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 "expl.s"
  30 
  31 #include "libm.h"
  32 LIBM_ANSI_PRAGMA_WEAK(expl,function)
  33 #include "libm_synonyms.h"
  34 
  35         .data
  36         .align  16
  37 ln2_hi: .4byte  0xd1d00000, 0xb17217f7, 0x3ffe, 0x0
  38 ln2_lo: .4byte  0x4c67fc0d, 0x8654361c, 0xbfce, 0x0
  39 
  40         ENTRY(expl)
  41         movl    16(%rsp),%ecx           / cx <--sign&bexp(x)
  42         andl    $0x7fff,%ecx            / ecx <-- zero_xtnd(bexp(x))
  43         cmpl    $0x3ffe,%ecx            / Is |x| < 0.5?
  44         jb      2f                      / If so, see which shortcut to take
  45         je      .check_tail             / More checking if 0.5 <= |x| < 1
  46 .general_case:                          / Here, |x| >= 1 or x is NaN
  47         cmpl    $0x7fff,%ecx            / bexp(|x|) = bexp(INF)?
  48         je      .not_finite             / if so, x is not finite
  49         cmpl    $0x400e,%ecx            / |x| < 32768 = 2^15?
  50         jb      .finite_non_special     / if so, proceed with argument reduction
  51         fldt    8(%rsp)                 / x
  52         fld1                            / 1, x
  53         jmp     1f
  54 .finite_non_special:                    / Here, ln(2) < |x| < 2^15
  55         fldt    8(%rsp)                 / x
  56         fld     %st(0)                  / x, x
  57         fldl2e                          / log2(e), x, x
  58         fmulp                           / z := x*log2(e), x
  59         frndint                         / [z], x
  60         fst     %st(2)                  / [z], x, [z]
  61         PIC_SETUP(1)
  62         fldt    PIC_L(ln2_hi)           / ln2_hi, [z], x, [z]
  63         fmulp                           / [z]*ln2_hi, x, [z]
  64         fsubrp  %st,%st(1)              / x-[z]*ln2_hi, [z]
  65         fldt    PIC_L(ln2_lo)           / ln2_lo, x-[z]*ln2_hi, [z]
  66         PIC_WRAPUP
  67         fmul    %st(2),%st              / [z]*ln2_lo, x-[z]*ln2_hi, [z]
  68         fsubrp  %st,%st(1)              / r := x-[z]*ln(2), [z]
  69         fldl2e                          / log2(e), r, [z]
  70         fmulp                           / f := r*log2(e), [z]
  71         f2xm1                           / 2^f-1,[z]
  72         fld1                            / 1, 2^f-1, [z]
  73         faddp   %st,%st(1)              / 2^f, [z]
  74 1:
  75         fscale                          / e^x, [z]
  76         fstp    %st(1)
  77         ret
  78 
  79 2:                                      / Here, |x| < 0.5
  80         cmpl    $0x3fbe,%ecx            / Is |x| >= 2^-65?
  81         jae     .shortcut               / If so, take a shortcut
  82         fldt    8(%rsp)                 / x
  83         fld1                            / 1, x
  84         faddp   %st,%st(1)              / 1+x (for inexact & directed rounding)
  85         ret
  86 
  87 .check_tail:
  88         movl    12(%rsp),%ecx           / ecx <-- hi_32(sgnfcnd(x))
  89         cmpl    $0xb17217f7,%ecx        / Is |x| < ln(2)?
  90         ja      .finite_non_special
  91         jb      .shortcut
  92         movl    8(%rsp),%edx            / edx <-- lo_32(x)
  93         cmpl    $0xd1cf79ab,%edx        / Is |x| slightly < ln(2)?
  94         ja      .finite_non_special     / branch if |x| slightly > ln(2)
  95 .shortcut:
  96         / Here, |x| < ln(2), so |z| = |x/ln(2)| < 1,
  97         / whence z is in f2xm1's domain.
  98         fldt    8(%rsp)                 / x
  99         fldl2e                          / log2(e), x
 100         fmulp                           / x*log2(e)
 101         f2xm1                           / 2^(x*log2(e))-1 = e^x-1
 102         fld1                            / 1, e^x-1
 103         faddp   %st,%st(1)              / e^x
 104         ret
 105 
 106 .not_finite:
 107         movl    12(%rsp),%ecx           / ecx <-- hi_32(sgnfcnd(x))
 108         cmpl    $0x80000000,%ecx        / hi_32(|x|) = hi_32(INF)?
 109         jne     .NaN_or_pinf            / if not, x is NaN
 110         movl    8(%rsp),%edx            / edx <-- lo_32(x)
 111         cmpl    $0,%edx                 / lo_32(x) = 0?
 112         jne     .NaN_or_pinf            / if not, x is NaN
 113         movl    16(%rsp),%eax           / ax <-- sign&bexp((x))
 114         andl    $0x8000,%eax            / here, x is infinite, but +/-?
 115         jz      .NaN_or_pinf            / branch if x = +INF
 116         fldz                            / Here, x = -inf, so return 0
 117         ret
 118 
 119 .NaN_or_pinf:
 120         / Here, x = NaN or +inf, so load x and return immediately.
 121         fldt    8(%rsp)
 122         fadd    %st(0),%st              / quiet SNaN
 123         ret
 124         .align  16
 125         SET_SIZE(expl)