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" 32LIBM_ANSI_PRAGMA_WEAK(expl,function) 33 34 .data 35 .align 16 36ln2_hi: .4byte 0xd1d00000, 0xb17217f7, 0x3ffe, 0x0 37ln2_lo: .4byte 0x4c67fc0d, 0x8654361c, 0xbfce, 0x0 38 39 ENTRY(expl) 40 movl 16(%rsp),%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.general_case: / Here, |x| >= 1 or x is NaN 46 cmpl $0x7fff,%ecx / bexp(|x|) = bexp(INF)? 47 je .not_finite / if so, x is not finite 48 cmpl $0x400e,%ecx / |x| < 32768 = 2^15? 49 jb .finite_non_special / if so, proceed with argument reduction 50 fldt 8(%rsp) / x 51 fld1 / 1, x 52 jmp 1f 53.finite_non_special: / Here, ln(2) < |x| < 2^15 54 fldt 8(%rsp) / x 55 fld %st(0) / x, x 56 fldl2e / log2(e), x, x 57 fmulp / z := x*log2(e), x 58 frndint / [z], x 59 fst %st(2) / [z], x, [z] 60 PIC_SETUP(1) 61 fldt PIC_L(ln2_hi) / ln2_hi, [z], x, [z] 62 fmulp / [z]*ln2_hi, x, [z] 63 fsubrp %st,%st(1) / x-[z]*ln2_hi, [z] 64 fldt PIC_L(ln2_lo) / ln2_lo, x-[z]*ln2_hi, [z] 65 PIC_WRAPUP 66 fmul %st(2),%st / [z]*ln2_lo, x-[z]*ln2_hi, [z] 67 fsubrp %st,%st(1) / r := x-[z]*ln(2), [z] 68 fldl2e / log2(e), r, [z] 69 fmulp / f := r*log2(e), [z] 70 f2xm1 / 2^f-1,[z] 71 fld1 / 1, 2^f-1, [z] 72 faddp %st,%st(1) / 2^f, [z] 731: 74 fscale / e^x, [z] 75 fstp %st(1) 76 ret 77 782: / Here, |x| < 0.5 79 cmpl $0x3fbe,%ecx / Is |x| >= 2^-65? 80 jae .shortcut / If so, take a shortcut 81 fldt 8(%rsp) / x 82 fld1 / 1, x 83 faddp %st,%st(1) / 1+x (for inexact & directed rounding) 84 ret 85 86.check_tail: 87 movl 12(%rsp),%ecx / ecx <-- hi_32(sgnfcnd(x)) 88 cmpl $0xb17217f7,%ecx / Is |x| < ln(2)? 89 ja .finite_non_special 90 jb .shortcut 91 movl 8(%rsp),%edx / edx <-- lo_32(x) 92 cmpl $0xd1cf79ab,%edx / Is |x| slightly < ln(2)? 93 ja .finite_non_special / branch if |x| slightly > ln(2) 94.shortcut: 95 / Here, |x| < ln(2), so |z| = |x/ln(2)| < 1, 96 / whence z is in f2xm1's domain. 97 fldt 8(%rsp) / x 98 fldl2e / log2(e), x 99 fmulp / x*log2(e) 100 f2xm1 / 2^(x*log2(e))-1 = e^x-1 101 fld1 / 1, e^x-1 102 faddp %st,%st(1) / e^x 103 ret 104 105.not_finite: 106 movl 12(%rsp),%ecx / ecx <-- hi_32(sgnfcnd(x)) 107 cmpl $0x80000000,%ecx / hi_32(|x|) = hi_32(INF)? 108 jne .NaN_or_pinf / if not, x is NaN 109 movl 8(%rsp),%edx / edx <-- lo_32(x) 110 cmpl $0,%edx / lo_32(x) = 0? 111 jne .NaN_or_pinf / if not, x is NaN 112 movl 16(%rsp),%eax / ax <-- sign&bexp((x)) 113 andl $0x8000,%eax / here, x is infinite, but +/-? 114 jz .NaN_or_pinf / branch if x = +INF 115 fldz / Here, x = -inf, so return 0 116 ret 117 118.NaN_or_pinf: 119 / Here, x = NaN or +inf, so load x and return immediately. 120 fldt 8(%rsp) 121 fadd %st(0),%st / quiet SNaN 122 ret 123 .align 16 124 SET_SIZE(expl) 125