | |
| 52 | | Step 2. Return ans := ans + sign(X)*2^(-126). Exit. |
| 53 | | Notes: This will always generate one exception -- inexact. |
| 54 | | |
| 55 | | |
| 56 | | setox |
| 57 | | ----- |
| 58 | | |
| 59 | | Step 1. Filter out extreme cases of input argument. |
| 60 | | 1.1 If |X| >= 2^(-65), go to Step 1.3. |
| 61 | | 1.2 Go to Step 7. |
| 62 | | 1.3 If |X| < 16380 log(2), go to Step 2. |
| 63 | | 1.4 Go to Step 8. |
| 64 | | Notes: The usual case should take the branches 1.1 -> 1.3 -> 2. |
| 65 | | To avoid the use of floating-point comparisons, a |
| 66 | | compact representation of |X| is used. This format is a |
| 67 | | 32-bit integer, the upper (more significant) 16 bits are |
| 68 | | the sign and biased exponent field of |X|; the lower 16 |
| 69 | | bits are the 16 most significant fraction (including the |
| 70 | | explicit bit) bits of |X|. Consequently, the comparisons |
| 71 | | in Steps 1.1 and 1.3 can be performed by integer comparison. |
| 72 | | Note also that the constant 16380 log(2) used in Step 1.3 |
| 73 | | is also in the compact form. Thus taking the branch |
| 74 | | to Step 2 guarantees |X| < 16380 log(2). There is no harm |
| 75 | | to have a small number of cases where |X| is less than, |
| 76 | | but close to, 16380 log(2) and the branch to Step 9 is |
| 77 | | taken. |
| 78 | | |
| 79 | | Step 2. Calculate N = round-to-nearest-int( X * 64/log2 ). |
| 80 | | 2.1 Set AdjFlag := 0 (indicates the branch 1.3 -> 2 was taken) |
| 81 | | 2.2 N := round-to-nearest-integer( X * 64/log2 ). |
| 82 | | 2.3 Calculate J = N mod 64; so J = 0,1,2,..., or 63. |
| 83 | | 2.4 Calculate M = (N - J)/64; so N = 64M + J. |
| 84 | | 2.5 Calculate the address of the stored value of 2^(J/64). |
| 85 | | 2.6 Create the value Scale = 2^M. |
| 86 | | Notes: The calculation in 2.2 is really performed by |
| 87 | | |
| 88 | | Z := X * constant |
| 89 | | N := round-to-nearest-integer(Z) |
| 90 | | |
| 91 | | where |
| 92 | | |
| 93 | | constant := single-precision( 64/log 2 ). |
| 94 | | |
| 95 | | Using a single-precision constant avoids memory access. |
| 96 | | Another effect of using a single-precision "constant" is |
| 97 | | that the calculated value Z is |
| 98 | | |
| 99 | | Z = X*(64/log2)*(1+eps), |eps| <= 2^(-24). |
| 100 | | |
| 101 | | This error has to be considered later in Steps 3 and 4. |
| 102 | | |
| 103 | | Step 3. Calculate X - N*log2/64. |
| 104 | | 3.1 R := X + N*L1, where L1 := single-precision(-log2/64). |
| 105 | | 3.2 R := R + N*L2, L2 := extended-precision(-log2/64 - L1). |
| 106 | | Notes: a) The way L1 and L2 are chosen ensures L1+L2 approximate |
| 107 | | the value -log2/64 to 88 bits of accuracy. |
| 108 | | b) N*L1 is exact because N is no longer than 22 bits and |
| 109 | | L1 is no longer than 24 bits. |
| 110 | | c) The calculation X+N*L1 is also exact due to cancellation. |
| 111 | | Thus, R is practically X+N(L1+L2) to full 64 bits. |
| 112 | | d) It is important to estimate how large can |R| be after |
| 113 | | Step 3.2. |
| 114 | | |
| 115 | | N = rnd-to-int( X*64/log2 (1+eps) ), |eps|<=2^(-24) |
| 116 | | X*64/log2 (1+eps) = N + f, |f| <= 0.5 |
| 117 | | X*64/log2 - N = f - eps*X 64/log2 |
| 118 | | X - N*log2/64 = f*log2/64 - eps*X |
| 119 | | |
| 120 | | |
| 121 | | Now |X| <= 16446 log2, thus |
| 122 | | |
| 123 | | |X - N*log2/64| <= (0.5 + 16446/2^(18))*log2/64 |
| 124 | | <= 0.57 log2/64. |
| 125 | | This bound will be used in Step 4. |
| 126 | | |
| 127 | | Step 4. Approximate exp(R)-1 by a polynomial |
| 128 | | p = R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5)))) |
| 129 | | Notes: a) In order to reduce memory access, the coefficients are |
| 130 | | made as "short" as possible: A1 (which is 1/2), A4 and A5 |
| 131 | | are single precision; A2 and A3 are double precision. |
| 132 | | b) Even with the restrictions above, |
| 133 | | |p - (exp(R)-1)| < 2^(-68.8) for all |R| <= 0.0062. |
| 134 | | Note that 0.0062 is slightly bigger than 0.57 log2/64. |
| 135 | | c) To fully utilize the pipeline, p is separated into |
| 136 | | two independent pieces of roughly equal complexities |
| 137 | | p = [ R + R*S*(A2 + S*A4) ] + |
| 138 | | [ S*(A1 + S*(A3 + S*A5)) ] |
| 139 | | where S = R*R. |
| 140 | | |
