1.file "sincosf.s" 2 3 4// Copyright (c) 2000 - 2005, Intel Corporation 5// All rights reserved. 6// 7// 8// Redistribution and use in source and binary forms, with or without 9// modification, are permitted provided that the following conditions are 10// met: 11// 12// * Redistributions of source code must retain the above copyright 13// notice, this list of conditions and the following disclaimer. 14// 15// * Redistributions in binary form must reproduce the above copyright 16// notice, this list of conditions and the following disclaimer in the 17// documentation and/or other materials provided with the distribution. 18// 19// * The name of Intel Corporation may not be used to endorse or promote 20// products derived from this software without specific prior written 21// permission. 22 23// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 24// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 25// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 26// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS 27// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 28// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 29// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 30// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 31// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING 32// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 33// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 34// 35// Intel Corporation is the author of this code, and requests that all 36// problem reports or change requests be submitted to it directly at 37// http://www.intel.com/software/products/opensource/libraries/num.htm. 38// 39// History 40//============================================================== 41// 02/02/00 Initial version 42// 04/02/00 Unwind support added. 43// 06/16/00 Updated tables to enforce symmetry 44// 08/31/00 Saved 2 cycles in main path, and 9 in other paths. 45// 09/20/00 The updated tables regressed to an old version, so reinstated them 46// 10/18/00 Changed one table entry to ensure symmetry 47// 01/03/01 Improved speed, fixed flag settings for small arguments. 48// 02/18/02 Large arguments processing routine excluded 49// 05/20/02 Cleaned up namespace and sf0 syntax 50// 06/03/02 Insure inexact flag set for large arg result 51// 09/05/02 Single precision version is made using double precision one as base 52// 02/10/03 Reordered header: .section, .global, .proc, .align 53// 03/31/05 Reformatted delimiters between data tables 54// 55// API 56//============================================================== 57// float sinf( float x); 58// float cosf( float x); 59// 60// Overview of operation 61//============================================================== 62// 63// Step 1 64// ====== 65// Reduce x to region -1/2*pi/2^k ===== 0 ===== +1/2*pi/2^k where k=4 66// divide x by pi/2^k. 67// Multiply by 2^k/pi. 68// nfloat = Round result to integer (round-to-nearest) 69// 70// r = x - nfloat * pi/2^k 71// Do this as (x - nfloat * HIGH(pi/2^k)) - nfloat * LOW(pi/2^k) 72 73// for increased accuracy. 