sysdeps/i386/fpu/e_powf.S

   1 /* ix87 specific implementation of pow function.
   2    Copyright (C) 1996, 1997, 1999, 2001, 2004, 2005
   3    Free Software Foundation, Inc.
   4    This file is part of the GNU C Library.
   5    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
   6
   7    The GNU C Library is free software; you can redistribute it and/or
   8    modify it under the terms of the GNU Lesser General Public
   9    License as published by the Free Software Foundation; either
  10    version 2.1 of the License, or (at your option) any later version.
  11
  12    The GNU C Library is distributed in the hope that it will be useful,
  13    but WITHOUT ANY WARRANTY; without even the implied warranty of
  14    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15    Lesser General Public License for more details.
  16
  17    You should have received a copy of the GNU Lesser General Public
  18    License along with the GNU C Library; if not, write to the Free
  19    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  20    02111-1307 USA.  */
  21
  22 #include <machine/asm.h>
  23
  24 #ifdef __ELF__
  25         .section .rodata
  26 #else
  27         .text
  28 #endif
  29
  30         .align ALIGNARG(4)
  31         ASM_TYPE_DIRECTIVE(infinity,@object)
  32 inf_zero:
  33 infinity:
  34         .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
  35         ASM_SIZE_DIRECTIVE(infinity)
  36         ASM_TYPE_DIRECTIVE(zero,@object)
  37 zero:   .double 0.0
  38         ASM_SIZE_DIRECTIVE(zero)
  39         ASM_TYPE_DIRECTIVE(minf_mzero,@object)
  40 minf_mzero:
  41 minfinity:
  42         .byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
  43 mzero:
  44         .byte 0, 0, 0, 0, 0, 0, 0, 0x80
  45         ASM_SIZE_DIRECTIVE(minf_mzero)
  46         ASM_TYPE_DIRECTIVE(one,@object)
  47 one:    .double 1.0
  48         ASM_SIZE_DIRECTIVE(one)
  49         ASM_TYPE_DIRECTIVE(limit,@object)
  50 limit:  .double 0.29
  51         ASM_SIZE_DIRECTIVE(limit)
  52         ASM_TYPE_DIRECTIVE(p31,@object)
  53 p31:    .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x41
  54         ASM_SIZE_DIRECTIVE(p31)
  55
  56 #ifdef PIC
  57 #define MO(op) op##@GOTOFF(%ecx)
  58 #define MOX(op,x,f) op##@GOTOFF(%ecx,x,f)
  59 #else
  60 #define MO(op) op
  61 #define MOX(op,x,f) op(,x,f)
  62 #endif
  63
  64         .text
  65 ENTRY(__ieee754_powf)
  66         flds    8(%esp) // y
  67         fxam
  68
  69 #ifdef  PIC
  70         LOAD_PIC_REG (cx)
  71 #endif
  72
  73         fnstsw
  74         movb    %ah, %dl
  75         andb    $0x45, %ah
  76         cmpb    $0x40, %ah      // is y == 0 ?
  77         je      11f
  78
  79         cmpb    $0x05, %ah      // is y == ±inf ?
  80         je      12f
  81
  82         cmpb    $0x01, %ah      // is y == NaN ?
