sysdeps/i386/fpu/e_powl.S

   1 /* ix87 specific implementation of pow function.
   2    Copyright (C) 1996-2015 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 Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the 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    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 #include <machine/asm.h>
  21
  22         .section .rodata.cst8,"aM",@progbits,8
  23
  24         .p2align 3
  25         .type one,@object
  26 one:    .double 1.0
  27         ASM_SIZE_DIRECTIVE(one)
  28         .type p3,@object
  29 p3:     .byte 0, 0, 0, 0, 0, 0, 0x20, 0x40
  30         ASM_SIZE_DIRECTIVE(p3)
  31         .type p63,@object
  32 p63:    .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
  33         ASM_SIZE_DIRECTIVE(p63)
  34         .type p64,@object
  35 p64:    .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43
  36         ASM_SIZE_DIRECTIVE(p64)
  37         .type p78,@object
  38 p78:    .byte 0, 0, 0, 0, 0, 0, 0xd0, 0x44
  39         ASM_SIZE_DIRECTIVE(p78)
  40         .type pm79,@object
  41 pm79:   .byte 0, 0, 0, 0, 0, 0, 0, 0x3b
  42         ASM_SIZE_DIRECTIVE(pm79)
  43
  44         .section .rodata.cst16,"aM",@progbits,16
  45
  46         .p2align 3
  47         .type infinity,@object
  48 inf_zero:
  49 infinity:
  50         .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
  51         ASM_SIZE_DIRECTIVE(infinity)
  52         .type zero,@object
  53 zero:   .double 0.0
  54         ASM_SIZE_DIRECTIVE(zero)
  55         .type minf_mzero,@object
  56 minf_mzero:
  57 minfinity:
  58         .byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
  59 mzero:
  60         .byte 0, 0, 0, 0, 0, 0, 0, 0x80
  61         ASM_SIZE_DIRECTIVE(minf_mzero)
  62
  63 #ifdef PIC
  64 # define MO(op) op##@GOTOFF(%ecx)
  65 # define MOX(op,x,f) op##@GOTOFF(%ecx,x,f)
  66 #else
  67 # define MO(op) op
  68 # define MOX(op,x,f) op(,x,f)
  69 #endif
  70
  71         .text
  72 ENTRY(__ieee754_powl)
  73         fldt    16(%esp)        // y
  74         fxam
  75
  76 #ifdef  PIC
  77         LOAD_PIC_REG (cx)
  78 #endif
  79
  80         fnstsw
  81         movb    %ah, %dl
  82         andb    $0x45, %ah
  83         cmpb    $0x40, %ah      // is y == 0 ?
  84         je      11f
  85
  86         cmpb    $0x05, %ah      // is y == ±inf ?
  87         je      12f
  88
  89         cmpb    $0x01, %ah      // is y == NaN ?
  90         je      30f
  91
  92         fldt    4(%esp)         // x : y
  93
  94         subl    $8,%esp
  95         cfi_adjust_cfa_offset (8)
  96
  97         fxam
  98         fnstsw
  99         movb    %ah, %dh
 100         andb    $0x45, %ah
 101         cmpb    $0x40, %ah
 102         je      20f             // x is ±0
 103
 104         cmpb    $0x05, %ah
 105         je      15f             // x is ±inf
 106
 107         cmpb    $0x01, %ah
 108         je      32f             // x is NaN
 109
 110         fxch                    // y : x
 111
 112         /* fistpll raises invalid exception for |y| >= 1L<<63.  */
 113         fld     %st             // y : y : x
 114         fabs                    // |y| : y : x
 115         fcompl  MO(p63)         // y : x
 116         fnstsw
 117         sahf
 118         jnc     2f
 119
 120         /* First see whether `y' is a natural number.  In this case we
 121            can use a more precise algorithm.  */
 122         fld     %st             // y : y : x
 123         fistpll (%esp)          // y : x
 124         fildll  (%esp)          // int(y) : y : x
 125         fucomp  %st(1)          // y : x
 126         fnstsw
 127         sahf
 128         je      9f
 129
 130         // If y has absolute value at most 0x1p-79, then any finite
 131         // nonzero x will result in 1.  Saturate y to those bounds to
 132         // avoid underflow in the calculation of y*log2(x).