74// pi/2^k is stored as two numbers that when added make pi/2^k. 75// pi/2^k = HIGH(pi/2^k) + LOW(pi/2^k) 76// HIGH part is rounded to zero, LOW - to nearest 77// 78// x = (nfloat * pi/2^k) + r 79// r is small enough that we can use a polynomial approximation 80// and is referred to as the reduced argument. 81// 82// Step 3 83// ====== 84// Take the unreduced part and remove the multiples of 2pi. 85// So nfloat = nfloat (with lower k+1 bits cleared) + lower k+1 bits 86// 87// nfloat (with lower k+1 bits cleared) is a multiple of 2^(k+1) 88// N * 2^(k+1) 89// nfloat * pi/2^k = N * 2^(k+1) * pi/2^k + (lower k+1 bits) * pi/2^k 90// nfloat * pi/2^k = N * 2 * pi + (lower k+1 bits) * pi/2^k 91// nfloat * pi/2^k = N2pi + M * pi/2^k 92// 93// 94// Sin(x) = Sin((nfloat * pi/2^k) + r) 95// = Sin(nfloat * pi/2^k) * Cos(r) + Cos(nfloat * pi/2^k) * Sin(r) 96// 97// Sin(nfloat * pi/2^k) = Sin(N2pi + Mpi/2^k) 98// = Sin(N2pi)Cos(Mpi/2^k) + Cos(N2pi)Sin(Mpi/2^k) 99// = Sin(Mpi/2^k) 100// 101// Cos(nfloat * pi/2^k) = Cos(N2pi + Mpi/2^k) 102// = Cos(N2pi)Cos(Mpi/2^k) + Sin(N2pi)Sin(Mpi/2^k) 103// = Cos(Mpi/2^k) 104// 105// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r) 106// 107// 108// Step 4 109// ====== 110// 0 <= M < 2^(k+1) 111// There are 2^(k+1) Sin entries in a table. 112// There are 2^(k+1) Cos entries in a table. 113// 114// Get Sin(Mpi/2^k) and Cos(Mpi/2^k) by table lookup. 115// 116// 117// Step 5 118// ====== 119// Calculate Cos(r) and Sin(r) by polynomial approximation. 120// 121// Cos(r) = 1 + r^2 q1 + r^4 q2 = Series for Cos 122// Sin(r) = r + r^3 p1 + r^5 p2 = Series for Sin 123// 124// and the coefficients q1, q2 and p1, p2 are stored in a table 125// 126// 127// Calculate 128// Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r) 129// 130// as follows 131// 132// S[m] = Sin(Mpi/2^k) and C[m] = Cos(Mpi/2^k) 133// rsq = r*r 134// 135// 136// P = P1 + r^2*P2 137// Q = Q1 + r^2*Q2 138// 139// rcub = r * rsq 140// Sin(r) = r + rcub * P 141// = r + r^3p1 + r^5p2 = Sin(r) 142// 143// The coefficients are not exactly these values, but almost. 144// 145// p1 = -1/6 = -1/3! 146// p2 = 1/120 = 1/5! 147// p3 = -1/5040 = -1/7! 148// p4 = 1/362889 = 1/9! 149// 150// P = r + r^3 * P 151// 152// Answer = S[m] Cos(r) + C[m] P 153// 154// Cos(r) = 1 + rsq Q 155// Cos(r) = 1 + r^2 Q 156// Cos(r) = 1 + r^2 (q1 + r^2q2) 157// Cos(r) = 1 + r^2q1 + r^4q2 158// 159// S[m] Cos(r) = S[m](1 + rsq Q) 160// S[m] Cos(r) = S[m] + S[m] rsq Q 161// S[m] Cos(r) = S[m] + s_rsq Q 162// Q = S[m] + s_rsq Q 163// 164// Then, 165// 166// Answer = Q + C[m] P 167 168 169// Registers used 170//============================================================== 171// general input registers: 172// r14 -> r19 173// r32 -> r45 174 175// predicate registers used: 176// p6 -> p14 177 178// floating-point registers used 179// f9 -> f15 180// f32 -> f61 181 182// Assembly macros 