  83         je      30f
  84
  85         flds    4(%esp)         // x : y
  86
  87         subl    $4, %esp
  88         cfi_adjust_cfa_offset (4)
  89
  90         fxam
  91         fnstsw
  92         movb    %ah, %dh
  93         andb    $0x45, %ah
  94         cmpb    $0x40, %ah
  95         je      20f             // x is ±0
  96
  97         cmpb    $0x05, %ah
  98         je      15f             // x is ±inf
  99
 100         fxch                    // y : x
 101
 102         /* fistpl raises invalid exception for |y| >= 1L<<31.  */
 103         fld     %st             // y : y : x
 104         fabs                    // |y| : y : x
 105         fcompl  MO(p31)         // y : x
 106         fnstsw
 107         sahf
 108         jnc     2f
 109
 110         /* First see whether `y' is a natural number.  In this case we
 111            can use a more precise algorithm.  */
 112         fld     %st             // y : y : x
 113         fistpl  (%esp)          // y : x
 114         fildl   (%esp)          // int(y) : y : x
 115         fucomp  %st(1)          // y : x
 116         fnstsw
 117         sahf
 118         jne     2f
 119
 120         /* OK, we have an integer value for y.  */
 121         popl    %edx
 122         cfi_adjust_cfa_offset (-4)
 123         orl     $0, %edx
 124         fstp    %st(0)          // x
 125         jns     4f              // y >= 0, jump
 126         fdivrl  MO(one)         // 1/x          (now referred to as x)
 127         negl    %edx
 128 4:      fldl    MO(one)         // 1 : x
 129         fxch
 130
 131 6:      shrl    $1, %edx
 132         jnc     5f
 133         fxch
 134         fmul    %st(1)          // x : ST*x
 135         fxch
 136 5:      fmul    %st(0), %st     // x*x : ST*x
 137         testl   %edx, %edx
 138         jnz     6b
 139         fstp    %st(0)          // ST*x
 140         ret
 141
 142         /* y is ±NAN */
 143 30:     flds    4(%esp)         // x : y
 144         fldl    MO(one)         // 1.0 : x : y
 145         fucomp  %st(1)          // x : y
 146         fnstsw
 147         sahf
 148         je      31f
 149         fxch                    // y : x
 150 31:     fstp    %st(1)
 151         ret
 152
 153         cfi_adjust_cfa_offset (4)
 154         .align ALIGNARG(4)
 155 2:      /* y is a real number.  */
 156         fxch                    // x : y
 157         fldl    MO(one)         // 1.0 : x : y
 158         fld     %st(1)          // x : 1.0 : x : y
 159         fsub    %st(1)          // x-1 : 1.0 : x : y
 160         fabs                    // |x-1| : 1.0 : x : y
 161         fcompl  MO(limit)       // 1.0 : x : y
 162         fnstsw
 163         fxch                    // x : 1.0 : y
 164         sahf
 165         ja      7f
 166         fsub    %st(1)          // x-1 : 1.0 : y
 167         fyl2xp1                 // log2(x) : y
 168         jmp     8f
 169
 170 7:      fyl2x                   // log2(x) : y
 171 8:      fmul    %st(1)          // y*log2(x) : y
 172         fst     %st(1)          // y*log2(x) : y*log2(x)
 173         frndint                 // int(y*log2(x)) : y*log2(x)
 174         fsubr   %st, %st(1)     // int(y*log2(x)) : fract(y*log2(x))
 175         fxch                    // fract(y*log2(x)) : int(y*log2(x))
 176         f2xm1                   // 2^fract(y*log2(x))-1 : int(y*log2(x))
 177         faddl   MO(one)         // 2^fract(y*log2(x)) : int(y*log2(x))
 178         fscale                  // 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
 179         addl    $4, %esp
 180         cfi_adjust_cfa_offset (-4)
 181         fstp    %st(1)          // 2^fract(y*log2(x))*2^int(y*log2(x))
 182         ret
 183
 184
 185         // pow(x,±0) = 1
 186         .align ALIGNARG(4)
 187 11:     fstp    %st(0)          // pop y
 188         fldl    MO(one)
 189         ret
 190
 191         // y == ±inf
 192         .align ALIGNARG(4)
 193 12:     fstp    %st(0)          // pop y
 194         flds    4(%esp)         // x
 195         fabs
 196         fcompl  MO(one)         // < 1, == 1, or > 1
 197         fnstsw
 198         andb    $0x45, %ah
 199         cmpb    $0x45, %ah
 200         je      13f             // jump if x is NaN
 201
 202         cmpb    $0x40, %ah
 203         je      14f             // jump if |x| == 1
 204
 205         shlb    $1, %ah
 206         xorb    %ah, %dl
 207         andl    $2, %edx
 208         fldl    MOX(inf_zero, %edx, 4)
 209         ret
 210
 211         .align ALIGNARG(4)
 212 14:     fldl    MO(one)
 213         ret
 214
 215         .align ALIGNARG(4)
 216 13:     flds    4(%esp)         // load x == NaN
 217         ret
 218
 219         cfi_adjust_cfa_offset (4)
 220         .align ALIGNARG(4)
 221         // x is ±inf
 222 15:     fstp    %st(0)          // y
 223         testb   $2, %dh
 224         jz      16f             // jump if x == +inf
 225
 226         // We must find out whether y is an odd integer.
