Laurent Vivier | 591596b | 2018-02-24 21:18:00 +0100 | [diff] [blame] | 1 | /* |
| 2 | * Ported from a work by Andreas Grabher for Previous, NeXT Computer Emulator, |
| 3 | * derived from NetBSD M68040 FPSP functions, |
| 4 | * derived from release 2a of the SoftFloat IEC/IEEE Floating-point Arithmetic |
| 5 | * Package. Those parts of the code (and some later contributions) are |
| 6 | * provided under that license, as detailed below. |
| 7 | * It has subsequently been modified by contributors to the QEMU Project, |
| 8 | * so some portions are provided under: |
| 9 | * the SoftFloat-2a license |
| 10 | * the BSD license |
| 11 | * GPL-v2-or-later |
| 12 | * |
| 13 | * Any future contributions to this file will be taken to be licensed under |
| 14 | * the Softfloat-2a license unless specifically indicated otherwise. |
| 15 | */ |
| 16 | |
| 17 | /* Portions of this work are licensed under the terms of the GNU GPL, |
| 18 | * version 2 or later. See the COPYING file in the top-level directory. |
| 19 | */ |
| 20 | |
| 21 | #include "qemu/osdep.h" |
| 22 | #include "softfloat.h" |
| 23 | #include "fpu/softfloat-macros.h" |
Laurent Vivier | 4b5c65b | 2018-03-05 21:39:04 +0100 | [diff] [blame] | 24 | #include "softfloat_fpsp_tables.h" |
Laurent Vivier | 591596b | 2018-02-24 21:18:00 +0100 | [diff] [blame] | 25 | |
Laurent Vivier | c84813b | 2018-03-12 21:27:24 +0100 | [diff] [blame] | 26 | #define pi_exp 0x4000 |
Laurent Vivier | 8c992ab | 2018-03-12 21:27:22 +0100 | [diff] [blame] | 27 | #define piby2_exp 0x3FFF |
| 28 | #define pi_sig LIT64(0xc90fdaa22168c235) |
| 29 | |
Laurent Vivier | 0d379c1 | 2018-02-24 21:18:02 +0100 | [diff] [blame] | 30 | static floatx80 propagateFloatx80NaNOneArg(floatx80 a, float_status *status) |
| 31 | { |
| 32 | if (floatx80_is_signaling_nan(a, status)) { |
| 33 | float_raise(float_flag_invalid, status); |
Richard Henderson | 1c0c951 | 2018-05-10 13:49:00 -0700 | [diff] [blame] | 34 | a = floatx80_silence_nan(a, status); |
Laurent Vivier | 0d379c1 | 2018-02-24 21:18:02 +0100 | [diff] [blame] | 35 | } |
| 36 | |
| 37 | if (status->default_nan_mode) { |
| 38 | return floatx80_default_nan(status); |
| 39 | } |
| 40 | |
Richard Henderson | 1c0c951 | 2018-05-10 13:49:00 -0700 | [diff] [blame] | 41 | return a; |
Laurent Vivier | 0d379c1 | 2018-02-24 21:18:02 +0100 | [diff] [blame] | 42 | } |
| 43 | |
Laurent Vivier | 591596b | 2018-02-24 21:18:00 +0100 | [diff] [blame] | 44 | /*---------------------------------------------------------------------------- |
| 45 | | Returns the modulo remainder of the extended double-precision floating-point |
| 46 | | value `a' with respect to the corresponding value `b'. |
| 47 | *----------------------------------------------------------------------------*/ |
| 48 | |
| 49 | floatx80 floatx80_mod(floatx80 a, floatx80 b, float_status *status) |
| 50 | { |
| 51 | flag aSign, zSign; |
| 52 | int32_t aExp, bExp, expDiff; |
| 53 | uint64_t aSig0, aSig1, bSig; |
| 54 | uint64_t qTemp, term0, term1; |
| 55 | |
| 56 | aSig0 = extractFloatx80Frac(a); |
| 57 | aExp = extractFloatx80Exp(a); |
| 58 | aSign = extractFloatx80Sign(a); |
| 59 | bSig = extractFloatx80Frac(b); |
| 60 | bExp = extractFloatx80Exp(b); |
| 61 | |
| 62 | if (aExp == 0x7FFF) { |
| 63 | if ((uint64_t) (aSig0 << 1) |
| 64 | || ((bExp == 0x7FFF) && (uint64_t) (bSig << 1))) { |
| 65 | return propagateFloatx80NaN(a, b, status); |
| 66 | } |
| 67 | goto invalid; |
| 68 | } |
| 69 | if (bExp == 0x7FFF) { |
| 70 | if ((uint64_t) (bSig << 1)) { |
| 71 | return propagateFloatx80NaN(a, b, status); |
| 72 | } |
| 73 | return a; |
| 74 | } |
| 75 | if (bExp == 0) { |
| 76 | if (bSig == 0) { |
| 77 | invalid: |
| 78 | float_raise(float_flag_invalid, status); |
| 79 | return floatx80_default_nan(status); |
| 80 | } |
| 81 | normalizeFloatx80Subnormal(bSig, &bExp, &bSig); |
| 82 | } |
| 83 | if (aExp == 0) { |
| 84 | if ((uint64_t) (aSig0 << 1) == 0) { |
| 85 | return a; |
| 86 | } |
| 87 | normalizeFloatx80Subnormal(aSig0, &aExp, &aSig0); |
| 88 | } |
| 89 | bSig |= LIT64(0x8000000000000000); |
| 90 | zSign = aSign; |
| 91 | expDiff = aExp - bExp; |
| 92 | aSig1 = 0; |
| 93 | if (expDiff < 0) { |
| 94 | return a; |
| 95 | } |
| 96 | qTemp = (bSig <= aSig0); |
| 97 | if (qTemp) { |
| 98 | aSig0 -= bSig; |
| 99 | } |
| 100 | expDiff -= 64; |
| 101 | while (0 < expDiff) { |
| 102 | qTemp = estimateDiv128To64(aSig0, aSig1, bSig); |
| 103 | qTemp = (2 < qTemp) ? qTemp - 2 : 0; |
| 104 | mul64To128(bSig, qTemp, &term0, &term1); |
| 105 | sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1); |
| 106 | shortShift128Left(aSig0, aSig1, 62, &aSig0, &aSig1); |
Laurent Vivier | 5a73e7f | 2018-05-08 22:39:37 +0200 | [diff] [blame] | 107 | expDiff -= 62; |
Laurent Vivier | 591596b | 2018-02-24 21:18:00 +0100 | [diff] [blame] | 108 | } |
| 109 | expDiff += 64; |
| 110 | if (0 < expDiff) { |
| 111 | qTemp = estimateDiv128To64(aSig0, aSig1, bSig); |
| 112 | qTemp = (2 < qTemp) ? qTemp - 2 : 0; |
| 113 | qTemp >>= 64 - expDiff; |
| 114 | mul64To128(bSig, qTemp << (64 - expDiff), &term0, &term1); |
| 115 | sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1); |
| 116 | shortShift128Left(0, bSig, 64 - expDiff, &term0, &term1); |
| 117 | while (le128(term0, term1, aSig0, aSig1)) { |
| 118 | ++qTemp; |
| 119 | sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1); |
| 120 | } |
| 121 | } |
| 122 | return |
| 123 | normalizeRoundAndPackFloatx80( |
| 124 | 80, zSign, bExp + expDiff, aSig0, aSig1, status); |
| 125 | } |
Laurent Vivier | 0d379c1 | 2018-02-24 21:18:02 +0100 | [diff] [blame] | 126 | |
| 127 | /*---------------------------------------------------------------------------- |
| 128 | | Returns the mantissa of the extended double-precision floating-point |
| 129 | | value `a'. |
| 130 | *----------------------------------------------------------------------------*/ |
| 131 | |
| 132 | floatx80 floatx80_getman(floatx80 a, float_status *status) |
| 133 | { |
| 134 | flag aSign; |
| 135 | int32_t aExp; |
| 136 | uint64_t aSig; |
| 137 | |
| 138 | aSig = extractFloatx80Frac(a); |
| 139 | aExp = extractFloatx80Exp(a); |
| 140 | aSign = extractFloatx80Sign(a); |
| 141 | |
| 142 | if (aExp == 0x7FFF) { |
| 143 | if ((uint64_t) (aSig << 1)) { |
| 144 | return propagateFloatx80NaNOneArg(a , status); |
| 145 | } |
| 146 | float_raise(float_flag_invalid , status); |
| 147 | return floatx80_default_nan(status); |
| 148 | } |
| 149 | |
| 150 | if (aExp == 0) { |
| 151 | if (aSig == 0) { |
| 152 | return packFloatx80(aSign, 0, 0); |
| 153 | } |
| 154 | normalizeFloatx80Subnormal(aSig, &aExp, &aSig); |
| 155 | } |
| 156 | |
| 157 | return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, |
| 158 | 0x3FFF, aSig, 0, status); |
| 159 | } |
| 160 | |
| 161 | /*---------------------------------------------------------------------------- |
| 162 | | Returns the exponent of the extended double-precision floating-point |
| 163 | | value `a' as an extended double-precision value. |
| 164 | *----------------------------------------------------------------------------*/ |
| 165 | |
| 166 | floatx80 floatx80_getexp(floatx80 a, float_status *status) |
| 167 | { |
| 168 | flag aSign; |
| 169 | int32_t aExp; |
| 170 | uint64_t aSig; |
| 171 | |
| 172 | aSig = extractFloatx80Frac(a); |
| 173 | aExp = extractFloatx80Exp(a); |
| 174 | aSign = extractFloatx80Sign(a); |
| 175 | |
| 176 | if (aExp == 0x7FFF) { |
| 177 | if ((uint64_t) (aSig << 1)) { |
| 178 | return propagateFloatx80NaNOneArg(a , status); |
| 179 | } |
| 180 | float_raise(float_flag_invalid , status); |
| 181 | return floatx80_default_nan(status); |
| 182 | } |
| 183 | |
| 184 | if (aExp == 0) { |
| 185 | if (aSig == 0) { |
| 186 | return packFloatx80(aSign, 0, 0); |
| 187 | } |
| 188 | normalizeFloatx80Subnormal(aSig, &aExp, &aSig); |
| 189 | } |
| 190 | |
| 191 | return int32_to_floatx80(aExp - 0x3FFF, status); |
| 192 | } |
| 193 | |
| 194 | /*---------------------------------------------------------------------------- |
| 195 | | Scales extended double-precision floating-point value in operand `a' by |
| 196 | | value `b'. The function truncates the value in the second operand 'b' to |
| 197 | | an integral value and adds that value to the exponent of the operand 'a'. |
| 198 | | The operation performed according to the IEC/IEEE Standard for Binary |
| 199 | | Floating-Point Arithmetic. |
| 200 | *----------------------------------------------------------------------------*/ |
| 201 | |
| 202 | floatx80 floatx80_scale(floatx80 a, floatx80 b, float_status *status) |
| 203 | { |
| 204 | flag aSign, bSign; |
| 205 | int32_t aExp, bExp, shiftCount; |
| 206 | uint64_t aSig, bSig; |
| 207 | |
| 208 | aSig = extractFloatx80Frac(a); |
| 209 | aExp = extractFloatx80Exp(a); |
| 210 | aSign = extractFloatx80Sign(a); |
| 211 | bSig = extractFloatx80Frac(b); |
| 212 | bExp = extractFloatx80Exp(b); |
| 213 | bSign = extractFloatx80Sign(b); |
| 214 | |
| 215 | if (bExp == 0x7FFF) { |
| 216 | if ((uint64_t) (bSig << 1) || |
| 217 | ((aExp == 0x7FFF) && (uint64_t) (aSig << 1))) { |
| 218 | return propagateFloatx80NaN(a, b, status); |
| 219 | } |
| 220 | float_raise(float_flag_invalid , status); |
| 221 | return floatx80_default_nan(status); |
| 222 | } |
| 223 | if (aExp == 0x7FFF) { |
| 224 | if ((uint64_t) (aSig << 1)) { |
| 225 | return propagateFloatx80NaN(a, b, status); |
| 226 | } |
| 227 | return packFloatx80(aSign, floatx80_infinity.high, |
| 228 | floatx80_infinity.low); |
| 229 | } |
| 230 | if (aExp == 0) { |
| 231 | if (aSig == 0) { |
| 232 | return packFloatx80(aSign, 0, 0); |
| 233 | } |
| 234 | if (bExp < 0x3FFF) { |
| 235 | return a; |
| 236 | } |
| 237 | normalizeFloatx80Subnormal(aSig, &aExp, &aSig); |
| 238 | } |
| 239 | |
| 240 | if (bExp < 0x3FFF) { |
| 241 | return a; |
| 242 | } |
| 243 | |
| 244 | if (0x400F < bExp) { |
| 245 | aExp = bSign ? -0x6001 : 0xE000; |
| 246 | return roundAndPackFloatx80(status->floatx80_rounding_precision, |
| 247 | aSign, aExp, aSig, 0, status); |
| 248 | } |
| 249 | |
| 250 | shiftCount = 0x403E - bExp; |
| 251 | bSig >>= shiftCount; |
| 252 | aExp = bSign ? (aExp - bSig) : (aExp + bSig); |
| 253 | |
| 254 | return roundAndPackFloatx80(status->floatx80_rounding_precision, |
| 255 | aSign, aExp, aSig, 0, status); |
| 256 | } |
Laurent Vivier | 9a06977 | 2018-03-05 21:39:03 +0100 | [diff] [blame] | 257 | |
| 258 | floatx80 floatx80_move(floatx80 a, float_status *status) |
| 259 | { |
| 260 | flag aSign; |
| 261 | int32_t aExp; |
| 262 | uint64_t aSig; |
| 263 | |
| 264 | aSig = extractFloatx80Frac(a); |
| 265 | aExp = extractFloatx80Exp(a); |
| 266 | aSign = extractFloatx80Sign(a); |
| 267 | |
| 268 | if (aExp == 0x7FFF) { |
| 269 | if ((uint64_t)(aSig << 1)) { |
| 270 | return propagateFloatx80NaNOneArg(a, status); |
| 271 | } |
| 272 | return a; |
| 273 | } |
| 274 | if (aExp == 0) { |
| 275 | if (aSig == 0) { |
| 276 | return a; |
| 277 | } |
| 278 | normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision, |
| 279 | aSign, aExp, aSig, 0, status); |
| 280 | } |
| 281 | return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, |
| 282 | aExp, aSig, 0, status); |
| 283 | } |
Laurent Vivier | 4b5c65b | 2018-03-05 21:39:04 +0100 | [diff] [blame] | 284 | |
| 285 | /*---------------------------------------------------------------------------- |
| 286 | | Algorithms for transcendental functions supported by MC68881 and MC68882 |
| 287 | | mathematical coprocessors. The functions are derived from FPSP library. |
| 288 | *----------------------------------------------------------------------------*/ |
| 289 | |
| 290 | #define one_exp 0x3FFF |
| 291 | #define one_sig LIT64(0x8000000000000000) |
| 292 | |
| 293 | /*---------------------------------------------------------------------------- |
| 294 | | Function for compactifying extended double-precision floating point values. |
| 295 | *----------------------------------------------------------------------------*/ |
| 296 | |
| 297 | static int32_t floatx80_make_compact(int32_t aExp, uint64_t aSig) |
| 298 | { |
| 299 | return (aExp << 16) | (aSig >> 48); |
| 300 | } |
| 301 | |
| 302 | /*---------------------------------------------------------------------------- |
| 303 | | Log base e of x plus 1 |
| 304 | *----------------------------------------------------------------------------*/ |
| 305 | |
| 306 | floatx80 floatx80_lognp1(floatx80 a, float_status *status) |
| 307 | { |
| 308 | flag aSign; |
| 309 | int32_t aExp; |
| 310 | uint64_t aSig, fSig; |
| 311 | |
| 312 | int8_t user_rnd_mode, user_rnd_prec; |
| 313 | |
| 314 | int32_t compact, j, k; |
| 315 | floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu; |
| 316 | |
| 317 | aSig = extractFloatx80Frac(a); |
| 318 | aExp = extractFloatx80Exp(a); |
| 319 | aSign = extractFloatx80Sign(a); |
| 320 | |
| 321 | if (aExp == 0x7FFF) { |
| 322 | if ((uint64_t) (aSig << 1)) { |
| 323 | propagateFloatx80NaNOneArg(a, status); |
| 324 | } |
| 325 | if (aSign) { |
| 326 | float_raise(float_flag_invalid, status); |
| 327 | return floatx80_default_nan(status); |
| 328 | } |
| 329 | return packFloatx80(0, floatx80_infinity.high, floatx80_infinity.low); |
| 330 | } |
| 331 | |
| 332 | if (aExp == 0 && aSig == 0) { |
| 333 | return packFloatx80(aSign, 0, 0); |
| 334 | } |
| 335 | |
| 336 | if (aSign && aExp >= one_exp) { |
| 337 | if (aExp == one_exp && aSig == one_sig) { |
| 338 | float_raise(float_flag_divbyzero, status); |
Laurent Vivier | 981348a | 2018-04-30 19:01:55 +0200 | [diff] [blame] | 339 | return packFloatx80(aSign, floatx80_infinity.high, |
| 340 | floatx80_infinity.low); |
Laurent Vivier | 4b5c65b | 2018-03-05 21:39:04 +0100 | [diff] [blame] | 341 | } |
| 342 | float_raise(float_flag_invalid, status); |
| 343 | return floatx80_default_nan(status); |
| 344 | } |
| 345 | |
| 346 | if (aExp < 0x3f99 || (aExp == 0x3f99 && aSig == one_sig)) { |
| 347 | /* <= min threshold */ |
| 348 | float_raise(float_flag_inexact, status); |
| 349 | return floatx80_move(a, status); |
| 350 | } |
| 351 | |
| 352 | user_rnd_mode = status->float_rounding_mode; |
| 353 | user_rnd_prec = status->floatx80_rounding_precision; |
| 354 | status->float_rounding_mode = float_round_nearest_even; |
| 355 | status->floatx80_rounding_precision = 80; |
| 356 | |
| 357 | compact = floatx80_make_compact(aExp, aSig); |
| 358 | |
| 359 | fp0 = a; /* Z */ |
| 360 | fp1 = a; |
| 361 | |
| 362 | fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), |
| 363 | status), status); /* X = (1+Z) */ |
| 364 | |
| 365 | aExp = extractFloatx80Exp(fp0); |
| 366 | aSig = extractFloatx80Frac(fp0); |
| 367 | |
| 368 | compact = floatx80_make_compact(aExp, aSig); |
| 369 | |
| 370 | if (compact < 0x3FFE8000 || compact > 0x3FFFC000) { |
| 371 | /* |X| < 1/2 or |X| > 3/2 */ |
| 372 | k = aExp - 0x3FFF; |
| 373 | fp1 = int32_to_floatx80(k, status); |