183//============================================================== 184sincosf_NORM_f8 = f9 185sincosf_W = f10 186sincosf_int_Nfloat = f11 187sincosf_Nfloat = f12 188 189sincosf_r = f13 190sincosf_rsq = f14 191sincosf_rcub = f15 192sincosf_save_tmp = f15 193 194sincosf_Inv_Pi_by_16 = f32 195sincosf_Pi_by_16_1 = f33 196sincosf_Pi_by_16_2 = f34 197 198sincosf_Inv_Pi_by_64 = f35 199 200sincosf_Pi_by_16_3 = f36 201 202sincosf_r_exact = f37 203 204sincosf_Sm = f38 205sincosf_Cm = f39 206 207sincosf_P1 = f40 208sincosf_Q1 = f41 209sincosf_P2 = f42 210sincosf_Q2 = f43 211sincosf_P3 = f44 212sincosf_Q3 = f45 213sincosf_P4 = f46 214sincosf_Q4 = f47 215 216sincosf_P_temp1 = f48 217sincosf_P_temp2 = f49 218 219sincosf_Q_temp1 = f50 220sincosf_Q_temp2 = f51 221 222sincosf_P = f52 223sincosf_Q = f53 224 225sincosf_srsq = f54 226 227sincosf_SIG_INV_PI_BY_16_2TO61 = f55 228sincosf_RSHF_2TO61 = f56 229sincosf_RSHF = f57 230sincosf_2TOM61 = f58 231sincosf_NFLOAT = f59 232sincosf_W_2TO61_RSH = f60 233 234fp_tmp = f61 235 236///////////////////////////////////////////////////////////// 237 238sincosf_AD_1 = r33 239sincosf_AD_2 = r34 240sincosf_exp_limit = r35 241sincosf_r_signexp = r36 242sincosf_AD_beta_table = r37 243sincosf_r_sincos = r38 244 245sincosf_r_exp = r39 246sincosf_r_17_ones = r40 247 248sincosf_GR_sig_inv_pi_by_16 = r14 249sincosf_GR_rshf_2to61 = r15 250sincosf_GR_rshf = r16 251sincosf_GR_exp_2tom61 = r17 252sincosf_GR_n = r18 253sincosf_GR_m = r19 254sincosf_GR_32m = r19 255sincosf_GR_all_ones = r19 256 257gr_tmp = r41 258GR_SAVE_PFS = r41 259GR_SAVE_B0 = r42 260GR_SAVE_GP = r43 261 262RODATA 263.align 16 264 265// Pi/16 parts 266LOCAL_OBJECT_START(double_sincosf_pi) 267 data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part 268 data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part 269LOCAL_OBJECT_END(double_sincosf_pi) 270 271// Coefficients for polynomials 272LOCAL_OBJECT_START(double_sincosf_pq_k4) 273 data8 0x3F810FABB668E9A2 // P2 274 data8 0x3FA552E3D6DE75C9 // Q2 275 data8 0xBFC555554447BC7F // P1 276 data8 0xBFDFFFFFC447610A // Q1 277LOCAL_OBJECT_END(double_sincosf_pq_k4) 278 279// Sincos table (S[m], C[m]) 280LOCAL_OBJECT_START(double_sin_cos_beta_k4) 281 data8 0x0000000000000000 // sin ( 0 Pi / 16 ) 282 data8 0x3FF0000000000000 // cos ( 0 Pi / 16 ) 283// 284 data8 0x3FC8F8B83C69A60B // sin ( 1 Pi / 16 ) 285 data8 0x3FEF6297CFF75CB0 // cos ( 1 Pi / 16 ) 286// 287 data8 0x3FD87DE2A6AEA963 // sin ( 2 Pi / 16 ) 288 data8 0x3FED906BCF328D46 // cos ( 2 Pi / 16 ) 289// 290 data8 0x3FE1C73B39AE68C8 // sin ( 3 Pi / 16 ) 291 data8 0x3FEA9B66290EA1A3 // cos ( 3 Pi / 16 ) 292// 293 data8 0x3FE6A09E667F3BCD // sin ( 4 Pi / 16 ) 294 data8 0x3FE6A09E667F3BCD // cos ( 4 Pi / 16 ) 295// 296 data8 0x3FEA9B66290EA1A3 // sin ( 5 Pi / 16 ) 297 data8 0x3FE1C73B39AE68C8 // cos ( 5 Pi / 16 ) 298// 299 data8 0x3FED906BCF328D46 // sin ( 6 Pi / 16 ) 300 data8 0x3FD87DE2A6AEA963 // cos ( 6 Pi / 16 ) 301// 302 data8 0x3FEF6297CFF75CB0 // sin ( 7 Pi / 16 ) 