n_argred.S revision 1.9
1 /* $NetBSD: n_argred.S,v 1.9 2007/04/19 00:37:20 matt Exp $ */ 2 /* 3 * Copyright (c) 1985, 1993 4 * The Regents of the University of California. All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 3. Neither the name of the University nor the names of its contributors 15 * may be used to endorse or promote products derived from this software 16 * without specific prior written permission. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 28 * SUCH DAMAGE. 29 * 30 * @(#)argred.s 8.1 (Berkeley) 6/4/93 31 */ 32 33 #include <machine/asm.h> 34 35 /* 36 * libm$argred implements Bob Corbett's argument reduction and 37 * libm$sincos implements Peter Tang's double precision sin/cos. 38 * 39 * Note: The two entry points libm$argred and libm$sincos are meant 40 * to be used only by _sin, _cos and _tan. 41 * 42 * method: true range reduction to [-pi/4,pi/4], P. Tang & B. Corbett 43 * S. McDonald, April 4, 1985 44 */ 45 46 .hidden __libm_argred 47 ENTRY(__libm_argred, 0) 48 /* 49 * Compare the argument with the largest possible that can 50 * be reduced by table lookup. %r3 := |x| will be used in table_lookup . 51 */ 52 movd %r0,%r3 53 bgeq abs1 54 mnegd %r3,%r3 55 abs1: 56 cmpd %r3,$0d+4.55530934770520019583e+01 57 blss small_arg 58 jsb trigred 59 rsb 60 small_arg: 61 jsb table_lookup 62 rsb 63 /* 64 * At this point, 65 * %r0 contains the quadrant number, 0, 1, 2, or 3; 66 * %r2/%r1 contains the reduced argument as a D-format number; 67 * %r3 contains a F-format extension to the reduced argument; 68 * %r4 contains a 0 or 1 corresponding to a sin or cos entry. 69 */ 70 71 .hidden __libm_sincos 72 ENTRY(__libm_sincos, 0) 73 /* 74 * Compensate for a cosine entry by adding one to the quadrant number. 75 */ 76 addl2 %r4,%r0 77 /* 78 * Polyd clobbers %r5-%r0 ; save X in %r7/%r6 . 79 * This can be avoided by rewriting trigred . 80 */ 81 movd %r1,%r6 82 /* 83 * Likewise, save alpha in %r8 . 84 * This can be avoided by rewriting trigred . 85 */ 86 movf %r3,%r8 87 /* 88 * Odd or even quadrant? cosine if odd, sine otherwise. 89 * Save floor(quadrant/2) in %r9 ; it determines the final sign. 90 */ 91 rotl $-1,%r0,%r9 92 blss cosine 93 sine: 94 muld2 %r1,%r1 # Xsq = X * X 95 cmpw $0x2480,%r1 # [zl] Xsq > 2^-56? 96 blss 1f # [zl] yes, go ahead and do polyd 97 clrq %r1 # [zl] work around 11/780 FPA polyd bug 98 1: 99 polyd %r1,$7,sin_coef # Q = P(Xsq) , of deg 7 100 mulf3 $0f3.0,%r8,%r4 # beta = 3 * alpha 101 mulf2 %r0,%r4 # beta = Q * beta 102 addf2 %r8,%r4 # beta = alpha + beta 103 muld2 %r6,%r0 # S(X) = X * Q 104 /* cvtfd %r4,%r4 ... %r5 = 0 after a polyd. */ 105 addd2 %r4,%r0 # S(X) = beta + S(X) 106 addd2 %r6,%r0 # S(X) = X + S(X) 107 jbr done 108 cosine: 109 muld2 %r6,%r6 # Xsq = X * X 110 beql zero_arg 111 mulf2 %r1,%r8 # beta = X * alpha 112 polyd %r6,$7,cos_coef /* Q = P'(Xsq) , of deg 7 */ 113 subd3 %r0,%r8,%r0 # beta = beta - Q 114 subw2 $0x80,%r6 # Xsq = Xsq / 2 115 addd2 %r0,%r6 # Xsq = Xsq + beta 116 zero_arg: 117 subd3 %r6,$0d1.0,%r0 # C(X) = 1 - Xsq 118 done: 119 blbc %r9,even 120 mnegd %r0,%r0 121 even: 122 rsb 123 124 #ifdef __ELF__ 125 .section .rodata 126 #else 127 .text 128 #endif 129 _ALIGN_TEXT 130 131 sin_coef: 132 .double 0d-7.53080332264191085773e-13 # s7 = 2^-29 -1.a7f2504ffc49f8.. 133 .double 0d+1.60573519267703489121e-10 # s6 = 2^-21 1.611adaede473c8.. 134 .double 0d-2.50520965150706067211e-08 # s5 = 2^-1a -1.ae644921ed8382.. 135 .double 0d+2.75573191800593885716e-06 # s4 = 2^-13 1.71de3a4b884278.. 136 .double 0d-1.98412698411850507950e-04 # s3 = 2^-0d -1.a01a01a0125e7d.. 137 .double 0d+8.33333333333325688985e-03 # s2 = 2^-07 1.11111111110e50 138 .double 0d-1.66666666666666664354e-01 # s1 = 2^-03 -1.55555555555554 139 .double 0d+0.00000000000000000000e+00 # s0 = 0 140 141 cos_coef: 142 .double 0d-1.13006966202629430300e-11 # s7 = 2^-25 -1.8D9BA04D1374BE.. 143 .double 0d+2.08746646574796004700e-09 # s6 = 2^-1D 1.1EE632650350BA.. 144 .double 0d-2.75573073031284417300e-07 # s5 = 2^-16 -1.27E4F31411719E.. 145 .double 0d+2.48015872682668025200e-05 # s4 = 2^-10 1.A01A0196B902E8.. 146 .double 0d-1.38888888888464709200e-03 # s3 = 2^-0A -1.6C16C16C11FACE.. 147 .double 0d+4.16666666666664761400e-02 # s2 = 2^-05 1.5555555555539E 148 .double 0d+0.00000000000000000000e+00 # s1 = 0 149 .double 0d+0.00000000000000000000e+00 # s0 = 0 150 151 /* 152 * Multiples of pi/2 expressed as the sum of three doubles, 153 * 154 * trailing: n * pi/2 , n = 0, 1, 2, ..., 29 155 * trailing[n] , 156 * 157 * middle: n * pi/2 , n = 0, 1, 2, ..., 29 158 * middle[n] , 159 * 160 * leading: n * pi/2 , n = 0, 1, 2, ..., 29 161 * leading[n] , 162 * 163 * where 164 * leading[n] := (n * pi/2) rounded, 165 * middle[n] := (n * pi/2 - leading[n]) rounded, 166 * trailing[n] := (( n * pi/2 - leading[n]) - middle[n]) rounded . 167 */ 168 trailing: 169 .double 0d+0.00000000000000000000e+00 # 0 * pi/2 trailing 170 .double 0d+4.33590506506189049611e-35 # 1 * pi/2 trailing 171 .double 0d+8.67181013012378099223e-35 # 2 * pi/2 trailing 172 .double 0d+1.30077151951856714215e-34 # 3 * pi/2 trailing 173 .double 0d+1.73436202602475619845e-34 # 4 * pi/2 trailing 174 .double 0d-1.68390735624352669192e-34 # 5 * pi/2 trailing 175 .double 0d+2.60154303903713428430e-34 # 6 * pi/2 trailing 176 .double 0d-8.16726343231148352150e-35 # 7 * pi/2 trailing 177 .double 0d+3.46872405204951239689e-34 # 8 * pi/2 trailing 178 .double 0d+3.90231455855570147991e-34 # 9 * pi/2 trailing 179 .double 0d-3.36781471248705338384e-34 # 10 * pi/2 trailing 180 .double 0d-1.06379439835298071785e-33 # 11 * pi/2 trailing 181 .double 0d+5.20308607807426856861e-34 # 12 * pi/2 trailing 182 .double 0d+5.63667658458045770509e-34 # 13 * pi/2 trailing 183 .double 0d-1.63345268646229670430e-34 # 14 * pi/2 trailing 184 .double 0d-1.19986217995610764801e-34 # 15 * pi/2 trailing 185 .double 0d+6.93744810409902479378e-34 # 16 * pi/2 trailing 186 .double 0d-8.03640094449267300110e-34 # 17 * pi/2 trailing 187 .double 0d+7.80462911711140295982e-34 # 18 * pi/2 trailing 188 .double 0d-7.16921993148029483506e-34 # 19 * pi/2 trailing 189 .double 0d-6.73562942497410676769e-34 # 20 * pi/2 trailing 190 .double 0d-6.30203891846791677593e-34 # 21 * pi/2 trailing 191 .double 0d-2.12758879670596143570e-33 # 22 * pi/2 trailing 192 .double 0d+2.53800212047402350390e-33 # 23 * pi/2 trailing 193 .double 0d+1.04061721561485371372e-33 # 24 * pi/2 trailing 194 .double 0d+6.11729905311472319056e-32 # 25 * pi/2 trailing 195 .double 0d+1.12733531691609154102e-33 # 26 * pi/2 trailing 196 .double 0d-3.70049587943078297272e-34 # 27 * pi/2 trailing 197 .double 0d-3.26690537292459340860e-34 # 28 * pi/2 trailing 198 .double 0d-1.14812616507957271361e-34 # 29 * pi/2 trailing 199 200 middle: 201 .double 0d+0.00000000000000000000e+00 # 0 * pi/2 middle 202 .double 0d+5.72118872610983179676e-18 # 1 * pi/2 middle 203 .double 0d+1.14423774522196635935e-17 # 2 * pi/2 middle 204 .double 0d-3.83475850529283316309e-17 # 3 * pi/2 middle 205 .double 0d+2.28847549044393271871e-17 # 4 * pi/2 middle 206 .double 0d-2.69052076007086676522e-17 # 5 * pi/2 middle 207 .double 0d-7.66951701058566632618e-17 # 6 * pi/2 middle 208 .double 0d-1.54628301484890040587e-17 # 7 * pi/2 middle 209 .double 0d+4.57695098088786543741e-17 # 8 * pi/2 middle 210 .double 0d+1.07001849766246313192e-16 # 9 * pi/2 middle 211 .double 0d-5.38104152014173353044e-17 # 10 * pi/2 middle 212 .double 0d-2.14622680169080983801e-16 # 11 * pi/2 middle 213 .double 0d-1.53390340211713326524e-16 # 12 * pi/2 middle 214 .double 0d-9.21580002543456677056e-17 # 13 * pi/2 middle 215 .double 0d-3.09256602969780081173e-17 # 14 * pi/2 middle 216 .double 0d+3.03066796603896507006e-17 # 15 * pi/2 middle 217 .double 0d+9.15390196177573087482e-17 # 16 * pi/2 middle 218 .double 0d+1.52771359575124969107e-16 # 17 * pi/2 middle 219 .double 0d+2.14003699532492626384e-16 # 18 * pi/2 middle 220 .double 0d-1.68853170360202329427e-16 # 19 * pi/2 middle 221 .double 0d-1.07620830402834670609e-16 # 20 * pi/2 middle 222 .double 0d+3.97700719404595604379e-16 # 21 * pi/2 middle 223 .double 0d-4.29245360338161967602e-16 # 22 * pi/2 middle 224 .double 0d-3.68013020380794313406e-16 # 23 * pi/2 middle 225 .double 0d-3.06780680423426653047e-16 # 24 * pi/2 middle 226 .double 0d-2.45548340466059054318e-16 # 25 * pi/2 middle 227 .double 0d-1.84316000508691335411e-16 # 26 * pi/2 middle 228 .double 0d-1.23083660551323675053e-16 # 27 * pi/2 middle 229 .double 0d-6.18513205939560162346e-17 # 28 * pi/2 middle 230 .double 