| 374 | |
| 375 | fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000); |
| 376 | j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */ |
| 377 | |
| 378 | f = packFloatx80(0, 0x3FFF, fSig); /* F */ |
| 379 | fp0 = packFloatx80(0, 0x3FFF, aSig); /* Y */ |
| 380 | |
| 381 | fp0 = floatx80_sub(fp0, f, status); /* Y-F */ |
| 382 | |
| 383 | lp1cont1: |
| 384 | /* LP1CONT1 */ |
| 385 | fp0 = floatx80_mul(fp0, log_tbl[j], status); /* FP0 IS U = (Y-F)/F */ |
| 386 | logof2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); |
| 387 | klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */ |
| 388 | fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */ |
| 389 | |
| 390 | fp3 = fp2; |
| 391 | fp1 = fp2; |
| 392 | |
| 393 | fp1 = floatx80_mul(fp1, float64_to_floatx80( |
| 394 | make_float64(0x3FC2499AB5E4040B), status), |
| 395 | status); /* V*A6 */ |
| 396 | fp2 = floatx80_mul(fp2, float64_to_floatx80( |
| 397 | make_float64(0xBFC555B5848CB7DB), status), |
| 398 | status); /* V*A5 */ |
| 399 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 400 | make_float64(0x3FC99999987D8730), status), |
| 401 | status); /* A4+V*A6 */ |
| 402 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 403 | make_float64(0xBFCFFFFFFF6F7E97), status), |
| 404 | status); /* A3+V*A5 */ |
| 405 | fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */ |
| 406 | fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */ |
| 407 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 408 | make_float64(0x3FD55555555555A4), status), |
| 409 | status); /* A2+V*(A4+V*A6) */ |
| 410 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 411 | make_float64(0xBFE0000000000008), status), |
| 412 | status); /* A1+V*(A3+V*A5) */ |
| 413 | fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */ |
| 414 | fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */ |
| 415 | fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */ |
| 416 | fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */ |
| 417 | |
| 418 | fp1 = floatx80_add(fp1, log_tbl[j + 1], |
| 419 | status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */ |
| 420 | fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */ |
| 421 | |
| 422 | status->float_rounding_mode = user_rnd_mode; |
| 423 | status->floatx80_rounding_precision = user_rnd_prec; |
| 424 | |
| 425 | a = floatx80_add(fp0, klog2, status); |
| 426 | |
| 427 | float_raise(float_flag_inexact, status); |
| 428 | |
| 429 | return a; |
| 430 | } else if (compact < 0x3FFEF07D || compact > 0x3FFF8841) { |
| 431 | /* |X| < 1/16 or |X| > -1/16 */ |
| 432 | /* LP1CARE */ |
| 433 | fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000); |
| 434 | f = packFloatx80(0, 0x3FFF, fSig); /* F */ |
| 435 | j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */ |
| 436 | |
| 437 | if (compact >= 0x3FFF8000) { /* 1+Z >= 1 */ |
| 438 | /* KISZERO */ |
| 439 | fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x3F800000), |
| 440 | status), f, status); /* 1-F */ |
| 441 | fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (1-F)+Z */ |
| 442 | fp1 = packFloatx80(0, 0, 0); /* K = 0 */ |
| 443 | } else { |
| 444 | /* KISNEG */ |
| 445 | fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x40000000), |
| 446 | status), f, status); /* 2-F */ |
| 447 | fp1 = floatx80_add(fp1, fp1, status); /* 2Z */ |
| 448 | fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (2-F)+2Z */ |
| 449 | fp1 = packFloatx80(1, one_exp, one_sig); /* K = -1 */ |
| 450 | } |
| 451 | goto lp1cont1; |
| 452 | } else { |
| 453 | /* LP1ONE16 */ |
| 454 | fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2Z */ |
| 455 | fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), |
| 456 | status), status); /* FP0 IS 1+X */ |
| 457 | |
| 458 | /* LP1CONT2 */ |
| 459 | fp1 = floatx80_div(fp1, fp0, status); /* U */ |
| 460 | saveu = fp1; |
| 461 | fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */ |
| 462 | fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */ |
| 463 | |
| 464 | fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6), |
| 465 | status); /* B5 */ |
| 466 | fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0), |
| 467 | status); /* B4 */ |
| 468 | fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */ |
| 469 | fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */ |
| 470 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 471 | make_float64(0x3F624924928BCCFF), status), |
| 472 | status); /* B3+W*B5 */ |
| 473 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 474 | make_float64(0x3F899999999995EC), status), |
| 475 | status); /* B2+W*B4 */ |
| 476 | fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */ |
| 477 | fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */ |
| 478 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 479 | make_float64(0x3FB5555555555555), status), |
| 480 | status); /* B1+W*(B3+W*B5) */ |
| 481 | |
| 482 | fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */ |
| 483 | fp1 = floatx80_add(fp1, fp2, |
| 484 | status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */ |
| 485 | fp0 = floatx80_mul(fp0, fp1, |
| 486 | status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */ |
| 487 | |
| 488 | status->float_rounding_mode = user_rnd_mode; |
| 489 | status->floatx80_rounding_precision = user_rnd_prec; |
| 490 | |
| 491 | a = floatx80_add(fp0, saveu, status); |
| 492 | |
| 493 | /*if (!floatx80_is_zero(a)) { */ |
| 494 | float_raise(float_flag_inexact, status); |
| 495 | /*} */ |
| 496 | |
| 497 | return a; |
| 498 | } |
| 499 | } |
Laurent Vivier | 50067bd | 2018-03-05 21:39:05 +0100 | [diff] [blame] | 500 | |
| 501 | /*---------------------------------------------------------------------------- |
| 502 | | Log base e |
| 503 | *----------------------------------------------------------------------------*/ |
| 504 | |
| 505 | floatx80 floatx80_logn(floatx80 a, float_status *status) |
| 506 | { |
| 507 | flag aSign; |
| 508 | int32_t aExp; |
| 509 | uint64_t aSig, fSig; |
| 510 | |
| 511 | int8_t user_rnd_mode, user_rnd_prec; |
| 512 | |
| 513 | int32_t compact, j, k, adjk; |
| 514 | floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu; |
| 515 | |
| 516 | aSig = extractFloatx80Frac(a); |
| 517 | aExp = extractFloatx80Exp(a); |
| 518 | aSign = extractFloatx80Sign(a); |
| 519 | |
| 520 | if (aExp == 0x7FFF) { |
| 521 | if ((uint64_t) (aSig << 1)) { |
| 522 | propagateFloatx80NaNOneArg(a, status); |
| 523 | } |
| 524 | if (aSign == 0) { |
| 525 | return packFloatx80(0, floatx80_infinity.high, |
| 526 | floatx80_infinity.low); |
| 527 | } |
| 528 | } |
| 529 | |
| 530 | adjk = 0; |
| 531 | |
| 532 | if (aExp == 0) { |
| 533 | if (aSig == 0) { /* zero */ |
| 534 | float_raise(float_flag_divbyzero, status); |
| 535 | return packFloatx80(1, floatx80_infinity.high, |
| 536 | floatx80_infinity.low); |
| 537 | } |
| 538 | if ((aSig & one_sig) == 0) { /* denormal */ |
| 539 | normalizeFloatx80Subnormal(aSig, &aExp, &aSig); |
| 540 | adjk = -100; |
| 541 | aExp += 100; |
| 542 | a = packFloatx80(aSign, aExp, aSig); |
| 543 | } |
| 544 | } |
| 545 | |
| 546 | if (aSign) { |
| 547 | float_raise(float_flag_invalid, status); |
| 548 | return floatx80_default_nan(status); |
| 549 | } |
| 550 | |
| 551 | user_rnd_mode = status->float_rounding_mode; |
| 552 | user_rnd_prec = status->floatx80_rounding_precision; |
| 553 | status->float_rounding_mode = float_round_nearest_even; |
| 554 | status->floatx80_rounding_precision = 80; |
| 555 | |
| 556 | compact = floatx80_make_compact(aExp, aSig); |
| 557 | |
| 558 | if (compact < 0x3FFEF07D || compact > 0x3FFF8841) { |
| 559 | /* |X| < 15/16 or |X| > 17/16 */ |
| 560 | k = aExp - 0x3FFF; |
| 561 | k += adjk; |
| 562 | fp1 = int32_to_floatx80(k, status); |
| 563 | |
| 564 | fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000); |
| 565 | j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */ |
| 566 | |
| 567 | f = packFloatx80(0, 0x3FFF, fSig); /* F */ |
| 568 | fp0 = packFloatx80(0, 0x3FFF, aSig); /* Y */ |
| 569 | |
| 570 | fp0 = floatx80_sub(fp0, f, status); /* Y-F */ |
| 571 | |
| 572 | /* LP1CONT1 */ |
| 573 | fp0 = floatx80_mul(fp0, log_tbl[j], status); /* FP0 IS U = (Y-F)/F */ |
| 574 | logof2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); |
| 575 | klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */ |
| 576 | fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */ |
| 577 | |
| 578 | fp3 = fp2; |
| 579 | fp1 = fp2; |
| 580 | |
| 581 | fp1 = floatx80_mul(fp1, float64_to_floatx80( |
| 582 | make_float64(0x3FC2499AB5E4040B), status), |
| 583 | status); /* V*A6 */ |
| 584 | fp2 = floatx80_mul(fp2, float64_to_floatx80( |
| 585 | make_float64(0xBFC555B5848CB7DB), status), |
| 586 | status); /* V*A5 */ |
| 587 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 588 | make_float64(0x3FC99999987D8730), status), |
| 589 | status); /* A4+V*A6 */ |
| 590 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 591 | make_float64(0xBFCFFFFFFF6F7E97), status), |
| 592 | status); /* A3+V*A5 */ |
| 593 | fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */ |
| 594 | fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */ |
| 595 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 596 | make_float64(0x3FD55555555555A4), status), |
| 597 | status); /* A2+V*(A4+V*A6) */ |
| 598 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 599 | make_float64(0xBFE0000000000008), status), |
| 600 | status); /* A1+V*(A3+V*A5) */ |
| 601 | fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */ |
| 602 | fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */ |
| 603 | fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */ |
| 604 | fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */ |
| 605 | |
| 606 | fp1 = floatx80_add(fp1, log_tbl[j + 1], |
| 607 | status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */ |
| 608 | fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */ |
| 609 | |
| 610 | status->float_rounding_mode = user_rnd_mode; |
| 611 | status->floatx80_rounding_precision = user_rnd_prec; |
| 612 | |
| 613 | a = floatx80_add(fp0, klog2, status); |
| 614 | |
| 615 | float_raise(float_flag_inexact, status); |
| 616 | |
| 617 | return a; |
| 618 | } else { /* |X-1| >= 1/16 */ |
| 619 | fp0 = a; |
| 620 | fp1 = a; |
| 621 | fp1 = floatx80_sub(fp1, float32_to_floatx80(make_float32(0x3F800000), |
| 622 | status), status); /* FP1 IS X-1 */ |
| 623 | fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), |
| 624 | status), status); /* FP0 IS X+1 */ |
| 625 | fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2(X-1) */ |
| 626 | |
| 627 | /* LP1CONT2 */ |
| 628 | fp1 = floatx80_div(fp1, fp0, status); /* U */ |
| 629 | saveu = fp1; |
| 630 | fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */ |
| 631 | fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */ |
| 632 | |
| 633 | fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6), |
| 634 | status); /* B5 */ |
| 635 | fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0), |
| 636 | status); /* B4 */ |
| 637 | fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */ |
| 638 | fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */ |
| 639 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 640 | make_float64(0x3F624924928BCCFF), status), |
| 641 | status); /* B3+W*B5 */ |
| 642 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 643 | make_float64(0x3F899999999995EC), status), |
| 644 | status); /* B2+W*B4 */ |
| 645 | fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */ |
| 646 | fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */ |
| 647 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 648 | make_float64(0x3FB5555555555555), status), |
| 649 | status); /* B1+W*(B3+W*B5) */ |
| 650 | |
| 651 | fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */ |
| 652 | fp1 = floatx80_add(fp1, fp2, status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */ |
| 653 | fp0 = floatx80_mul(fp0, fp1, |
| 654 | status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */ |
| 655 | |
| 656 | status->float_rounding_mode = user_rnd_mode; |
| 657 | status->floatx80_rounding_precision = user_rnd_prec; |
| 658 | |
| 659 | a = floatx80_add(fp0, saveu, status); |
| 660 | |
| 661 | /*if (!floatx80_is_zero(a)) { */ |
| 662 | float_raise(float_flag_inexact, status); |
| 663 | /*} */ |
| 664 | |
| 665 | return a; |
| 666 | } |
| 667 | } |
Laurent Vivier | 248efb6 | 2018-03-05 21:39:06 +0100 | [diff] [blame] | 668 | |
| 669 | /*---------------------------------------------------------------------------- |
| 670 | | Log base 10 |
| 671 | *----------------------------------------------------------------------------*/ |
| 672 | |
| 673 | floatx80 floatx80_log10(floatx80 a, float_status *status) |
| 674 | { |
| 675 | flag aSign; |
| 676 | int32_t aExp; |
| 677 | uint64_t aSig; |
| 678 | |
| 679 | int8_t user_rnd_mode, user_rnd_prec; |
| 680 | |
| 681 | floatx80 fp0, fp1; |
| 682 | |
| 683 | aSig = extractFloatx80Frac(a); |
| 684 | aExp = extractFloatx80Exp(a); |
| 685 | aSign = extractFloatx80Sign(a); |
| 686 | |
| 687 | if (aExp == 0x7FFF) { |
| 688 | if ((uint64_t) (aSig << 1)) { |
| 689 | propagateFloatx80NaNOneArg(a, status); |
| 690 | } |
| 691 | if (aSign == 0) { |
| 692 | return packFloatx80(0, floatx80_infinity.high, |
| 693 | floatx80_infinity.low); |
| 694 | } |
| 695 | } |
| 696 | |
| 697 | if (aExp == 0 && aSig == 0) { |
| 698 | float_raise(float_flag_divbyzero, status); |
| 699 | return packFloatx80(1, floatx80_infinity.high, |
| 700 | floatx80_infinity.low); |
| 701 | } |
| 702 | |
| 703 | if (aSign) { |
| 704 | float_raise(float_flag_invalid, status); |
| 705 | return floatx80_default_nan(status); |
| 706 | } |
| 707 | |
| 708 | user_rnd_mode = status->float_rounding_mode; |
| 709 | user_rnd_prec = status->floatx80_rounding_precision; |
| 710 | status->float_rounding_mode = float_round_nearest_even; |
| 711 | status->floatx80_rounding_precision = 80; |
| 712 | |
| 713 | fp0 = floatx80_logn(a, status); |
| 714 | fp1 = packFloatx80(0, 0x3FFD, LIT64(0xDE5BD8A937287195)); /* INV_L10 */ |
| 715 | |
| 716 | status->float_rounding_mode = user_rnd_mode; |
| 717 | status->floatx80_rounding_precision = user_rnd_prec; |
| 718 | |
| 719 | a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L10 */ |
| 720 | |
| 721 | float_raise(float_flag_inexact, status); |
| 722 | |
| 723 | return a; |
| 724 | } |
Laurent Vivier | 67b453e | 2018-03-05 21:39:07 +0100 | [diff] [blame] | 725 | |
| 726 | /*---------------------------------------------------------------------------- |
| 727 | | Log base 2 |
| 728 | *----------------------------------------------------------------------------*/ |
| 729 | |
| 730 | floatx80 floatx80_log2(floatx80 a, float_status *status) |
| 731 | { |
| 732 | flag aSign; |
| 733 | int32_t aExp; |