303 data8 0x3FC8F8B83C69A60B // cos ( 7 Pi / 16 ) 304// 305 data8 0x3FF0000000000000 // sin ( 8 Pi / 16 ) 306 data8 0x0000000000000000 // cos ( 8 Pi / 16 ) 307// 308 data8 0x3FEF6297CFF75CB0 // sin ( 9 Pi / 16 ) 309 data8 0xBFC8F8B83C69A60B // cos ( 9 Pi / 16 ) 310// 311 data8 0x3FED906BCF328D46 // sin ( 10 Pi / 16 ) 312 data8 0xBFD87DE2A6AEA963 // cos ( 10 Pi / 16 ) 313// 314 data8 0x3FEA9B66290EA1A3 // sin ( 11 Pi / 16 ) 315 data8 0xBFE1C73B39AE68C8 // cos ( 11 Pi / 16 ) 316// 317 data8 0x3FE6A09E667F3BCD // sin ( 12 Pi / 16 ) 318 data8 0xBFE6A09E667F3BCD // cos ( 12 Pi / 16 ) 319// 320 data8 0x3FE1C73B39AE68C8 // sin ( 13 Pi / 16 ) 321 data8 0xBFEA9B66290EA1A3 // cos ( 13 Pi / 16 ) 322// 323 data8 0x3FD87DE2A6AEA963 // sin ( 14 Pi / 16 ) 324 data8 0xBFED906BCF328D46 // cos ( 14 Pi / 16 ) 325// 326 data8 0x3FC8F8B83C69A60B // sin ( 15 Pi / 16 ) 327 data8 0xBFEF6297CFF75CB0 // cos ( 15 Pi / 16 ) 328// 329 data8 0x0000000000000000 // sin ( 16 Pi / 16 ) 330 data8 0xBFF0000000000000 // cos ( 16 Pi / 16 ) 331// 332 data8 0xBFC8F8B83C69A60B // sin ( 17 Pi / 16 ) 333 data8 0xBFEF6297CFF75CB0 // cos ( 17 Pi / 16 ) 334// 335 data8 0xBFD87DE2A6AEA963 // sin ( 18 Pi / 16 ) 336 data8 0xBFED906BCF328D46 // cos ( 18 Pi / 16 ) 337// 338 data8 0xBFE1C73B39AE68C8 // sin ( 19 Pi / 16 ) 339 data8 0xBFEA9B66290EA1A3 // cos ( 19 Pi / 16 ) 340// 341 data8 0xBFE6A09E667F3BCD // sin ( 20 Pi / 16 ) 342 data8 0xBFE6A09E667F3BCD // cos ( 20 Pi / 16 ) 343// 344 data8 0xBFEA9B66290EA1A3 // sin ( 21 Pi / 16 ) 345 data8 0xBFE1C73B39AE68C8 // cos ( 21 Pi / 16 ) 346// 347 data8 0xBFED906BCF328D46 // sin ( 22 Pi / 16 ) 348 data8 0xBFD87DE2A6AEA963 // cos ( 22 Pi / 16 ) 349// 350 data8 0xBFEF6297CFF75CB0 // sin ( 23 Pi / 16 ) 351 data8 0xBFC8F8B83C69A60B // cos ( 23 Pi / 16 ) 352// 353 data8 0xBFF0000000000000 // sin ( 24 Pi / 16 ) 354 data8 0x0000000000000000 // cos ( 24 Pi / 16 ) 355// 356 data8 0xBFEF6297CFF75CB0 // sin ( 25 Pi / 16 ) 357 data8 0x3FC8F8B83C69A60B // cos ( 25 Pi / 16 ) 358// 359 data8 0xBFED906BCF328D46 // sin ( 26 Pi / 16 ) 360 data8 0x3FD87DE2A6AEA963 // cos ( 26 Pi / 16 ) 361// 362 data8 0xBFEA9B66290EA1A3 // sin ( 27 Pi / 16 ) 363 data8 0x3FE1C73B39AE68C8 // cos ( 27 Pi / 16 ) 364// 365 data8 0xBFE6A09E667F3BCD // sin ( 28 Pi / 16 ) 366 data8 0x3FE6A09E667F3BCD // cos ( 28 Pi / 16 ) 367// 368 data8 0xBFE1C73B39AE68C8 // sin ( 29 Pi / 16 ) 369 data8 0x3FEA9B66290EA1A3 // cos ( 29 Pi / 16 ) 370// 371 data8 0xBFD87DE2A6AEA963 // sin ( 30 Pi / 16 ) 372 data8 0x3FED906BCF328D46 // cos ( 30 Pi / 16 ) 373// 374 data8 0xBFC8F8B83C69A60B // sin ( 31 Pi / 16 ) 375 data8 0x3FEF6297CFF75CB0 // cos ( 31 Pi / 16 ) 376// 377 data8 0x0000000000000000 // sin ( 32 Pi / 16 ) 378 data8 0x3FF0000000000000 // cos ( 32 Pi / 16 ) 379LOCAL_OBJECT_END(double_sin_cos_beta_k4) 380 381.section .text 382 383//////////////////////////////////////////////////////// 384// There are two entry points: sin and cos 385// If from sin, p8 is true 386// If from cos, p9 is true 387 