1.file "nextafter.s" 2 3 4// Copyright (c) 2000 - 2004, 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// 03/03/00 Modified to conform to C9X, and improve speed of main path 43// 03/14/00 Fixed case where x is a power of 2, and x > y, improved speed 44// 04/04/00 Unwind support added 45// 05/12/00 Fixed erroneous denormal flag setting for exponent change cases 1,3 46// 08/15/00 Bundle added after call to __libm_error_support to properly 47// set [the previously overwritten] GR_Parameter_RESULT. 48// 09/09/00 Updated fcmp so that qnans do not raise invalid 49// 12/15/00 Corrected behavior when both args are zero to conform to C99, and 50// fixed flag settings for several cases 51// 05/20/02 Cleaned up namespace and sf0 syntax 52// 02/10/03 Reordered header: .section, .global, .proc, .align 53// 12/14/04 Added error handling on underflow. 54// 55// API 56//============================================================== 57// double nextafter( double x, double y ); 58// input floating point f8, f9 59// output floating point f8 60// 61// Registers used 62//============================================================== 63GR_max_pexp = r14 64GR_min_pexp = r15 65GR_exp = r16 66GR_sig = r17 67GR_lnorm_sig = r18 68GR_sign_mask = r19 69GR_exp_mask = r20 70GR_sden_sig = r21 71GR_new_sig = r22 72GR_new_exp = r23 73GR_lden_sig = r24 74GR_snorm_sig = r25 75GR_exp1 = r26 76GR_x_exp = r27 77GR_min_den_rexp = r28 78// r36-39 parameters for libm_error_support 79 80GR_SAVE_B0 = r34 81GR_SAVE_GP = r35 82GR_SAVE_PFS = r32 83 84GR_Parameter_X = r36 85GR_Parameter_Y = r37 86GR_Parameter_RESULT = r38 87GR_Parameter_TAG = r39 88 89FR_lnorm_sig = f10 90FR_lnorm_exp = f11 91FR_lnorm = f12 92FR_sden_sig = f13 93FR_sden_exp = f14 94FR_sden = f15 95FR_save_f8 = f33 96FR_new_exp = f34 97FR_new_sig = f35 98FR_lden_sig = f36 99FR_snorm_sig = f37 100FR_exp1 = f38 101FR_tmp = f39 102 103// 104// Overview of operation 105//============================================================== 106// nextafter determines the next representable value 107// after x in the direction of y. 108 109 110.section .text 111GLOBAL_LIBM_ENTRY(nextafter) 112 113// Extract signexp from x 114// Is x < y ? p10 if yes, p11 if no 115// Form smallest denormal significand = ulp size 116{ .mfi 117 getf.exp GR_exp = f8 118 fcmp.lt.s1 p10,p11 = f8, f9 119 addl GR_sden_sig = 0x800, r0 120} 121// Form largest normal significand 0xfffffffffffff800 122// Form smallest normal exponent 123{ .mfi 124 addl GR_lnorm_sig = -0x800,r0 125 nop.f 999 126 addl GR_min_pexp = 0x0fc01, r0 ;; 127} 128// Extract significand from x 129// Is x=y? 130// Form largest normal exponent 131{ .mfi 132 getf.sig GR_sig = f8 133 fcmp.eq.s0 p6,p0 = f8, f9 134 addl GR_max_pexp = 0x103fe, r0 135} 136// Move largest normal significand to fp reg for special cases 137{ .mfi 138 setf.sig FR_lnorm_sig = GR_lnorm_sig 139 nop.f 999 140 addl GR_sign_mask = 0x20000, r0 ;; 141} 142 143// Move smallest denormal significand and signexp to fp regs 144// Is x=nan? 145// Set p12 and p13 based on whether significand increases or