| 141 | | Step 5. Compute 2^(J/64)*exp(R) = 2^(J/64)*(1+p) by |
| 142 | | ans := T + ( T*p + t) |
| 143 | | where T and t are the stored values for 2^(J/64). |
| 144 | | Notes: 2^(J/64) is stored as T and t where T+t approximates |
| 145 | | 2^(J/64) to roughly 85 bits; T is in extended precision |
| 146 | | and t is in single precision. Note also that T is rounded |
| 147 | | to 62 bits so that the last two bits of T are zero. The |
| 148 | | reason for such a special form is that T-1, T-2, and T-8 |
| 149 | | will all be exact --- a property that will give much |
| 150 | | more accurate computation of the function EXPM1. |
| 151 | | |
| 152 | | Step 6. Reconstruction of exp(X) |
| 153 | | exp(X) = 2^M * 2^(J/64) * exp(R). |
| 154 | | 6.1 If AdjFlag = 0, go to 6.3 |
| 155 | | 6.2 ans := ans * AdjScale |
| 156 | | 6.3 Restore the user FPCR |
| 157 | | 6.4 Return ans := ans * Scale. Exit. |
| 158 | | Notes: If AdjFlag = 0, we have X = Mlog2 + Jlog2/64 + R, |
| 159 | | |M| <= 16380, and Scale = 2^M. Moreover, exp(X) will |
| 160 | | neither overflow nor underflow. If AdjFlag = 1, that |
| 161 | | means that |
| 162 | | X = (M1+M)log2 + Jlog2/64 + R, |M1+M| >= 16380. |
| 163 | | Hence, exp(X) may overflow or underflow or neither. |
| 164 | | When that is the case, AdjScale = 2^(M1) where M1 is |
| 165 | | approximately M. Thus 6.2 will never cause over/underflow. |
| 166 | | Possible exception in 6.4 is overflow or underflow. |
| 167 | | The inexact exception is not generated in 6.4. Although |
| 168 | | one can argue that the inexact flag should always be |
| 169 | | raised, to simulate that exception cost to much than the |
| 170 | | flag is worth in practical uses. |
| 171 | | |
| 172 | | Step 7. Return 1 + X. |
| 173 | | 7.1 ans := X |
| 174 | | 7.2 Restore user FPCR. |
| 175 | | 7.3 Return ans := 1 + ans. Exit |
| 176 | | Notes: For non-zero X, the inexact exception will always be |
| 177 | | raised by 7.3. That is the only exception raised by 7.3. |
| 178 | | Note also that we use the FMOVEM instruction to move X |
| 179 | | in Step 7.1 to avoid unnecessary trapping. (Although |
| 180 | | the FMOVEM may not seem relevant since X is normalized, |
| 181 | | the precaution will be useful in the library version of |
| 182 | | this code where the separate entry for denormalized inputs |
| 183 | | will be done away with.) |
| 184 | | |
| 185 | | Step 8. Handle exp(X) where |X| >= 16380log2. |
| 186 | | 8.1 If |X| > 16480 log2, go to Step 9. |
| 187 | | (mimic 2.2 - 2.6) |
| 188 | | 8.2 N := round-to-integer( X * 64/log2 ) |
| 189 | | 8.3 Calculate J = N mod 64, J = 0,1,...,63 |
| 190 | | 8.4 K := (N-J)/64, M1 := truncate(K/2), M = K-M1, AdjFlag := 1. |
| 191 | | 8.5 Calculate the address of the stored value 2^(J/64). |
| 192 | | 8.6 Create the values Scale = 2^M, AdjScale = 2^M1. |
| 193 | | 8.7 Go to Step 3. |
| 194 | | Notes: Refer to notes for 2.2 - 2.6. |
| 195 | | |
| 196 | | Step 9. Handle exp(X), |X| > 16480 log2. |
| 197 | | 9.1 If X < 0, go to 9.3 |
| 198 | | 9.2 ans := Huge, go to 9.4 |
| 199 | | 9.3 ans := Tiny. |
| 200 | | 9.4 Restore user FPCR. |
| 201 | | 9.5 Return ans := ans * ans. Exit. |
| 202 | | Notes: Exp(X) will surely overflow or underflow, depending on |
| 203 | | X's sign. "Huge" and "Tiny" are respectively large/tiny |
| 204 | | extended-precision numbers whose square over/underflow |
| 205 | | with an inexact result. Thus, 9.5 always raises the |
| 206 | | inexact together with either overflow or underflow. |
| 207 | | |
| 208 | | |
| 209 | | setoxm1d |
| 210 | | -------- |
| 211 | | |
| 212 | | Step 1. Set ans := 0 |
| 213 | | |
| 214 | | Step 2. Return ans := X + ans. Exit. |
| 215 | | Notes: This will return X with the appropriate rounding |
| 216 | | precision prescribed by the user FPCR. |
| 217 | | |
| 218 | | setoxm1 |
| 219 | | ------- |
| 220 | | |
| 221 | | Step 1. Check |X| |
| 222 | | 1.1 If |X| >= 1/4, go to Step 1.3. |
| 223 | | 1.2 Go to Step 7. |
| 224 | | 1.3 If |X| < 70 log(2), go to Step 2. |
| 225 | | 1.4 Go to Step 10. |
| 226 | | Notes: The usual case should take the branches 1.1 -> 1.3 -> 2. |
| 227 | | However, it is conceivable |X| can be small very often |
| 228 | | because EXPM1 is intended to evaluate exp(X)-1 accurately |
