1.file "hypot.s" 2 3 4// Copyright (c) 2000 - 2003, 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//********************************************************************* 40// 41// History: 42// 02/02/00 hand-optimized 43// 04/04/00 Unwind support added 44// 06/20/00 new version 45// 08/15/00 Bundle added after call to __libm_error_support to properly 46// set [the previously overwritten] GR_Parameter_RESULT. 47// 05/20/02 Cleaned up namespace and sf0 syntax 48// 02/10/03 Reordered header: .section, .global, .proc, .align 49// 04/17/03 Added missing mutex directive 50// 51//********************************************************************* 52// ___________ 53// Function: hypot(x,y) = |(x^2 + y^2) = for double precision values 54// x and y 55// Also provides cabs functionality. 56// 57//********************************************************************* 58// 59// Resources Used: 60// 61// Floating-Point Registers: f8 (Input and Return Value) 62// f9 (Input) 63// f6 -f15, f32-f34 64// 65// General Purpose Registers: 66// r2,r3,r29 (Scratch) 67// r32-r36 (Locals) 68// r37-r40 (Used to pass arguments to error handling routine) 69// 70// Predicate Registers: p6 - p10 71// 72//********************************************************************* 73// 74// IEEE Special Conditions: 75// 76// All faults and exceptions should be raised correctly. 77// Overflow can occur. 78// hypot(Infinity and anything) = +Infinity 79// hypot(QNaN and anything) = QNaN 80// hypot(SNaN and anything ) = QNaN 81// 82//********************************************************************* 83// 84// Implementation: 85// x2 = x * x in double-extended 86// y2 = y * y in double-extended 87// temp = x2 + y2 in double-extended 88// sqrt(temp) rounded to double 89// 90//********************************************************************* 91 92GR_SAVE_PFS = r33 93GR_SAVE_B0 = r34 94GR_SAVE_GP = r35 95GR_Parameter_X = r36 96GR_Parameter_Y = r37 97GR_Parameter_RESULT = r38 98GR_Parameter_TAG = r39 99 100FR_X = f32 101FR_Y = f33 102FR_RESULT = f8 103 104.section .text 105 106LOCAL_LIBM_ENTRY(cabs) 107LOCAL_LIBM_END(cabs) 108 109GLOBAL_IEEE754_ENTRY(hypot) 110 111{.mfi 112 alloc r32= ar.pfs,0,4,4,0 113 // Compute x*x 114 fma.s1 f10=f8,f8,f0 115 // r2=bias-1 116 mov r2=0xfffe 117} 118{.mfi 119 // 63/8 120 mov r3=0x40fc //0000 121 // y*y 122 fma.s1 f11=f9,f9,f0 123 // r29=429/16 124 mov r29=0x41d68;; //000 125} 126 127{ .mfi 128 nop.m 0 129// Check if x is an Inf - if so return Inf even 130// if y is a NaN (C9X) 131 fclass.m.unc p7, p6 = f8, 0x023 132 shl r3=r3,16 133} 134{.mfi 135 nop.m 0 136 // if possible overflow, copy f8 to f32 137 // set Denormal, if necessary 138 // (p8) 139 fma.d.s0 f32=f8,f1,f0 140 nop.i 