388GLOBAL_IEEE754_ENTRY(sinf) 389 390{ .mlx 391 alloc r32 = ar.pfs,1,13,0,0 392 movl sincosf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A //signd of 16/pi 393} 394{ .mlx 395 addl sincosf_AD_1 = @ltoff(double_sincosf_pi), gp 396 movl sincosf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) 397};; 398 399{ .mfi 400 ld8 sincosf_AD_1 = [sincosf_AD_1] 401 fnorm.s1 sincosf_NORM_f8 = f8 // Normalize argument 402 cmp.eq p8,p9 = r0, r0 // set p8 (clear p9) for sin 403} 404{ .mib 405 mov sincosf_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 406 mov sincosf_r_sincos = 0x0 // 0 for sin 407 br.cond.sptk _SINCOSF_COMMON // go to common part 408};; 409 410GLOBAL_IEEE754_END(sinf) 411libm_alias_float_other (__sin, sin) 412 413GLOBAL_IEEE754_ENTRY(cosf) 414 415{ .mlx 416 alloc r32 = ar.pfs,1,13,0,0 417 movl sincosf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A //signd of 16/pi 418} 419{ .mlx 420 addl sincosf_AD_1 = @ltoff(double_sincosf_pi), gp 421 movl sincosf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) 422};; 423 424{ .mfi 425 ld8 sincosf_AD_1 = [sincosf_AD_1] 426 fnorm.s1 sincosf_NORM_f8 = f8 // Normalize argument 427 cmp.eq p9,p8 = r0, r0 // set p9 (clear p8) for cos 428} 429{ .mib 430 mov sincosf_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 431 mov sincosf_r_sincos = 0x8 // 8 for cos 432 nop.b 999 433};; 434 435//////////////////////////////////////////////////////// 436// All entry points end up here. 437// If from sin, sincosf_r_sincos is 0 and p8 is true 438// If from cos, sincosf_r_sincos is 8 = 2^(k-1) and p9 is true 439// We add sincosf_r_sincos to N 440 441///////////// Common sin and cos part ////////////////// 442_SINCOSF_COMMON: 443 444// Form two constants we need 445// 16/pi * 2^-2 * 2^63, scaled by 2^61 since we just loaded the significand 446// 1.1000...000 * 2^(63+63-2) to right shift int(W) into the low significand 447// fcmp used to set denormal, and invalid on snans 448{ .mfi 449 setf.sig sincosf_SIG_INV_PI_BY_16_2TO61 = sincosf_GR_sig_inv_pi_by_16 450 fclass.m p6,p0 = f8, 0xe7 // if x=0,inf,nan 451 mov sincosf_exp_limit = 0x10017 452} 453{ .mlx 454 setf.d sincosf_RSHF_2TO61 = sincosf_GR_rshf_2to61 455 movl sincosf_GR_rshf = 0x43e8000000000000 // 1.1000 2^63 456};; // Right shift 457 458// Form another constant 459// 2^-61 for scaling Nfloat 460// 0x10017 is register_bias + 24. 461// So if f8 >= 2^24, go to large argument routines 462{ .mmi 463 getf.exp sincosf_r_signexp = f8 464 setf.exp sincosf_2TOM61 = sincosf_GR_exp_2tom61 465 addl gr_tmp = -1,r0 // For "inexect" constant create 466};; 467 468// Load the two pieces of pi/16 469// Form another constant 470// 1.1000...000 * 2^63, the right shift constant 471{ .mmb 472 ldfe sincosf_Pi_by_16_1 = [sincosf_AD_1],16 473 setf.d sincosf_RSHF = sincosf_GR_rshf 474(p6) br.cond.spnt _SINCOSF_SPECIAL_ARGS 475};; 476 477// Getting argument's exp for "large arguments" filtering 478{ .mmi 479 ldfe sincosf_Pi_by_16_2 = [sincosf_AD_1],16 480 setf.sig fp_tmp = gr_tmp // constant for inexact set 481 nop.i 999 482};; 483 484// Polynomial coefficients (Q2, Q1, P2, P1) loading 485{ .mmi 486 ldfpd sincosf_P2,sincosf_Q2 = [sincosf_AD_1],16 487 nop.m 999 488 nop.i 999 489};; 490 491// Select exponent (17 lsb) 492{ .mmi 493 ldfpd sincosf_P1,sincosf_Q1 = [sincosf_AD_1],16 494 nop.m 999 495 dep.z sincosf_r_exp = sincosf_r_signexp, 0, 17 496};; 497 498// p10 is true if we must call routines to handle larger arguments 499// p10 is true if f8 exp is >= 0x10017 (2^24) 500{ .mfb 501 cmp.ge p10,p0 = sincosf_r_exp,sincosf_exp_limit 502 nop.f 999 503(p10) br.cond.spnt _SINCOSF_LARGE_ARGS // Go to "large args" routine 504};; 505 506// sincosf_W = x * sincosf_Inv_Pi_by_16 507// Multiply x by scaled 16/pi and add large const to shift integer part of W to 508// rightmost bits of significand 509{ .mfi 510 nop.m 999 511 fma.s1 sincosf_W_2TO61_RSH = sincosf_NORM_f8, sincosf_SIG_INV_PI_BY_16_2TO61, sincosf_RSHF_2TO61 512 nop.i 999 513};; 514 515// sincosf_NFLOAT = Round_Int_Nearest(sincosf_W) 516// This is done by scaling back by 2^-61 and subtracting the shift constant 517{ .mfi 518 nop.m 999 519 fms.s1 sincosf_NFLOAT = sincosf_W_2TO61_RSH,sincosf_2TOM61,sincosf_RSHF 520 nop.i 999 521};; 522 523// get N = (int)sincosf_int_Nfloat 524{ .mfi 525 getf.sig sincosf_GR_n = sincosf_W_2TO61_RSH // integer N value 526 nop.f 999 527 nop.i 999 528};; 529 530// Add 2^(k-1) (which is in sincosf_r_sincos=8) to N 531// sincosf_r = -sincosf_Nfloat * sincosf_Pi_by_16_1 + x 532{ .mfi 533 add sincosf_GR_n = sincosf_GR_n, sincosf_r_sincos 534 fnma.s1 sincosf_r = sincosf_NFLOAT, sincosf_Pi_by_16_1, sincosf_NORM_f8 535 nop.i 999 536};; 537 538// Get M (least k+1 bits of N) 539{ .mmi 540 and sincosf_GR_m = 0x1f,sincosf_GR_n // Put mask 0x1F - 541 nop.m 999 // - select k+1 bits 542 nop.i 999 543};; 544 545// Add 16*M to address of sin_cos_beta table 546{ .mfi 547 shladd sincosf_AD_2 = sincosf_GR_32m, 4, sincosf_AD_1 548(p8) fclass.m.unc p10,p0 = f8,0x0b // If sin denormal input - 549 nop.i 999 550};; 551 552// Load Sin and Cos table value using obtained index m (sincosf_AD_2) 553{ .mfi 554 ldfd sincosf_Sm = [sincosf_AD_2],8 // Sin value S[m] 555(p9) fclass.m.unc p11,p0 = f8,0x0b // If cos denormal input - 556 nop.i 999 // - set denormal 557};; 558 559// sincosf_r = sincosf_r -sincosf_Nfloat * sincosf_Pi_by_16_2 560{ .mfi 561 ldfd sincosf_Cm = [sincosf_AD_2] // Cos table value C[m] 562 fnma.s1 sincosf_r_exact = sincosf_NFLOAT, sincosf_Pi_by_16_2, sincosf_r 563 nop.i 999 564} 565// get rsq = r*r 566{ .mfi 567 nop.m 999 568 fma.s1 sincosf_rsq = sincosf_r, sincosf_r, f0 // r^2 = r*r 569 nop.i 999 570};; 571 572{ .mfi 573 nop.m 999 574 fmpy.s0 fp_tmp = fp_tmp, fp_tmp // forces inexact flag 575 nop.i 999 576};; 577 578// Polynomials calculation 579// Q = Q2*r^2 + Q1 580// P = P2*r^2 + P1 581{ .mfi 582 nop.m 999 583 fma.s1 sincosf_Q = sincosf_rsq, sincosf_Q2, sincosf_Q1 584 nop.i 999 585} 586{ .mfi 587 nop.m 999 588 fma.s1 sincosf_P = sincosf_rsq, sincosf_P2, sincosf_P1 589 nop.i 999 590};; 591 592// get rcube and S[m]*r^2 593{ .mfi 594 nop.m 999 595 fmpy.s1 sincosf_srsq = sincosf_Sm,sincosf_rsq // r^2*S[m] 596 nop.i 999 597} 598{ .mfi 599 nop.m 999 600 fmpy.s1 sincosf_rcub = sincosf_r_exact, sincosf_rsq 601 nop.i 999 602};; 603 604// Get final P and Q 605// Q = Q*S[m]*r^2 + S[m] 606// P = P*r^3 + r 607{ .mfi 608 nop.m 999 609 fma.s1 sincosf_Q = sincosf_srsq,sincosf_Q, sincosf_Sm 610 nop.i 999 611} 612{ .mfi 613 nop.m 999 614 fma.s1 sincosf_P = sincosf_rcub,sincosf_P,sincosf_r_exact 615 nop.i 999 616};; 617 618// If sinf(denormal) - force underflow to be set 619.pred.rel "mutex",p10,p11 620{ .mfi 621 nop.m 999 622(p10) fmpy.s.s0 fp_tmp = f8,f8 // forces underflow flag 623 nop.i 999 // for denormal sine args 624} 625// If cosf(denormal) - force denormal to be set 626{ .mfi 627 nop.m 999 628(p11) fma.s.s0 fp_tmp = f8, f1, f8 // forces denormal flag 629 nop.i 999 // for denormal cosine args 630};; 631 632 633// Final calculation 634// result = C[m]*P + Q 635{ .mfb 636 nop.m 999 637 fma.s.s0 f8 = sincosf_Cm, sincosf_P, sincosf_Q 638 br.ret.sptk b0 // Exit for common path 639};; 640 641////////// x = 0/Inf/NaN path ////////////////// 642_SINCOSF_SPECIAL_ARGS: 643.pred.rel "mutex",p8,p9 644// sinf(+/-0) = +/-0 645// sinf(Inf) = NaN 646// sinf(NaN) = NaN 647{ .mfi 648 nop.m 999 649(p8) fma.s.s0 f8 = f8, f0, f0 // sinf(+/-0,NaN,Inf) 650 nop.i 999 651} 652// cosf(+/-0) = 1.0 653// cosf(Inf) = NaN 654// cosf(NaN) = NaN 655{ .mfb 656 nop.m 999 657(p9) fma.s.s0 f8 = f8, f0, f1 // cosf(+/-0,NaN,Inf) 658 br.ret.sptk b0 // Exit for x = 0/Inf/NaN path 659};; 660 661GLOBAL_IEEE754_END(cosf) 662libm_alias_float_other (__cos, cos) 663 664//////////// x >= 2^24 - large arguments routine call //////////// 665LOCAL_LIBM_ENTRY(__libm_callout_sincosf) 666_SINCOSF_LARGE_ARGS: 667.prologue 668{ .mfi 669 mov sincosf_GR_all_ones = -1 // 0xffffffff 670 nop.f 999 671.save ar.pfs,GR_SAVE_PFS 672 mov GR_SAVE_PFS = ar.pfs 673} 674;; 675 676{ .mfi 677 mov GR_SAVE_GP = gp 678 nop.f 999 679.save b0, GR_SAVE_B0 680 mov GR_SAVE_B0 = b0 681} 682.body 683 684{ .mbb 685 setf.sig sincosf_save_tmp = sincosf_GR_all_ones // inexact set 686 nop.b 999 687(p8) br.call.sptk.many b0 = __libm_sin_large# // sinf(large_X) 688};; 689 690{ .mbb 691 cmp.ne p9,p0 = sincosf_r_sincos, r0 // set p9 if cos 692 nop.b 999 693(p9) br.call.sptk.many b0 = __libm_cos_large# // cosf(large_X) 694};; 695 696{ .mfi 697 mov gp = GR_SAVE_GP 698 fma.s.s0 f8 = f8, f1, f0 // Round result to single 699 mov b0 = GR_SAVE_B0 700} 701{ .mfi // force inexact set 702 nop.m 999 703 fmpy.s0 sincosf_save_tmp = sincosf_save_tmp, sincosf_save_tmp 704 nop.i 999 705};; 706 707{ .mib 708 nop.m 999 709 mov ar.pfs = GR_SAVE_PFS 710 br.ret.sptk b0 // Exit for large arguments routine call 711};; 712LOCAL_LIBM_END(__libm_callout_sincosf) 713 714.type __libm_sin_large#, @function 715.global __libm_sin_large# 716.type __libm_cos_large#, @function 717.global __libm_cos_large# 718