| 229 | | when |X| is small. For further details on the comparisons, |
| 230 | | see the notes on Step 1 of setox. |
| 231 | | |
| 232 | | Step 2. Calculate N = round-to-nearest-int( X * 64/log2 ). |
| 233 | | 2.1 N := round-to-nearest-integer( X * 64/log2 ). |
| 234 | | 2.2 Calculate J = N mod 64; so J = 0,1,2,..., or 63. |
| 235 | | 2.3 Calculate M = (N - J)/64; so N = 64M + J. |
| 236 | | 2.4 Calculate the address of the stored value of 2^(J/64). |
| 237 | | 2.5 Create the values Sc = 2^M and OnebySc := -2^(-M). |
| 238 | | Notes: See the notes on Step 2 of setox. |
| 239 | | |
| 240 | | Step 3. Calculate X - N*log2/64. |
| 241 | | 3.1 R := X + N*L1, where L1 := single-precision(-log2/64). |
| 242 | | 3.2 R := R + N*L2, L2 := extended-precision(-log2/64 - L1). |
| 243 | | Notes: Applying the analysis of Step 3 of setox in this case |
| 244 | | shows that |R| <= 0.0055 (note that |X| <= 70 log2 in |
| 245 | | this case). |
| 246 | | |
| 247 | | Step 4. Approximate exp(R)-1 by a polynomial |
| 248 | | p = R+R*R*(A1+R*(A2+R*(A3+R*(A4+R*(A5+R*A6))))) |
| 249 | | Notes: a) In order to reduce memory access, the coefficients are |
| 250 | | made as "short" as possible: A1 (which is 1/2), A5 and A6 |
| 251 | | are single precision; A2, A3 and A4 are double precision. |
| 252 | | b) Even with the restriction above, |
| 253 | | |p - (exp(R)-1)| < |R| * 2^(-72.7) |
| 254 | | for all |R| <= 0.0055. |
| 255 | | c) To fully utilize the pipeline, p is separated into |
| 256 | | two independent pieces of roughly equal complexity |
| 257 | | p = [ R*S*(A2 + S*(A4 + S*A6)) ] + |
| 258 | | [ R + S*(A1 + S*(A3 + S*A5)) ] |
| 259 | | where S = R*R. |
| 260 | | |
| 261 | | Step 5. Compute 2^(J/64)*p by |
| 262 | | p := T*p |
| 263 | | where T and t are the stored values for 2^(J/64). |
| 264 | | Notes: 2^(J/64) is stored as T and t where T+t approximates |
| 265 | | 2^(J/64) to roughly 85 bits; T is in extended precision |
| 266 | | and t is in single precision. Note also that T is rounded |
| 267 | | to 62 bits so that the last two bits of T are zero. The |
| 268 | | reason for such a special form is that T-1, T-2, and T-8 |
| 269 | | will all be exact --- a property that will be exploited |
| 270 | | in Step 6 below. The total relative error in p is no |
| 271 | | bigger than 2^(-67.7) compared to the final result. |
| 272 | | |
| 273 | | Step 6. Reconstruction of exp(X)-1 |
| 274 | | exp(X)-1 = 2^M * ( 2^(J/64) + p - 2^(-M) ). |
| 275 | | 6.1 If M <= 63, go to Step 6.3. |
| 276 | | 6.2 ans := T + (p + (t + OnebySc)). Go to 6.6 |
| 277 | | 6.3 If M >= -3, go to 6.5. |
| 278 | | 6.4 ans := (T + (p + t)) + OnebySc. Go to 6.6 |
| 279 | | 6.5 ans := (T + OnebySc) + (p + t). |
| 280 | | 6.6 Restore user FPCR. |
| 281 | | 6.7 Return ans := Sc * ans. Exit. |
| 282 | | Notes: The various arrangements of the expressions give accurate |
| 283 | | evaluations. |
| 284 | | |
| 285 | | Step 7. exp(X)-1 for |X| < 1/4. |
| 286 | | 7.1 If |X| >= 2^(-65), go to Step 9. |
| 287 | | 7.2 Go to Step 8. |
| 288 | | |
| 289 | | Step 8. Calculate exp(X)-1, |X| < 2^(-65). |
| 290 | | 8.1 If |X| < 2^(-16312), goto 8.3 |
| 291 | | 8.2 Restore FPCR; return ans := X - 2^(-16382). Exit. |
| 292 | | 8.3 X := X * 2^(140). |
| 293 | | 8.4 Restore FPCR; ans := ans - 2^(-16382). |
| 294 | | Return ans := ans*2^(140). Exit |
| 295 | | Notes: The idea is to return "X - tiny" under the user |
| 296 | | precision and rounding modes. To avoid unnecessary |
| 297 | | inefficiency, we stay away from denormalized numbers the |
| 298 | | best we can. For |X| >= 2^(-16312), the straightforward |
| 299 | | 8.2 generates the inexact exception as the case warrants. |
| 300 | | |
| 301 | | Step 9. Calculate exp(X)-1, |X| < 1/4, by a polynomial |
| 302 | | p = X + X*X*(B1 + X*(B2 + ... + X*B12)) |
| 303 | | Notes: a) In order to reduce memory access, the coefficients are |
| 304 | | made as "short" as possible: B1 (which is 1/2), B9 to B12 |
| 305 | | are single precision; B3 to B8 are double precision; and |
| 306 | | B2 is double extended. |
| 307 | | b) Even with the restriction above, |
| 308 | | |p - (exp(X)-1)| < |X| 2^(-70.6) |
| 309 | | for all |X| <= 0.251. |
| 310 | | Note that 0.251 is slightly bigger than 1/4. |
