/* ix87 specific implementation of arcsinh. Copyright (C) 1996-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, see <http://www.gnu.org/licenses/>. */ #include <machine/asm.h> .section .rodata.cst8,"aM",@progbits,8 .p2align 3 .type one,@object one: .double 1.0 ASM_SIZE_DIRECTIVE(one) .type limit,@object limit: .double 0.29 ASM_SIZE_DIRECTIVE(limit) #ifdef PIC #define MO(op) op##@GOTOFF(%edx) #else #define MO(op) op #endif .text ENTRY(__ieee754_acoshf) movl 4(%esp), %ecx cmpl $0x3f800000, %ecx jl 5f // < 1 => invalid fldln2 // log(2) flds 4(%esp) // x : log(2) cmpl $0x47000000, %ecx ja 3f // x > 2^14 #ifdef PIC LOAD_PIC_REG (dx) #endif cmpl $0x40000000, %ecx ja 4f // x > 2 // 1 <= x <= 2 => y = log1p(x-1+sqrt(2*(x-1)+(x-1)^2)) fsubl MO(one) // x-1 : log(2) fabs // acosh(1) is +0 in all rounding modes fld %st // x-1 : x-1 : log(2) fmul %st(1) // (x-1)^2 : x-1 : log(2) fadd %st(1) // x-1+(x-1)^2 : x-1 : log(2) fadd %st(1) // 2*(x-1)+(x-1)^2 : x-1 : log(2) fsqrt // sqrt(2*(x-1)+(x-1)^2) : x-1 : log(2) faddp // x-1+sqrt(2*(x-1)+(x-1)^2) : log(2) fcoml MO(limit) fnstsw sahf ja 2f fyl2xp1 // log1p(x-1+sqrt(2*(x-1)+(x-1)^2)) ret 2: faddl MO(one) // x+sqrt(2*(x-1)+(x-1)^2) : log(2) fyl2x // log(x+sqrt(2*(x-1)+(x-1)^2)) ret // x > 2^14 => y = log(x) + log(2) .align ALIGNARG(4) 3: fyl2x // log(x) fldln2 // log(2) : log(x) faddp // log(x)+log(2) ret // 2^28 > x > 2 => y = log(2*x - 1/(x+sqrt(x*x-1))) .align ALIGNARG(4) 4: fld %st // x : x : log(2) fadd %st, %st(1) // x : 2*x : log(2) fld %st // x : x : 2*x : log(2) fmul %st(1) // x^2 : x : 2*x : log(2) fsubl MO(one) // x^2-1 : x : 2*x : log(2) fsqrt // sqrt(x^2-1) : x : 2*x : log(2) faddp // x+sqrt(x^2-1) : 2*x : log(2) fdivrl MO(one) // 1/(x+sqrt(x^2-1)) : 2*x : log(2) fsubrp // 2*x+1/(x+sqrt(x^2)-1) : log(2) fyl2x // log(2*x+1/(x+sqrt(x^2-1))) ret // x < 1 (or -NaN) => NaN .align ALIGNARG(4) 5: flds 4(%esp) fsub %st fdiv %st, %st(0) ret END(__ieee754_acoshf) strong_alias (__ieee754_acoshf, __acoshf_finite)