0d-6.18980636588357585202e-19 # 29 * pi/2 middle 231 232 leading: 233 .double 0d+0.00000000000000000000e+00 # 0 * pi/2 leading 234 .double 0d+1.57079632679489661351e+00 # 1 * pi/2 leading 235 .double 0d+3.14159265358979322702e+00 # 2 * pi/2 leading 236 .double 0d+4.71238898038468989604e+00 # 3 * pi/2 leading 237 .double 0d+6.28318530717958645404e+00 # 4 * pi/2 leading 238 .double 0d+7.85398163397448312306e+00 # 5 * pi/2 leading 239 .double 0d+9.42477796076937979208e+00 # 6 * pi/2 leading 240 .double 0d+1.09955742875642763501e+01 # 7 * pi/2 leading 241 .double 0d+1.25663706143591729081e+01 # 8 * pi/2 leading 242 .double 0d+1.41371669411540694661e+01 # 9 * pi/2 leading 243 .double 0d+1.57079632679489662461e+01 # 10 * pi/2 leading 244 .double 0d+1.72787595947438630262e+01 # 11 * pi/2 leading 245 .double 0d+1.88495559215387595842e+01 # 12 * pi/2 leading 246 .double 0d+2.04203522483336561422e+01 # 13 * pi/2 leading 247 .double 0d+2.19911485751285527002e+01 # 14 * pi/2 leading 248 .double 0d+2.35619449019234492582e+01 # 15 * pi/2 leading 249 .double 0d+2.51327412287183458162e+01 # 16 * pi/2 leading 250 .double 0d+2.67035375555132423742e+01 # 17 * pi/2 leading 251 .double 0d+2.82743338823081389322e+01 # 18 * pi/2 leading 252 .double 0d+2.98451302091030359342e+01 # 19 * pi/2 leading 253 .double 0d+3.14159265358979324922e+01 # 20 * pi/2 leading 254 .double 0d+3.29867228626928286062e+01 # 21 * pi/2 leading 255 .double 0d+3.45575191894877260523e+01 # 22 * pi/2 leading 256 .double 0d+3.61283155162826226103e+01 # 23 * pi/2 leading 257 .double 0d+3.76991118430775191683e+01 # 24 * pi/2 leading 258 .double 0d+3.92699081698724157263e+01 # 25 * pi/2 leading 259 .double 0d+4.08407044966673122843e+01 # 26 * pi/2 leading 260 .double 0d+4.24115008234622088423e+01 # 27 * pi/2 leading 261 .double 0d+4.39822971502571054003e+01 # 28 * pi/2 leading 262 .double 0d+4.55530934770520019583e+01 # 29 * pi/2 leading 263 264 twoOverPi: 265 .double 0d+6.36619772367581343076e-01 266 267 .text 268 _ALIGN_TEXT 269 270 table_lookup: 271 muld3 %r3,twoOverPi,%r0 272 cvtrdl %r0,%r0 # n = nearest int to ((2/pi)*|x|) rnded 273 subd2 leading[%r0],%r3 # p = (|x| - leading n*pi/2) exactly 274 subd3 middle[%r0],%r3,%r1 # q = (p - middle n*pi/2) rounded 275 subd2 %r1,%r3 # r = (p - q) 276 subd2 middle[%r0],%r3 # r = r - middle n*pi/2 277 subd2 trailing[%r0],%r3 # r = r - trailing n*pi/2 rounded 278 /* 279 * If the original argument was negative, 280 * negate the reduce argument and 281 * adjust the octant/quadrant number. 282 */ 283 tstw 4(%ap) 284 bgeq abs2 285 mnegf %r1,%r1 286 mnegf %r3,%r3 287 /* subb3 %r0,$8,%r0 ...used for pi/4 reduction -S.McD */ 288 subb3 %r0,$4,%r0 289 abs2: 290 /* 291 * Clear all unneeded octant/quadrant bits. 292 */ 293 /* bicb2 $0xf8,%r0 ...used for pi/4 reduction -S.McD */ 294 bicb2 $0xfc,%r0 295 rsb 296 /* 297 * p.0 298 */ 299 #ifdef __ELF__ 300 .section .rodata 301 #else 302 .text 303 #endif 304 _ALIGN_TEXT 305 /* 306 * Only 256 (actually 225) bits of 2/pi are needed for VAX double 307 * precision; this was determined by enumerating all the nearest 308 * machine integer multiples of pi/2 using continued fractions. 