| 311 | | c) To fully preserve accuracy, the polynomial is computed |
| 312 | | as X + ( S*B1 + Q ) where S = X*X and |
| 313 | | Q = X*S*(B2 + X*(B3 + ... + X*B12)) |
| 314 | | d) To fully utilize the pipeline, Q is separated into |
| 315 | | two independent pieces of roughly equal complexity |
| 316 | | Q = [ X*S*(B2 + S*(B4 + ... + S*B12)) ] + |
| 317 | | [ S*S*(B3 + S*(B5 + ... + S*B11)) ] |
| 318 | | |
| 319 | | Step 10. Calculate exp(X)-1 for |X| >= 70 log 2. |
| 320 | | 10.1 If X >= 70log2 , exp(X) - 1 = exp(X) for all practical |
| 321 | | purposes. Therefore, go to Step 1 of setox. |
| 322 | | 10.2 If X <= -70log2, exp(X) - 1 = -1 for all practical purposes. |
| 323 | | ans := -1 |
| 324 | | Restore user FPCR |
| 325 | | Return ans := ans + 2^(-126). Exit. |
| 326 | | Notes: 10.2 will always create an inexact and return -1 + tiny |
| 327 | | in the user rounding precision and mode. |
| 328 | | |
| 329 | | |
| 330 | |
| 331 | | Copyright (C) Motorola, Inc. 1990 |
| 332 | | All Rights Reserved |
| 333 | | |
Matt Waddel | e00d82d | 2006-02-11 17:55:48 -0800 | [diff] [blame] | 334 | | For details on the license for this file, please see the |
| 335 | | file, README, in this same directory. |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 336 | |
| 337 | |setox idnt 2,1 | Motorola 040 Floating Point Software Package |
| 338 | |
| 339 | |section 8 |
| 340 | |
| 341 | #include "fpsp.h" |
| 342 | |
| 343 | L2: .long 0x3FDC0000,0x82E30865,0x4361C4C6,0x00000000 |
| 344 | |
| 345 | EXPA3: .long 0x3FA55555,0x55554431 |
| 346 | EXPA2: .long 0x3FC55555,0x55554018 |
| 347 | |
| 348 | HUGE: .long 0x7FFE0000,0xFFFFFFFF,0xFFFFFFFF,0x00000000 |
| 349 | TINY: .long 0x00010000,0xFFFFFFFF,0xFFFFFFFF,0x00000000 |
| 350 | |
| 351 | EM1A4: .long 0x3F811111,0x11174385 |
| 352 | EM1A3: .long 0x3FA55555,0x55554F5A |
| 353 | |
| 354 | EM1A2: .long 0x3FC55555,0x55555555,0x00000000,0x00000000 |
| 355 | |
| 356 | EM1B8: .long 0x3EC71DE3,0xA5774682 |
| 357 | EM1B7: .long 0x3EFA01A0,0x19D7CB68 |
| 358 | |
| 359 | EM1B6: .long 0x3F2A01A0,0x1A019DF3 |
| 360 | EM1B5: .long 0x3F56C16C,0x16C170E2 |
| 361 | |
| 362 | EM1B4: .long 0x3F811111,0x11111111 |
| 363 | EM1B3: .long 0x3FA55555,0x55555555 |
| 364 | |
| 365 | EM1B2: .long 0x3FFC0000,0xAAAAAAAA,0xAAAAAAAB |
| 366 | .long 0x00000000 |
| 367 | |
| 368 | TWO140: .long 0x48B00000,0x00000000 |
| 369 | TWON140: .long 0x37300000,0x00000000 |
| 370 | |
| 371 | EXPTBL: |
| 372 | .long 0x3FFF0000,0x80000000,0x00000000,0x00000000 |
| 373 | .long 0x3FFF0000,0x8164D1F3,0xBC030774,0x9F841A9B |
| 374 | .long 0x3FFF0000,0x82CD8698,0xAC2BA1D8,0x9FC1D5B9 |
| 375 | .long 0x3FFF0000,0x843A28C3,0xACDE4048,0xA0728369 |
| 376 | .long 0x3FFF0000,0x85AAC367,0xCC487B14,0x1FC5C95C |
| 377 | .long 0x3FFF0000,0x871F6196,0x9E8D1010,0x1EE85C9F |
| 378 | .long 0x3FFF0000,0x88980E80,0x92DA8528,0x9FA20729 |
| 379 | .long 0x3FFF0000,0x8A14D575,0x496EFD9C,0xA07BF9AF |
| 380 | .long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E8,0xA0020DCF |
| 381 | .long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E4,0x205A63DA |
| 382 | .long 0x3FFF0000,0x8EA4398B,0x45CD53C0,0x1EB70051 |
| 383 | .long 0x3FFF0000,0x9031DC43,0x1466B1DC,0x1F6EB029 |
| 384 | .long 0x3FFF0000,0x91C3D373,0xAB11C338,0xA0781494 |
| 385 | .long 0x3FFF0000,0x935A2B2F,0x13E6E92C,0x9EB319B0 |
| 386 | .long 0x3FFF0000,0x94F4EFA8,0xFEF70960,0x2017457D |
| 387 | .long 0x3FFF0000,0x96942D37,0x20185A00,0x1F11D537 |
| 388 | .long 0x3FFF0000,0x9837F051,0x8DB8A970,0x9FB952DD |
| 389 | .long 0x3FFF0000,0x99E04593,0x20B7FA64,0x1FE43087 |
| 390 | .long 0x3FFF0000,0x9B8D39B9,0xD54E5538,0x1FA2A818 |
| 391 | .long 0x3FFF0000,0x9D3ED9A7,0x2CFFB750,0x1FDE494D |
| 392 | .long 0x3FFF0000,0x9EF53260,0x91A111AC,0x20504890 |
| 393 | .long 0x3FFF0000,0xA0B0510F,0xB9714FC4,0xA073691C |
| 394 | .long 0x3FFF0000,0xA2704303,0x0C496818,0x1F9B7A05 |
| 395 | .long 0x3FFF0000,0xA43515AE,0x09E680A0,0xA0797126 |
| 396 | .long 0x3FFF0000,0xA5FED6A9,0xB15138EC,0xA071A140 |
| 397 | .long 0x3FFF0000,0xA7CD93B4,0xE9653568,0x204F62DA |
| 398 | .long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x1F283C4A |
| 399 | .long 0x3FFF0000,0xAB7A39B5,0xA93ED338,0x9F9A7FDC |
| 400 | .long 0x3FFF0000,0xAD583EEA,0x42A14AC8,0xA05B3FAC |