| 734 | uint64_t aSig; |
| 735 | |
| 736 | int8_t user_rnd_mode, user_rnd_prec; |
| 737 | |
| 738 | floatx80 fp0, fp1; |
| 739 | |
| 740 | aSig = extractFloatx80Frac(a); |
| 741 | aExp = extractFloatx80Exp(a); |
| 742 | aSign = extractFloatx80Sign(a); |
| 743 | |
| 744 | if (aExp == 0x7FFF) { |
| 745 | if ((uint64_t) (aSig << 1)) { |
| 746 | propagateFloatx80NaNOneArg(a, status); |
| 747 | } |
| 748 | if (aSign == 0) { |
| 749 | return packFloatx80(0, floatx80_infinity.high, |
| 750 | floatx80_infinity.low); |
| 751 | } |
| 752 | } |
| 753 | |
| 754 | if (aExp == 0) { |
| 755 | if (aSig == 0) { |
| 756 | float_raise(float_flag_divbyzero, status); |
| 757 | return packFloatx80(1, floatx80_infinity.high, |
| 758 | floatx80_infinity.low); |
| 759 | } |
| 760 | normalizeFloatx80Subnormal(aSig, &aExp, &aSig); |
| 761 | } |
| 762 | |
| 763 | if (aSign) { |
| 764 | float_raise(float_flag_invalid, status); |
| 765 | return floatx80_default_nan(status); |
| 766 | } |
| 767 | |
| 768 | user_rnd_mode = status->float_rounding_mode; |
| 769 | user_rnd_prec = status->floatx80_rounding_precision; |
| 770 | status->float_rounding_mode = float_round_nearest_even; |
| 771 | status->floatx80_rounding_precision = 80; |
| 772 | |
| 773 | if (aSig == one_sig) { /* X is 2^k */ |
| 774 | status->float_rounding_mode = user_rnd_mode; |
| 775 | status->floatx80_rounding_precision = user_rnd_prec; |
| 776 | |
| 777 | a = int32_to_floatx80(aExp - 0x3FFF, status); |
| 778 | } else { |
| 779 | fp0 = floatx80_logn(a, status); |
| 780 | fp1 = packFloatx80(0, 0x3FFF, LIT64(0xB8AA3B295C17F0BC)); /* INV_L2 */ |
| 781 | |
| 782 | status->float_rounding_mode = user_rnd_mode; |
| 783 | status->floatx80_rounding_precision = user_rnd_prec; |
| 784 | |
| 785 | a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L2 */ |
| 786 | } |
| 787 | |
| 788 | float_raise(float_flag_inexact, status); |
| 789 | |
| 790 | return a; |
| 791 | } |
Laurent Vivier | 40ad087 | 2018-03-05 21:39:08 +0100 | [diff] [blame] | 792 | |
| 793 | /*---------------------------------------------------------------------------- |
| 794 | | e to x |
| 795 | *----------------------------------------------------------------------------*/ |
| 796 | |
| 797 | floatx80 floatx80_etox(floatx80 a, float_status *status) |
| 798 | { |
| 799 | flag aSign; |
| 800 | int32_t aExp; |
| 801 | uint64_t aSig; |
| 802 | |
| 803 | int8_t user_rnd_mode, user_rnd_prec; |
| 804 | |
| 805 | int32_t compact, n, j, k, m, m1; |
| 806 | floatx80 fp0, fp1, fp2, fp3, l2, scale, adjscale; |
| 807 | flag adjflag; |
| 808 | |
| 809 | aSig = extractFloatx80Frac(a); |
| 810 | aExp = extractFloatx80Exp(a); |
| 811 | aSign = extractFloatx80Sign(a); |
| 812 | |
| 813 | if (aExp == 0x7FFF) { |
| 814 | if ((uint64_t) (aSig << 1)) { |
| 815 | return propagateFloatx80NaNOneArg(a, status); |
| 816 | } |
| 817 | if (aSign) { |
| 818 | return packFloatx80(0, 0, 0); |
| 819 | } |
| 820 | return packFloatx80(0, floatx80_infinity.high, |
| 821 | floatx80_infinity.low); |
| 822 | } |
| 823 | |
| 824 | if (aExp == 0 && aSig == 0) { |
| 825 | return packFloatx80(0, one_exp, one_sig); |
| 826 | } |
| 827 | |
| 828 | user_rnd_mode = status->float_rounding_mode; |
| 829 | user_rnd_prec = status->floatx80_rounding_precision; |
| 830 | status->float_rounding_mode = float_round_nearest_even; |
| 831 | status->floatx80_rounding_precision = 80; |
| 832 | |
| 833 | adjflag = 0; |
| 834 | |
| 835 | if (aExp >= 0x3FBE) { /* |X| >= 2^(-65) */ |
| 836 | compact = floatx80_make_compact(aExp, aSig); |
| 837 | |
| 838 | if (compact < 0x400CB167) { /* |X| < 16380 log2 */ |
| 839 | fp0 = a; |
| 840 | fp1 = a; |
| 841 | fp0 = floatx80_mul(fp0, float32_to_floatx80( |
| 842 | make_float32(0x42B8AA3B), status), |
| 843 | status); /* 64/log2 * X */ |
| 844 | adjflag = 0; |
| 845 | n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */ |
| 846 | fp0 = int32_to_floatx80(n, status); |
| 847 | |
| 848 | j = n & 0x3F; /* J = N mod 64 */ |
| 849 | m = n / 64; /* NOTE: this is really arithmetic right shift by 6 */ |
| 850 | if (n < 0 && j) { |
| 851 | /* arithmetic right shift is division and |
| 852 | * round towards minus infinity |
| 853 | */ |
| 854 | m--; |
| 855 | } |
| 856 | m += 0x3FFF; /* biased exponent of 2^(M) */ |
| 857 | |
| 858 | expcont1: |
| 859 | fp2 = fp0; /* N */ |
| 860 | fp0 = floatx80_mul(fp0, float32_to_floatx80( |
| 861 | make_float32(0xBC317218), status), |
| 862 | status); /* N * L1, L1 = lead(-log2/64) */ |
| 863 | l2 = packFloatx80(0, 0x3FDC, LIT64(0x82E308654361C4C6)); |
| 864 | fp2 = floatx80_mul(fp2, l2, status); /* N * L2, L1+L2 = -log2/64 */ |
| 865 | fp0 = floatx80_add(fp0, fp1, status); /* X + N*L1 */ |
| 866 | fp0 = floatx80_add(fp0, fp2, status); /* R */ |
| 867 | |
| 868 | fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ |
| 869 | fp2 = float32_to_floatx80(make_float32(0x3AB60B70), |
| 870 | status); /* A5 */ |
| 871 | fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*A5 */ |
| 872 | fp3 = floatx80_mul(float32_to_floatx80(make_float32(0x3C088895), |
| 873 | status), fp1, |
| 874 | status); /* fp3 is S*A4 */ |
| 875 | fp2 = floatx80_add(fp2, float64_to_floatx80(make_float64( |
| 876 | 0x3FA5555555554431), status), |
| 877 | status); /* fp2 is A3+S*A5 */ |
| 878 | fp3 = floatx80_add(fp3, float64_to_floatx80(make_float64( |
| 879 | 0x3FC5555555554018), status), |
| 880 | status); /* fp3 is A2+S*A4 */ |
| 881 | fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*(A3+S*A5) */ |
| 882 | fp3 = floatx80_mul(fp3, fp1, status); /* fp3 is S*(A2+S*A4) */ |
| 883 | fp2 = floatx80_add(fp2, float32_to_floatx80( |
| 884 | make_float32(0x3F000000), status), |
| 885 | status); /* fp2 is A1+S*(A3+S*A5) */ |
| 886 | fp3 = floatx80_mul(fp3, fp0, status); /* fp3 IS R*S*(A2+S*A4) */ |
| 887 | fp2 = floatx80_mul(fp2, fp1, |
| 888 | status); /* fp2 IS S*(A1+S*(A3+S*A5)) */ |
| 889 | fp0 = floatx80_add(fp0, fp3, status); /* fp0 IS R+R*S*(A2+S*A4) */ |
| 890 | fp0 = floatx80_add(fp0, fp2, status); /* fp0 IS EXP(R) - 1 */ |
| 891 | |
| 892 | fp1 = exp_tbl[j]; |
| 893 | fp0 = floatx80_mul(fp0, fp1, status); /* 2^(J/64)*(Exp(R)-1) */ |
| 894 | fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status), |
| 895 | status); /* accurate 2^(J/64) */ |
| 896 | fp0 = floatx80_add(fp0, fp1, |
| 897 | status); /* 2^(J/64) + 2^(J/64)*(Exp(R)-1) */ |
| 898 | |
| 899 | scale = packFloatx80(0, m, one_sig); |
| 900 | if (adjflag) { |
| 901 | adjscale = packFloatx80(0, m1, one_sig); |
| 902 | fp0 = floatx80_mul(fp0, adjscale, status); |
| 903 | } |
| 904 | |
| 905 | status->float_rounding_mode = user_rnd_mode; |
| 906 | status->floatx80_rounding_precision = user_rnd_prec; |
| 907 | |
| 908 | a = floatx80_mul(fp0, scale, status); |
| 909 | |
| 910 | float_raise(float_flag_inexact, status); |
| 911 | |
| 912 | return a; |
| 913 | } else { /* |X| >= 16380 log2 */ |
| 914 | if (compact > 0x400CB27C) { /* |X| >= 16480 log2 */ |
| 915 | status->float_rounding_mode = user_rnd_mode; |
| 916 | status->floatx80_rounding_precision = user_rnd_prec; |
| 917 | if (aSign) { |
| 918 | a = roundAndPackFloatx80( |
| 919 | status->floatx80_rounding_precision, |
| 920 | 0, -0x1000, aSig, 0, status); |
| 921 | } else { |
| 922 | a = roundAndPackFloatx80( |
| 923 | status->floatx80_rounding_precision, |
| 924 | 0, 0x8000, aSig, 0, status); |
| 925 | } |
| 926 | float_raise(float_flag_inexact, status); |
| 927 | |
| 928 | return a; |
| 929 | } else { |
| 930 | fp0 = a; |
| 931 | fp1 = a; |
| 932 | fp0 = floatx80_mul(fp0, float32_to_floatx80( |
| 933 | make_float32(0x42B8AA3B), status), |
| 934 | status); /* 64/log2 * X */ |
| 935 | adjflag = 1; |
| 936 | n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */ |
| 937 | fp0 = int32_to_floatx80(n, status); |
| 938 | |
| 939 | j = n & 0x3F; /* J = N mod 64 */ |
| 940 | /* NOTE: this is really arithmetic right shift by 6 */ |
| 941 | k = n / 64; |
| 942 | if (n < 0 && j) { |
| 943 | /* arithmetic right shift is division and |
| 944 | * round towards minus infinity |
| 945 | */ |
| 946 | k--; |
| 947 | } |
| 948 | /* NOTE: this is really arithmetic right shift by 1 */ |
| 949 | m1 = k / 2; |
| 950 | if (k < 0 && (k & 1)) { |
| 951 | /* arithmetic right shift is division and |
| 952 | * round towards minus infinity |
| 953 | */ |
| 954 | m1--; |
| 955 | } |
| 956 | m = k - m1; |
| 957 | m1 += 0x3FFF; /* biased exponent of 2^(M1) */ |
| 958 | m += 0x3FFF; /* biased exponent of 2^(M) */ |
| 959 | |
| 960 | goto expcont1; |
| 961 | } |
| 962 | } |
| 963 | } else { /* |X| < 2^(-65) */ |
| 964 | status->float_rounding_mode = user_rnd_mode; |
| 965 | status->floatx80_rounding_precision = user_rnd_prec; |
| 966 | |
| 967 | a = floatx80_add(a, float32_to_floatx80(make_float32(0x3F800000), |
| 968 | status), status); /* 1 + X */ |
| 969 | |
| 970 | float_raise(float_flag_inexact, status); |
| 971 | |
| 972 | return a; |
| 973 | } |
| 974 | } |
Laurent Vivier | 068f161 | 2018-03-05 21:39:09 +0100 | [diff] [blame] | 975 | |
| 976 | /*---------------------------------------------------------------------------- |
| 977 | | 2 to x |
| 978 | *----------------------------------------------------------------------------*/ |
| 979 | |
| 980 | floatx80 floatx80_twotox(floatx80 a, float_status *status) |
| 981 | { |
| 982 | flag aSign; |
| 983 | int32_t aExp; |
| 984 | uint64_t aSig; |
| 985 | |
| 986 | int8_t user_rnd_mode, user_rnd_prec; |
| 987 | |
| 988 | int32_t compact, n, j, l, m, m1; |
| 989 | floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2; |
| 990 | |
| 991 | aSig = extractFloatx80Frac(a); |
| 992 | aExp = extractFloatx80Exp(a); |
| 993 | aSign = extractFloatx80Sign(a); |
| 994 | |
| 995 | if (aExp == 0x7FFF) { |
| 996 | if ((uint64_t) (aSig << 1)) { |
| 997 | return propagateFloatx80NaNOneArg(a, status); |
| 998 | } |
| 999 | if (aSign) { |
| 1000 | return packFloatx80(0, 0, 0); |
| 1001 | } |
| 1002 | return packFloatx80(0, floatx80_infinity.high, |
| 1003 | floatx80_infinity.low); |
| 1004 | } |
| 1005 | |
| 1006 | if (aExp == 0 && aSig == 0) { |
| 1007 | return packFloatx80(0, one_exp, one_sig); |
| 1008 | } |
| 1009 | |
| 1010 | user_rnd_mode = status->float_rounding_mode; |
| 1011 | user_rnd_prec = status->floatx80_rounding_precision; |
| 1012 | status->float_rounding_mode = float_round_nearest_even; |
| 1013 | status->floatx80_rounding_precision = 80; |
| 1014 | |
| 1015 | fp0 = a; |
| 1016 | |
| 1017 | compact = floatx80_make_compact(aExp, aSig); |
| 1018 | |
| 1019 | if (compact < 0x3FB98000 || compact > 0x400D80C0) { |
| 1020 | /* |X| > 16480 or |X| < 2^(-70) */ |
| 1021 | if (compact > 0x3FFF8000) { /* |X| > 16480 */ |
| 1022 | status->float_rounding_mode = user_rnd_mode; |
| 1023 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1024 | |
| 1025 | if (aSign) { |
| 1026 | return roundAndPackFloatx80(status->floatx80_rounding_precision, |
| 1027 | 0, -0x1000, aSig, 0, status); |
| 1028 | } else { |
| 1029 | return roundAndPackFloatx80(status->floatx80_rounding_precision, |
| 1030 | 0, 0x8000, aSig, 0, status); |
| 1031 | } |
| 1032 | } else { /* |X| < 2^(-70) */ |
| 1033 | status->float_rounding_mode = user_rnd_mode; |
| 1034 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1035 | |
| 1036 | a = floatx80_add(fp0, float32_to_floatx80( |
| 1037 | make_float32(0x3F800000), status), |
| 1038 | status); /* 1 + X */ |
| 1039 | |
| 1040 | float_raise(float_flag_inexact, status); |
| 1041 | |
| 1042 | return a; |
| 1043 | } |
| 1044 | } else { /* 2^(-70) <= |X| <= 16480 */ |
| 1045 | fp1 = fp0; /* X */ |
| 1046 | fp1 = floatx80_mul(fp1, float32_to_floatx80( |
| 1047 | make_float32(0x42800000), status), |
| 1048 | status); /* X * 64 */ |
| 1049 | n = floatx80_to_int32(fp1, status); |
| 1050 | fp1 = int32_to_floatx80(n, status); |
| 1051 | j = n & 0x3F; |
| 1052 | l = n / 64; /* NOTE: this is really arithmetic right shift by 6 */ |
| 1053 | if (n < 0 && j) { |
| 1054 | /* arithmetic right shift is division and |
| 1055 | * round towards minus infinity |
| 1056 | */ |
| 1057 | l--; |
| 1058 | } |
| 1059 | m = l / 2; /* NOTE: this is really arithmetic right shift by 1 */ |
| 1060 | if (l < 0 && (l & 1)) { |
| 1061 | /* arithmetic right shift is division and |
| 1062 | * round towards minus infinity |
| 1063 | */ |
| 1064 | m--; |
| 1065 | } |
| 1066 | m1 = l - m; |
| 1067 | m1 += 0x3FFF; /* ADJFACT IS 2^(M') */ |
| 1068 | |
| 1069 | adjfact = packFloatx80(0, m1, one_sig); |
| 1070 | fact1 = exp2_tbl[j]; |
| 1071 | fact1.high += m; |
| 1072 | fact2.high = exp2_tbl2[j] >> 16; |
| 1073 | fact2.high += m; |
| 1074 | fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF); |
| 1075 | fact2.low <<= 48; |
| 1076 | |
| 1077 | fp1 = floatx80_mul(fp1, float32_to_floatx80( |
| 1078 | make_float32(0x3C800000), status), |
| 1079 | status); /* (1/64)*N */ |
| 1080 | fp0 = floatx80_sub(fp0, fp1, status); /* X - (1/64)*INT(64 X) */ |
| 1081 | fp2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); /* LOG2 */ |
| 1082 | fp0 = floatx80_mul(fp0, fp2, status); /* R */ |
| 1083 | |
| 1084 | /* EXPR */ |
| 1085 | fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ |
| 1086 | fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2), |
| 1087 | status); /* A5 */ |
| 1088 | fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C), |
| 1089 | status); /* A4 */ |
| 1090 | fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */ |
| 1091 | fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */ |
| 1092 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 1093 | make_float64(0x3FA5555555554CC1), status), |
| 1094 | status); /* A3+S*A5 */ |
| 1095 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 1096 | make_float64(0x3FC5555555554A54), status), |
| 1097 | status); /* A2+S*A4 */ |
| 1098 | fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */ |
| 1099 | fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */ |
| 1100 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 1101 | make_float64(0x3FE0000000000000), status), |
| 1102 | status); /* A1+S*(A3+S*A5) */ |
| 1103 | fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */ |
| 1104 | |
| 1105 | fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */ |
| 1106 | fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */ |
| 1107 | fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */ |
| 1108 | |
| 1109 | fp0 = floatx80_mul(fp0, fact1, status); |
| 1110 | fp0 = floatx80_add(fp0, fact2, status); |
| 1111 | fp0 = floatx80_add(fp0, fact1, status); |
| 1112 | |
| 1113 | status->float_rounding_mode = user_rnd_mode; |
| 1114 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1115 | |
| 1116 | a = floatx80_mul(fp0, adjfact, status); |
| 1117 | |
| 1118 | float_raise(float_flag_inexact, status); |
| 1119 | |
| 1120 | return a; |
| 1121 | } |
| 1122 | } |
Laurent Vivier | 6c25be6 | 2018-03-05 21:39:10 +0100 | [diff] [blame] | 1123 | |