309 * (8a8d3673775b7ff7 required the most bits.) -S.McD 310 */ 311 .long 0 312 .long 0 313 .long 0xaef1586d 314 .long 0x9458eaf7 315 .long 0x10e4107f 316 .long 0xd8a5664f 317 .long 0x4d377036 318 .long 0x09d5f47d 319 .long 0x91054a7f 320 .long 0xbe60db93 321 bits2opi: 322 .long 0x00000028 323 .long 0 324 /* 325 * Note: wherever you see the word `octant', read `quadrant'. 326 * Currently this code is set up for pi/2 argument reduction. 327 * By uncommenting/commenting the appropriate lines, it will 328 * also serve as a pi/4 argument reduction code. 329 */ 330 .text 331 332 /* p.1 333 * Trigred preforms argument reduction 334 * for the trigonometric functions. It 335 * takes one input argument, a D-format 336 * number in %r1/%r0 . The magnitude of 337 * the input argument must be greater 338 * than or equal to 1/2 . Trigred produces 339 * three results: the number of the octant 340 * occupied by the argument, the reduced 341 * argument, and an extension of the 342 * reduced argument. The octant number is 343 * returned in %r0 . The reduced argument 344 * is returned as a D-format number in 345 * %r2/%r1 . An 8 bit extension of the 346 * reduced argument is returned as an 347 * F-format number in %r3. 348 * p.2 349 */ 350 trigred: 351 /* 352 * Save the sign of the input argument. 353 */ 354 movw %r0,-(%sp) 355 /* 356 * Extract the exponent field. 357 */ 358 extzv $7,$7,%r0,%r2 359 /* 360 * Convert the fraction part of the input 361 * argument into a quadword integer. 362 */ 363 bicw2 $0xff80,%r0 364 bisb2 $0x80,%r0 # -S.McD 365 rotl $16,%r0,%r0 366 rotl $16,%r1,%r1 367 /* 368 * If %r1 is negative, add 1 to %r0 . This 369 * adjustment is made so that the two's 370 * complement multiplications done later 371 * will produce unsigned results. 372 */ 373 bgeq posmid 374 incl %r0 375 posmid: 376 /* p.3 377 * 378 * Set %r3 to the address of the first quadword 379 * used to obtain the needed portion of 2/pi . 380 * The address is longword aligned to ensure 381 * efficient access. 382 */ 383 ashl $-3,%r2,%r3 384 bicb2 $3,%r3 385 mnegl %r3,%r3 386 movab bits2opi[%r3],%r3 387 /* 388 * Set %r2 to the size of the shift needed to 389 * obtain the correct portion of 2/pi . 390 */ 391 bicb2 $0xe0,%r2 392 /* p.4 393 * 394 * Move the needed 128 bits of 2/pi into 395 * %r11 - %r8 . Adjust the numbers to allow 396 * for unsigned multiplication. 