| 401 | .long 0x3FFF0000,0xAF3B78AD,0x690A4374,0x1FDF2610 |
| 402 | .long 0x3FFF0000,0xB123F581,0xD2AC2590,0x9F705F90 |
| 403 | .long 0x3FFF0000,0xB311C412,0xA9112488,0x201F678A |
| 404 | .long 0x3FFF0000,0xB504F333,0xF9DE6484,0x1F32FB13 |
| 405 | .long 0x3FFF0000,0xB6FD91E3,0x28D17790,0x20038B30 |
| 406 | .long 0x3FFF0000,0xB8FBAF47,0x62FB9EE8,0x200DC3CC |
| 407 | .long 0x3FFF0000,0xBAFF5AB2,0x133E45FC,0x9F8B2AE6 |
| 408 | .long 0x3FFF0000,0xBD08A39F,0x580C36C0,0xA02BBF70 |
| 409 | .long 0x3FFF0000,0xBF1799B6,0x7A731084,0xA00BF518 |
| 410 | .long 0x3FFF0000,0xC12C4CCA,0x66709458,0xA041DD41 |
| 411 | .long 0x3FFF0000,0xC346CCDA,0x24976408,0x9FDF137B |
| 412 | .long 0x3FFF0000,0xC5672A11,0x5506DADC,0x201F1568 |
| 413 | .long 0x3FFF0000,0xC78D74C8,0xABB9B15C,0x1FC13A2E |
| 414 | .long 0x3FFF0000,0xC9B9BD86,0x6E2F27A4,0xA03F8F03 |
| 415 | .long 0x3FFF0000,0xCBEC14FE,0xF2727C5C,0x1FF4907D |
| 416 | .long 0x3FFF0000,0xCE248C15,0x1F8480E4,0x9E6E53E4 |
| 417 | .long 0x3FFF0000,0xD06333DA,0xEF2B2594,0x1FD6D45C |
| 418 | .long 0x3FFF0000,0xD2A81D91,0xF12AE45C,0xA076EDB9 |
| 419 | .long 0x3FFF0000,0xD4F35AAB,0xCFEDFA20,0x9FA6DE21 |
| 420 | .long 0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x1EE69A2F |
| 421 | .long 0x3FFF0000,0xD99D15C2,0x78AFD7B4,0x207F439F |
| 422 | .long 0x3FFF0000,0xDBFBB797,0xDAF23754,0x201EC207 |
| 423 | .long 0x3FFF0000,0xDE60F482,0x5E0E9124,0x9E8BE175 |
| 424 | .long 0x3FFF0000,0xE0CCDEEC,0x2A94E110,0x20032C4B |
| 425 | .long 0x3FFF0000,0xE33F8972,0xBE8A5A50,0x2004DFF5 |
| 426 | .long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x1E72F47A |
| 427 | .long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x1F722F22 |
| 428 | .long 0x3FFF0000,0xEAC0C6E7,0xDD243930,0xA017E945 |
| 429 | .long 0x3FFF0000,0xED4F301E,0xD9942B84,0x1F401A5B |
| 430 | .long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CC,0x9FB9A9E3 |
| 431 | .long 0x3FFF0000,0xF281773C,0x59FFB138,0x20744C05 |
| 432 | .long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x1F773A19 |
| 433 | .long 0x3FFF0000,0xF7D0DF73,0x0AD13BB8,0x1FFE90D5 |
| 434 | .long 0x3FFF0000,0xFA83B2DB,0x722A033C,0xA041ED22 |
| 435 | .long 0x3FFF0000,0xFD3E0C0C,0xF486C174,0x1F853F3A |
| 436 | |
| 437 | .set ADJFLAG,L_SCR2 |
| 438 | .set SCALE,FP_SCR1 |
| 439 | .set ADJSCALE,FP_SCR2 |
| 440 | .set SC,FP_SCR3 |
| 441 | .set ONEBYSC,FP_SCR4 |
| 442 | |
| 443 | | xref t_frcinx |
| 444 | |xref t_extdnrm |
| 445 | |xref t_unfl |
| 446 | |xref t_ovfl |
| 447 | |
| 448 | .global setoxd |
| 449 | setoxd: |
| 450 | |--entry point for EXP(X), X is denormalized |
| 451 | movel (%a0),%d0 |
| 452 | andil #0x80000000,%d0 |
| 453 | oril #0x00800000,%d0 | ...sign(X)*2^(-126) |
| 454 | movel %d0,-(%sp) |
| 455 | fmoves #0x3F800000,%fp0 |
| 456 | fmovel %d1,%fpcr |
| 457 | fadds (%sp)+,%fp0 |
| 458 | bra t_frcinx |
| 459 | |
| 460 | .global setox |
| 461 | setox: |
| 462 | |--entry point for EXP(X), here X is finite, non-zero, and not NaN's |
| 463 | |
| 464 | |--Step 1. |
| 465 | movel (%a0),%d0 | ...load part of input X |
| 466 | andil #0x7FFF0000,%d0 | ...biased expo. of X |
| 467 | cmpil #0x3FBE0000,%d0 | ...2^(-65) |
| 468 | bges EXPC1 | ...normal case |
| 469 | bra EXPSM |
| 470 | |
| 471 | EXPC1: |
| 472 | |--The case |X| >= 2^(-65) |
| 473 | movew 4(%a0),%d0 | ...expo. and partial sig. of |X| |
| 474 | cmpil #0x400CB167,%d0 | ...16380 log2 trunc. 16 bits |
| 475 | blts EXPMAIN | ...normal case |
| 476 | bra EXPBIG |
| 477 | |
| 478 | EXPMAIN: |
| 479 | |--Step 2. |
| 480 | |--This is the normal branch: 2^(-65) <= |X| < 16380 log2. |
| 481 | fmovex (%a0),%fp0 | ...load input from (a0) |
| 482 | |
| 483 | fmovex %fp0,%fp1 |
| 484 | fmuls #0x42B8AA3B,%fp0 | ...64/log2 * X |
| 485 | fmovemx %fp2-%fp2/%fp3,-(%a7) | ...save fp2 |
| 486 | movel #0,ADJFLAG(%a6) |
| 487 | fmovel %fp0,%d0 | ...N = int( X * 64/log2 ) |
| 488 | lea EXPTBL,%a1 |
| 489 | fmovel %d0,%fp0 | ...convert to floating-format |
| 490 | |
| 491 | movel %d0,L_SCR1(%a6) | ...save N temporarily |
| 492 | andil #0x3F,%d0 | ...D0 is J = N mod 64 |
| 493 | lsll #4,%d0 |
| 494 | addal %d0,%a1 | ...address of 2^(J/64) |
| 495 | movel L_SCR1(%a6),%d0 |
| 496 | asrl #6,%d0 | ...D0 is M |
| 497 | addiw #0x3FFF,%d0 | ...biased expo. of 2^(M) |