0;; 141} 142{ .mfi 143 nop.m 0 144// Check if y is an Inf - if so return Inf even 145// if x is a NaN (C9X) 146 fclass.m.unc p8, p9 = f9, 0x023 147 shl r29=r29,12 148} 149{ .mfb 150 // f7=0.5 151 setf.exp f7=r2 152// For x=inf, multiply y by 1 to raise invalid on y an SNaN 153// (p7) fma.s0 f9=f9,f1,f0 154 // copy f9 to f33; set Denormal, if necessary 155 fma.d.s0 f33=f9,f1,f0 156 nop.b 0;; 157} 158{.mfb 159 // f13=63/8 160 setf.s f13=r3 161 // is y Zero ? 162 (p6) fclass.m p6,p0=f9,0x7 163 nop.b 0 164} 165{.mlx 166 nop.m 0 167 movl r2=0x408c0000;; 168} 169 170{.mfi 171 // f34=429/16 172 setf.s f34=r29 173 // is x Zero ? 174 (p9) fclass.m p9,p0=f8,0x7 175 // 231/16 176 mov r3=0x4167;; //0000 177} 178{.mfi 179 nop.m 0 180 // a=x2+y2 181 fma.s1 f12=f10,f1,f11 182 nop.i 0;; 183} 184{.mfi 185 nop.m 0 186 // y not NaN ? 187 (p9) fclass.m p8,p0=f9,0x3f 188 shl r3=r3,16 189} 190{.mfi 191 nop.m 0 192 // f6=2 193 fma.s1 f6=f1,f1,f1 194 nop.i 0;; 195} 196 197 198{.mfi 199 nop.m 0 200 // x not NaN ? 201 (p6) fclass.m p7,p0=f8,0x3f 202 nop.i 0;; 203} 204{.mfi 205 // f9=35/8 206 setf.s f9=r2 207 nop.f 0 208 // 2*emax-2 209 mov r2=0x107fb;; 210} 211 212.pred.rel "mutex",p7,p8 213{.mfb 214 nop.m 0 215 // if f8=Infinity or f9=Zero, return |f8| 216 (p7) fmerge.s f8=f0,f32 217 (p7) br.ret.spnt b0 218} 219{.mfb 220 nop.m 0 221 // if f9=Infinity or f8=Zero, return |f9| 222 (p8) fmerge.s f8=f0,f33 223 (p8) br.ret.spnt b0;; 224} 225 226 227{.mfi 228 // f10 =231/16 229 setf.s f10=r3 230 // z0=frsqrta(a) 231 frsqrta.s1 f8,p6=f12 232 nop.i 0;; 233} 234 235{ .mfi 236 nop.m 0 237// Identify Natvals, Infs, NaNs, and Zeros 238// and return result 239 fclass.m.unc p7, p0 = f12, 0x1E7 240 nop.i 0;; 241} 242{.mfb 243 // get exponent of x^2+y^2 244 getf.exp r3=f12 245 // if special case, set f8 246 (p7) mov f8=f12 247 (p7) br.ret.spnt b0;; 248} 249 250 251{.mfi 252 nop.m 0 253 // S0=a*z0 254 (p6) fma.s1 f14=f12,f8,f0 255 nop.i 0 256} 257{.mfi 258 nop.m 0 259 // H0=0.5*z0 260 (p6) fma.s1 f15=f8,f7,f0 261 nop.i 0;; 262} 263 264 265{.mfi 266 nop.m 0 267 // f6=5/2 268 fma.s1 f6=f7,f1,f6 269 nop.i 0 270} 271{.mfi 272 nop.m 0 273 // f11=3/2 274 fma.s1 f11=f7,f1,f1 275 nop.i 0;; 276} 277 278{.mfi 279 nop.m 0 280 // d=0.5-S0*H0 281 (p6) fnma.s1 f7=f14,f15,f7 282 nop.i 0;; 283} 284 285{.mfi 286 nop.m 0 287 // P67=231/16+429/16*d 288 (p6) fma.s1 f10=f34,f7,f10 289 nop.i 0 290} 291{.mfi 292 nop.m 0 293 // P45=63/8*d+35/8 294 (p6) fma.s1 f9=f13,f7,f9 295 nop.i 0;; 296} 297{.mfi 298 nop.m 0 299 // P23=5/2*d+3/2 300 (p6) fma.s1 f11=f6,f7,f11 301 nop.i 0 302} 303{.mfi 304 nop.m 0 305 // d2=d*d 306 (p6) fma.s1 f13=f7,f7,f0 307 nop.i 0;; 308} 309 310{.mfi 311 nop.m 0 312 // P47=d2*P67+P45 313 (p6) fma.s1 f10=f10,f13,f9 314 nop.i 0 315} 316{.mfi 317 nop.m 0 318 // P13=d*P23+1 319 (p6) fma.s1 f11=f11,f7,f1 320 nop.i 0;; 321} 322{.mfi 323 nop.m 0 324 // d3=d2*d 325 (p6) fma.s1 f13=f13,f7,f0 326 nop.i 0;; 327} 328 329{.mfi 330 nop.m 0 331 // T0=d*S0 332 (p6) fma.s1 f15=f7,f14,f0 333 nop.i 0 334} 335{.mfi 336 // Is x^2 + y^2 well less than the overflow 337 // threshold? 