sysdeps/i386/fpu/s_expm1f.S

   1 /* ix87 specific implementation of exp(x)-1.
   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    Based on code by John C. Bowman <bowman@ipp-garching.mpg.de>.
   6    Corrections by H.J. Lu (hjl@gnu.ai.mit.edu), 1997.
   7
   8    The GNU C Library is free software; you can redistribute it and/or
   9    modify it under the terms of the GNU Lesser General Public
  10    License as published by the Free Software Foundation; either
  11    version 2.1 of the License, or (at your option) any later version.
  12
  13    The GNU C Library is distributed in the hope that it will be useful,
  14    but WITHOUT ANY WARRANTY; without even the implied warranty of
  15    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  16    Lesser General Public License for more details.
  17
  18    You should have received a copy of the GNU Lesser General Public
  19    License along with the GNU C Library; if not, see
  20    <http://www.gnu.org/licenses/>.  */
  21
  22         /* Using: e^x - 1 = 2^(x * log2(e)) - 1 */
  23
  24 #include <sysdep.h>
  25 #include <machine/asm.h>
  26
  27         .section .rodata
  28
  29         .align ALIGNARG(4)
  30         .type minus1,@object
  31 minus1: .double -1.0
  32         ASM_SIZE_DIRECTIVE(minus1)
  33         .type one,@object
  34 one:    .double 1.0
  35         ASM_SIZE_DIRECTIVE(one)
  36         .type l2e,@object
  37 l2e:    .tfloat 1.442695040888963407359924681002
  38         ASM_SIZE_DIRECTIVE(l2e)
  39
  40         .section .rodata.cst4,"aM",@progbits,4
  41
  42         .p2align 2
  43         .type flt_min,@object
  44 flt_min:        .byte 0, 0, 0x80, 0
  45         ASM_SIZE_DIRECTIVE(flt_min)
  46
  47 #ifdef PIC
  48 #define MO(op) op##@GOTOFF(%edx)
  49 #else
  50 #define MO(op) op
  51 #endif
  52
  53         .text
  54 ENTRY(__expm1f)
  55         movzwl  4+2(%esp), %eax
  56         xorb    $0x80, %ah      // invert sign bit (now 1 is "positive")
  57         cmpl    $0xc2b1, %eax   // is num >= 88.5?
  58         jae     HIDDEN_JUMPTARGET (__expf)
  59
  60         flds    4(%esp)         // x
  61         fxam                    // Is NaN, +-Inf or +-0?
  62         xorb    $0x80, %ah
  63         cmpl    $0xc190, %eax   // is num <= -18.0?
  64         fstsw   %ax
  65         movb    $0x45, %ch
  66         jb      4f
  67
  68         // Below -18.0 (may be -NaN or -Inf).
  69         andb    %ah, %ch
  70 #ifdef  PIC
  71         LOAD_PIC_REG (dx)
  72 #endif
  73         cmpb    $0x01, %ch
  74         je      5f              // If -NaN, jump.
  75         jmp     2f              // -large, possibly -Inf.
  76
  77 4:      // In range -18.0 to 88.5 (may be +-0 but not NaN or +-Inf).
  78         andb    %ah, %ch
  79         cmpb    $0x40, %ch
  80         je      3f              // If +-0, jump.
  81 #ifdef  PIC
  82         LOAD_PIC_REG (dx)
  83 #endif
  84         fld     %st
  85         fabs
  86         fcoms   MO(flt_min)
  87         fstp    %st
  88         fnstsw
  89         sahf
  90         jae     5f
  91         subl    $4, %esp
  92         cfi_adjust_cfa_offset (4)
  93         fld     %st(0)
  94         fmul    %st(0)
  95         fstps   (%esp)
  96         addl    $4, %esp
  97         cfi_adjust_cfa_offset (-4)
  98         ret
  99
 100 5:      fldt    MO(l2e)         // log2(e) : x
 101         fmulp                   // log2(e)*x
 102         fld     %st             // log2(e)*x : log2(e)*x
 103         // Set round-to-nearest temporarily.
 104         subl    $8, %esp
 105         cfi_adjust_cfa_offset (8)
 106         fstcw   4(%esp)
 107         movl    $0xf3ff, %ecx
 108         andl    4(%esp), %ecx
 109         movl    %ecx, (%esp)
 110         fldcw   (%esp)
 111         frndint                 // int(log2(e)*x) : log2(e)*x
 112         fldcw   4(%esp)
 113         addl    $8, %esp
 114         cfi_adjust_cfa_offset (-8)
 115         fsubr   %st, %st(1)     // int(log2(e)*x) : fract(log2(e)*x)
 116         fxch                    // fract(log2(e)*x) : int(log2(e)*x)
 117         f2xm1                   // 2^fract(log2(e)*x)-1 : int(log2(e)*x)
 118         fscale                  // 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x)
 119         fxch                    // int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
 120         fldl    MO(one)         // 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
 121         fscale                  // 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
 122         fsubrl  MO(one)         // 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
 123         fstp    %st(1)          // 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
 124         fsubrp  %st, %st(1)     // 2^(log2(e)*x)
 125         ret
 126
 127 2:      fstp    %st
 128         fldl    MO(minus1)      // Set result to -1.0.
 129 3:      ret
 130 END(__expm1f)
 131 weak_alias (__expm1f, expm1f)