decreases 146// It increases (p12 set) if x<y and x>=0 or if x>y and x<0 147// It decreases (p13 set) if x<y and x<0 or if x>y and x>=0 148{ .mfi 149 setf.sig FR_sden_sig = GR_sden_sig 150 fclass.m p8,p0 = f8, 0xc3 151(p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask 152} 153{ .mfi 154 setf.exp FR_sden_exp = GR_min_pexp 155(p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;; 156} 157 158.pred.rel "mutex",p12,p13 159 160// Form expected new significand, adding or subtracting 1 ulp increment 161// If x=y set result to y 162// Form smallest normal significand and largest denormal significand 163{ .mfi 164(p12) add GR_new_sig = GR_sig, GR_sden_sig 165(p6) fmerge.s f8=f9,f9 166 dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000 167} 168{ .mlx 169(p13) sub GR_new_sig = GR_sig, GR_sden_sig 170 movl GR_lden_sig = 0x7ffffffffffff800 ;; 171} 172 173// Move expected result significand and signexp to fp regs 174// Is y=nan? 175// Form new exponent in case result exponent needs incrementing or decrementing 176{ .mfi 177 setf.exp FR_new_exp = GR_exp 178 fclass.m p9,p0 = f9, 0xc3 179(p12) add GR_exp1 = 1, GR_exp 180} 181{ .mib 182 setf.sig FR_new_sig = GR_new_sig 183(p13) add GR_exp1 = -1, GR_exp 184(p6) br.ret.spnt b0 ;; // Exit if x=y 185} 186 187// Move largest normal signexp to fp reg for special cases 188// Is x=zero? 189{ .mfi 190 setf.exp FR_lnorm_exp = GR_max_pexp 191 fclass.m p7,p0 = f8, 0x7 192 nop.i 999 193} 194{ .mfb 195 nop.m 999 196(p8) fma.s0 f8 = f8,f1,f9 197(p8) br.ret.spnt b0 ;; // Exit if x=nan 198} 199 200// Move exp+-1 and smallest normal significand to fp regs for special cases 201// Is x=inf? 202{ .mfi 203 setf.exp FR_exp1 = GR_exp1 204 fclass.m p6,p0 = f8, 0x23 205 addl GR_exp_mask = 0x1ffff, r0 206} 207{ .mfb 208 setf.sig FR_snorm_sig = GR_snorm_sig 209(p9) fma.s0 f8 = f8,f1,f9 210(p9) br.ret.spnt b0 ;; // Exit if y=nan 211} 212 213// Move largest denormal significand to fp regs for special cases 214// Save x 215{ .mfb 216 setf.sig FR_lden_sig = GR_lden_sig 217 mov FR_save_f8 = f8 218(p7) br.cond.spnt NEXT_ZERO ;; // Exit if x=0 219} 220 221// Mask off the sign to get x_exp 222{ .mfb 223 and GR_x_exp = GR_exp_mask, GR_exp 224 nop.f 999 225(p6) br.cond.spnt NEXT_INF ;; // Exit if x=inf 226} 227 228// Check 6 special cases when significand rolls over: 229// 1 sig size incr, x_sig=max_sig, x_exp < max_exp 230// Set p6, result is sig=min_sig, exp++ 231// 2 sig size incr, x_sig=max_sig, x_exp >= max_exp 232// Set p7, result is inf, signal overflow 233// 3 sig size decr, x_sig=min_sig, x_exp > min_exp 234// Set p8, result is sig=max_sig, exp-- 235// 4 sig size decr, x_sig=min_sig, x_exp = min_exp 236// Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact 237// 5 sig size decr, x_sig=min_den_sig, x_exp = min_exp 238// Set p10, result is zero, sign of x, signal underflow and inexact 239// 6 sig size decr, x_sig=min_sig, x_exp < min_exp 240// Set p14, result is zero, sign of x, signal underflow and inexact 241// 242// Form exponent of smallest double denormal (if normalized register format) 