397 */ 398 ashq %r2,(%r3),%r10 399 400 subl2 $4,%r3 401 ashq %r2,(%r3),%r9 402 bgeq signoff1 403 incl %r11 404 signoff1: 405 subl2 $4,%r3 406 ashq %r2,(%r3),%r8 407 bgeq signoff2 408 incl %r10 409 signoff2: 410 subl2 $4,%r3 411 ashq %r2,(%r3),%r7 412 bgeq signoff3 413 incl %r9 414 signoff3: 415 /* p.5 416 * 417 * Multiply the contents of %r0/%r1 by the 418 * slice of 2/pi in %r11 - %r8 . 419 */ 420 emul %r0,%r8,$0,%r4 421 emul %r0,%r9,%r5,%r5 422 emul %r0,%r10,%r6,%r6 423 424 emul %r1,%r8,$0,%r7 425 emul %r1,%r9,%r8,%r8 426 emul %r1,%r10,%r9,%r9 427 emul %r1,%r11,%r10,%r10 428 429 addl2 %r4,%r8 430 adwc %r5,%r9 431 adwc %r6,%r10 432 /* p.6 433 * 434 * If there are more than five leading zeros 435 * after the first two quotient bits or if there 436 * are more than five leading ones after the first 437 * two quotient bits, generate more fraction bits. 438 * Otherwise, branch to code to produce the result. 439 */ 440 bicl3 $0xc1ffffff,%r10,%r4 441 beql more1 442 cmpl $0x3e000000,%r4 443 bneq result 444 more1: 445 /* p.7 446 * 447 * generate another 32 result bits. 448 */ 449 subl2 $4,%r3 450 ashq %r2,(%r3),%r5 451 bgeq signoff4 452 453 emul %r1,%r6,$0,%r4 454 addl2 %r1,%r5 455 emul %r0,%r6,%r5,%r5 456 addl2 %r0,%r6 457 jbr addbits1 458 459 signoff4: 460 emul %r1,%r6,$0,%r4 461 emul %r0,%r6,%r5,%r5 462 463 addbits1: 464 addl2 %r5,%r7 465 adwc %r6,%r8 466 adwc $0,%r9 467 adwc $0,%r10 468 /* p.8 469 * 470 * Check for massive cancellation. 471 */ 472 bicl3 $0xc0000000,%r10,%r6 473 /* bneq more2 -S.McD Test was backwards */ 474 beql more2 475 cmpl $0x3fffffff,%r6 476 bneq result 477 more2: 478 /* p.9 479 * 480 * If massive cancellation has occurred, 481 * generate another 24 result bits. 482 * Testing has shown there will always be 483 * enough bits after this point. 484 */ 485 subl2 $4,%r3 486 ashq %r2,(%r3),%r5 487 bgeq signoff5 488 489 emul %r0,%r6,%r4,%r5 490 addl2 %r0,%r6 491 jbr addbits2 492 493 signoff5: 494 emul %r0,%r6,%r4,%r5 495 496 addbits2: 497 addl2 %r6,%r7 498 adwc $0,%r8 499 adwc $0,%r9 500 adwc $0,%r10 501 /* p.10 502 * 503 * The following code produces the reduced 504 * argument from the product bits contained 505 * in %r10 - %r7 . 506 */ 507 result: 508 /* 509 * Extract the octant number from %r10 . 510 */ 511 /* extzv $29,$3,%r10,%r0 ...used for pi/4 reduction -S.McD */ 512 extzv $30,$2,%r10,%r0 513 /* 514 * Clear the octant bits in %r10 . 515 */ 516 /* bicl2 $0xe0000000,%r10 ...used for pi/4 reduction -S.McD */ 517 bicl2 $0xc0000000,%r10 518 /* 519 * Zero the sign flag. 520 */ 521 clrl %r5 522 /* p.11 523 * 524 * Check to see if the fraction is greater than 525 * or equal to one-half. If it is, add one 526 * to the octant number, set the sign flag 527 * on, and replace the fraction with 1 minus 528 * the fraction. 