| 498 | movew L2,L_SCR1(%a6) | ...prefetch L2, no need in CB |
| 499 | |
| 500 | EXPCONT1: |
| 501 | |--Step 3. |
| 502 | |--fp1,fp2 saved on the stack. fp0 is N, fp1 is X, |
| 503 | |--a0 points to 2^(J/64), D0 is biased expo. of 2^(M) |
| 504 | fmovex %fp0,%fp2 |
| 505 | fmuls #0xBC317218,%fp0 | ...N * L1, L1 = lead(-log2/64) |
| 506 | fmulx L2,%fp2 | ...N * L2, L1+L2 = -log2/64 |
| 507 | faddx %fp1,%fp0 | ...X + N*L1 |
| 508 | faddx %fp2,%fp0 | ...fp0 is R, reduced arg. |
| 509 | | MOVE.W #$3FA5,EXPA3 ...load EXPA3 in cache |
| 510 | |
| 511 | |--Step 4. |
| 512 | |--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL |
| 513 | |-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5)))) |
| 514 | |--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R |
| 515 | |--[R+R*S*(A2+S*A4)] + [S*(A1+S*(A3+S*A5))] |
| 516 | |
| 517 | fmovex %fp0,%fp1 |
| 518 | fmulx %fp1,%fp1 | ...fp1 IS S = R*R |
| 519 | |
| 520 | fmoves #0x3AB60B70,%fp2 | ...fp2 IS A5 |
| 521 | | MOVE.W #0,2(%a1) ...load 2^(J/64) in cache |
| 522 | |
| 523 | fmulx %fp1,%fp2 | ...fp2 IS S*A5 |
| 524 | fmovex %fp1,%fp3 |
| 525 | fmuls #0x3C088895,%fp3 | ...fp3 IS S*A4 |
| 526 | |
| 527 | faddd EXPA3,%fp2 | ...fp2 IS A3+S*A5 |
| 528 | faddd EXPA2,%fp3 | ...fp3 IS A2+S*A4 |
| 529 | |
| 530 | fmulx %fp1,%fp2 | ...fp2 IS S*(A3+S*A5) |
| 531 | movew %d0,SCALE(%a6) | ...SCALE is 2^(M) in extended |
| 532 | clrw SCALE+2(%a6) |
| 533 | movel #0x80000000,SCALE+4(%a6) |
| 534 | clrl SCALE+8(%a6) |
| 535 | |
| 536 | fmulx %fp1,%fp3 | ...fp3 IS S*(A2+S*A4) |
| 537 | |
| 538 | fadds #0x3F000000,%fp2 | ...fp2 IS A1+S*(A3+S*A5) |
| 539 | fmulx %fp0,%fp3 | ...fp3 IS R*S*(A2+S*A4) |
| 540 | |
| 541 | fmulx %fp1,%fp2 | ...fp2 IS S*(A1+S*(A3+S*A5)) |
| 542 | faddx %fp3,%fp0 | ...fp0 IS R+R*S*(A2+S*A4), |
| 543 | | ...fp3 released |
| 544 | |
| 545 | fmovex (%a1)+,%fp1 | ...fp1 is lead. pt. of 2^(J/64) |
| 546 | faddx %fp2,%fp0 | ...fp0 is EXP(R) - 1 |
| 547 | | ...fp2 released |
| 548 | |
| 549 | |--Step 5 |
| 550 | |--final reconstruction process |
| 551 | |--EXP(X) = 2^M * ( 2^(J/64) + 2^(J/64)*(EXP(R)-1) ) |
| 552 | |
| 553 | fmulx %fp1,%fp0 | ...2^(J/64)*(Exp(R)-1) |
| 554 | fmovemx (%a7)+,%fp2-%fp2/%fp3 | ...fp2 restored |
| 555 | fadds (%a1),%fp0 | ...accurate 2^(J/64) |
| 556 | |
| 557 | faddx %fp1,%fp0 | ...2^(J/64) + 2^(J/64)*... |
| 558 | movel ADJFLAG(%a6),%d0 |
| 559 | |
| 560 | |--Step 6 |
| 561 | tstl %d0 |
| 562 | beqs NORMAL |
| 563 | ADJUST: |
| 564 | fmulx ADJSCALE(%a6),%fp0 |
| 565 | NORMAL: |
| 566 | fmovel %d1,%FPCR | ...restore user FPCR |
| 567 | fmulx SCALE(%a6),%fp0 | ...multiply 2^(M) |
| 568 | bra t_frcinx |
| 569 | |
| 570 | EXPSM: |
| 571 | |--Step 7 |
| 572 | fmovemx (%a0),%fp0-%fp0 | ...in case X is denormalized |
| 573 | fmovel %d1,%FPCR |
| 574 | fadds #0x3F800000,%fp0 | ...1+X in user mode |
| 575 | bra t_frcinx |
| 576 | |
| 577 | EXPBIG: |
| 578 | |--Step 8 |
| 579 | cmpil #0x400CB27C,%d0 | ...16480 log2 |
| 580 | bgts EXP2BIG |
| 581 | |--Steps 8.2 -- 8.6 |
| 582 | fmovex (%a0),%fp0 | ...load input from (a0) |
| 583 | |
| 584 | fmovex %fp0,%fp1 |
| 585 | fmuls #0x42B8AA3B,%fp0 | ...64/log2 * X |
| 586 | fmovemx %fp2-%fp2/%fp3,-(%a7) | ...save fp2 |
| 587 | movel #1,ADJFLAG(%a6) |
| 588 | fmovel %fp0,%d0 | ...N = int( X * 64/log2 ) |
| 589 | lea EXPTBL,%a1 |
| 590 | fmovel %d0,%fp0 | ...convert to floating-format |
| 591 | movel %d0,L_SCR1(%a6) | ...save N temporarily |
| 592 | andil #0x3F,%d0 | ...D0 is J = N mod 64 |
| 593 | lsll #4,%d0 |
| 594 | addal %d0,%a1 | ...address of 2^(J/64) |
| 595 | movel L_SCR1(%a6),%d0 |
| 596 | asrl #6,%d0 | ...D0 is K |
| 597 | movel %d0,L_SCR1(%a6) | ...save K temporarily |
| 598 | asrl #1,%d0 | ...D0 is M1 |
| 599 | subl %d0,L_SCR1(%a6) | ...a1 is M |
| 600 | addiw #0x3FFF,%d0 | ...biased expo. of 2^(M1) |
| 601 | movew %d0,ADJSCALE(%a6) | ...ADJSCALE := 2^(M1) |
| 602 | clrw ADJSCALE+2(%a6) |
| 603 | movel #0x80000000,ADJSCALE+4(%a6) |
| 604 | clrl ADJSCALE+8(%a6) |
| 605 | movel L_SCR1(%a6),%d0 | ...D0 is M |
| 606 | addiw #0x3FFF,%d0 | ...biased expo. of 2^(M) |
| 607 | bra EXPCONT1 | ...go back to Step 3 |
| 608 | |
| 609 | EXP2BIG: |
| 610 | |--Step 9 |
| 611 | fmovel %d1,%FPCR |
| 612 | movel (%a0),%d0 |
| 613 | bclrb #sign_bit,(%a0) | ...setox always returns positive |