243{ .mmi 244 adds GR_min_den_rexp = -52, GR_min_pexp 245(p12) cmp.eq.unc p6,p0 = GR_new_sig, r0 246(p13) cmp.eq.unc p8,p10 = GR_new_sig, GR_lden_sig ;; 247} 248 249{ .mmi 250(p6) cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp 251(p8) cmp.gt.unc p8,p9 = GR_x_exp, GR_min_pexp 252(p10) cmp.eq.unc p10,p0 = GR_new_sig, r0 ;; 253} 254 255// Create small normal in case need to generate underflow flag 256{ .mfi 257(p10) cmp.le.unc p10,p0 = GR_x_exp, GR_min_pexp 258 fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig 259(p9) cmp.gt.unc p9,p14 = GR_x_exp, GR_min_den_rexp 260} 261// Branch if cases 1, 2, 3 262{ .bbb 263(p6) br.cond.spnt NEXT_EXPUP 264(p7) br.cond.spnt NEXT_OVERFLOW 265(p8) br.cond.spnt NEXT_EXPDOWN ;; 266} 267 268// Branch if cases 4, 5, 6 269{ .bbb 270(p9) br.cond.spnt NEXT_NORM_TO_DENORM 271(p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO 272(p14) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO ;; 273} 274 275// Here if no special cases 276// Set p6 if result will be a denormal, so can force underflow flag 277// Case 1: x_exp=min_exp, x_sig=unnormalized 278// Case 2: x_exp<min_exp 279{ .mfi 280 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp 281 fmerge.se f8 = FR_new_exp, FR_new_sig 282 nop.i 999 ;; 283} 284 285{ .mfi 286 nop.m 999 287 nop.f 999 288(p7) tbit.z p6,p0 = GR_new_sig, 63 ;; 289} 290 291NEXT_COMMON_FINISH: 292// Force underflow and inexact if denormal result 293{ .mfi 294 nop.m 999 295(p6) fma.d.s0 FR_tmp = FR_tmp,FR_tmp,f0 296 nop.i 999 297} 298{ .mfb 299 nop.m 999 300 fnorm.d.s0 f8 = f8 // Final normalization to result precision 301(p6) br.cond.spnt NEXT_UNDERFLOW ;; 302} 303 304{ .mfb 305 nop.m 999 306 nop.f 999 307 br.ret.sptk b0;; 308} 309 310//Special cases 311NEXT_EXPUP: 312{ .mfb 313 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp 314 fmerge.se f8 = FR_exp1, FR_snorm_sig 315 br.cond.sptk NEXT_COMMON_FINISH ;; 316} 317 318NEXT_EXPDOWN: 319{ .mfb 320 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp 321 fmerge.se f8 = FR_exp1, FR_lnorm_sig 322 br.cond.sptk NEXT_COMMON_FINISH ;; 323} 324 325NEXT_NORM_TO_DENORM: 326{ .mfi 327 nop.m 999 328 fmerge.se f8 = FR_new_exp, FR_lden_sig 329 nop.i 999 330} 331// Force underflow and inexact if denormal result 332{ .mfb 333 nop.m 999 334 fma.d.s0 FR_tmp = FR_tmp,FR_tmp,f0 335 br.cond.sptk NEXT_UNDERFLOW ;; 336} 337 338NEXT_UNDERFLOW_TO_ZERO: 339{ .mfb 340 cmp.eq p6,p0 = r0,r0 341 fmerge.s f8 = FR_save_f8,f0 342 br.cond.sptk NEXT_COMMON_FINISH ;; 343} 344 345NEXT_INF: 346// Here if f8 is +- infinity 347// INF 348// if f8 is +inf, no matter what y is return largest double 349// if f8 is -inf, no matter what y is return -largest double 350 351{ .mfi 352 nop.m 999 353 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig 354 nop.i 999 ;; 355} 356 357{ .mfb 358 nop.m 999 359 fmerge.s f8 = f8,FR_lnorm 360 br.ret.sptk b0 ;; 361} 362 363NEXT_ZERO: 364 365// Here if f8 is +- zero 366// ZERO 367// if f8 is zero and y is +, return + smallest double denormal 368// if f8 is zero and y is -, return - smallest double denormal 