529 */ 530 /* bitl $0x10000000,%r10 ...used for pi/4 reduction -S.McD */ 531 bitl $0x20000000,%r10 532 beql small 533 incl %r0 534 incl %r5 535 /* subl3 %r10,$0x1fffffff,%r10 ...used for pi/4 reduction -S.McD */ 536 subl3 %r10,$0x3fffffff,%r10 537 mcoml %r9,%r9 538 mcoml %r8,%r8 539 mcoml %r7,%r7 540 small: 541 /* p.12 542 * 543 * Test whether the first 29 bits of the ...used for pi/4 reduction -S.McD 544 * Test whether the first 30 bits of the 545 * fraction are zero. 546 */ 547 tstl %r10 548 beql tiny 549 /* 550 * Find the position of the first one bit in %r10 . 551 */ 552 cvtld %r10,%r1 553 extzv $7,$7,%r1,%r1 554 /* 555 * Compute the size of the shift needed. 556 */ 557 subl3 %r1,$32,%r6 558 /* 559 * Shift up the high order 64 bits of the 560 * product. 561 */ 562 ashq %r6,%r9,%r10 563 ashq %r6,%r8,%r9 564 jbr mult 565 /* p.13 566 * 567 * Test to see if the sign bit of %r9 is on. 568 */ 569 tiny: 570 tstl %r9 571 bgeq tinier 572 /* 573 * If it is, shift the product bits up 32 bits. 574 */ 575 movl $32,%r6 576 movq %r8,%r10 577 tstl %r10 578 jbr mult 579 /* p.14 580 * 581 * Test whether %r9 is zero. It is probably 582 * impossible for both %r10 and %r9 to be 583 * zero, but until proven to be so, the test 584 * must be made. 585 */ 586 tinier: 587 beql zero 588 /* 589 * Find the position of the first one bit in %r9 . 590 */ 591 cvtld %r9,%r1 592 extzv $7,$7,%r1,%r1 593 /* 594 * Compute the size of the shift needed. 595 */ 596 subl3 %r1,$32,%r1 597 addl3 $32,%r1,%r6 598 /* 599 * Shift up the high order 64 bits of the 600 * product. 601 */ 602 ashq %r1,%r8,%r10 603 ashq %r1,%r7,%r9 604 jbr mult 605 /* p.15 606 * 607 * The following code sets the reduced 608 * argument to zero. 609 */ 610 zero: 611 clrl %r1 612 clrl %r2 613 clrl %r3 614 jbr return 615 /* p.16 616 * 617 * At this point, %r0 contains the octant number, 618 * %r6 indicates the number of bits the fraction 619 * has been shifted, %r5 indicates the sign of 620 * the fraction, %r11/%r10 contain the high order 621 * 64 bits of the fraction, and the condition 622 * codes indicate where the sign bit of %r10 623 * is on. The following code multiplies the 624 * fraction by pi/2 . 625 */ 626 mult: 627 /* 628 * Save %r11/%r10 in %r4/%r1 . -S.McD 629 */ 630 movl %r11,%r4 631 movl %r10,%r1 632 /* 633 * If the sign bit of %r10 is on, add 1 to %r11 . 634 */ 635 bgeq signoff6 636 incl %r11 637 signoff6: 638 /* p.17 639 * 640 * Move pi/2 into %r3/%r2 . 641 */ 642 movq $0xc90fdaa22168c235,%r2 643 /* 644 * Multiply the fraction by the portion of pi/2 645 * in %r2 . 646 */ 647 emul %r2,%r10,$0,%r7 648 emul %r2,%r11,%r8,%r7 649 /* 650 * Multiply the fraction by the portion of pi/2 651 * in %r3 . 652 */ 653 emul %r3,%r10,$0,%r9 654 emul %r3,%r11,%r10,%r10 655 /* 656 * Add the product bits together. 657 */ 658 addl2 %r7,%r9 659 adwc %r8,%r10 660 adwc $0,%r11 661 /* 662 * Compensate for not sign extending %r8 above.