1*5d9d9091SRichard Lowe/* 2*5d9d9091SRichard Lowe * CDDL HEADER START 3*5d9d9091SRichard Lowe * 4*5d9d9091SRichard Lowe * The contents of this file are subject to the terms of the 5*5d9d9091SRichard Lowe * Common Development and Distribution License (the "License"). 6*5d9d9091SRichard Lowe * You may not use this file except in compliance with the License. 7*5d9d9091SRichard Lowe * 8*5d9d9091SRichard Lowe * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9*5d9d9091SRichard Lowe * or http://www.opensolaris.org/os/licensing. 10*5d9d9091SRichard Lowe * See the License for the specific language governing permissions 11*5d9d9091SRichard Lowe * and limitations under the License. 12*5d9d9091SRichard Lowe * 13*5d9d9091SRichard Lowe * When distributing Covered Code, include this CDDL HEADER in each 14*5d9d9091SRichard Lowe * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15*5d9d9091SRichard Lowe * If applicable, add the following below this CDDL HEADER, with the 16*5d9d9091SRichard Lowe * fields enclosed by brackets "[]" replaced with your own identifying 17*5d9d9091SRichard Lowe * information: Portions Copyright [yyyy] [name of copyright owner] 18*5d9d9091SRichard Lowe * 19*5d9d9091SRichard Lowe * CDDL HEADER END 20*5d9d9091SRichard Lowe */ 21*5d9d9091SRichard Lowe/* 22*5d9d9091SRichard Lowe * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 23*5d9d9091SRichard Lowe */ 24*5d9d9091SRichard Lowe/* 25*5d9d9091SRichard Lowe * Copyright 2005 Sun Microsystems, Inc. All rights reserved. 26*5d9d9091SRichard Lowe * Use is subject to license terms. 27*5d9d9091SRichard Lowe */ 28*5d9d9091SRichard Lowe 29*5d9d9091SRichard Lowe .file "expm1l.s" 30*5d9d9091SRichard Lowe 31*5d9d9091SRichard Lowe#include "libm.h" 32*5d9d9091SRichard LoweLIBM_ANSI_PRAGMA_WEAK(expm1l,function) 33*5d9d9091SRichard Lowe 34*5d9d9091SRichard Lowe .data 35*5d9d9091SRichard Lowe .align 16 36*5d9d9091SRichard Loweln2_hi: .4byte 0xd1d00000, 0xb17217f7, 0x3ffe, 0x0 37*5d9d9091SRichard Loweln2_lo: .4byte 0x4c67fc0d, 0x8654361c, 0xbfce, 0x0 38*5d9d9091SRichard Lowe 39*5d9d9091SRichard Lowe ENTRY(expm1l) 40*5d9d9091SRichard Lowe movl 16(%rsp),%ecx / cx <--sign&bexp(x) 41*5d9d9091SRichard Lowe movl %ecx,%eax / ax <--sign&bexp(x) 42*5d9d9091SRichard Lowe andl $0x7fff,%ecx / ecx <-- zero_xtnd(bexp(x)) 43*5d9d9091SRichard Lowe cmpl $0x3ffe,%ecx / Is |x| < ln(2)? 44*5d9d9091SRichard Lowe jb .shortcut / If so, take a shortcut. 45*5d9d9091SRichard Lowe je .check_tail / |x| may be only slightly < ln(2) 46*5d9d9091SRichard Lowe.general_case: / Here, |x| > ln(2) or x is NaN 47*5d9d9091SRichard Lowe cmpl $0x7fff,%ecx / bexp(|x|) = bexp(INF)? 48*5d9d9091SRichard Lowe je .not_finite / if so, x is not finite 49*5d9d9091SRichard Lowe andl $0xffff,%eax / eax <-- sign&bexp(x) 50*5d9d9091SRichard Lowe cmpl $0xc006,%eax / x <= -128? 51*5d9d9091SRichard Lowe jae 1f / if so, simply return -1 52*5d9d9091SRichard Lowe cmpl $0x400d,%ecx / |x| < 16384 = 2^14? 