sysdeps/i386/fpu/e_powf.S

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