| 614 | cmpil #0,%d0 |
| 615 | blt t_unfl |
| 616 | bra t_ovfl |
| 617 | |
| 618 | .global setoxm1d |
| 619 | setoxm1d: |
| 620 | |--entry point for EXPM1(X), here X is denormalized |
| 621 | |--Step 0. |
| 622 | bra t_extdnrm |
| 623 | |
| 624 | |
| 625 | .global setoxm1 |
| 626 | setoxm1: |
| 627 | |--entry point for EXPM1(X), here X is finite, non-zero, non-NaN |
| 628 | |
| 629 | |--Step 1. |
| 630 | |--Step 1.1 |
| 631 | movel (%a0),%d0 | ...load part of input X |
| 632 | andil #0x7FFF0000,%d0 | ...biased expo. of X |
| 633 | cmpil #0x3FFD0000,%d0 | ...1/4 |
| 634 | bges EM1CON1 | ...|X| >= 1/4 |
| 635 | bra EM1SM |
| 636 | |
| 637 | EM1CON1: |
| 638 | |--Step 1.3 |
| 639 | |--The case |X| >= 1/4 |
| 640 | movew 4(%a0),%d0 | ...expo. and partial sig. of |X| |
| 641 | cmpil #0x4004C215,%d0 | ...70log2 rounded up to 16 bits |
| 642 | bles EM1MAIN | ...1/4 <= |X| <= 70log2 |
| 643 | bra EM1BIG |
| 644 | |
| 645 | EM1MAIN: |
| 646 | |--Step 2. |
| 647 | |--This is the case: 1/4 <= |X| <= 70 log2. |
| 648 | fmovex (%a0),%fp0 | ...load input from (a0) |
| 649 | |
| 650 | fmovex %fp0,%fp1 |
| 651 | fmuls #0x42B8AA3B,%fp0 | ...64/log2 * X |
| 652 | fmovemx %fp2-%fp2/%fp3,-(%a7) | ...save fp2 |
| 653 | | MOVE.W #$3F81,EM1A4 ...prefetch in CB mode |
| 654 | fmovel %fp0,%d0 | ...N = int( X * 64/log2 ) |
| 655 | lea EXPTBL,%a1 |
| 656 | fmovel %d0,%fp0 | ...convert to floating-format |
| 657 | |
| 658 | movel %d0,L_SCR1(%a6) | ...save N temporarily |
| 659 | andil #0x3F,%d0 | ...D0 is J = N mod 64 |
| 660 | lsll #4,%d0 |
| 661 | addal %d0,%a1 | ...address of 2^(J/64) |
| 662 | movel L_SCR1(%a6),%d0 |
| 663 | asrl #6,%d0 | ...D0 is M |
| 664 | movel %d0,L_SCR1(%a6) | ...save a copy of M |
| 665 | | MOVE.W #$3FDC,L2 ...prefetch L2 in CB mode |
| 666 | |
| 667 | |--Step 3. |
| 668 | |--fp1,fp2 saved on the stack. fp0 is N, fp1 is X, |
| 669 | |--a0 points to 2^(J/64), D0 and a1 both contain M |
| 670 | fmovex %fp0,%fp2 |
| 671 | fmuls #0xBC317218,%fp0 | ...N * L1, L1 = lead(-log2/64) |
| 672 | fmulx L2,%fp2 | ...N * L2, L1+L2 = -log2/64 |
| 673 | faddx %fp1,%fp0 | ...X + N*L1 |
| 674 | faddx %fp2,%fp0 | ...fp0 is R, reduced arg. |
| 675 | | MOVE.W #$3FC5,EM1A2 ...load EM1A2 in cache |
| 676 | addiw #0x3FFF,%d0 | ...D0 is biased expo. of 2^M |
| 677 | |
| 678 | |--Step 4. |
| 679 | |--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL |
| 680 | |-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*(A5 + R*A6))))) |
| 681 | |--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R |
| 682 | |--[R*S*(A2+S*(A4+S*A6))] + [R+S*(A1+S*(A3+S*A5))] |
| 683 | |
| 684 | fmovex %fp0,%fp1 |
| 685 | fmulx %fp1,%fp1 | ...fp1 IS S = R*R |
| 686 | |
| 687 | fmoves #0x3950097B,%fp2 | ...fp2 IS a6 |
| 688 | | MOVE.W #0,2(%a1) ...load 2^(J/64) in cache |
| 689 | |
| 690 | fmulx %fp1,%fp2 | ...fp2 IS S*A6 |
| 691 | fmovex %fp1,%fp3 |
| 692 | fmuls #0x3AB60B6A,%fp3 | ...fp3 IS S*A5 |
| 693 | |
| 694 | faddd EM1A4,%fp2 | ...fp2 IS A4+S*A6 |
| 695 | faddd EM1A3,%fp3 | ...fp3 IS A3+S*A5 |
| 696 | movew %d0,SC(%a6) | ...SC is 2^(M) in extended |
| 697 | clrw SC+2(%a6) |
| 698 | movel #0x80000000,SC+4(%a6) |
| 699 | clrl SC+8(%a6) |
| 700 | |
| 701 | fmulx %fp1,%fp2 | ...fp2 IS S*(A4+S*A6) |
| 702 | movel L_SCR1(%a6),%d0 | ...D0 is M |
| 703 | negw %d0 | ...D0 is -M |
| 704 | fmulx %fp1,%fp3 | ...fp3 IS S*(A3+S*A5) |
| 705 | addiw #0x3FFF,%d0 | ...biased expo. of 2^(-M) |
| 706 | faddd EM1A2,%fp2 | ...fp2 IS A2+S*(A4+S*A6) |
| 707 | fadds #0x3F000000,%fp3 | ...fp3 IS A1+S*(A3+S*A5) |
| 708 | |
| 709 | fmulx %fp1,%fp2 | ...fp2 IS S*(A2+S*(A4+S*A6)) |
| 710 | oriw #0x8000,%d0 | ...signed/expo. of -2^(-M) |
| 711 | movew %d0,ONEBYSC(%a6) | ...OnebySc is -2^(-M) |
| 712 | clrw ONEBYSC+2(%a6) |
| 713 | movel #0x80000000,ONEBYSC+4(%a6) |
| 714 | clrl ONEBYSC+8(%a6) |
| 715 | fmulx %fp3,%fp1 | ...fp1 IS S*(A1+S*(A3+S*A5)) |
| 716 | | ...fp3 released |
| 717 | |
| 718 | fmulx %fp0,%fp2 | ...fp2 IS R*S*(A2+S*(A4+S*A6)) |
| 719 | faddx %fp1,%fp0 | ...fp0 IS R+S*(A1+S*(A3+S*A5)) |
| 720 | | ...fp1 released |
| 721 | |
| 722 | faddx %fp2,%fp0 | ...fp0 IS EXP(R)-1 |
| 723 | | ...fp2 released |
| 724 | fmovemx (%a7)+,%fp2-%fp2/%fp3 | ...fp2 restored |
| 725 | |
| 726 | |--Step 5 |
