1/* ix87 specific implementation of exp(x)-1. 2 Copyright (C) 1996,1997,2001,2002,2008,2009 Free Software Foundation, Inc. 3 This file is part of the GNU C Library. 4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996. 5 Based on code by John C. Bowman <bowman@ipp-garching.mpg.de>. 6 Corrections by H.J. Lu (hjl@gnu.ai.mit.edu), 1997. 7 8 The GNU C Library is free software; you can redistribute it and/or 9 modify it under the terms of the GNU Lesser General Public 10 License as published by the Free Software Foundation; either 11 version 2.1 of the License, or (at your option) any later version. 12 13 The GNU C Library is distributed in the hope that it will be useful, 14 but WITHOUT ANY WARRANTY; without even the implied warranty of 15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 16 Lesser General Public License for more details. 17 18 You should have received a copy of the GNU Lesser General Public 19 License along with the GNU C Library; if not, write to the Free 20 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 21 02111-1307 USA. */ 22 23 /* Using: e^x - 1 = 2^(x * log2(e)) - 1 */ 24 25#include <machine/asm.h> 26 27#ifdef __ELF__ 28 .section .rodata 29#else 30 .text 31#endif 32 .align ALIGNARG(4) 33 ASM_TYPE_DIRECTIVE(minus1,@object) 34minus1: .double -1.0 35 ASM_SIZE_DIRECTIVE(minus1) 36 ASM_TYPE_DIRECTIVE(one,@object) 37one: .double 1.0 38 ASM_SIZE_DIRECTIVE(one) 39 ASM_TYPE_DIRECTIVE(l2e,@object) 40l2e: .tfloat 1.442695040888963407359924681002 41 ASM_SIZE_DIRECTIVE(l2e) 42 43#ifdef PIC 44#define MO(op) op##(%rip) 45#else 46#define MO(op) op 47#endif 48 49 .text 50ENTRY(__expm1l) 51 movzwl 8+8(%rsp), %eax // load sign bit and 15-bit exponent 52 xorb $0x80, %ah // invert sign bit (now 1 is "positive") 53 cmpl $0xc006, %eax // is num positive and exp >= 6 (number is >= 128.0)? 54 jae __expl@PLT // (if num is denormal, it is at least >= 64.0) 55 56 fldt 8(%rsp) // x 57 fxam // Is NaN or +-Inf? 58 fstsw %ax 59 movb $0x45, %ch 60 andb %ah, %ch 61 cmpb $0x40, %ch 62 je 3f // If +-0, jump. 63 cmpb $0x05, %ch 64 je 2f // If +-Inf, jump. 65 66 fldt MO(l2e) // log2(e) : x 67 fmulp // log2(e)*x 68 fld %st // log2(e)*x : log2(e)*x 69 frndint // int(log2(e)*x) : log2(e)*x 70 fsubr %st, %st(1) // int(log2(e)*x) : fract(log2(e)*x) 71 fxch // fract(log2(e)*x) : int(log2(e)*x) 72 f2xm1 // 2^fract(log2(e)*x)-1 : int(log2(e)*x) 73 fscale // 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x) 74 fxch // int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x) 75 fldl MO(one) // 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x) 76 fscale // 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x) 77 fsubrl MO(one) // 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x) 78 fstp %st(1) // 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x) 79 fsubrp %st, %st(1) // 2^(log2(e)*x)-1 80 ret 81 822: testl $0x200, %eax // Test sign. 83 jz 3f // If positive, jump. 84 fstp %st 85 fldl MO(minus1) // Set result to -1.0. 863: ret 87END(__expm1l) 88libm_hidden_def (__expm1l) 89weak_alias (__expm1l, expm1l) 90