53*5d9d9091SRichard Lowe jb .finite_non_special / if so, proceed with argument reduction 54*5d9d9091SRichard Lowe fldt 8(%rsp) / x >= 16384; x 55*5d9d9091SRichard Lowe fld1 / 1, x 56*5d9d9091SRichard Lowe fscale / +Inf, x 57*5d9d9091SRichard Lowe fstp %st(1) / +Inf 58*5d9d9091SRichard Lowe ret 59*5d9d9091SRichard Lowe 60*5d9d9091SRichard Lowe.finite_non_special: / -128 < x < -ln(2) || ln(2) < x < 2^14 61*5d9d9091SRichard Lowe fldt 8(%rsp) / x 62*5d9d9091SRichard Lowe fld %st(0) / x, x 63*5d9d9091SRichard Lowe fldl2e / log2(e), x, x 64*5d9d9091SRichard Lowe fmulp / z := x*log2(e), x 65*5d9d9091SRichard Lowe frndint / [z], x 66*5d9d9091SRichard Lowe fst %st(2) / [z], x, [z] 67*5d9d9091SRichard Lowe PIC_SETUP(1) 68*5d9d9091SRichard Lowe fldt PIC_L(ln2_hi) / ln2_hi, [z], x, [z] 69*5d9d9091SRichard Lowe fmulp / [z]*ln2_hi, x, [z] 70*5d9d9091SRichard Lowe fsubrp %st,%st(1) / x-[z]*ln2_hi, [z] 71*5d9d9091SRichard Lowe fldt PIC_L(ln2_lo) / ln2_lo, x-[z]*ln2_hi, [z] 72*5d9d9091SRichard Lowe PIC_WRAPUP 73*5d9d9091SRichard Lowe fmul %st(2),%st / [z]*ln2_lo, x-[z]*ln2_hi, [z] 74*5d9d9091SRichard Lowe fsubrp %st,%st(1) / r := x-[z]*ln(2), [z] 75*5d9d9091SRichard Lowe fldl2e / log2(e), r, [z] 76*5d9d9091SRichard Lowe fmulp / f := r*log2(e), [z] 77*5d9d9091SRichard Lowe f2xm1 / 2^f-1,[z] 78*5d9d9091SRichard Lowe fld1 / 1, 2^f-1, [z] 79*5d9d9091SRichard Lowe faddp %st,%st(1) / 2^f, [z] 80*5d9d9091SRichard Lowe fscale / e^x, [z] 81*5d9d9091SRichard Lowe fstp %st(1) / e^x 82*5d9d9091SRichard Lowe fld1 / 1, e^x 83*5d9d9091SRichard Lowe fsubrp %st,%st(1) / e^x-1 84*5d9d9091SRichard Lowe ret 85*5d9d9091SRichard Lowe 86*5d9d9091SRichard Lowe.check_tail: 87*5d9d9091SRichard Lowe movl 12(%rsp),%ecx / ecx <-- hi_32(sgnfcnd(x)) 88*5d9d9091SRichard Lowe cmpl $0xb17217f7,%ecx / Is |x| < ln(2)? 89*5d9d9091SRichard Lowe ja .finite_non_special 90*5d9d9091SRichard Lowe jb .shortcut 91*5d9d9091SRichard Lowe movl 8(%rsp),%edx / edx <-- lo_32(x) 92*5d9d9091SRichard Lowe cmpl $0xd1cf79ab,%edx / Is |x| slightly < ln(2)? 93*5d9d9091SRichard Lowe ja .finite_non_special / branch if |x| slightly > ln(2) 94*5d9d9091SRichard Lowe.shortcut: 95*5d9d9091SRichard Lowe / Here, |x| < ln(2), so |z| = |x/ln(2)| < 1, 96*5d9d9091SRichard Lowe / whence z is in f2xm1's domain. 97*5d9d9091SRichard Lowe fldt 8(%rsp) / x 98*5d9d9091SRichard Lowe fldl2e / log2(e), x 99*5d9d9091SRichard Lowe fmulp / z := x*log2(e) 100*5d9d9091SRichard Lowe f2xm1 / 2^(x*log2(e))-1 = e^x-1 101*5d9d9091SRichard Lowe ret 102*5d9d9091SRichard Lowe 103*5d9d9091SRichard Lowe.not_finite: 104*5d9d9091SRichard Lowe movl 12(%rsp),%ecx / ecx <-- hi_32(sgnfcnd(x)) 105*5d9d9091SRichard Lowe cmpl $0x80000000,%ecx / hi_32(|x|) = hi_32(INF)? 106*5d9d9091SRichard Lowe jne .NaN_or_pinf / if not, x is NaN 107*5d9d9091SRichard Lowe movl 8(%rsp),%edx / edx <-- lo_32(x) 108*5d9d9091SRichard Lowe cmpl $0,%edx / lo_32(x) = 0? 109*5d9d9091SRichard Lowe jne .NaN_or_pinf / if not, x is NaN 110*5d9d9091SRichard Lowe movl 16(%rsp),%eax / ax <-- sign&bexp((x)) 111*5d9d9091SRichard Lowe andl $0x8000,%eax / here, x is infinite, but +/-? 112*5d9d9091SRichard Lowe jz .NaN_or_pinf / branch if x = +INF 113*5d9d9091SRichard Lowe1: 114*5d9d9091SRichard Lowe fld1 / Here, x = -inf, so return -1 115*5d9d9091SRichard Lowe fchs 116*5d9d9091SRichard Lowe ret 117*5d9d9091SRichard Lowe 118*5d9d9091SRichard Lowe.NaN_or_pinf: 119*5d9d9091SRichard Lowe / Here, x = NaN or +inf, so load x and return immediately. 120*5d9d9091SRichard Lowe fldt 8(%rsp) 121*5d9d9091SRichard Lowe ret 122*5d9d9091SRichard Lowe .align 16 123*5d9d9091SRichard Lowe SET_SIZE(expm1l) 124