usr/src/lib/libm/i386/src/expm1f.s

   1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 /*
  22  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  23  */
  24 /*
  25  * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
  26  * Use is subject to license terms.
  27  */
  28
  29         .file "expm1f.s"
  30
  31 #include "libm.h"
  32 LIBM_ANSI_PRAGMA_WEAK(expm1f,function)
  33
  34         .data
  35         .align  4
  36 .mhundred:      .float  -100.0
  37
  38         ENTRY(expm1f)
  39         movl    4(%esp),%ecx            / ecx <-- x
  40         andl    $0x7fffffff,%ecx        / ecx <-- |x|
  41         cmpl    $0x3f317217,%ecx        / Is |x| < ln(2)?
  42         jbe     .shortcut               / If so, take a shortcut.
  43         cmpl    $0x7f800000,%ecx        / |x| >= INF?
  44         jae     .not_finite             / if so, x is not finite
  45         flds    4(%esp)                 / push x
  46
  47         subl    $8,%esp                 / save RP and set round-to-64-bits
  48         fstcw   (%esp)
  49         movw    (%esp),%ax
  50         movw    %ax,4(%esp)
  51         orw     $0x0300,%ax
  52         movw    %ax,(%esp)
  53         fldcw   (%esp)
  54
  55         fldl2e                          / push log2e   }not for xtndd_dbl
  56         fmulp   %st,%st(1)              / z = x*log2e  }not for xtndd_dbl
  57         fld     %st(0)                  / duplicate stack top
  58         frndint                         / [z],z
  59         fucom                           / This and the next 3 instructions
  60         fstsw   %ax                     / add 10 clocks to runtime of the
  61         sahf                            / main branch, but save about 265
  62         je      .z_integral             / upon detection of integral z.
  63         / [z] != 0, compute exp(x) and then subtract one to get expm1(x)
  64         fxch                            / z,[z]
  65         fsub    %st(1),%st              / z-[z],[z]
  66         f2xm1                           / 2**(z-[z])-1,[z]
  67         / avoid spurious underflow when scaling to compute exp(x)
  68         PIC_SETUP(1)
  69         flds    PIC_L(.mhundred)
  70         PIC_WRAPUP
  71         fucom   %st(2)                  / if -100 !< [z], then use -100
  72         fstsw   %ax
  73         sahf
  74         jb      .got_int_part
  75         fxch    %st(2)
  76 .got_int_part:
  77         fstp    %st(0)                  /   2**(z-[z])-1,max([z],-100)
  78         fld1                            / 1,2**(z-[z])-1,max([z],-100)
  79         faddp   %st,%st(1)              /   2**(z-[z])  ,max([z],-100)
  80         fscale                          /   exp(x)      ,max([z],-100)
  81         fld1                            / 1,exp(x)      ,max([z],-100)
  82         fsubrp  %st,%st(1)              /   exp(x)-1    ,max([z],-100)
  83         fstp    %st(1)
  84
  85         fstcw   (%esp)                  / restore old RP
  86         movw    (%esp),%dx
  87         andw    $0xfcff,%dx
  88         movw    4(%esp),%cx
  89         andw    $0x0300,%cx
  90         orw     %dx,%cx
  91         movw    %cx,(%esp)
  92         fldcw   (%esp)
  93         add     $8,%esp
  94
  95         ret
  96
  97 .z_integral:                            / here, z is integral
  98         fstp    %st(0)                  / ,z
  99         / avoid spurious underflow when scaling to compute exp(x)
 100         PIC_SETUP(2)
 101         flds    PIC_L(.mhundred)
 102         PIC_WRAPUP
 103         fucom   %st(1)                  / if -100 !< [z], then use -100
 104         fstsw   %ax
 105         sahf
 106         jb      .scale_wont_ovfl
 107         fxch    %st(1)
 108 .scale_wont_ovfl:
 109         fstp    %st(0)                  /   max([z],-100)
 110         fld1                            / 1,max([z],-100)
 111         fscale                          /   exp(x)      ,max([z],-100)
 112         fld1                            / 1,exp(x)      ,max([z],-100)
 113         fsubrp  %st,%st(1)              /   exp(x)-1    ,max([z],-100)
 114         fstp    %st(1)
 115
 116         fstcw   (%esp)                  / restore old RP
 117         movw    (%esp),%dx
 118         andw    $0xfcff,%dx
 119         movw    4(%esp),%cx
 120         andw    $0x0300,%cx
 121         orw     %dx,%cx
 122         movw    %cx,(%esp)
 123         fldcw   (%esp)
 124         add     $8,%esp
 125
 126         ret
 127
 128 .shortcut:
 129         / Here, |x| < ln(2), so |z| = |x*log2(e)| < 1,
 130         / whence z is in f2xm1's domain.
 131         flds    4(%esp)                 / push x
 132         fldl2e                          / push log2e  }not for xtndd_dbl
 133         fmulp   %st,%st(1)              / z = x*log2e }not for xtndd_dbl
 134         f2xm1                           / 2**(x*log2(e))-1 = e**x - 1
 135         ret
 136
 137 .not_finite:
 138         ja      .NaN_or_pinf            / branch if x is NaN
 139         movl    4(%esp),%eax            / eax <-- x
 140         andl    $0x80000000,%eax        / here, x is infinite, but +/-?
 141         jz      .NaN_or_pinf            / branch if x = +INF
 142         fld1                            / Here, x = -inf, so return -1
 143         fchs
 144         ret
 145
 146 .NaN_or_pinf:
 147         / Here, x = NaN or +inf, so load x and return immediately.
 148         flds    4(%esp)
 149         fwait
 150         ret
 151         .align  4
 152         SET_SIZE(expm1f)