| 727 | |--Compute 2^(J/64)*p |
| 728 | |
| 729 | fmulx (%a1),%fp0 | ...2^(J/64)*(Exp(R)-1) |
| 730 | |
| 731 | |--Step 6 |
| 732 | |--Step 6.1 |
| 733 | movel L_SCR1(%a6),%d0 | ...retrieve M |
| 734 | cmpil #63,%d0 |
| 735 | bles MLE63 |
| 736 | |--Step 6.2 M >= 64 |
| 737 | fmoves 12(%a1),%fp1 | ...fp1 is t |
| 738 | faddx ONEBYSC(%a6),%fp1 | ...fp1 is t+OnebySc |
| 739 | faddx %fp1,%fp0 | ...p+(t+OnebySc), fp1 released |
| 740 | faddx (%a1),%fp0 | ...T+(p+(t+OnebySc)) |
| 741 | bras EM1SCALE |
| 742 | MLE63: |
| 743 | |--Step 6.3 M <= 63 |
| 744 | cmpil #-3,%d0 |
| 745 | bges MGEN3 |
| 746 | MLTN3: |
| 747 | |--Step 6.4 M <= -4 |
| 748 | fadds 12(%a1),%fp0 | ...p+t |
| 749 | faddx (%a1),%fp0 | ...T+(p+t) |
| 750 | faddx ONEBYSC(%a6),%fp0 | ...OnebySc + (T+(p+t)) |
| 751 | bras EM1SCALE |
| 752 | MGEN3: |
| 753 | |--Step 6.5 -3 <= M <= 63 |
| 754 | fmovex (%a1)+,%fp1 | ...fp1 is T |
| 755 | fadds (%a1),%fp0 | ...fp0 is p+t |
| 756 | faddx ONEBYSC(%a6),%fp1 | ...fp1 is T+OnebySc |
| 757 | faddx %fp1,%fp0 | ...(T+OnebySc)+(p+t) |
| 758 | |
| 759 | EM1SCALE: |
| 760 | |--Step 6.6 |
| 761 | fmovel %d1,%FPCR |
| 762 | fmulx SC(%a6),%fp0 |
| 763 | |
| 764 | bra t_frcinx |
| 765 | |
| 766 | EM1SM: |
| 767 | |--Step 7 |X| < 1/4. |
| 768 | cmpil #0x3FBE0000,%d0 | ...2^(-65) |
| 769 | bges EM1POLY |
| 770 | |
| 771 | EM1TINY: |
| 772 | |--Step 8 |X| < 2^(-65) |
| 773 | cmpil #0x00330000,%d0 | ...2^(-16312) |
| 774 | blts EM12TINY |
| 775 | |--Step 8.2 |
| 776 | movel #0x80010000,SC(%a6) | ...SC is -2^(-16382) |
| 777 | movel #0x80000000,SC+4(%a6) |
| 778 | clrl SC+8(%a6) |
| 779 | fmovex (%a0),%fp0 |
| 780 | fmovel %d1,%FPCR |
| 781 | faddx SC(%a6),%fp0 |
| 782 | |
| 783 | bra t_frcinx |
| 784 | |
| 785 | EM12TINY: |
| 786 | |--Step 8.3 |
| 787 | fmovex (%a0),%fp0 |
| 788 | fmuld TWO140,%fp0 |
| 789 | movel #0x80010000,SC(%a6) |
| 790 | movel #0x80000000,SC+4(%a6) |
| 791 | clrl SC+8(%a6) |
| 792 | faddx SC(%a6),%fp0 |
| 793 | fmovel %d1,%FPCR |
| 794 | fmuld TWON140,%fp0 |
| 795 | |
| 796 | bra t_frcinx |
| 797 | |
| 798 | EM1POLY: |
| 799 | |--Step 9 exp(X)-1 by a simple polynomial |
| 800 | fmovex (%a0),%fp0 | ...fp0 is X |
| 801 | fmulx %fp0,%fp0 | ...fp0 is S := X*X |
| 802 | fmovemx %fp2-%fp2/%fp3,-(%a7) | ...save fp2 |
| 803 | fmoves #0x2F30CAA8,%fp1 | ...fp1 is B12 |
| 804 | fmulx %fp0,%fp1 | ...fp1 is S*B12 |
| 805 | fmoves #0x310F8290,%fp2 | ...fp2 is B11 |
| 806 | fadds #0x32D73220,%fp1 | ...fp1 is B10+S*B12 |
| 807 | |
| 808 | fmulx %fp0,%fp2 | ...fp2 is S*B11 |
| 809 | fmulx %fp0,%fp1 | ...fp1 is S*(B10 + ... |
| 810 | |
| 811 | fadds #0x3493F281,%fp2 | ...fp2 is B9+S*... |
| 812 | faddd EM1B8,%fp1 | ...fp1 is B8+S*... |
| 813 | |
| 814 | fmulx %fp0,%fp2 | ...fp2 is S*(B9+... |
| 815 | fmulx %fp0,%fp1 | ...fp1 is S*(B8+... |
| 816 | |
| 817 | faddd EM1B7,%fp2 | ...fp2 is B7+S*... |
| 818 | faddd EM1B6,%fp1 | ...fp1 is B6+S*... |
| 819 | |
| 820 | fmulx %fp0,%fp2 | ...fp2 is S*(B7+... |
| 821 | fmulx %fp0,%fp1 | ...fp1 is S*(B6+... |
| 822 | |
| 823 | faddd EM1B5,%fp2 | ...fp2 is B5+S*... |
| 824 | faddd EM1B4,%fp1 | ...fp1 is B4+S*... |
| 825 | |
| 826 | fmulx %fp0,%fp2 | ...fp2 is S*(B5+... |
| 827 | fmulx %fp0,%fp1 | ...fp1 is S*(B4+... |
| 828 | |
| 829 | faddd EM1B3,%fp2 | ...fp2 is B3+S*... |
| 830 | faddx EM1B2,%fp1 | ...fp1 is B2+S*... |
| 831 | |
| 832 | fmulx %fp0,%fp2 | ...fp2 is S*(B3+... |
| 833 | fmulx %fp0,%fp1 | ...fp1 is S*(B2+... |
| 834 | |
| 835 | fmulx %fp0,%fp2 | ...fp2 is S*S*(B3+...) |
| 836 | fmulx (%a0),%fp1 | ...fp1 is X*S*(B2... |
| 837 | |
| 838 | fmuls #0x3F000000,%fp0 | ...fp0 is S*B1 |
| 839 | faddx %fp2,%fp1 | ...fp1 is Q |
| 840 | | ...fp2 released |
| 841 | |
| 842 | fmovemx (%a7)+,%fp2-%fp2/%fp3 | ...fp2 restored |
| 843 | |
| 844 | faddx %fp1,%fp0 | ...fp0 is S*B1+Q |
| 845 | | ...fp1 released |
| 846 | |
| 847 | fmovel %d1,%FPCR |
| 848 | faddx (%a0),%fp0 |
| 849 | |
| 850 | bra t_frcinx |
| 851 | |
| 852 | EM1BIG: |
| 853 | |--Step 10 |X| > 70 log2 |
| 854 | movel (%a0),%d0 |
| 855 | cmpil #0,%d0 |
| 856 | bgt EXPC1 |
| 857 | |--Step 10.2 |
| 858 | fmoves #0xBF800000,%fp0 | ...fp0 is -1 |
| 859 | fmovel %d1,%FPCR |
| 860 | fadds #0x00800000,%fp0 | ...-1 + 2^(-126) |
| 861 | |
| 862 | bra t_frcinx |
| 863 | |
| 864 | |end |