-S.McD 663 */ 664 tstl %r8 665 bgeq signoff6a 666 decl %r11 667 signoff6a: 668 /* 669 * Compensate for %r11/%r10 being unsigned. -S.McD 670 */ 671 addl2 %r2,%r10 672 adwc %r3,%r11 673 /* 674 * Compensate for %r3/%r2 being unsigned. -S.McD 675 */ 676 addl2 %r1,%r10 677 adwc %r4,%r11 678 /* p.18 679 * 680 * If the sign bit of %r11 is zero, shift the 681 * product bits up one bit and increment %r6 . 682 */ 683 blss signon 684 incl %r6 685 ashq $1,%r10,%r10 686 tstl %r9 687 bgeq signoff7 688 incl %r10 689 signoff7: 690 signon: 691 /* p.19 692 * 693 * Shift the 56 most significant product 694 * bits into %r9/%r8 . The sign extension 695 * will be handled later. 696 */ 697 ashq $-8,%r10,%r8 698 /* 699 * Convert the low order 8 bits of %r10 700 * into an F-format number. 701 */ 702 cvtbf %r10,%r3 703 /* 704 * If the result of the conversion was 705 * negative, add 1 to %r9/%r8 . 706 */ 707 bgeq chop 708 incl %r8 709 adwc $0,%r9 710 /* 711 * If %r9 is now zero, branch to special 712 * code to handle that possibility. 713 */ 714 beql carryout 715 chop: 716 /* p.20 717 * 718 * Convert the number in %r9/%r8 into 719 * D-format number in %r2/%r1 . 720 */ 721 rotl $16,%r8,%r2 722 rotl $16,%r9,%r1 723 /* 724 * Set the exponent field to the appropriate 725 * value. Note that the extra bits created by 726 * sign extension are now eliminated. 727 */ 728 subw3 %r6,$131,%r6 729 insv %r6,$7,$9,%r1 730 /* 731 * Set the exponent field of the F-format 732 * number in %r3 to the appropriate value. 733 */ 734 tstf %r3 735 beql return 736 /* extzv $7,$8,%r3,%r4 -S.McD */ 737 extzv $7,$7,%r3,%r4 738 addw2 %r4,%r6 739 /* subw2 $217,%r6 -S.McD */ 740 subw2 $64,%r6 741 insv %r6,$7,$8,%r3 742 jbr return 743 /* p.21 744 * 745 * The following code generates the appropriate 746 * result for the unlikely possibility that 747 * rounding the number in %r9/%r8 resulted in 748 * a carry out. 749 */ 750 carryout: 751 clrl %r1 752 clrl %r2 753 subw3 %r6,$132,%r6 754 insv %r6,$7,$9,%r1 755 tstf %r3 756 beql return 757 extzv $7,$8,%r3,%r4 758 addw2 %r4,%r6 759 subw2 $218,%r6 760 insv %r6,$7,$8,%r3 761 /* p.22 762 * 763 * The following code makes an needed 764 * adjustments to the signs of the 765 * results or to the octant number, and 766 * then returns. 767 */ 768 return: 769 /* 770 * Test if the fraction was greater than or 771 * equal to 1/2 . If so, negate the reduced 772 * argument. 773 */ 774 blbc %r5,signoff8 775 mnegf %r1,%r1 776 mnegf %r3,%r3 777 signoff8: 778 /* p.23 779 * 780 * If the original argument was negative, 781 * negate the reduce argument and 782 * adjust the octant number. 783 */ 784 tstw (%sp)+ 785 bgeq signoff9 786 mnegf %r1,%r1 787 mnegf %r3,%r3 788 /* subb3 %r0,$8,%r0 ...used for pi/4 reduction -S.McD */ 789 subb3 %r0,$4,%r0 790 signoff9: 791 /* 792 * Clear all unneeded octant bits. 793 * 794 * bicb2 $0xf8,%r0 ...used for pi/4 reduction -S.McD */ 795 bicb2 $0xfc,%r0 796 /* 797 * Return. 798 */ 799 rsb 800
Indexes created Tue Sep 30 17:09:57 GMT 2025