 133         fld     %st             // y : y : x
 134         fabs                    // |y| : y : x
 135         fcompl  MO(pm79)        // y : x
 136         fnstsw
 137         sahf
 138         jnc     3f
 139         fstp    %st(0)          // pop y
 140         fldl    MO(pm79)        // 0x1p-79 : x
 141         testb   $2, %dl
 142         jnz     3f              // y > 0
 143         fchs                    // -0x1p-79 : x
 144         jmp     3f
 145
 146 9:      /* OK, we have an integer value for y.  Unless very small
 147            (we use < 8), use the algorithm for real exponent to avoid
 148            accumulation of errors.  */
 149         fld     %st             // y : y : x
 150         fabs                    // |y| : y : x
 151         fcompl  MO(p3)          // y : x
 152         fnstsw
 153         sahf
 154         jnc     3f
 155         popl    %eax
 156         cfi_adjust_cfa_offset (-4)
 157         popl    %edx
 158         cfi_adjust_cfa_offset (-4)
 159         orl     $0, %edx
 160         fstp    %st(0)          // x
 161         jns     4f              // y >= 0, jump
 162         fdivrl  MO(one)         // 1/x          (now referred to as x)
 163         negl    %eax
 164         adcl    $0, %edx
 165         negl    %edx
 166 4:      fldl    MO(one)         // 1 : x
 167         fxch
 168
 169         /* If y is even, take the absolute value of x.  Otherwise,
 170            ensure all intermediate values that might overflow have the
 171            sign of x.  */
 172         testb   $1, %al
 173         jnz     6f
 174         fabs
 175
 176 6:      shrdl   $1, %edx, %eax
 177         jnc     5f
 178         fxch
 179         fabs
 180         fmul    %st(1)          // x : ST*x
 181         fxch
 182 5:      fld     %st             // x : x : ST*x
 183         fabs                    // |x| : x : ST*x
 184         fmulp                   // |x|*x : ST*x
 185         shrl    $1, %edx
 186         movl    %eax, %ecx
 187         orl     %edx, %ecx
 188         jnz     6b
 189         fstp    %st(0)          // ST*x
 190         ret
 191
 192         /* y is ±NAN */
 193 30:     fldt    4(%esp)         // x : y
 194         fldl    MO(one)         // 1.0 : x : y
 195         fucomp  %st(1)          // x : y
 196         fnstsw
 197         sahf
 198         je      31f
 199         fxch                    // y : x
 200 31:     fstp    %st(1)
 201         ret
 202
 203         cfi_adjust_cfa_offset (8)
 204 32:     addl    $8, %esp
 205         cfi_adjust_cfa_offset (-8)
 206         fstp    %st(1)
 207         ret
 208
 209         cfi_adjust_cfa_offset (8)
 210         .align ALIGNARG(4)
 211 2:      // y is a large integer (absolute value at least 1L<<63).
 212         // If y has absolute value at least 1L<<78, then any finite
 213         // nonzero x will result in 0 (underflow), 1 or infinity (overflow).
 214         // Saturate y to those bounds to avoid overflow in the calculation
 215         // of y*log2(x).
 216         fld     %st             // y : y : x
 217         fabs                    // |y| : y : x
 218         fcompl  MO(p78)         // y : x
 219         fnstsw
 220         sahf
 221         jc      3f
 222         fstp    %st(0)          // pop y
 223         fldl    MO(p78)         // 1L<<78 : x
 224         testb   $2, %dl
 225         jz      3f              // y > 0
 226         fchs                    // -(1L<<78) : x
 227         .align ALIGNARG(4)
 228 3:      /* y is a real number.  */
 229         subl    $28, %esp
 230         cfi_adjust_cfa_offset (28)
 231         fstpt   12(%esp)        // x
 232         fstpt   (%esp)          // <empty>
 233         call    HIDDEN_JUMPTARGET (__powl_helper)       // <result>
 234         addl    $36, %esp
 235         cfi_adjust_cfa_offset (-36)
 236         ret
 237
 238         // pow(x,±0) = 1
 239         .align ALIGNARG(4)
 240 11:     fstp    %st(0)          // pop y
 241         fldl    MO(one)
 242         ret
 243
 244         // y == ±inf
 245         .align ALIGNARG(4)
 246 12:     fstp    %st(0)          // pop y
 247         fldl    MO(one)         // 1
 248         fldt    4(%esp)         // x : 1
 249         fabs                    // abs(x) : 1
 250         fucompp                 // < 1, == 1, or > 1
 251         fnstsw
 252         andb    $0x45, %ah
 253         cmpb    $0x45, %ah
 254         je      13f             // jump if x is NaN
 255
 256         cmpb    $0x40, %ah
 257         je      14f             // jump if |x| == 1
 258
 259         shlb    $1, %ah
 260         xorb    %ah, %dl
 261         andl    $2, %edx
 262         fldl    MOX(inf_zero, %edx, 4)
 263         ret
 264
 265         .align ALIGNARG(4)
 266 14:     fldl    MO(one)
 267         ret
 268
 269         .align ALIGNARG(4)
 270 13:     fldt    4(%esp)         // load x == NaN
 271         ret
 272
 273         cfi_adjust_cfa_offset (8)
 274         .align ALIGNARG(4)
 275         // x is ±inf
 276 15:     fstp    %st(0)          // y
 277         testb   $2, %dh
 278         jz      16f             // jump if x == +inf
 279
 280         // fistpll raises invalid exception for |y| >= 1L<<63, but y
 281         // may be odd unless we know |y| >= 1L<<64.
 282         fld     %st             // y : y
 283         fabs                    // |y| : y
 284         fcompl  MO(p64)         // y
 285         fnstsw
 286         sahf
 287         jnc     16f
 288         fldl    MO(p63)         // p63 : y
 289         fxch                    // y : p63
 290         fprem                   // y%p63 : p63
 291         fstp    %st(1)          // y%p63
 292
 293         // We must find out whether y is an odd integer.