| 1124 | /*---------------------------------------------------------------------------- |
| 1125 | | 10 to x |
| 1126 | *----------------------------------------------------------------------------*/ |
| 1127 | |
| 1128 | floatx80 floatx80_tentox(floatx80 a, float_status *status) |
| 1129 | { |
| 1130 | flag aSign; |
| 1131 | int32_t aExp; |
| 1132 | uint64_t aSig; |
| 1133 | |
| 1134 | int8_t user_rnd_mode, user_rnd_prec; |
| 1135 | |
| 1136 | int32_t compact, n, j, l, m, m1; |
| 1137 | floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2; |
| 1138 | |
| 1139 | aSig = extractFloatx80Frac(a); |
| 1140 | aExp = extractFloatx80Exp(a); |
| 1141 | aSign = extractFloatx80Sign(a); |
| 1142 | |
| 1143 | if (aExp == 0x7FFF) { |
| 1144 | if ((uint64_t) (aSig << 1)) { |
| 1145 | return propagateFloatx80NaNOneArg(a, status); |
| 1146 | } |
| 1147 | if (aSign) { |
| 1148 | return packFloatx80(0, 0, 0); |
| 1149 | } |
| 1150 | return packFloatx80(0, floatx80_infinity.high, |
| 1151 | floatx80_infinity.low); |
| 1152 | } |
| 1153 | |
| 1154 | if (aExp == 0 && aSig == 0) { |
| 1155 | return packFloatx80(0, one_exp, one_sig); |
| 1156 | } |
| 1157 | |
| 1158 | user_rnd_mode = status->float_rounding_mode; |
| 1159 | user_rnd_prec = status->floatx80_rounding_precision; |
| 1160 | status->float_rounding_mode = float_round_nearest_even; |
| 1161 | status->floatx80_rounding_precision = 80; |
| 1162 | |
| 1163 | fp0 = a; |
| 1164 | |
| 1165 | compact = floatx80_make_compact(aExp, aSig); |
| 1166 | |
| 1167 | if (compact < 0x3FB98000 || compact > 0x400B9B07) { |
| 1168 | /* |X| > 16480 LOG2/LOG10 or |X| < 2^(-70) */ |
| 1169 | if (compact > 0x3FFF8000) { /* |X| > 16480 */ |
| 1170 | status->float_rounding_mode = user_rnd_mode; |
| 1171 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1172 | |
| 1173 | if (aSign) { |
| 1174 | return roundAndPackFloatx80(status->floatx80_rounding_precision, |
| 1175 | 0, -0x1000, aSig, 0, status); |
| 1176 | } else { |
| 1177 | return roundAndPackFloatx80(status->floatx80_rounding_precision, |
| 1178 | 0, 0x8000, aSig, 0, status); |
| 1179 | } |
| 1180 | } else { /* |X| < 2^(-70) */ |
| 1181 | status->float_rounding_mode = user_rnd_mode; |
| 1182 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1183 | |
| 1184 | a = floatx80_add(fp0, float32_to_floatx80( |
| 1185 | make_float32(0x3F800000), status), |
| 1186 | status); /* 1 + X */ |
| 1187 | |
| 1188 | float_raise(float_flag_inexact, status); |
| 1189 | |
| 1190 | return a; |
| 1191 | } |
| 1192 | } else { /* 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10 */ |
| 1193 | fp1 = fp0; /* X */ |
| 1194 | fp1 = floatx80_mul(fp1, float64_to_floatx80( |
| 1195 | make_float64(0x406A934F0979A371), |
| 1196 | status), status); /* X*64*LOG10/LOG2 */ |
| 1197 | n = floatx80_to_int32(fp1, status); /* N=INT(X*64*LOG10/LOG2) */ |
| 1198 | fp1 = int32_to_floatx80(n, status); |
| 1199 | |
| 1200 | j = n & 0x3F; |
| 1201 | l = n / 64; /* NOTE: this is really arithmetic right shift by 6 */ |
| 1202 | if (n < 0 && j) { |
| 1203 | /* arithmetic right shift is division and |
| 1204 | * round towards minus infinity |
| 1205 | */ |
| 1206 | l--; |
| 1207 | } |
| 1208 | m = l / 2; /* NOTE: this is really arithmetic right shift by 1 */ |
| 1209 | if (l < 0 && (l & 1)) { |
| 1210 | /* arithmetic right shift is division and |
| 1211 | * round towards minus infinity |
| 1212 | */ |
| 1213 | m--; |
| 1214 | } |
| 1215 | m1 = l - m; |
| 1216 | m1 += 0x3FFF; /* ADJFACT IS 2^(M') */ |
| 1217 | |
| 1218 | adjfact = packFloatx80(0, m1, one_sig); |
| 1219 | fact1 = exp2_tbl[j]; |
| 1220 | fact1.high += m; |
| 1221 | fact2.high = exp2_tbl2[j] >> 16; |
| 1222 | fact2.high += m; |
| 1223 | fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF); |
| 1224 | fact2.low <<= 48; |
| 1225 | |
| 1226 | fp2 = fp1; /* N */ |
| 1227 | fp1 = floatx80_mul(fp1, float64_to_floatx80( |
| 1228 | make_float64(0x3F734413509F8000), status), |
| 1229 | status); /* N*(LOG2/64LOG10)_LEAD */ |
| 1230 | fp3 = packFloatx80(1, 0x3FCD, LIT64(0xC0219DC1DA994FD2)); |
| 1231 | fp2 = floatx80_mul(fp2, fp3, status); /* N*(LOG2/64LOG10)_TRAIL */ |
| 1232 | fp0 = floatx80_sub(fp0, fp1, status); /* X - N L_LEAD */ |
| 1233 | fp0 = floatx80_sub(fp0, fp2, status); /* X - N L_TRAIL */ |
| 1234 | fp2 = packFloatx80(0, 0x4000, LIT64(0x935D8DDDAAA8AC17)); /* LOG10 */ |
| 1235 | fp0 = floatx80_mul(fp0, fp2, status); /* R */ |
| 1236 | |
| 1237 | /* EXPR */ |
| 1238 | fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ |
| 1239 | fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2), |
| 1240 | status); /* A5 */ |
| 1241 | fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C), |
| 1242 | status); /* A4 */ |
| 1243 | fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */ |
| 1244 | fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */ |
| 1245 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 1246 | make_float64(0x3FA5555555554CC1), status), |
| 1247 | status); /* A3+S*A5 */ |
| 1248 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 1249 | make_float64(0x3FC5555555554A54), status), |
| 1250 | status); /* A2+S*A4 */ |
| 1251 | fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */ |
| 1252 | fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */ |
| 1253 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 1254 | make_float64(0x3FE0000000000000), status), |
| 1255 | status); /* A1+S*(A3+S*A5) */ |
| 1256 | fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */ |
| 1257 | |
| 1258 | fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */ |
| 1259 | fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */ |
| 1260 | fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */ |
| 1261 | |
| 1262 | fp0 = floatx80_mul(fp0, fact1, status); |
| 1263 | fp0 = floatx80_add(fp0, fact2, status); |
| 1264 | fp0 = floatx80_add(fp0, fact1, status); |
| 1265 | |
| 1266 | status->float_rounding_mode = user_rnd_mode; |
| 1267 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1268 | |
| 1269 | a = floatx80_mul(fp0, adjfact, status); |
| 1270 | |
| 1271 | float_raise(float_flag_inexact, status); |
| 1272 | |
| 1273 | return a; |
| 1274 | } |
| 1275 | } |
Laurent Vivier | 2734018 | 2018-03-12 21:27:18 +0100 | [diff] [blame] | 1276 | |
| 1277 | /*---------------------------------------------------------------------------- |
| 1278 | | Tangent |
| 1279 | *----------------------------------------------------------------------------*/ |
| 1280 | |
| 1281 | floatx80 floatx80_tan(floatx80 a, float_status *status) |
| 1282 | { |
| 1283 | flag aSign, xSign; |
| 1284 | int32_t aExp, xExp; |
| 1285 | uint64_t aSig, xSig; |
| 1286 | |
| 1287 | int8_t user_rnd_mode, user_rnd_prec; |
| 1288 | |
| 1289 | int32_t compact, l, n, j; |
| 1290 | floatx80 fp0, fp1, fp2, fp3, fp4, fp5, invtwopi, twopi1, twopi2; |
| 1291 | float32 twoto63; |
| 1292 | flag endflag; |
| 1293 | |
| 1294 | aSig = extractFloatx80Frac(a); |
| 1295 | aExp = extractFloatx80Exp(a); |
| 1296 | aSign = extractFloatx80Sign(a); |
| 1297 | |
| 1298 | if (aExp == 0x7FFF) { |
| 1299 | if ((uint64_t) (aSig << 1)) { |
| 1300 | return propagateFloatx80NaNOneArg(a, status); |
| 1301 | } |
| 1302 | float_raise(float_flag_invalid, status); |
| 1303 | return floatx80_default_nan(status); |
| 1304 | } |
| 1305 | |
| 1306 | if (aExp == 0 && aSig == 0) { |
| 1307 | return packFloatx80(aSign, 0, 0); |
| 1308 | } |
| 1309 | |
| 1310 | user_rnd_mode = status->float_rounding_mode; |
| 1311 | user_rnd_prec = status->floatx80_rounding_precision; |
| 1312 | status->float_rounding_mode = float_round_nearest_even; |
| 1313 | status->floatx80_rounding_precision = 80; |
| 1314 | |
| 1315 | compact = floatx80_make_compact(aExp, aSig); |
| 1316 | |
| 1317 | fp0 = a; |
| 1318 | |
| 1319 | if (compact < 0x3FD78000 || compact > 0x4004BC7E) { |
| 1320 | /* 2^(-40) > |X| > 15 PI */ |
| 1321 | if (compact > 0x3FFF8000) { /* |X| >= 15 PI */ |
| 1322 | /* REDUCEX */ |
| 1323 | fp1 = packFloatx80(0, 0, 0); |
| 1324 | if (compact == 0x7FFEFFFF) { |
| 1325 | twopi1 = packFloatx80(aSign ^ 1, 0x7FFE, |
| 1326 | LIT64(0xC90FDAA200000000)); |
| 1327 | twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, |
| 1328 | LIT64(0x85A308D300000000)); |
| 1329 | fp0 = floatx80_add(fp0, twopi1, status); |
| 1330 | fp1 = fp0; |
| 1331 | fp0 = floatx80_add(fp0, twopi2, status); |
| 1332 | fp1 = floatx80_sub(fp1, fp0, status); |
| 1333 | fp1 = floatx80_add(fp1, twopi2, status); |
| 1334 | } |
| 1335 | loop: |
| 1336 | xSign = extractFloatx80Sign(fp0); |
| 1337 | xExp = extractFloatx80Exp(fp0); |
| 1338 | xExp -= 0x3FFF; |
| 1339 | if (xExp <= 28) { |
| 1340 | l = 0; |
| 1341 | endflag = 1; |
| 1342 | } else { |
| 1343 | l = xExp - 27; |
| 1344 | endflag = 0; |
| 1345 | } |
| 1346 | invtwopi = packFloatx80(0, 0x3FFE - l, |
| 1347 | LIT64(0xA2F9836E4E44152A)); /* INVTWOPI */ |
| 1348 | twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000)); |
| 1349 | twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(0x85A308D300000000)); |
| 1350 | |
| 1351 | /* SIGN(INARG)*2^63 IN SGL */ |
| 1352 | twoto63 = packFloat32(xSign, 0xBE, 0); |
| 1353 | |
| 1354 | fp2 = floatx80_mul(fp0, invtwopi, status); |
| 1355 | fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), |
| 1356 | status); /* THE FRACT PART OF FP2 IS ROUNDED */ |
| 1357 | fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status), |
| 1358 | status); /* FP2 is N */ |
| 1359 | fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */ |
| 1360 | fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */ |
| 1361 | fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */ |
| 1362 | fp4 = floatx80_sub(fp4, fp3, status); /* W-P */ |
| 1363 | fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */ |
| 1364 | fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */ |
| 1365 | fp3 = fp0; /* FP3 is A */ |
| 1366 | fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */ |
| 1367 | fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */ |
| 1368 | |
| 1369 | if (endflag > 0) { |
| 1370 | n = floatx80_to_int32(fp2, status); |
| 1371 | goto tancont; |
| 1372 | } |
| 1373 | fp3 = floatx80_sub(fp3, fp0, status); /* A-R */ |
| 1374 | fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */ |
| 1375 | goto loop; |
| 1376 | } else { |
| 1377 | status->float_rounding_mode = user_rnd_mode; |
| 1378 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1379 | |
| 1380 | a = floatx80_move(a, status); |
| 1381 | |
| 1382 | float_raise(float_flag_inexact, status); |
| 1383 | |
| 1384 | return a; |
| 1385 | } |
| 1386 | } else { |
| 1387 | fp1 = floatx80_mul(fp0, float64_to_floatx80( |
| 1388 | make_float64(0x3FE45F306DC9C883), status), |
| 1389 | status); /* X*2/PI */ |
| 1390 | |
| 1391 | n = floatx80_to_int32(fp1, status); |
| 1392 | j = 32 + n; |
| 1393 | |
| 1394 | fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */ |
| 1395 | fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status), |
| 1396 | status); /* FP0 IS R = (X-Y1)-Y2 */ |
| 1397 | |
| 1398 | tancont: |
| 1399 | if (n & 1) { |
| 1400 | /* NODD */ |
| 1401 | fp1 = fp0; /* R */ |
| 1402 | fp0 = floatx80_mul(fp0, fp0, status); /* S = R*R */ |
| 1403 | fp3 = float64_to_floatx80(make_float64(0x3EA0B759F50F8688), |
| 1404 | status); /* Q4 */ |
| 1405 | fp2 = float64_to_floatx80(make_float64(0xBEF2BAA5A8924F04), |
| 1406 | status); /* P3 */ |
| 1407 | fp3 = floatx80_mul(fp3, fp0, status); /* SQ4 */ |
| 1408 | fp2 = floatx80_mul(fp2, fp0, status); /* SP3 */ |
| 1409 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 1410 | make_float64(0xBF346F59B39BA65F), status), |
| 1411 | status); /* Q3+SQ4 */ |
| 1412 | fp4 = packFloatx80(0, 0x3FF6, LIT64(0xE073D3FC199C4A00)); |
| 1413 | fp2 = floatx80_add(fp2, fp4, status); /* P2+SP3 */ |
| 1414 | fp3 = floatx80_mul(fp3, fp0, status); /* S(Q3+SQ4) */ |
| 1415 | fp2 = floatx80_mul(fp2, fp0, status); /* S(P2+SP3) */ |
| 1416 | fp4 = packFloatx80(0, 0x3FF9, LIT64(0xD23CD68415D95FA1)); |
| 1417 | fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */ |
| 1418 | fp4 = packFloatx80(1, 0x3FFC, LIT64(0x8895A6C5FB423BCA)); |
| 1419 | fp2 = floatx80_add(fp2, fp4, status); /* P1+S(P2+SP3) */ |
| 1420 | fp3 = floatx80_mul(fp3, fp0, status); /* S(Q2+S(Q3+SQ4)) */ |
| 1421 | fp2 = floatx80_mul(fp2, fp0, status); /* S(P1+S(P2+SP3)) */ |
| 1422 | fp4 = packFloatx80(1, 0x3FFD, LIT64(0xEEF57E0DA84BC8CE)); |
| 1423 | fp3 = floatx80_add(fp3, fp4, status); /* Q1+S(Q2+S(Q3+SQ4)) */ |
| 1424 | fp2 = floatx80_mul(fp2, fp1, status); /* RS(P1+S(P2+SP3)) */ |
| 1425 | fp0 = floatx80_mul(fp0, fp3, status); /* S(Q1+S(Q2+S(Q3+SQ4))) */ |
| 1426 | fp1 = floatx80_add(fp1, fp2, status); /* R+RS(P1+S(P2+SP3)) */ |
| 1427 | fp0 = floatx80_add(fp0, float32_to_floatx80( |
| 1428 | make_float32(0x3F800000), status), |
| 1429 | status); /* 1+S(Q1+S(Q2+S(Q3+SQ4))) */ |
| 1430 | |
| 1431 | xSign = extractFloatx80Sign(fp1); |
| 1432 | xExp = extractFloatx80Exp(fp1); |
| 1433 | xSig = extractFloatx80Frac(fp1); |
| 1434 | xSign ^= 1; |
| 1435 | fp1 = packFloatx80(xSign, xExp, xSig); |
| 1436 | |
| 1437 | status->float_rounding_mode = user_rnd_mode; |
| 1438 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1439 | |
| 1440 | a = floatx80_div(fp0, fp1, status); |
| 1441 | |
| 1442 | float_raise(float_flag_inexact, status); |
| 1443 | |
| 1444 | return a; |
| 1445 | } else { |
| 1446 | fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ |
| 1447 | fp3 = float64_to_floatx80(make_float64(0x3EA0B759F50F8688), |
| 1448 | status); /* Q4 */ |
| 1449 | fp2 = float64_to_floatx80(make_float64(0xBEF2BAA5A8924F04), |
| 1450 | status); /* P3 */ |
| 1451 | fp3 = floatx80_mul(fp3, fp1, status); /* SQ4 */ |
| 1452 | fp2 = floatx80_mul(fp2, fp1, status); /* SP3 */ |
| 1453 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 1454 | make_float64(0xBF346F59B39BA65F), status), |
| 1455 | status); /* Q3+SQ4 */ |
| 1456 | fp4 = packFloatx80(0, 0x3FF6, LIT64(0xE073D3FC199C4A00)); |
| 1457 | fp2 = floatx80_add(fp2, fp4, status); /* P2+SP3 */ |
| 1458 | fp3 = floatx80_mul(fp3, fp1, status); /* S(Q3+SQ4) */ |
| 1459 | fp2 = floatx80_mul(fp2, fp1, status); /* S(P2+SP3) */ |
| 1460 | fp4 = packFloatx80(0, 0x3FF9, LIT64(0xD23CD68415D95FA1)); |
| 1461 | fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */ |
| 1462 | fp4 = packFloatx80(1, 0x3FFC, LIT64(0x8895A6C5FB423BCA)); |
| 1463 | fp2 = floatx80_add(fp2, fp4, status); /* P1+S(P2+SP3) */ |
| 1464 | fp3 = floatx80_mul(fp3, fp1, status); /* S(Q2+S(Q3+SQ4)) */ |
| 1465 | fp2 = floatx80_mul(fp2, fp1, status); /* S(P1+S(P2+SP3)) */ |
| 1466 | fp4 = packFloatx80(1, 0x3FFD, LIT64(0xEEF57E0DA84BC8CE)); |
| 1467 | fp3 = floatx80_add(fp3, fp4, status); /* Q1+S(Q2+S(Q3+SQ4)) */ |
| 1468 | fp2 = floatx80_mul(fp2, fp0, status); /* RS(P1+S(P2+SP3)) */ |
| 1469 | fp1 = floatx80_mul(fp1, fp3, status); /* S(Q1+S(Q2+S(Q3+SQ4))) */ |
| 1470 | fp0 = floatx80_add(fp0, fp2, status); /* R+RS(P1+S(P2+SP3)) */ |
