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 2006 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 
  34         .data
  35         .align  4
  36 ln2_hi: .long   0xd1d00000, 0xb17217f7, 0x00003ffe
  37 ln2_lo: .long   0x4c67fc0d, 0x8654361c, 0x0000bfce
  38 
  39         ENTRY(expl)
  40         movl    12(%esp),%ecx           / cx <--sign&bexp(x)
  41         andl    $0x7fff,%ecx            / ecx <-- zero_xtnd(bexp(x))
  42         cmpl    $0x3ffe,%ecx            / Is |x| < 0.5?
  43         jb      2f                      / If so, see which shortcut to take
  44         je      .check_tail             / More checking if 0.5 <= |x| < 1
  45         cmpl    $0x00007fff,%ecx        / bexp(|x|) = bexp(INF)?
  46         je      .not_finite             / if so, x is not finite
  47         cmpl    $0x0000400e,%ecx        / |x| < 32768 = 2^15?
  48         jb      .finite_non_special     / if so, proceed with argument reduction
  49         fldt    4(%esp)                 / x
  50         fld1                            / 1, x
  51         jmp     1f
  52 .finite_non_special:                    / Here, ln(2) < |x| < 2^15
  53         fldt    4(%esp)                 / x
  54         fld     %st(0)                  / x, x
  55         fldl2e                          / log2(e), x, x
  56         fmulp                           / z := x*log2(e), x
  57         frndint                         / [z], x
  58         fst     %st(2)                  / [z], x, [z]
  59         PIC_SETUP(1)
  60         fldt    PIC_L(ln2_hi)           / ln2_hi, [z], x, [z]
  61         fmulp                           / [z]*ln2_hi, x, [z]
  62         fsubrp  %st,%st(1)              / x-[z]*ln2_hi, [z]
  63         fldt    PIC_L(ln2_lo)           / ln2_lo, x-[z]*ln2_hi, [z]
  64         PIC_WRAPUP
  65         fmul    %st(2),%st              / [z]*ln2_lo, x-[z]*ln2_hi, [z]
  66         fsubrp  %st,%st(1)              / r := x-[z]*ln(2), [z]
  67         fldl2e                          / log2(e), r, [z]
  68         fmulp                           / f := r*log2(e), [z]
  69         f2xm1                           / 2^f-1,[z]
  70         fld1                            / 1, 2^f-1, [z]
  71         faddp   %st,%st(1)              / 2^f, [z]
  72 1:
  73         fscale                          / e^x, [z]
  74         fstp    %st(1)
  75         ret
  76 
  77 2:                                      / Here, |x| < 0.5
  78         cmpl    $0x3fbe,%ecx            / Is |x| >= 2^-65?
  79         jae     .shortcut               / If so, take a shortcut
  80         fldt    4(%esp)                 / x
  81         fld1                            / 1, x
  82         faddp   %st,%st(1)              / 1+x (for inexact & directed rounding)
  83         ret
  84 
  85 .check_tail:
  86         movl    8(%esp),%ecx            / ecx <-- hi_32(sgnfcnd(x))
  87         cmpl    $0xb17217f7,%ecx        / Is |x| < ln(2)?
  88         ja      .finite_non_special
  89         jb      .shortcut
  90         movl    4(%esp),%edx            / edx <-- lo_32(x)
  91         cmpl    $0xd1cf79ab,%edx        / Is |x| slightly < ln(2)?
  92         ja      .finite_non_special     / branch if |x| slightly > ln(2)
  93 .shortcut:
  94         / Here, |x| < ln(2), so |z| = |x/ln(2)| < 1,
  95         / whence z is in f2xm1's domain.
  96         fldt    4(%esp)                 / x
  97         fldl2e                          / log2(e), x
  98         fmulp                           / x*log2(e)
  99         f2xm1                           / 2^(x*log2(e))-1 = e^x-1
 100         fld1                            / 1, e^x-1
 101         faddp   %st,%st(1)              / e^x
 102         ret
 103 
 104 .not_finite:
 105         movl    8(%esp),%ecx            / ecx <-- hi_32(sgnfcnd(x))
 106         cmpl    $0x80000000,%ecx        / hi_32(|x|) = hi_32(INF)?
 107         jne     .NaN_or_pinf            / if not, x is NaN 
 108         movl    4(%esp),%edx            / edx <-- lo_32(x)
 109         cmpl    $0,%edx                 / lo_32(x) = 0?
 110         jne     .NaN_or_pinf            / if not, x is NaN
 111         movl    12(%esp),%eax           / ax <-- sign&bexp((x))
 112         andl    $0x00008000,%eax        / here, x is infinite, but +/-?
 113         jz      .NaN_or_pinf            / branch if x = +INF
 114         fldz                            / Here, x = -inf, so return 0
 115         ret
 116 
 117 .NaN_or_pinf:
 118         / Here, x = NaN or +inf, so load x and return immediately.
 119         fldt    4(%esp)
 120         fadd    %st(0),%st              / quiet SNaN
 121         ret
 122         .align  4
 123         SET_SIZE(expl)