 294         fld     %st             // y : y
 295         fistpll (%esp)          // y
 296         fildll  (%esp)          // int(y) : y
 297         fucompp                 // <empty>
 298         fnstsw
 299         sahf
 300         jne     17f
 301
 302         // OK, the value is an integer, but is it odd?
 303         popl    %eax
 304         cfi_adjust_cfa_offset (-4)
 305         popl    %edx
 306         cfi_adjust_cfa_offset (-4)
 307         andb    $1, %al
 308         jz      18f             // jump if not odd
 309         // It's an odd integer.
 310         shrl    $31, %edx
 311         fldl    MOX(minf_mzero, %edx, 8)
 312         ret
 313
 314         cfi_adjust_cfa_offset (8)
 315         .align ALIGNARG(4)
 316 16:     fcompl  MO(zero)
 317         addl    $8, %esp
 318         cfi_adjust_cfa_offset (-8)
 319         fnstsw
 320         shrl    $5, %eax
 321         andl    $8, %eax
 322         fldl    MOX(inf_zero, %eax, 1)
 323         ret
 324
 325         cfi_adjust_cfa_offset (8)
 326         .align ALIGNARG(4)
 327 17:     shll    $30, %edx       // sign bit for y in right position
 328         addl    $8, %esp
 329         cfi_adjust_cfa_offset (-8)
 330 18:     shrl    $31, %edx
 331         fldl    MOX(inf_zero, %edx, 8)
 332         ret
 333
 334         cfi_adjust_cfa_offset (8)
 335         .align ALIGNARG(4)
 336         // x is ±0
 337 20:     fstp    %st(0)          // y
 338         testb   $2, %dl
 339         jz      21f             // y > 0
 340
 341         // x is ±0 and y is < 0.  We must find out whether y is an odd integer.
 342         testb   $2, %dh
 343         jz      25f
 344
 345         // fistpll raises invalid exception for |y| >= 1L<<63, but y
 346         // may be odd unless we know |y| >= 1L<<64.
 347         fld     %st             // y : y
 348         fabs                    // |y| : y
 349         fcompl  MO(p64)         // y
 350         fnstsw
 351         sahf
 352         jnc     25f
 353         fldl    MO(p63)         // p63 : y
 354         fxch                    // y : p63
 355         fprem                   // y%p63 : p63
 356         fstp    %st(1)          // y%p63
 357
 358         fld     %st             // y : y
 359         fistpll (%esp)          // y
 360         fildll  (%esp)          // int(y) : y
 361         fucompp                 // <empty>
 362         fnstsw
 363         sahf
 364         jne     26f
 365
 366         // OK, the value is an integer, but is it odd?
 367         popl    %eax
 368         cfi_adjust_cfa_offset (-4)
 369         popl    %edx
 370         cfi_adjust_cfa_offset (-4)
 371         andb    $1, %al
 372         jz      27f             // jump if not odd
 373         // It's an odd integer.
 374         // Raise divide-by-zero exception and get minus infinity value.
 375         fldl    MO(one)
 376         fdivl   MO(zero)
 377         fchs
 378         ret
 379
 380         cfi_adjust_cfa_offset (8)
 381 25:     fstp    %st(0)
 382 26:     addl    $8, %esp
 383         cfi_adjust_cfa_offset (-8)
 384 27:     // Raise divide-by-zero exception and get infinity value.
 385         fldl    MO(one)
 386         fdivl   MO(zero)
 387         ret
 388
 389         cfi_adjust_cfa_offset (8)
 390         .align ALIGNARG(4)
 391         // x is ±0 and y is > 0.  We must find out whether y is an odd integer.
 392 21:     testb   $2, %dh
 393         jz      22f
 394
 395         // fistpll raises invalid exception for |y| >= 1L<<63, but y
 396         // may be odd unless we know |y| >= 1L<<64.
 397         fld     %st             // y : y
 398         fcompl  MO(p64)         // y
 399         fnstsw
 400         sahf
 401         jnc     22f
 402         fldl    MO(p63)         // p63 : y
 403         fxch                    // y : p63
 404         fprem                   // y%p63 : p63
 405         fstp    %st(1)          // y%p63
 406
 407         fld     %st             // y : y
 408         fistpll (%esp)          // y
 409         fildll  (%esp)          // int(y) : y
 410         fucompp                 // <empty>
 411         fnstsw
 412         sahf
 413         jne     23f
 414
 415         // OK, the value is an integer, but is it odd?
 416         popl    %eax
 417         cfi_adjust_cfa_offset (-4)
 418         popl    %edx
 419         cfi_adjust_cfa_offset (-4)
 420         andb    $1, %al
 421         jz      24f             // jump if not odd
 422         // It's an odd integer.
 423         fldl    MO(mzero)
 424         ret
 425
 426         cfi_adjust_cfa_offset (8)
 427 22:     fstp    %st(0)
 428 23:     addl    $8, %esp        // Don't use 2 x pop
 429         cfi_adjust_cfa_offset (-8)
 430 24:     fldl    MO(zero)
 431         ret
 432
 433 END(__ieee754_powl)
 434 strong_alias (__ieee754_powl, __powl_finite)