| 1471 | fp1 = floatx80_add(fp1, float32_to_floatx80( |
| 1472 | make_float32(0x3F800000), status), |
| 1473 | status); /* 1+S(Q1+S(Q2+S(Q3+SQ4))) */ |
| 1474 | |
| 1475 | status->float_rounding_mode = user_rnd_mode; |
| 1476 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1477 | |
| 1478 | a = floatx80_div(fp0, fp1, status); |
| 1479 | |
| 1480 | float_raise(float_flag_inexact, status); |
| 1481 | |
| 1482 | return a; |
| 1483 | } |
| 1484 | } |
| 1485 | } |
Laurent Vivier | 5add1ac | 2018-03-12 21:27:19 +0100 | [diff] [blame] | 1486 | |
| 1487 | /*---------------------------------------------------------------------------- |
| 1488 | | Sine |
| 1489 | *----------------------------------------------------------------------------*/ |
| 1490 | |
| 1491 | floatx80 floatx80_sin(floatx80 a, float_status *status) |
| 1492 | { |
| 1493 | flag aSign, xSign; |
| 1494 | int32_t aExp, xExp; |
| 1495 | uint64_t aSig, xSig; |
| 1496 | |
| 1497 | int8_t user_rnd_mode, user_rnd_prec; |
| 1498 | |
| 1499 | int32_t compact, l, n, j; |
| 1500 | floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2; |
| 1501 | float32 posneg1, twoto63; |
Laurent Vivier | 6361d29 | 2018-04-30 19:01:56 +0200 | [diff] [blame] | 1502 | flag endflag; |
Laurent Vivier | 5add1ac | 2018-03-12 21:27:19 +0100 | [diff] [blame] | 1503 | |
| 1504 | aSig = extractFloatx80Frac(a); |
| 1505 | aExp = extractFloatx80Exp(a); |
| 1506 | aSign = extractFloatx80Sign(a); |
| 1507 | |
| 1508 | if (aExp == 0x7FFF) { |
| 1509 | if ((uint64_t) (aSig << 1)) { |
| 1510 | return propagateFloatx80NaNOneArg(a, status); |
| 1511 | } |
| 1512 | float_raise(float_flag_invalid, status); |
| 1513 | return floatx80_default_nan(status); |
| 1514 | } |
| 1515 | |
| 1516 | if (aExp == 0 && aSig == 0) { |
| 1517 | return packFloatx80(aSign, 0, 0); |
| 1518 | } |
| 1519 | |
Laurent Vivier | 5add1ac | 2018-03-12 21:27:19 +0100 | [diff] [blame] | 1520 | user_rnd_mode = status->float_rounding_mode; |
| 1521 | user_rnd_prec = status->floatx80_rounding_precision; |
| 1522 | status->float_rounding_mode = float_round_nearest_even; |
| 1523 | status->floatx80_rounding_precision = 80; |
| 1524 | |
| 1525 | compact = floatx80_make_compact(aExp, aSig); |
| 1526 | |
| 1527 | fp0 = a; |
| 1528 | |
| 1529 | if (compact < 0x3FD78000 || compact > 0x4004BC7E) { |
| 1530 | /* 2^(-40) > |X| > 15 PI */ |
| 1531 | if (compact > 0x3FFF8000) { /* |X| >= 15 PI */ |
| 1532 | /* REDUCEX */ |
| 1533 | fp1 = packFloatx80(0, 0, 0); |
| 1534 | if (compact == 0x7FFEFFFF) { |
| 1535 | twopi1 = packFloatx80(aSign ^ 1, 0x7FFE, |
| 1536 | LIT64(0xC90FDAA200000000)); |
| 1537 | twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, |
| 1538 | LIT64(0x85A308D300000000)); |
| 1539 | fp0 = floatx80_add(fp0, twopi1, status); |
| 1540 | fp1 = fp0; |
| 1541 | fp0 = floatx80_add(fp0, twopi2, status); |
| 1542 | fp1 = floatx80_sub(fp1, fp0, status); |
| 1543 | fp1 = floatx80_add(fp1, twopi2, status); |
| 1544 | } |
| 1545 | loop: |
| 1546 | xSign = extractFloatx80Sign(fp0); |
| 1547 | xExp = extractFloatx80Exp(fp0); |
| 1548 | xExp -= 0x3FFF; |
| 1549 | if (xExp <= 28) { |
| 1550 | l = 0; |
| 1551 | endflag = 1; |
| 1552 | } else { |
| 1553 | l = xExp - 27; |
| 1554 | endflag = 0; |
| 1555 | } |
| 1556 | invtwopi = packFloatx80(0, 0x3FFE - l, |
| 1557 | LIT64(0xA2F9836E4E44152A)); /* INVTWOPI */ |
| 1558 | twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000)); |
| 1559 | twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(0x85A308D300000000)); |
| 1560 | |
| 1561 | /* SIGN(INARG)*2^63 IN SGL */ |
| 1562 | twoto63 = packFloat32(xSign, 0xBE, 0); |
| 1563 | |
| 1564 | fp2 = floatx80_mul(fp0, invtwopi, status); |
| 1565 | fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), |
| 1566 | status); /* THE FRACT PART OF FP2 IS ROUNDED */ |
| 1567 | fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status), |
| 1568 | status); /* FP2 is N */ |
| 1569 | fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */ |
| 1570 | fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */ |
| 1571 | fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */ |
| 1572 | fp4 = floatx80_sub(fp4, fp3, status); /* W-P */ |
| 1573 | fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */ |
| 1574 | fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */ |
| 1575 | fp3 = fp0; /* FP3 is A */ |
| 1576 | fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */ |
| 1577 | fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */ |
| 1578 | |
| 1579 | if (endflag > 0) { |
| 1580 | n = floatx80_to_int32(fp2, status); |
| 1581 | goto sincont; |
| 1582 | } |
| 1583 | fp3 = floatx80_sub(fp3, fp0, status); /* A-R */ |
| 1584 | fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */ |
| 1585 | goto loop; |
| 1586 | } else { |
| 1587 | /* SINSM */ |
| 1588 | fp0 = float32_to_floatx80(make_float32(0x3F800000), |
| 1589 | status); /* 1 */ |
| 1590 | |
| 1591 | status->float_rounding_mode = user_rnd_mode; |
| 1592 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1593 | |
Laurent Vivier | 6361d29 | 2018-04-30 19:01:56 +0200 | [diff] [blame] | 1594 | /* SINTINY */ |
| 1595 | a = floatx80_move(a, status); |
Laurent Vivier | 5add1ac | 2018-03-12 21:27:19 +0100 | [diff] [blame] | 1596 | float_raise(float_flag_inexact, status); |
| 1597 | |
| 1598 | return a; |
| 1599 | } |
| 1600 | } else { |
| 1601 | fp1 = floatx80_mul(fp0, float64_to_floatx80( |
| 1602 | make_float64(0x3FE45F306DC9C883), status), |
| 1603 | status); /* X*2/PI */ |
| 1604 | |
| 1605 | n = floatx80_to_int32(fp1, status); |
| 1606 | j = 32 + n; |
| 1607 | |
| 1608 | fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */ |
| 1609 | fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status), |
| 1610 | status); /* FP0 IS R = (X-Y1)-Y2 */ |
| 1611 | |
| 1612 | sincont: |
Laurent Vivier | 6361d29 | 2018-04-30 19:01:56 +0200 | [diff] [blame] | 1613 | if (n & 1) { |
Laurent Vivier | 5add1ac | 2018-03-12 21:27:19 +0100 | [diff] [blame] | 1614 | /* COSPOLY */ |
| 1615 | fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */ |
| 1616 | fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */ |
| 1617 | fp2 = float64_to_floatx80(make_float64(0x3D2AC4D0D6011EE3), |
| 1618 | status); /* B8 */ |
| 1619 | fp3 = float64_to_floatx80(make_float64(0xBDA9396F9F45AC19), |
| 1620 | status); /* B7 */ |
| 1621 | |
| 1622 | xSign = extractFloatx80Sign(fp0); /* X IS S */ |
| 1623 | xExp = extractFloatx80Exp(fp0); |
| 1624 | xSig = extractFloatx80Frac(fp0); |
| 1625 | |
Laurent Vivier | 6361d29 | 2018-04-30 19:01:56 +0200 | [diff] [blame] | 1626 | if ((n >> 1) & 1) { |
Laurent Vivier | 5add1ac | 2018-03-12 21:27:19 +0100 | [diff] [blame] | 1627 | xSign ^= 1; |
| 1628 | posneg1 = make_float32(0xBF800000); /* -1 */ |
| 1629 | } else { |
| 1630 | xSign ^= 0; |
| 1631 | posneg1 = make_float32(0x3F800000); /* 1 */ |
| 1632 | } /* X IS NOW R'= SGN*R */ |
| 1633 | |
| 1634 | fp2 = floatx80_mul(fp2, fp1, status); /* TB8 */ |
| 1635 | fp3 = floatx80_mul(fp3, fp1, status); /* TB7 */ |
| 1636 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 1637 | make_float64(0x3E21EED90612C972), status), |
| 1638 | status); /* B6+TB8 */ |
| 1639 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 1640 | make_float64(0xBE927E4FB79D9FCF), status), |
| 1641 | status); /* B5+TB7 */ |
| 1642 | fp2 = floatx80_mul(fp2, fp1, status); /* T(B6+TB8) */ |
| 1643 | fp3 = floatx80_mul(fp3, fp1, status); /* T(B5+TB7) */ |
| 1644 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 1645 | make_float64(0x3EFA01A01A01D423), status), |
| 1646 | status); /* B4+T(B6+TB8) */ |
| 1647 | fp4 = packFloatx80(1, 0x3FF5, LIT64(0xB60B60B60B61D438)); |
| 1648 | fp3 = floatx80_add(fp3, fp4, status); /* B3+T(B5+TB7) */ |
| 1649 | fp2 = floatx80_mul(fp2, fp1, status); /* T(B4+T(B6+TB8)) */ |
| 1650 | fp1 = floatx80_mul(fp1, fp3, status); /* T(B3+T(B5+TB7)) */ |
| 1651 | fp4 = packFloatx80(0, 0x3FFA, LIT64(0xAAAAAAAAAAAAAB5E)); |
| 1652 | fp2 = floatx80_add(fp2, fp4, status); /* B2+T(B4+T(B6+TB8)) */ |
| 1653 | fp1 = floatx80_add(fp1, float32_to_floatx80( |
| 1654 | make_float32(0xBF000000), status), |
| 1655 | status); /* B1+T(B3+T(B5+TB7)) */ |
| 1656 | fp0 = floatx80_mul(fp0, fp2, status); /* S(B2+T(B4+T(B6+TB8))) */ |
| 1657 | fp0 = floatx80_add(fp0, fp1, status); /* [B1+T(B3+T(B5+TB7))]+ |
| 1658 | * [S(B2+T(B4+T(B6+TB8)))] |
| 1659 | */ |
| 1660 | |
| 1661 | x = packFloatx80(xSign, xExp, xSig); |
| 1662 | fp0 = floatx80_mul(fp0, x, status); |
| 1663 | |
| 1664 | status->float_rounding_mode = user_rnd_mode; |
| 1665 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1666 | |
| 1667 | a = floatx80_add(fp0, float32_to_floatx80(posneg1, status), status); |
| 1668 | |
| 1669 | float_raise(float_flag_inexact, status); |
| 1670 | |
| 1671 | return a; |
| 1672 | } else { |
| 1673 | /* SINPOLY */ |
| 1674 | xSign = extractFloatx80Sign(fp0); /* X IS R */ |
| 1675 | xExp = extractFloatx80Exp(fp0); |
| 1676 | xSig = extractFloatx80Frac(fp0); |
| 1677 | |
Laurent Vivier | 6361d29 | 2018-04-30 19:01:56 +0200 | [diff] [blame] | 1678 | xSign ^= (n >> 1) & 1; /* X IS NOW R'= SGN*R */ |
Laurent Vivier | 5add1ac | 2018-03-12 21:27:19 +0100 | [diff] [blame] | 1679 | |
| 1680 | fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */ |
| 1681 | fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */ |
| 1682 | fp3 = float64_to_floatx80(make_float64(0xBD6AAA77CCC994F5), |
| 1683 | status); /* A7 */ |
| 1684 | fp2 = float64_to_floatx80(make_float64(0x3DE612097AAE8DA1), |
| 1685 | status); /* A6 */ |
| 1686 | fp3 = floatx80_mul(fp3, fp1, status); /* T*A7 */ |
| 1687 | fp2 = floatx80_mul(fp2, fp1, status); /* T*A6 */ |
| 1688 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 1689 | make_float64(0xBE5AE6452A118AE4), status), |
| 1690 | status); /* A5+T*A7 */ |
| 1691 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 1692 | make_float64(0x3EC71DE3A5341531), status), |
| 1693 | status); /* A4+T*A6 */ |
| 1694 | fp3 = floatx80_mul(fp3, fp1, status); /* T(A5+TA7) */ |
| 1695 | fp2 = floatx80_mul(fp2, fp1, status); /* T(A4+TA6) */ |
| 1696 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 1697 | make_float64(0xBF2A01A01A018B59), status), |
| 1698 | status); /* A3+T(A5+TA7) */ |
| 1699 | fp4 = packFloatx80(0, 0x3FF8, LIT64(0x88888888888859AF)); |
| 1700 | fp2 = floatx80_add(fp2, fp4, status); /* A2+T(A4+TA6) */ |
| 1701 | fp1 = floatx80_mul(fp1, fp3, status); /* T(A3+T(A5+TA7)) */ |
| 1702 | fp2 = floatx80_mul(fp2, fp0, status); /* S(A2+T(A4+TA6)) */ |
| 1703 | fp4 = packFloatx80(1, 0x3FFC, LIT64(0xAAAAAAAAAAAAAA99)); |
| 1704 | fp1 = floatx80_add(fp1, fp4, status); /* A1+T(A3+T(A5+TA7)) */ |
| 1705 | fp1 = floatx80_add(fp1, fp2, |
| 1706 | status); /* [A1+T(A3+T(A5+TA7))]+ |
| 1707 | * [S(A2+T(A4+TA6))] |
| 1708 | */ |
| 1709 | |
| 1710 | x = packFloatx80(xSign, xExp, xSig); |
| 1711 | fp0 = floatx80_mul(fp0, x, status); /* R'*S */ |
| 1712 | fp0 = floatx80_mul(fp0, fp1, status); /* SIN(R')-R' */ |
| 1713 | |
| 1714 | status->float_rounding_mode = user_rnd_mode; |
| 1715 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1716 | |
| 1717 | a = floatx80_add(fp0, x, status); |
| 1718 | |
| 1719 | float_raise(float_flag_inexact, status); |
| 1720 | |
| 1721 | return a; |
| 1722 | } |
| 1723 | } |
| 1724 | } |
Laurent Vivier | 68d0ed3 | 2018-03-12 21:27:20 +0100 | [diff] [blame] | 1725 | |
| 1726 | /*---------------------------------------------------------------------------- |
| 1727 | | Cosine |
| 1728 | *----------------------------------------------------------------------------*/ |
| 1729 | |
| 1730 | floatx80 floatx80_cos(floatx80 a, float_status *status) |
| 1731 | { |
| 1732 | flag aSign, xSign; |
| 1733 | int32_t aExp, xExp; |
| 1734 | uint64_t aSig, xSig; |
| 1735 | |
| 1736 | int8_t user_rnd_mode, user_rnd_prec; |
| 1737 | |
| 1738 | int32_t compact, l, n, j; |
| 1739 | floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2; |
| 1740 | float32 posneg1, twoto63; |
Laurent Vivier | 6361d29 | 2018-04-30 19:01:56 +0200 | [diff] [blame] | 1741 | flag endflag; |
Laurent Vivier | 68d0ed3 | 2018-03-12 21:27:20 +0100 | [diff] [blame] | 1742 | |
| 1743 | aSig = extractFloatx80Frac(a); |
| 1744 | aExp = extractFloatx80Exp(a); |
| 1745 | aSign = extractFloatx80Sign(a); |
| 1746 | |
| 1747 | if (aExp == 0x7FFF) { |
| 1748 | if ((uint64_t) (aSig << 1)) { |
| 1749 | return propagateFloatx80NaNOneArg(a, status); |
| 1750 | } |
| 1751 | float_raise(float_flag_invalid, status); |
| 1752 | return floatx80_default_nan(status); |
| 1753 | } |
| 1754 | |
| 1755 | if (aExp == 0 && aSig == 0) { |
| 1756 | return packFloatx80(0, one_exp, one_sig); |
| 1757 | } |
| 1758 | |
Laurent Vivier | 68d0ed3 | 2018-03-12 21:27:20 +0100 | [diff] [blame] | 1759 | user_rnd_mode = status->float_rounding_mode; |
| 1760 | user_rnd_prec = status->floatx80_rounding_precision; |
| 1761 | status->float_rounding_mode = float_round_nearest_even; |
| 1762 | status->floatx80_rounding_precision = 80; |
| 1763 | |
| 1764 | compact = floatx80_make_compact(aExp, aSig); |
| 1765 | |
| 1766 | fp0 = a; |
| 1767 | |
| 1768 | if (compact < 0x3FD78000 || compact > 0x4004BC7E) { |
| 1769 | /* 2^(-40) > |X| > 15 PI */ |
| 1770 | if (compact > 0x3FFF8000) { /* |X| >= 15 PI */ |
| 1771 | /* REDUCEX */ |
| 1772 | fp1 = packFloatx80(0, 0, 0); |
| 1773 | if (compact == 0x7FFEFFFF) { |
| 1774 | twopi1 = packFloatx80(aSign ^ 1, 0x7FFE, |
| 1775 | LIT64(0xC90FDAA200000000)); |
| 1776 | twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, |
| 1777 | LIT64(0x85A308D300000000)); |
| 1778 | fp0 = floatx80_add(fp0, twopi1, status); |
| 1779 | fp1 = fp0; |
| 1780 | fp0 = floatx80_add(fp0, twopi2, status); |
| 1781 | fp1 = floatx80_sub(fp1, fp0, status); |
| 1782 | fp1 = floatx80_add(fp1, twopi2, status); |
| 1783 | } |
| 1784 | loop: |
| 1785 | xSign = extractFloatx80Sign(fp0); |
| 1786 | xExp = extractFloatx80Exp(fp0); |
| 1787 | xExp -= 0x3FFF; |
| 1788 | if (xExp <= 28) { |
| 1789 | l = 0; |
| 1790 | endflag = 1; |
| 1791 | } else { |
| 1792 | l = xExp - 27; |
| 1793 | endflag = 0; |
| 1794 | } |
| 1795 | invtwopi = packFloatx80(0, 0x3FFE - l, |
| 1796 | LIT64(0xA2F9836E4E44152A)); /* INVTWOPI */ |
| 1797 | twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000)); |
| 1798 | twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(0x85A308D300000000)); |
| 1799 | |
| 1800 | /* SIGN(INARG)*2^63 IN SGL */ |
| 1801 | twoto63 = packFloat32(xSign, 0xBE, 0); |
| 1802 | |
| 1803 | fp2 = floatx80_mul(fp0, invtwopi, status); |
| 1804 | fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), |
| 1805 | status); /* THE FRACT PART OF FP2 IS ROUNDED */ |
| 1806 | fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status), |
| 1807 | status); /* FP2 is N */ |
| 1808 | fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */ |
| 1809 | fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */ |
| 1810 | fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */ |
| 1811 | fp4 = floatx80_sub(fp4, fp3, status); /* W-P */ |
| 1812 | fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */ |
| 1813 | fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */ |
| 1814 | fp3 = fp0; /* FP3 is A */ |
| 1815 | fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */ |
| 1816 | fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */ |
| 1817 | |
| 1818 | if (endflag > 0) { |
| 1819 | n = floatx80_to_int32(fp2, status); |
| 1820 | goto sincont; |
| 1821 | } |
| 1822 | fp3 = floatx80_sub(fp3, fp0, status); /* A-R */ |
| 1823 | fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */ |
| 1824 | goto loop; |
| 1825 | } else { |
| 1826 | /* SINSM */ |
| 1827 | fp0 = float32_to_floatx80(make_float32(0x3F800000), status); /* 1 */ |
| 1828 | |
| 1829 | status->float_rounding_mode = user_rnd_mode; |
| 1830 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1831 | |
Laurent Vivier | 6361d29 | 2018-04-30 19:01:56 +0200 | [diff] [blame] | 1832 | /* COSTINY */ |
| 1833 | a = floatx80_sub(fp0, float32_to_floatx80( |
| 1834 | make_float32(0x00800000), status), |
| 1835 | status); |
Laurent Vivier | 68d0ed3 | 2018-03-12 21:27:20 +0100 | [diff] [blame] | 1836 | float_raise(float_flag_inexact, status); |
| 1837 | |
| 1838 | return a; |
| 1839 | } |
| 1840 | } else { |
| 1841 | fp1 = floatx80_mul(fp0, float64_to_floatx80( |
| 1842 | make_float64(0x3FE45F306DC9C883), status), |
| 1843 | status); /* X*2/PI */ |
| 1844 | |
| 1845 | n = floatx80_to_int32(fp1, status); |
| 1846 | j = 32 + n; |
| 1847 | |
| 1848 | fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */ |
| 1849 | fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status), |
| 1850 | status); /* FP0 IS R = (X-Y1)-Y2 */ |
| 1851 | |
| 1852 | sincont: |
Laurent Vivier | 6361d29 | 2018-04-30 19:01:56 +0200 | [diff] [blame] | 1853 | if ((n + 1) & 1) { |
Laurent Vivier | 68d0ed3 | 2018-03-12 21:27:20 +0100 | [diff] [blame] | 1854 | /* COSPOLY */ |
| 1855 | fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */ |
| 1856 | fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */ |
| 1857 | fp2 = float64_to_floatx80(make_float64(0x3D2AC4D0D6011EE3), |
| 1858 | status); /* B8 */ |
| 1859 | fp3 = float64_to_floatx80(make_float64(0xBDA9396F9F45AC19), |
| 1860 | status); /* B7 */ |
| 1861 | |
| 1862 | xSign = extractFloatx80Sign(fp0); /* X IS S */ |
| 1863 | xExp = extractFloatx80Exp(fp0); |
| 1864 | xSig = extractFloatx80Frac(fp0); |
| 1865 | |
Laurent Vivier | 6361d29 | 2018-04-30 19:01:56 +0200 | [diff] [blame] | 1866 | if (((n + 1) >> 1) & 1) { |
Laurent Vivier | 68d0ed3 | 2018-03-12 21:27:20 +0100 | [diff] [blame] | 1867 | xSign ^= 1; |
| 1868 | posneg1 = make_float32(0xBF800000); /* -1 */ |
| 1869 | } else { |
| 1870 | xSign ^= 0; |
| 1871 | posneg1 = make_float32(0x3F800000); /* 1 */ |
| 1872 | } /* X IS NOW R'= SGN*R */ |
| 1873 | |
| 1874 | fp2 = floatx80_mul(fp2, fp1, status); /* TB8 */ |
| 1875 | fp3 = floatx80_mul(fp3, fp1, status); /* TB7 */ |
| 1876 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 1877 | make_float64(0x3E21EED90612C972), status), |
| 1878 | status); /* B6+TB8 */ |
| 1879 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 1880 | make_float64(0xBE927E4FB79D9FCF), status), |
| 1881 | status); /* B5+TB7 */ |
| 1882 | fp2 = floatx80_mul(fp2, fp1, status); /* T(B6+TB8) */ |
| 1883 | fp3 = floatx80_mul(fp3, fp1, status); /* T(B5+TB7) */ |
| 1884 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 1885 | make_float64(0x3EFA01A01A01D423), status), |
| 1886 | status); /* B4+T(B6+TB8) */ |
| 1887 | fp4 = packFloatx80(1, 0x3FF5, LIT64(0xB60B60B60B61D438)); |
| 1888 | fp3 = floatx80_add(fp3, fp4, status); /* B3+T(B5+TB7) */ |
| 1889 | fp2 = floatx80_mul(fp2, fp1, status); /* T(B4+T(B6+TB8)) */ |
| 1890 | fp1 = floatx80_mul(fp1, fp3, status); /* T(B3+T(B5+TB7)) */ |
| 1891 | fp4 = packFloatx80(0, 0x3FFA, LIT64(0xAAAAAAAAAAAAAB5E)); |
| 1892 | fp2 = floatx80_add(fp2, fp4, status); /* B2+T(B4+T(B6+TB8)) */ |
| 1893 | fp1 = floatx80_add(fp1, float32_to_floatx80( |
| 1894 | make_float32(0xBF000000), status), |
| 1895 | status); /* B1+T(B3+T(B5+TB7)) */ |
| 1896 | fp0 = floatx80_mul(fp0, fp2, status); /* S(B2+T(B4+T(B6+TB8))) */ |
| 1897 | fp0 = floatx80_add(fp0, fp1, status); |
| 1898 | /* [B1+T(B3+T(B5+TB7))]+[S(B2+T(B4+T(B6+TB8)))] */ |
| 1899 | |
| 1900 | x = packFloatx80(xSign, xExp, xSig); |
| 1901 | fp0 = floatx80_mul(fp0, x, status); |
| 1902 | |
| 1903 | status->float_rounding_mode = user_rnd_mode; |
| 1904 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1905 | |
| 1906 | a = floatx80_add(fp0, float32_to_floatx80(posneg1, status), status); |
| 1907 | |
| 1908 | float_raise(float_flag_inexact, status); |
| 1909 | |
| 1910 | return a; |
| 1911 | } else { |
| 1912 | /* SINPOLY */ |
| 1913 | xSign = extractFloatx80Sign(fp0); /* X IS R */ |
| 1914 | xExp = extractFloatx80Exp(fp0); |
| 1915 | xSig = extractFloatx80Frac(fp0); |
| 1916 | |
Laurent Vivier | 6361d29 | 2018-04-30 19:01:56 +0200 | [diff] [blame] | 1917 | xSign ^= ((n + 1) >> 1) & 1; /* X IS NOW R'= SGN*R */ |
Laurent Vivier | 68d0ed3 | 2018-03-12 21:27:20 +0100 | [diff] [blame] | 1918 | |
| 1919 | fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */ |
| 1920 | fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */ |
| 1921 | fp3 = float64_to_floatx80(make_float64(0xBD6AAA77CCC994F5), |
| 1922 | status); /* A7 */ |
| 1923 | fp2 = float64_to_floatx80(make_float64(0x3DE612097AAE8DA1), |
| 1924 | status); /* A6 */ |
| 1925 | fp3 = floatx80_mul(fp3, fp1, status); /* T*A7 */ |
| 1926 | fp2 = floatx80_mul(fp2, fp1, status); /* T*A6 */ |
| 1927 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 1928 | make_float64(0xBE5AE6452A118AE4), status), |
| 1929 | status); /* A5+T*A7 */ |
| 1930 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 1931 | make_float64(0x3EC71DE3A5341531), status), |
| 1932 | status); /* A4+T*A6 */ |
| 1933 | fp3 = floatx80_mul(fp3, fp1, status); /* T(A5+TA7) */ |
| 1934 | fp2 = floatx80_mul(fp2, fp1, status); /* T(A4+TA6) */ |
| 1935 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 1936 | make_float64(0xBF2A01A01A018B59), status), |
| 1937 | status); /* A3+T(A5+TA7) */ |
| 1938 | fp4 = packFloatx80(0, 0x3FF8, LIT64(0x88888888888859AF)); |
| 1939 | fp2 = floatx80_add(fp2, fp4, status); /* A2+T(A4+TA6) */ |
| 1940 | fp1 = floatx80_mul(fp1, fp3, status); /* T(A3+T(A5+TA7)) */ |
| 1941 | fp2 = floatx80_mul(fp2, fp0, status); /* S(A2+T(A4+TA6)) */ |
| 1942 | fp4 = packFloatx80(1, 0x3FFC, LIT64(0xAAAAAAAAAAAAAA99)); |
| 1943 | fp1 = floatx80_add(fp1, fp4, status); /* A1+T(A3+T(A5+TA7)) */ |
| 1944 | fp1 = floatx80_add(fp1, fp2, status); |
| 1945 | /* [A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))] */ |
| 1946 | |
| 1947 | x = packFloatx80(xSign, xExp, xSig); |
| 1948 | fp0 = floatx80_mul(fp0, x, status); /* R'*S */ |
| 1949 | fp0 = floatx80_mul(fp0, fp1, status); /* SIN(R')-R' */ |
| 1950 | |
| 1951 | status->float_rounding_mode = user_rnd_mode; |
| 1952 | status->floatx80_rounding_precision = user_rnd_prec; |
| 1953 | |
| 1954 | a = floatx80_add(fp0, x, status); |
| 1955 | |
| 1956 | float_raise(float_flag_inexact, status); |
| 1957 | |
| 1958 | return a; |
| 1959 | } |
| 1960 | } |
| 1961 | } |
Laurent Vivier | 8c992ab | 2018-03-12 21:27:22 +0100 | [diff] [blame] | 1962 | |
| 1963 | /*---------------------------------------------------------------------------- |
| 1964 | | Arc tangent |
| 1965 | *----------------------------------------------------------------------------*/ |
| 1966 | |
| 1967 | floatx80 floatx80_atan(floatx80 a, float_status *status) |
| 1968 | { |
| 1969 | flag aSign; |
| 1970 | int32_t aExp; |
| 1971 | uint64_t aSig; |
| 1972 | |
| 1973 | int8_t user_rnd_mode, user_rnd_prec; |
| 1974 | |
| 1975 | int32_t compact, tbl_index; |
| 1976 | floatx80 fp0, fp1, fp2, fp3, xsave; |
| 1977 | |
| 1978 | aSig = extractFloatx80Frac(a); |
| 1979 | aExp = extractFloatx80Exp(a); |
| 1980 | aSign = extractFloatx80Sign(a); |
| 1981 | |
| 1982 | if (aExp == 0x7FFF) { |
| 1983 | if ((uint64_t) (aSig << 1)) { |
| 1984 | return propagateFloatx80NaNOneArg(a, status); |
| 1985 | } |
| 1986 | a = packFloatx80(aSign, piby2_exp, pi_sig); |
| 1987 | float_raise(float_flag_inexact, status); |
| 1988 | return floatx80_move(a, status); |
| 1989 | } |
| 1990 | |
| 1991 | if (aExp == 0 && aSig == 0) { |
| 1992 | return packFloatx80(aSign, 0, 0); |
| 1993 | } |
| 1994 | |
| 1995 | compact = floatx80_make_compact(aExp, aSig); |
| 1996 | |
| 1997 | user_rnd_mode = status->float_rounding_mode; |
| 1998 | user_rnd_prec = status->floatx80_rounding_precision; |
| 1999 | status->float_rounding_mode = float_round_nearest_even; |
| 2000 | status->floatx80_rounding_precision = 80; |
| 2001 | |
| 2002 | if (compact < 0x3FFB8000 || compact > 0x4002FFFF) { |
| 2003 | /* |X| >= 16 or |X| < 1/16 */ |
| 2004 | if (compact > 0x3FFF8000) { /* |X| >= 16 */ |
| 2005 | if (compact > 0x40638000) { /* |X| > 2^(100) */ |
| 2006 | fp0 = packFloatx80(aSign, piby2_exp, pi_sig); |
| 2007 | fp1 = packFloatx80(aSign, 0x0001, one_sig); |
| 2008 | |
| 2009 | status->float_rounding_mode = user_rnd_mode; |
| 2010 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2011 | |
| 2012 | a = floatx80_sub(fp0, fp1, status); |
| 2013 | |
| 2014 | float_raise(float_flag_inexact, status); |
| 2015 | |
| 2016 | return a; |
| 2017 | } else { |
| 2018 | fp0 = a; |
| 2019 | fp1 = packFloatx80(1, one_exp, one_sig); /* -1 */ |
| 2020 | fp1 = floatx80_div(fp1, fp0, status); /* X' = -1/X */ |
| 2021 | xsave = fp1; |
| 2022 | fp0 = floatx80_mul(fp1, fp1, status); /* Y = X'*X' */ |
| 2023 | fp1 = floatx80_mul(fp0, fp0, status); /* Z = Y*Y */ |
| 2024 | fp3 = float64_to_floatx80(make_float64(0xBFB70BF398539E6A), |
| 2025 | status); /* C5 */ |
| 2026 | fp2 = float64_to_floatx80(make_float64(0x3FBC7187962D1D7D), |
| 2027 | status); /* C4 */ |
| 2028 | fp3 = floatx80_mul(fp3, fp1, status); /* Z*C5 */ |
| 2029 | fp2 = floatx80_mul(fp2, fp1, status); /* Z*C4 */ |
| 2030 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 2031 | make_float64(0xBFC24924827107B8), status), |
| 2032 | status); /* C3+Z*C5 */ |
| 2033 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 2034 | make_float64(0x3FC999999996263E), status), |
| 2035 | status); /* C2+Z*C4 */ |
| 2036 | fp1 = floatx80_mul(fp1, fp3, status); /* Z*(C3+Z*C5) */ |
| 2037 | fp2 = floatx80_mul(fp2, fp0, status); /* Y*(C2+Z*C4) */ |
| 2038 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 2039 | make_float64(0xBFD5555555555536), status), |
| 2040 | status); /* C1+Z*(C3+Z*C5) */ |
| 2041 | fp0 = floatx80_mul(fp0, xsave, status); /* X'*Y */ |
| 2042 | /* [Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)] */ |
| 2043 | fp1 = floatx80_add(fp1, fp2, status); |
| 2044 | /* X'*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) ?? */ |
| 2045 | fp0 = floatx80_mul(fp0, fp1, status); |
| 2046 | fp0 = floatx80_add(fp0, xsave, status); |
| 2047 | fp1 = packFloatx80(aSign, piby2_exp, pi_sig); |
| 2048 | |
| 2049 | status->float_rounding_mode = user_rnd_mode; |
| 2050 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2051 | |
| 2052 | a = floatx80_add(fp0, fp1, status); |
| 2053 | |
| 2054 | float_raise(float_flag_inexact, status); |
| 2055 | |
| 2056 | return a; |
| 2057 | } |
| 2058 | } else { /* |X| < 1/16 */ |
| 2059 | if (compact < 0x3FD78000) { /* |X| < 2^(-40) */ |
| 2060 | status->float_rounding_mode = user_rnd_mode; |
| 2061 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2062 | |
| 2063 | a = floatx80_move(a, status); |
| 2064 | |
| 2065 | float_raise(float_flag_inexact, status); |
| 2066 | |
| 2067 | return a; |
| 2068 | } else { |
| 2069 | fp0 = a; |
| 2070 | xsave = a; |
| 2071 | fp0 = floatx80_mul(fp0, fp0, status); /* Y = X*X */ |
| 2072 | fp1 = floatx80_mul(fp0, fp0, status); /* Z = Y*Y */ |
| 2073 | fp2 = float64_to_floatx80(make_float64(0x3FB344447F876989), |
| 2074 | status); /* B6 */ |
| 2075 | fp3 = float64_to_floatx80(make_float64(0xBFB744EE7FAF45DB), |
| 2076 | status); /* B5 */ |
| 2077 | fp2 = floatx80_mul(fp2, fp1, status); /* Z*B6 */ |
| 2078 | fp3 = floatx80_mul(fp3, fp1, status); /* Z*B5 */ |
| 2079 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 2080 | make_float64(0x3FBC71C646940220), status), |
| 2081 | status); /* B4+Z*B6 */ |
| 2082 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 2083 | make_float64(0xBFC24924921872F9), |
| 2084 | status), status); /* B3+Z*B5 */ |
| 2085 | fp2 = floatx80_mul(fp2, fp1, status); /* Z*(B4+Z*B6) */ |
| 2086 | fp1 = floatx80_mul(fp1, fp3, status); /* Z*(B3+Z*B5) */ |
| 2087 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 2088 | make_float64(0x3FC9999999998FA9), status), |
| 2089 | status); /* B2+Z*(B4+Z*B6) */ |
| 2090 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 2091 | make_float64(0xBFD5555555555555), status), |
| 2092 | status); /* B1+Z*(B3+Z*B5) */ |
| 2093 | fp2 = floatx80_mul(fp2, fp0, status); /* Y*(B2+Z*(B4+Z*B6)) */ |
| 2094 | fp0 = floatx80_mul(fp0, xsave, status); /* X*Y */ |
| 2095 | /* [B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))] */ |
| 2096 | fp1 = floatx80_add(fp1, fp2, status); |
| 2097 | /* X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) */ |
| 2098 | fp0 = floatx80_mul(fp0, fp1, status); |
| 2099 | |
| 2100 | status->float_rounding_mode = user_rnd_mode; |
| 2101 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2102 | |
| 2103 | a = floatx80_add(fp0, xsave, status); |
| 2104 | |
| 2105 | float_raise(float_flag_inexact, status); |
| 2106 | |
| 2107 | return a; |
| 2108 | } |
| 2109 | } |
| 2110 | } else { |
| 2111 | aSig &= LIT64(0xF800000000000000); |
| 2112 | aSig |= LIT64(0x0400000000000000); |
| 2113 | xsave = packFloatx80(aSign, aExp, aSig); /* F */ |
| 2114 | fp0 = a; |
| 2115 | fp1 = a; /* X */ |
| 2116 | fp2 = packFloatx80(0, one_exp, one_sig); /* 1 */ |
| 2117 | fp1 = floatx80_mul(fp1, xsave, status); /* X*F */ |
| 2118 | fp0 = floatx80_sub(fp0, xsave, status); /* X-F */ |
| 2119 | fp1 = floatx80_add(fp1, fp2, status); /* 1 + X*F */ |
| 2120 | fp0 = floatx80_div(fp0, fp1, status); /* U = (X-F)/(1+X*F) */ |
| 2121 | |
| 2122 | tbl_index = compact; |
| 2123 | |
| 2124 | tbl_index &= 0x7FFF0000; |
| 2125 | tbl_index -= 0x3FFB0000; |
| 2126 | tbl_index >>= 1; |
| 2127 | tbl_index += compact & 0x00007800; |
| 2128 | tbl_index >>= 11; |
| 2129 | |
| 2130 | fp3 = atan_tbl[tbl_index]; |
| 2131 | |
| 2132 | fp3.high |= aSign ? 0x8000 : 0; /* ATAN(F) */ |
| 2133 | |
| 2134 | fp1 = floatx80_mul(fp0, fp0, status); /* V = U*U */ |
| 2135 | fp2 = float64_to_floatx80(make_float64(0xBFF6687E314987D8), |
| 2136 | status); /* A3 */ |
| 2137 | fp2 = floatx80_add(fp2, fp1, status); /* A3+V */ |
| 2138 | fp2 = floatx80_mul(fp2, fp1, status); /* V*(A3+V) */ |