369 370{ .mfi 371 nop.m 999 372 fmerge.se FR_sden = FR_sden_exp,FR_sden_sig 373 nop.i 999 ;; 374} 375 376// Create small normal to generate underflow flag 377{ .mfi 378 nop.m 999 379 fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig 380 nop.i 999 ;; 381} 382 383// Add correct sign from direction arg 384{ .mfi 385 nop.m 999 386 fmerge.s f8 = f9,FR_sden 387 nop.i 999 ;; 388} 389 390// Force underflow and inexact flags 391{ .mfb 392 nop.m 999 393 fma.d.s0 FR_tmp = FR_tmp,FR_tmp,f0 394 br.cond.sptk NEXT_UNDERFLOW ;; 395} 396 397NEXT_UNDERFLOW: 398// Here if result is a denorm, or input is finite and result is zero 399// Call error support to report possible range error 400{ .mib 401 alloc r32=ar.pfs,2,2,4,0 402 mov GR_Parameter_TAG = 268 // Error code 403 br.cond.sptk __libm_error_region // Branch to error call 404} 405;; 406 407NEXT_OVERFLOW: 408// Here if input is finite, but result will be infinite 409// Use frcpa to generate infinity of correct sign 410// Call error support to report possible range error 411{ .mfi 412 alloc r32=ar.pfs,2,2,4,0 413 frcpa.s1 f8,p6 = FR_save_f8, f0 414 nop.i 999 ;; 415} 416 417// Create largest double 418{ .mfi 419 nop.m 999 420 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig 421 nop.i 999 ;; 422} 423 424// Force overflow and inexact flags to be set 425{ .mfb 426 mov GR_Parameter_TAG = 154 // Error code 427 fma.d.s0 FR_tmp = FR_lnorm,FR_lnorm,f0 428 br.cond.sptk __libm_error_region // Branch to error call 429} 430;; 431 432GLOBAL_LIBM_END(nextafter) 433libm_alias_double_other (nextafter, nextafter) 434 435 436LOCAL_LIBM_ENTRY(__libm_error_region) 437.prologue 438 439// (1) 440{ .mfi 441 add GR_Parameter_Y=-32,sp // Parameter 2 value 442 nop.f 0 443.save ar.pfs,GR_SAVE_PFS 444 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs 445} 446{ .mfi 447.fframe 64 448 add sp=-64,sp // Create new stack 449 nop.f 0 450 mov GR_SAVE_GP=gp // Save gp 451};; 452 453 454// (2) 455{ .mmi 456 stfd [GR_Parameter_Y] = f9,16 // STORE Parameter 2 on stack 457 add GR_Parameter_X = 16,sp // Parameter 1 address 458.save b0, GR_SAVE_B0 459 mov GR_SAVE_B0=b0 // Save b0 460};; 461 462.body 463// (3) 464{ .mib 465 stfd [GR_Parameter_X] = FR_save_f8 // STORE Parameter 1 on stack 466 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address 467 nop.b 0 468} 469{ .mib 470 stfd [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack 471 add GR_Parameter_Y = -16,GR_Parameter_Y 472 br.call.sptk b0=__libm_error_support# // Call error handling function 473};; 474{ .mmi 475 nop.m 0 476 nop.m 0 477 add GR_Parameter_RESULT = 48,sp 478};; 479 480// (4) 481{ .mmi 482 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack 483.restore sp 484 add sp = 64,sp // Restore stack pointer 485 mov b0 = GR_SAVE_B0 // Restore return address 486};; 487{ .mib 488 mov gp = GR_SAVE_GP // Restore gp 489 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 490 br.ret.sptk b0 // Return 491};; 492 493LOCAL_LIBM_END(__libm_error_region) 494 495 496.type __libm_error_support#,@function 497.global __libm_error_support# 498