338 (p6) cmp.lt.unc p7, p8 = r3,r2 339 // P=P13+d3*P47 340 (p6) fma.s1 f10=f13,f10,f11 341 nop.i 0;; 342} 343 344{.mfb 345 nop.m 0 346 // S=P*T0+S0 347 fma.d.s0 f8=f10,f15,f14 348 // No overflow in this case 349 (p7) br.ret.sptk b0;; 350} 351 352{ .mfi 353 nop.m 0 354(p8) fsetc.s2 0x7F,0x42 355 // Possible overflow path, must detect by 356 // Setting widest range exponent with prevailing 357 // rounding mode. 358 nop.i 0 ;; 359} 360 361 362{ .mfi 363 // bias+0x400 (bias+EMAX+1) 364 (p8) mov r2=0x103ff 365 // S=P*T0+S0 366 (p8) fma.d.s2 f12=f10,f15,f14 367 nop.i 0 ;; 368} 369{ .mfi 370(p8) setf.exp f11 = r2 371(p8) fsetc.s2 0x7F,0x40 372// Restore Original Mode in S2 373 nop.i 0 ;; 374} 375{ .mfi 376 nop.m 0 377(p8) fcmp.lt.unc.s1 p9, p10 = f12, f11 378 nop.i 0 ;; 379} 380{ .mib 381 nop.m 0 382 mov GR_Parameter_TAG = 46 383 // No overflow 384(p9) br.ret.sptk b0;; 385} 386GLOBAL_IEEE754_END(hypot) 387libm_alias_double_other (__hypot, hypot) 388 389LOCAL_LIBM_ENTRY(__libm_error_region) 390.prologue 391{ .mfi 392 add GR_Parameter_Y=-32,sp // Parameter 2 value 393 nop.f 0 394.save ar.pfs,GR_SAVE_PFS 395 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs 396} 397{ .mfi 398.fframe 64 399 add sp=-64,sp // Create new stack 400 nop.f 0 401 mov GR_SAVE_GP=gp // Save gp 402};; 403{ .mmi 404 stfd [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack 405 add GR_Parameter_X = 16,sp // Parameter 1 address 406.save b0, GR_SAVE_B0 407 mov GR_SAVE_B0=b0 // Save b0 408};; 409.body 410{ .mib 411 stfd [GR_Parameter_X] = FR_X // Store Parameter 1 on stack 412 add GR_Parameter_RESULT = 0,GR_Parameter_Y 413 nop.b 0 // Parameter 3 address 414} 415{ .mib 416 stfd [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack 417 add GR_Parameter_Y = -16,GR_Parameter_Y 418 br.call.sptk b0=__libm_error_support# // Call error handling function 419};; 420{ .mmi 421 nop.m 0 422 nop.m 0 423 add GR_Parameter_RESULT = 48,sp 424};; 425{ .mmi 426 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack 427.restore sp 428 add sp = 64,sp // Restore stack pointer 429 mov b0 = GR_SAVE_B0 // Restore return address 430};; 431{ .mib 432 mov gp = GR_SAVE_GP // Restore gp 433 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 434 br.ret.sptk b0 // Return 435};; 436LOCAL_LIBM_END(__libm_error_region#) 437.type __libm_error_support#,@function 438.global __libm_error_support# 439