| 2139 | fp1 = floatx80_mul(fp1, fp0, status); /* U*V */ |
| 2140 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 2141 | make_float64(0x4002AC6934A26DB3), status), |
| 2142 | status); /* A2+V*(A3+V) */ |
| 2143 | fp1 = floatx80_mul(fp1, float64_to_floatx80( |
| 2144 | make_float64(0xBFC2476F4E1DA28E), status), |
| 2145 | status); /* A1+U*V */ |
| 2146 | fp1 = floatx80_mul(fp1, fp2, status); /* A1*U*V*(A2+V*(A3+V)) */ |
| 2147 | fp0 = floatx80_add(fp0, fp1, status); /* ATAN(U) */ |
| 2148 | |
| 2149 | status->float_rounding_mode = user_rnd_mode; |
| 2150 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2151 | |
| 2152 | a = floatx80_add(fp0, fp3, status); /* ATAN(X) */ |
| 2153 | |
| 2154 | float_raise(float_flag_inexact, status); |
| 2155 | |
| 2156 | return a; |
| 2157 | } |
| 2158 | } |
Laurent Vivier | bc20b34 | 2018-03-12 21:27:23 +0100 | [diff] [blame] | 2159 | |
| 2160 | /*---------------------------------------------------------------------------- |
| 2161 | | Arc sine |
| 2162 | *----------------------------------------------------------------------------*/ |
| 2163 | |
| 2164 | floatx80 floatx80_asin(floatx80 a, float_status *status) |
| 2165 | { |
| 2166 | flag aSign; |
| 2167 | int32_t aExp; |
| 2168 | uint64_t aSig; |
| 2169 | |
| 2170 | int8_t user_rnd_mode, user_rnd_prec; |
| 2171 | |
| 2172 | int32_t compact; |
| 2173 | floatx80 fp0, fp1, fp2, one; |
| 2174 | |
| 2175 | aSig = extractFloatx80Frac(a); |
| 2176 | aExp = extractFloatx80Exp(a); |
| 2177 | aSign = extractFloatx80Sign(a); |
| 2178 | |
| 2179 | if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) { |
| 2180 | return propagateFloatx80NaNOneArg(a, status); |
| 2181 | } |
| 2182 | |
| 2183 | if (aExp == 0 && aSig == 0) { |
| 2184 | return packFloatx80(aSign, 0, 0); |
| 2185 | } |
| 2186 | |
| 2187 | compact = floatx80_make_compact(aExp, aSig); |
| 2188 | |
| 2189 | if (compact >= 0x3FFF8000) { /* |X| >= 1 */ |
| 2190 | if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */ |
| 2191 | float_raise(float_flag_inexact, status); |
| 2192 | a = packFloatx80(aSign, piby2_exp, pi_sig); |
| 2193 | return floatx80_move(a, status); |
| 2194 | } else { /* |X| > 1 */ |
| 2195 | float_raise(float_flag_invalid, status); |
| 2196 | return floatx80_default_nan(status); |
| 2197 | } |
| 2198 | |
| 2199 | } /* |X| < 1 */ |
| 2200 | |
| 2201 | user_rnd_mode = status->float_rounding_mode; |
| 2202 | user_rnd_prec = status->floatx80_rounding_precision; |
| 2203 | status->float_rounding_mode = float_round_nearest_even; |
| 2204 | status->floatx80_rounding_precision = 80; |
| 2205 | |
| 2206 | one = packFloatx80(0, one_exp, one_sig); |
| 2207 | fp0 = a; |
| 2208 | |
| 2209 | fp1 = floatx80_sub(one, fp0, status); /* 1 - X */ |
| 2210 | fp2 = floatx80_add(one, fp0, status); /* 1 + X */ |
| 2211 | fp1 = floatx80_mul(fp2, fp1, status); /* (1+X)*(1-X) */ |
| 2212 | fp1 = floatx80_sqrt(fp1, status); /* SQRT((1+X)*(1-X)) */ |
| 2213 | fp0 = floatx80_div(fp0, fp1, status); /* X/SQRT((1+X)*(1-X)) */ |
| 2214 | |
| 2215 | status->float_rounding_mode = user_rnd_mode; |
| 2216 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2217 | |
| 2218 | a = floatx80_atan(fp0, status); /* ATAN(X/SQRT((1+X)*(1-X))) */ |
| 2219 | |
| 2220 | float_raise(float_flag_inexact, status); |
| 2221 | |
| 2222 | return a; |
| 2223 | } |
Laurent Vivier | c84813b | 2018-03-12 21:27:24 +0100 | [diff] [blame] | 2224 | |
| 2225 | /*---------------------------------------------------------------------------- |
| 2226 | | Arc cosine |
| 2227 | *----------------------------------------------------------------------------*/ |
| 2228 | |
| 2229 | floatx80 floatx80_acos(floatx80 a, float_status *status) |
| 2230 | { |
| 2231 | flag aSign; |
| 2232 | int32_t aExp; |
| 2233 | uint64_t aSig; |
| 2234 | |
| 2235 | int8_t user_rnd_mode, user_rnd_prec; |
| 2236 | |
| 2237 | int32_t compact; |
| 2238 | floatx80 fp0, fp1, one; |
| 2239 | |
| 2240 | aSig = extractFloatx80Frac(a); |
| 2241 | aExp = extractFloatx80Exp(a); |
| 2242 | aSign = extractFloatx80Sign(a); |
| 2243 | |
| 2244 | if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) { |
| 2245 | return propagateFloatx80NaNOneArg(a, status); |
| 2246 | } |
| 2247 | if (aExp == 0 && aSig == 0) { |
| 2248 | float_raise(float_flag_inexact, status); |
| 2249 | return roundAndPackFloatx80(status->floatx80_rounding_precision, 0, |
| 2250 | piby2_exp, pi_sig, 0, status); |
| 2251 | } |
| 2252 | |
| 2253 | compact = floatx80_make_compact(aExp, aSig); |
| 2254 | |
| 2255 | if (compact >= 0x3FFF8000) { /* |X| >= 1 */ |
| 2256 | if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */ |
| 2257 | if (aSign) { /* X == -1 */ |
| 2258 | a = packFloatx80(0, pi_exp, pi_sig); |
| 2259 | float_raise(float_flag_inexact, status); |
| 2260 | return floatx80_move(a, status); |
| 2261 | } else { /* X == +1 */ |
| 2262 | return packFloatx80(0, 0, 0); |
| 2263 | } |
| 2264 | } else { /* |X| > 1 */ |
| 2265 | float_raise(float_flag_invalid, status); |
| 2266 | return floatx80_default_nan(status); |
| 2267 | } |
| 2268 | } /* |X| < 1 */ |
| 2269 | |
| 2270 | user_rnd_mode = status->float_rounding_mode; |
| 2271 | user_rnd_prec = status->floatx80_rounding_precision; |
| 2272 | status->float_rounding_mode = float_round_nearest_even; |
| 2273 | status->floatx80_rounding_precision = 80; |
| 2274 | |
| 2275 | one = packFloatx80(0, one_exp, one_sig); |
| 2276 | fp0 = a; |
| 2277 | |
| 2278 | fp1 = floatx80_add(one, fp0, status); /* 1 + X */ |
| 2279 | fp0 = floatx80_sub(one, fp0, status); /* 1 - X */ |
| 2280 | fp0 = floatx80_div(fp0, fp1, status); /* (1-X)/(1+X) */ |
| 2281 | fp0 = floatx80_sqrt(fp0, status); /* SQRT((1-X)/(1+X)) */ |
| 2282 | fp0 = floatx80_atan(fp0, status); /* ATAN(SQRT((1-X)/(1+X))) */ |
| 2283 | |
| 2284 | status->float_rounding_mode = user_rnd_mode; |
| 2285 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2286 | |
| 2287 | a = floatx80_add(fp0, fp0, status); /* 2 * ATAN(SQRT((1-X)/(1+X))) */ |
| 2288 | |
| 2289 | float_raise(float_flag_inexact, status); |
| 2290 | |
| 2291 | return a; |
| 2292 | } |
Laurent Vivier | e3655af | 2018-03-12 21:27:25 +0100 | [diff] [blame] | 2293 | |
| 2294 | /*---------------------------------------------------------------------------- |
| 2295 | | Hyperbolic arc tangent |
| 2296 | *----------------------------------------------------------------------------*/ |
| 2297 | |
| 2298 | floatx80 floatx80_atanh(floatx80 a, float_status *status) |
| 2299 | { |
| 2300 | flag aSign; |
| 2301 | int32_t aExp; |
| 2302 | uint64_t aSig; |
| 2303 | |
| 2304 | int8_t user_rnd_mode, user_rnd_prec; |
| 2305 | |
| 2306 | int32_t compact; |
| 2307 | floatx80 fp0, fp1, fp2, one; |
| 2308 | |
| 2309 | aSig = extractFloatx80Frac(a); |
| 2310 | aExp = extractFloatx80Exp(a); |
| 2311 | aSign = extractFloatx80Sign(a); |
| 2312 | |
| 2313 | if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) { |
| 2314 | return propagateFloatx80NaNOneArg(a, status); |
| 2315 | } |
| 2316 | |
| 2317 | if (aExp == 0 && aSig == 0) { |
| 2318 | return packFloatx80(aSign, 0, 0); |
| 2319 | } |
| 2320 | |
| 2321 | compact = floatx80_make_compact(aExp, aSig); |
| 2322 | |
| 2323 | if (compact >= 0x3FFF8000) { /* |X| >= 1 */ |
| 2324 | if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */ |
| 2325 | float_raise(float_flag_divbyzero, status); |
| 2326 | return packFloatx80(aSign, floatx80_infinity.high, |
| 2327 | floatx80_infinity.low); |
| 2328 | } else { /* |X| > 1 */ |
| 2329 | float_raise(float_flag_invalid, status); |
| 2330 | return floatx80_default_nan(status); |
| 2331 | } |
| 2332 | } /* |X| < 1 */ |
| 2333 | |
| 2334 | user_rnd_mode = status->float_rounding_mode; |
| 2335 | user_rnd_prec = status->floatx80_rounding_precision; |
| 2336 | status->float_rounding_mode = float_round_nearest_even; |
| 2337 | status->floatx80_rounding_precision = 80; |
| 2338 | |
| 2339 | one = packFloatx80(0, one_exp, one_sig); |
| 2340 | fp2 = packFloatx80(aSign, 0x3FFE, one_sig); /* SIGN(X) * (1/2) */ |
| 2341 | fp0 = packFloatx80(0, aExp, aSig); /* Y = |X| */ |
| 2342 | fp1 = packFloatx80(1, aExp, aSig); /* -Y */ |
| 2343 | fp0 = floatx80_add(fp0, fp0, status); /* 2Y */ |
| 2344 | fp1 = floatx80_add(fp1, one, status); /* 1-Y */ |
| 2345 | fp0 = floatx80_div(fp0, fp1, status); /* Z = 2Y/(1-Y) */ |
| 2346 | fp0 = floatx80_lognp1(fp0, status); /* LOG1P(Z) */ |
| 2347 | |
| 2348 | status->float_rounding_mode = user_rnd_mode; |
| 2349 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2350 | |
| 2351 | a = floatx80_mul(fp0, fp2, |
| 2352 | status); /* ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z) */ |
| 2353 | |
| 2354 | float_raise(float_flag_inexact, status); |
| 2355 | |
| 2356 | return a; |
| 2357 | } |
Laurent Vivier | 9937b02 | 2018-03-12 21:27:26 +0100 | [diff] [blame] | 2358 | |
| 2359 | /*---------------------------------------------------------------------------- |
| 2360 | | e to x minus 1 |
| 2361 | *----------------------------------------------------------------------------*/ |
| 2362 | |
| 2363 | floatx80 floatx80_etoxm1(floatx80 a, float_status *status) |
| 2364 | { |
| 2365 | flag aSign; |
| 2366 | int32_t aExp; |
| 2367 | uint64_t aSig; |
| 2368 | |
| 2369 | int8_t user_rnd_mode, user_rnd_prec; |
| 2370 | |
| 2371 | int32_t compact, n, j, m, m1; |
| 2372 | floatx80 fp0, fp1, fp2, fp3, l2, sc, onebysc; |
| 2373 | |
| 2374 | aSig = extractFloatx80Frac(a); |
| 2375 | aExp = extractFloatx80Exp(a); |
| 2376 | aSign = extractFloatx80Sign(a); |
| 2377 | |
| 2378 | if (aExp == 0x7FFF) { |
| 2379 | if ((uint64_t) (aSig << 1)) { |
| 2380 | return propagateFloatx80NaNOneArg(a, status); |
| 2381 | } |
| 2382 | if (aSign) { |
| 2383 | return packFloatx80(aSign, one_exp, one_sig); |
| 2384 | } |
| 2385 | return packFloatx80(0, floatx80_infinity.high, |
| 2386 | floatx80_infinity.low); |
| 2387 | } |
| 2388 | |
| 2389 | if (aExp == 0 && aSig == 0) { |
| 2390 | return packFloatx80(aSign, 0, 0); |
| 2391 | } |
| 2392 | |
| 2393 | user_rnd_mode = status->float_rounding_mode; |
| 2394 | user_rnd_prec = status->floatx80_rounding_precision; |
| 2395 | status->float_rounding_mode = float_round_nearest_even; |
| 2396 | status->floatx80_rounding_precision = 80; |
| 2397 | |
| 2398 | if (aExp >= 0x3FFD) { /* |X| >= 1/4 */ |
| 2399 | compact = floatx80_make_compact(aExp, aSig); |
| 2400 | |
| 2401 | if (compact <= 0x4004C215) { /* |X| <= 70 log2 */ |
| 2402 | fp0 = a; |
| 2403 | fp1 = a; |
| 2404 | fp0 = floatx80_mul(fp0, float32_to_floatx80( |
| 2405 | make_float32(0x42B8AA3B), status), |
| 2406 | status); /* 64/log2 * X */ |
| 2407 | n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */ |
| 2408 | fp0 = int32_to_floatx80(n, status); |
| 2409 | |
| 2410 | j = n & 0x3F; /* J = N mod 64 */ |
| 2411 | m = n / 64; /* NOTE: this is really arithmetic right shift by 6 */ |
| 2412 | if (n < 0 && j) { |
| 2413 | /* arithmetic right shift is division and |
| 2414 | * round towards minus infinity |
| 2415 | */ |
| 2416 | m--; |
| 2417 | } |
| 2418 | m1 = -m; |
| 2419 | /*m += 0x3FFF; // biased exponent of 2^(M) */ |
| 2420 | /*m1 += 0x3FFF; // biased exponent of -2^(-M) */ |
| 2421 | |
| 2422 | fp2 = fp0; /* N */ |
| 2423 | fp0 = floatx80_mul(fp0, float32_to_floatx80( |
| 2424 | make_float32(0xBC317218), status), |
| 2425 | status); /* N * L1, L1 = lead(-log2/64) */ |
| 2426 | l2 = packFloatx80(0, 0x3FDC, LIT64(0x82E308654361C4C6)); |
| 2427 | fp2 = floatx80_mul(fp2, l2, status); /* N * L2, L1+L2 = -log2/64 */ |
| 2428 | fp0 = floatx80_add(fp0, fp1, status); /* X + N*L1 */ |
| 2429 | fp0 = floatx80_add(fp0, fp2, status); /* R */ |
| 2430 | |
| 2431 | fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ |
| 2432 | fp2 = float32_to_floatx80(make_float32(0x3950097B), |
| 2433 | status); /* A6 */ |
| 2434 | fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*A6 */ |
| 2435 | fp3 = floatx80_mul(float32_to_floatx80(make_float32(0x3AB60B6A), |
| 2436 | status), fp1, status); /* fp3 is S*A5 */ |
| 2437 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 2438 | make_float64(0x3F81111111174385), status), |
| 2439 | status); /* fp2 IS A4+S*A6 */ |
| 2440 | fp3 = floatx80_add(fp3, float64_to_floatx80( |
| 2441 | make_float64(0x3FA5555555554F5A), status), |
| 2442 | status); /* fp3 is A3+S*A5 */ |
| 2443 | fp2 = floatx80_mul(fp2, fp1, status); /* fp2 IS S*(A4+S*A6) */ |
| 2444 | fp3 = floatx80_mul(fp3, fp1, status); /* fp3 IS S*(A3+S*A5) */ |
| 2445 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 2446 | make_float64(0x3FC5555555555555), status), |
| 2447 | status); /* fp2 IS A2+S*(A4+S*A6) */ |
| 2448 | fp3 = floatx80_add(fp3, float32_to_floatx80( |
| 2449 | make_float32(0x3F000000), status), |
| 2450 | status); /* fp3 IS A1+S*(A3+S*A5) */ |
| 2451 | fp2 = floatx80_mul(fp2, fp1, |
| 2452 | status); /* fp2 IS S*(A2+S*(A4+S*A6)) */ |
| 2453 | fp1 = floatx80_mul(fp1, fp3, |
| 2454 | status); /* fp1 IS S*(A1+S*(A3+S*A5)) */ |
| 2455 | fp2 = floatx80_mul(fp2, fp0, |
| 2456 | status); /* fp2 IS R*S*(A2+S*(A4+S*A6)) */ |
| 2457 | fp0 = floatx80_add(fp0, fp1, |
| 2458 | status); /* fp0 IS R+S*(A1+S*(A3+S*A5)) */ |
| 2459 | fp0 = floatx80_add(fp0, fp2, status); /* fp0 IS EXP(R) - 1 */ |
| 2460 | |
| 2461 | fp0 = floatx80_mul(fp0, exp_tbl[j], |
| 2462 | status); /* 2^(J/64)*(Exp(R)-1) */ |
| 2463 | |
| 2464 | if (m >= 64) { |
| 2465 | fp1 = float32_to_floatx80(exp_tbl2[j], status); |
| 2466 | onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */ |
| 2467 | fp1 = floatx80_add(fp1, onebysc, status); |
| 2468 | fp0 = floatx80_add(fp0, fp1, status); |
| 2469 | fp0 = floatx80_add(fp0, exp_tbl[j], status); |
| 2470 | } else if (m < -3) { |
| 2471 | fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], |
| 2472 | status), status); |
| 2473 | fp0 = floatx80_add(fp0, exp_tbl[j], status); |
| 2474 | onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */ |
| 2475 | fp0 = floatx80_add(fp0, onebysc, status); |
| 2476 | } else { /* -3 <= m <= 63 */ |
| 2477 | fp1 = exp_tbl[j]; |
| 2478 | fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], |
| 2479 | status), status); |
| 2480 | onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */ |
| 2481 | fp1 = floatx80_add(fp1, onebysc, status); |
| 2482 | fp0 = floatx80_add(fp0, fp1, status); |
| 2483 | } |
| 2484 | |
| 2485 | sc = packFloatx80(0, m + 0x3FFF, one_sig); |
| 2486 | |
| 2487 | status->float_rounding_mode = user_rnd_mode; |
| 2488 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2489 | |
| 2490 | a = floatx80_mul(fp0, sc, status); |
| 2491 | |
| 2492 | float_raise(float_flag_inexact, status); |
| 2493 | |
| 2494 | return a; |
| 2495 | } else { /* |X| > 70 log2 */ |
| 2496 | if (aSign) { |
| 2497 | fp0 = float32_to_floatx80(make_float32(0xBF800000), |
| 2498 | status); /* -1 */ |
| 2499 | |
| 2500 | status->float_rounding_mode = user_rnd_mode; |
| 2501 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2502 | |