 227         fld     %st             // y : y
 228         fistpl  (%esp)          // y
 229         fildl   (%esp)          // int(y) : y
 230         fucompp                 // <empty>
 231         fnstsw
 232         sahf
 233         jne     17f
 234
 235         // OK, the value is an integer, but is the number of bits small
 236         // enough so that all are coming from the mantissa?
 237         popl    %edx
 238         cfi_adjust_cfa_offset (-4)
 239         testb   $1, %dl
 240         jz      18f             // jump if not odd
 241         movl    %edx, %eax
 242         orl     %edx, %edx
 243         jns     155f
 244         negl    %eax
 245 155:    cmpl    $0x01000000, %eax
 246         ja      18f             // does not fit in mantissa bits
 247         // It's an odd integer.
 248         shrl    $31, %edx
 249         fldl    MOX(minf_mzero, %edx, 8)
 250         ret
 251
 252         cfi_adjust_cfa_offset (4)
 253         .align ALIGNARG(4)
 254 16:     fcompl  MO(zero)
 255         addl    $4, %esp
 256         cfi_adjust_cfa_offset (-4)
 257         fnstsw
 258         shrl    $5, %eax
 259         andl    $8, %eax
 260         fldl    MOX(inf_zero, %eax, 1)
 261         ret
 262
 263         cfi_adjust_cfa_offset (4)
 264         .align ALIGNARG(4)
 265 17:     shll    $30, %edx       // sign bit for y in right position
 266         addl    $4, %esp
 267         cfi_adjust_cfa_offset (-4)
 268 18:     shrl    $31, %edx
 269         fldl    MOX(inf_zero, %edx, 8)
 270         ret
 271
 272         cfi_adjust_cfa_offset (4)
 273         .align ALIGNARG(4)
 274         // x is ±0
 275 20:     fstp    %st(0)          // y
 276         testb   $2, %dl
 277         jz      21f             // y > 0
 278
 279         // x is ±0 and y is < 0.  We must find out whether y is an odd integer.
 280         testb   $2, %dh
 281         jz      25f
 282
 283         fld     %st             // y : y
 284         fistpl  (%esp)          // y
 285         fildl   (%esp)          // int(y) : y
 286         fucompp                 // <empty>
 287         fnstsw
 288         sahf
 289         jne     26f
 290
 291         // OK, the value is an integer, but is the number of bits small
 292         // enough so that all are coming from the mantissa?
 293         popl    %edx
 294         cfi_adjust_cfa_offset (-4)
 295         testb   $1, %dl
 296         jz      27f             // jump if not odd
 297         cmpl    $0xff000000, %edx
 298         jbe     27f             // does not fit in mantissa bits
 299         // It's an odd integer.
 300         // Raise divide-by-zero exception and get minus infinity value.
 301         fldl    MO(one)
 302         fdivl   MO(zero)
 303         fchs
 304         ret
 305
 306         cfi_adjust_cfa_offset (4)
 307 25:     fstp    %st(0)
 308 26:     addl    $4, %esp
 309         cfi_adjust_cfa_offset (-4)
 310 27:     // Raise divide-by-zero exception and get infinity value.
 311         fldl    MO(one)
 312         fdivl   MO(zero)
 313         ret
 314
 315         cfi_adjust_cfa_offset (4)
 316         .align ALIGNARG(4)
 317         // x is ±0 and y is > 0.  We must find out whether y is an odd integer.
 318 21:     testb   $2, %dh
 319         jz      22f
 320
 321         fld     %st             // y : y
 322         fistpl  (%esp)          // y
 323         fildl   (%esp)          // int(y) : y
 324         fucompp                 // <empty>
 325         fnstsw
 326         sahf
 327         jne     23f
 328
 329         // OK, the value is an integer, but is the number of bits small
 330         // enough so that all are coming from the mantissa?
 331         popl    %edx
 332         cfi_adjust_cfa_offset (-4)
 333         testb   $1, %dl
 334         jz      24f             // jump if not odd
 335         cmpl    $0xff000000, %edx
 336         jae     24f             // does not fit in mantissa bits
 337         // It's an odd integer.
 338         fldl    MO(mzero)
 339         ret
 340
 341         cfi_adjust_cfa_offset (4)
 342 22:     fstp    %st(0)
 343 23:     addl    $4, %esp        // Don't use pop.
 344         cfi_adjust_cfa_offset (-4)
 345 24:     fldl    MO(zero)
 346         ret
 347
 348 END(__ieee754_powf)