| 2503 | a = floatx80_add(fp0, float32_to_floatx80( |
| 2504 | make_float32(0x00800000), status), |
| 2505 | status); /* -1 + 2^(-126) */ |
| 2506 | |
| 2507 | float_raise(float_flag_inexact, status); |
| 2508 | |
| 2509 | return a; |
| 2510 | } else { |
| 2511 | status->float_rounding_mode = user_rnd_mode; |
| 2512 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2513 | |
| 2514 | return floatx80_etox(a, status); |
| 2515 | } |
| 2516 | } |
| 2517 | } else { /* |X| < 1/4 */ |
| 2518 | if (aExp >= 0x3FBE) { |
| 2519 | fp0 = a; |
| 2520 | fp0 = floatx80_mul(fp0, fp0, status); /* S = X*X */ |
| 2521 | fp1 = float32_to_floatx80(make_float32(0x2F30CAA8), |
| 2522 | status); /* B12 */ |
| 2523 | fp1 = floatx80_mul(fp1, fp0, status); /* S * B12 */ |
| 2524 | fp2 = float32_to_floatx80(make_float32(0x310F8290), |
| 2525 | status); /* B11 */ |
| 2526 | fp1 = floatx80_add(fp1, float32_to_floatx80( |
| 2527 | make_float32(0x32D73220), status), |
| 2528 | status); /* B10 */ |
| 2529 | fp2 = floatx80_mul(fp2, fp0, status); |
| 2530 | fp1 = floatx80_mul(fp1, fp0, status); |
| 2531 | fp2 = floatx80_add(fp2, float32_to_floatx80( |
| 2532 | make_float32(0x3493F281), status), |
| 2533 | status); /* B9 */ |
| 2534 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 2535 | make_float64(0x3EC71DE3A5774682), status), |
| 2536 | status); /* B8 */ |
| 2537 | fp2 = floatx80_mul(fp2, fp0, status); |
| 2538 | fp1 = floatx80_mul(fp1, fp0, status); |
| 2539 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 2540 | make_float64(0x3EFA01A019D7CB68), status), |
| 2541 | status); /* B7 */ |
| 2542 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 2543 | make_float64(0x3F2A01A01A019DF3), status), |
| 2544 | status); /* B6 */ |
| 2545 | fp2 = floatx80_mul(fp2, fp0, status); |
| 2546 | fp1 = floatx80_mul(fp1, fp0, status); |
| 2547 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 2548 | make_float64(0x3F56C16C16C170E2), status), |
| 2549 | status); /* B5 */ |
| 2550 | fp1 = floatx80_add(fp1, float64_to_floatx80( |
| 2551 | make_float64(0x3F81111111111111), status), |
| 2552 | status); /* B4 */ |
| 2553 | fp2 = floatx80_mul(fp2, fp0, status); |
| 2554 | fp1 = floatx80_mul(fp1, fp0, status); |
| 2555 | fp2 = floatx80_add(fp2, float64_to_floatx80( |
| 2556 | make_float64(0x3FA5555555555555), status), |
| 2557 | status); /* B3 */ |
| 2558 | fp3 = packFloatx80(0, 0x3FFC, LIT64(0xAAAAAAAAAAAAAAAB)); |
| 2559 | fp1 = floatx80_add(fp1, fp3, status); /* B2 */ |
| 2560 | fp2 = floatx80_mul(fp2, fp0, status); |
| 2561 | fp1 = floatx80_mul(fp1, fp0, status); |
| 2562 | |
| 2563 | fp2 = floatx80_mul(fp2, fp0, status); |
| 2564 | fp1 = floatx80_mul(fp1, a, status); |
| 2565 | |
| 2566 | fp0 = floatx80_mul(fp0, float32_to_floatx80( |
| 2567 | make_float32(0x3F000000), status), |
| 2568 | status); /* S*B1 */ |
| 2569 | fp1 = floatx80_add(fp1, fp2, status); /* Q */ |
| 2570 | fp0 = floatx80_add(fp0, fp1, status); /* S*B1+Q */ |
| 2571 | |
| 2572 | status->float_rounding_mode = user_rnd_mode; |
| 2573 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2574 | |
| 2575 | a = floatx80_add(fp0, a, status); |
| 2576 | |
| 2577 | float_raise(float_flag_inexact, status); |
| 2578 | |
| 2579 | return a; |
| 2580 | } else { /* |X| < 2^(-65) */ |
| 2581 | sc = packFloatx80(1, 1, one_sig); |
| 2582 | fp0 = a; |
| 2583 | |
| 2584 | if (aExp < 0x0033) { /* |X| < 2^(-16382) */ |
| 2585 | fp0 = floatx80_mul(fp0, float64_to_floatx80( |
| 2586 | make_float64(0x48B0000000000000), status), |
| 2587 | status); |
| 2588 | fp0 = floatx80_add(fp0, sc, status); |
| 2589 | |
| 2590 | status->float_rounding_mode = user_rnd_mode; |
| 2591 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2592 | |
| 2593 | a = floatx80_mul(fp0, float64_to_floatx80( |
| 2594 | make_float64(0x3730000000000000), status), |
| 2595 | status); |
| 2596 | } else { |
| 2597 | status->float_rounding_mode = user_rnd_mode; |
| 2598 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2599 | |
| 2600 | a = floatx80_add(fp0, sc, status); |
| 2601 | } |
| 2602 | |
| 2603 | float_raise(float_flag_inexact, status); |
| 2604 | |
| 2605 | return a; |
| 2606 | } |
| 2607 | } |
| 2608 | } |
| 2609 | |
| 2610 | /*---------------------------------------------------------------------------- |
| 2611 | | Hyperbolic tangent |
| 2612 | *----------------------------------------------------------------------------*/ |
| 2613 | |
| 2614 | floatx80 floatx80_tanh(floatx80 a, float_status *status) |
| 2615 | { |
| 2616 | flag aSign, vSign; |
| 2617 | int32_t aExp, vExp; |
| 2618 | uint64_t aSig, vSig; |
| 2619 | |
| 2620 | int8_t user_rnd_mode, user_rnd_prec; |
| 2621 | |
| 2622 | int32_t compact; |
| 2623 | floatx80 fp0, fp1; |
| 2624 | uint32_t sign; |
| 2625 | |
| 2626 | aSig = extractFloatx80Frac(a); |
| 2627 | aExp = extractFloatx80Exp(a); |
| 2628 | aSign = extractFloatx80Sign(a); |
| 2629 | |
| 2630 | if (aExp == 0x7FFF) { |
| 2631 | if ((uint64_t) (aSig << 1)) { |
| 2632 | return propagateFloatx80NaNOneArg(a, status); |
| 2633 | } |
| 2634 | return packFloatx80(aSign, one_exp, one_sig); |
| 2635 | } |
| 2636 | |
| 2637 | if (aExp == 0 && aSig == 0) { |
| 2638 | return packFloatx80(aSign, 0, 0); |
| 2639 | } |
| 2640 | |
| 2641 | user_rnd_mode = status->float_rounding_mode; |
| 2642 | user_rnd_prec = status->floatx80_rounding_precision; |
| 2643 | status->float_rounding_mode = float_round_nearest_even; |
| 2644 | status->floatx80_rounding_precision = 80; |
| 2645 | |
| 2646 | compact = floatx80_make_compact(aExp, aSig); |
| 2647 | |
| 2648 | if (compact < 0x3FD78000 || compact > 0x3FFFDDCE) { |
| 2649 | /* TANHBORS */ |
| 2650 | if (compact < 0x3FFF8000) { |
| 2651 | /* TANHSM */ |
| 2652 | status->float_rounding_mode = user_rnd_mode; |
| 2653 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2654 | |
| 2655 | a = floatx80_move(a, status); |
| 2656 | |
| 2657 | float_raise(float_flag_inexact, status); |
| 2658 | |
| 2659 | return a; |
| 2660 | } else { |
| 2661 | if (compact > 0x40048AA1) { |
| 2662 | /* TANHHUGE */ |
| 2663 | sign = 0x3F800000; |
| 2664 | sign |= aSign ? 0x80000000 : 0x00000000; |
| 2665 | fp0 = float32_to_floatx80(make_float32(sign), status); |
| 2666 | sign &= 0x80000000; |
| 2667 | sign ^= 0x80800000; /* -SIGN(X)*EPS */ |
| 2668 | |
| 2669 | status->float_rounding_mode = user_rnd_mode; |
| 2670 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2671 | |
| 2672 | a = floatx80_add(fp0, float32_to_floatx80(make_float32(sign), |
| 2673 | status), status); |
| 2674 | |
| 2675 | float_raise(float_flag_inexact, status); |
| 2676 | |
| 2677 | return a; |
| 2678 | } else { |
| 2679 | fp0 = packFloatx80(0, aExp + 1, aSig); /* Y = 2|X| */ |
| 2680 | fp0 = floatx80_etox(fp0, status); /* FP0 IS EXP(Y) */ |
| 2681 | fp0 = floatx80_add(fp0, float32_to_floatx80( |
| 2682 | make_float32(0x3F800000), |
| 2683 | status), status); /* EXP(Y)+1 */ |
| 2684 | sign = aSign ? 0x80000000 : 0x00000000; |
| 2685 | fp1 = floatx80_div(float32_to_floatx80(make_float32( |
| 2686 | sign ^ 0xC0000000), status), fp0, |
| 2687 | status); /* -SIGN(X)*2 / [EXP(Y)+1] */ |
| 2688 | fp0 = float32_to_floatx80(make_float32(sign | 0x3F800000), |
| 2689 | status); /* SIGN */ |
| 2690 | |
| 2691 | status->float_rounding_mode = user_rnd_mode; |
| 2692 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2693 | |
| 2694 | a = floatx80_add(fp1, fp0, status); |
| 2695 | |
| 2696 | float_raise(float_flag_inexact, status); |
| 2697 | |
| 2698 | return a; |
| 2699 | } |
| 2700 | } |
| 2701 | } else { /* 2**(-40) < |X| < (5/2)LOG2 */ |
| 2702 | fp0 = packFloatx80(0, aExp + 1, aSig); /* Y = 2|X| */ |
| 2703 | fp0 = floatx80_etoxm1(fp0, status); /* FP0 IS Z = EXPM1(Y) */ |
| 2704 | fp1 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x40000000), |
| 2705 | status), |
| 2706 | status); /* Z+2 */ |
| 2707 | |
| 2708 | vSign = extractFloatx80Sign(fp1); |
| 2709 | vExp = extractFloatx80Exp(fp1); |
| 2710 | vSig = extractFloatx80Frac(fp1); |
| 2711 | |
| 2712 | fp1 = packFloatx80(vSign ^ aSign, vExp, vSig); |
| 2713 | |
| 2714 | status->float_rounding_mode = user_rnd_mode; |
| 2715 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2716 | |
| 2717 | a = floatx80_div(fp0, fp1, status); |
| 2718 | |
| 2719 | float_raise(float_flag_inexact, status); |
| 2720 | |
| 2721 | return a; |
| 2722 | } |
| 2723 | } |
Laurent Vivier | eee6b89 | 2018-03-12 21:27:27 +0100 | [diff] [blame] | 2724 | |
| 2725 | /*---------------------------------------------------------------------------- |
| 2726 | | Hyperbolic sine |
| 2727 | *----------------------------------------------------------------------------*/ |
| 2728 | |
| 2729 | floatx80 floatx80_sinh(floatx80 a, float_status *status) |
| 2730 | { |
| 2731 | flag aSign; |
| 2732 | int32_t aExp; |
| 2733 | uint64_t aSig; |
| 2734 | |
| 2735 | int8_t user_rnd_mode, user_rnd_prec; |
| 2736 | |
| 2737 | int32_t compact; |
| 2738 | floatx80 fp0, fp1, fp2; |
| 2739 | float32 fact; |
| 2740 | |
| 2741 | aSig = extractFloatx80Frac(a); |
| 2742 | aExp = extractFloatx80Exp(a); |
| 2743 | aSign = extractFloatx80Sign(a); |
| 2744 | |
| 2745 | if (aExp == 0x7FFF) { |
| 2746 | if ((uint64_t) (aSig << 1)) { |
| 2747 | return propagateFloatx80NaNOneArg(a, status); |
| 2748 | } |
| 2749 | return packFloatx80(aSign, floatx80_infinity.high, |
| 2750 | floatx80_infinity.low); |
| 2751 | } |
| 2752 | |
| 2753 | if (aExp == 0 && aSig == 0) { |
| 2754 | return packFloatx80(aSign, 0, 0); |
| 2755 | } |
| 2756 | |
| 2757 | user_rnd_mode = status->float_rounding_mode; |
| 2758 | user_rnd_prec = status->floatx80_rounding_precision; |
| 2759 | status->float_rounding_mode = float_round_nearest_even; |
| 2760 | status->floatx80_rounding_precision = 80; |
| 2761 | |
| 2762 | compact = floatx80_make_compact(aExp, aSig); |
| 2763 | |
| 2764 | if (compact > 0x400CB167) { |
| 2765 | /* SINHBIG */ |
| 2766 | if (compact > 0x400CB2B3) { |
| 2767 | status->float_rounding_mode = user_rnd_mode; |
| 2768 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2769 | |
| 2770 | return roundAndPackFloatx80(status->floatx80_rounding_precision, |
| 2771 | aSign, 0x8000, aSig, 0, status); |
| 2772 | } else { |
| 2773 | fp0 = floatx80_abs(a); /* Y = |X| */ |
| 2774 | fp0 = floatx80_sub(fp0, float64_to_floatx80( |
| 2775 | make_float64(0x40C62D38D3D64634), status), |
| 2776 | status); /* (|X|-16381LOG2_LEAD) */ |
| 2777 | fp0 = floatx80_sub(fp0, float64_to_floatx80( |
| 2778 | make_float64(0x3D6F90AEB1E75CC7), status), |
| 2779 | status); /* |X| - 16381 LOG2, ACCURATE */ |
| 2780 | fp0 = floatx80_etox(fp0, status); |
| 2781 | fp2 = packFloatx80(aSign, 0x7FFB, one_sig); |
| 2782 | |
| 2783 | status->float_rounding_mode = user_rnd_mode; |
| 2784 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2785 | |
| 2786 | a = floatx80_mul(fp0, fp2, status); |
| 2787 | |
| 2788 | float_raise(float_flag_inexact, status); |
| 2789 | |
| 2790 | return a; |
| 2791 | } |
| 2792 | } else { /* |X| < 16380 LOG2 */ |
| 2793 | fp0 = floatx80_abs(a); /* Y = |X| */ |
| 2794 | fp0 = floatx80_etoxm1(fp0, status); /* FP0 IS Z = EXPM1(Y) */ |
| 2795 | fp1 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), |
| 2796 | status), status); /* 1+Z */ |
| 2797 | fp2 = fp0; |
| 2798 | fp0 = floatx80_div(fp0, fp1, status); /* Z/(1+Z) */ |
| 2799 | fp0 = floatx80_add(fp0, fp2, status); |
| 2800 | |
| 2801 | fact = packFloat32(aSign, 0x7E, 0); |
| 2802 | |
| 2803 | status->float_rounding_mode = user_rnd_mode; |
| 2804 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2805 | |
| 2806 | a = floatx80_mul(fp0, float32_to_floatx80(fact, status), status); |
| 2807 | |
| 2808 | float_raise(float_flag_inexact, status); |
| 2809 | |
| 2810 | return a; |
| 2811 | } |
| 2812 | } |
Laurent Vivier | 02f9124 | 2018-03-12 21:27:28 +0100 | [diff] [blame] | 2813 | |
| 2814 | /*---------------------------------------------------------------------------- |
| 2815 | | Hyperbolic cosine |
| 2816 | *----------------------------------------------------------------------------*/ |
| 2817 | |
| 2818 | floatx80 floatx80_cosh(floatx80 a, float_status *status) |
| 2819 | { |
| 2820 | int32_t aExp; |
| 2821 | uint64_t aSig; |
| 2822 | |
| 2823 | int8_t user_rnd_mode, user_rnd_prec; |
| 2824 | |
| 2825 | int32_t compact; |
| 2826 | floatx80 fp0, fp1; |
| 2827 | |
| 2828 | aSig = extractFloatx80Frac(a); |
| 2829 | aExp = extractFloatx80Exp(a); |
| 2830 | |
| 2831 | if (aExp == 0x7FFF) { |
| 2832 | if ((uint64_t) (aSig << 1)) { |
| 2833 | return propagateFloatx80NaNOneArg(a, status); |
| 2834 | } |
| 2835 | return packFloatx80(0, floatx80_infinity.high, |
| 2836 | floatx80_infinity.low); |
| 2837 | } |
| 2838 | |
| 2839 | if (aExp == 0 && aSig == 0) { |
| 2840 | return packFloatx80(0, one_exp, one_sig); |
| 2841 | } |
| 2842 | |
| 2843 | user_rnd_mode = status->float_rounding_mode; |
| 2844 | user_rnd_prec = status->floatx80_rounding_precision; |
| 2845 | status->float_rounding_mode = float_round_nearest_even; |
| 2846 | status->floatx80_rounding_precision = 80; |
| 2847 | |
| 2848 | compact = floatx80_make_compact(aExp, aSig); |
| 2849 | |
| 2850 | if (compact > 0x400CB167) { |
| 2851 | if (compact > 0x400CB2B3) { |
| 2852 | status->float_rounding_mode = user_rnd_mode; |
| 2853 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2854 | return roundAndPackFloatx80(status->floatx80_rounding_precision, 0, |
| 2855 | 0x8000, one_sig, 0, status); |
| 2856 | } else { |
| 2857 | fp0 = packFloatx80(0, aExp, aSig); |
| 2858 | fp0 = floatx80_sub(fp0, float64_to_floatx80( |
| 2859 | make_float64(0x40C62D38D3D64634), status), |
| 2860 | status); |
| 2861 | fp0 = floatx80_sub(fp0, float64_to_floatx80( |
| 2862 | make_float64(0x3D6F90AEB1E75CC7), status), |
| 2863 | status); |
| 2864 | fp0 = floatx80_etox(fp0, status); |
| 2865 | fp1 = packFloatx80(0, 0x7FFB, one_sig); |
| 2866 | |
| 2867 | status->float_rounding_mode = user_rnd_mode; |
| 2868 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2869 | |
| 2870 | a = floatx80_mul(fp0, fp1, status); |
| 2871 | |
| 2872 | float_raise(float_flag_inexact, status); |
| 2873 | |
| 2874 | return a; |
| 2875 | } |
| 2876 | } |
| 2877 | |
| 2878 | fp0 = packFloatx80(0, aExp, aSig); /* |X| */ |
| 2879 | fp0 = floatx80_etox(fp0, status); /* EXP(|X|) */ |
| 2880 | fp0 = floatx80_mul(fp0, float32_to_floatx80(make_float32(0x3F000000), |
| 2881 | status), status); /* (1/2)*EXP(|X|) */ |
| 2882 | fp1 = float32_to_floatx80(make_float32(0x3E800000), status); /* 1/4 */ |
| 2883 | fp1 = floatx80_div(fp1, fp0, status); /* 1/(2*EXP(|X|)) */ |
| 2884 | |
| 2885 | status->float_rounding_mode = user_rnd_mode; |
| 2886 | status->floatx80_rounding_precision = user_rnd_prec; |
| 2887 | |
| 2888 | a = floatx80_add(fp0, fp1, status); |
| 2889 | |
| 2890 | float_raise(float_flag_inexact, status); |
| 2891 | |
| 2892 | return a; |
| 2893 | } |