/* ix87 specific implementation of pow function. Copyright (C) 1996-1999, 2001, 2004, 2007, 2011-2012 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper , 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, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. */ #include .section .rodata.cst8,"aM",@progbits,8 .p2align 3 ASM_TYPE_DIRECTIVE(one,@object) one: .double 1.0 ASM_SIZE_DIRECTIVE(one) ASM_TYPE_DIRECTIVE(limit,@object) limit: .double 0.29 ASM_SIZE_DIRECTIVE(limit) ASM_TYPE_DIRECTIVE(p63,@object) p63: .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43 ASM_SIZE_DIRECTIVE(p63) .section .rodata.cst16,"aM",@progbits,16 .p2align 3 ASM_TYPE_DIRECTIVE(infinity,@object) inf_zero: infinity: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f ASM_SIZE_DIRECTIVE(infinity) ASM_TYPE_DIRECTIVE(zero,@object) zero: .double 0.0 ASM_SIZE_DIRECTIVE(zero) ASM_TYPE_DIRECTIVE(minf_mzero,@object) minf_mzero: minfinity: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff mzero: .byte 0, 0, 0, 0, 0, 0, 0, 0x80 ASM_SIZE_DIRECTIVE(minf_mzero) #ifdef PIC # define MO(op) op##(%rip) #else # define MO(op) op #endif .text ENTRY(__ieee754_powl) fldt 24(%rsp) // y fxam fnstsw movb %ah, %dl andb $0x45, %ah cmpb $0x40, %ah // is y == 0 ? je 11f cmpb $0x05, %ah // is y == ±inf ? je 12f cmpb $0x01, %ah // is y == NaN ? je 30f fldt 8(%rsp) // x : y fxam fnstsw movb %ah, %dh andb $0x45, %ah cmpb $0x40, %ah je 20f // x is ±0 cmpb $0x05, %ah je 15f // x is ±inf fxch // y : x /* fistpll raises invalid exception for |y| >= 1L<<63. */ fldl MO(p63) // 1L<<63 : y : x fld %st(1) // y : 1L<<63 : y : x fabs // |y| : 1L<<63 : y : x fcomip %st(1), %st // 1L<<63 : y : x fstp %st(0) // y : x jnc 2f /* First see whether `y' is a natural number. In this case we can use a more precise algorithm. */ fld %st // y : y : x fistpll -8(%rsp) // y : x fildll -8(%rsp) // int(y) : y : x fucomip %st(1),%st // y : x jne 2f /* OK, we have an integer value for y. */ mov -8(%rsp),%eax mov -4(%rsp),%edx orl $0, %edx fstp %st(0) // x jns 4f // y >= 0, jump fdivrl MO(one) // 1/x (now referred to as x) negl %eax adcl $0, %edx negl %edx 4: fldl MO(one) // 1 : x fxch 6: shrdl $1, %edx, %eax jnc 5f fxch fmul %st(1) // x : ST*x fxch 5: fmul %st(0), %st // x*x : ST*x shrl $1, %edx movl %eax, %ecx orl %edx, %ecx jnz 6b fstp %st(0) // ST*x ret /* y is ±NAN */ 30: fldt 8(%rsp) // x : y fldl MO(one) // 1.0 : x : y fucomip %st(1),%st // x : y je 31f fxch // y : x 31: fstp %st(1) ret .align ALIGNARG(4) 2: /* y is a real number. */ fxch // x : y fldl MO(one) // 1.0 : x : y fldl MO(limit) // 0.29 : 1.0 : x : y fld %st(2) // x : 0.29 : 1.0 : x : y fsub %st(2) // x-1 : 0.29 : 1.0 : x : y fabs // |x-1| : 0.29 : 1.0 : x : y fucompp // 1.0 : x : y fnstsw fxch // x : 1.0 : y test $0x4500,%eax jz 7f fsub %st(1) // x-1 : 1.0 : y fyl2xp1 // log2(x) : y jmp 8f 7: fyl2x // log2(x) : y 8: fmul %st(1) // y*log2(x) : y fxam fnstsw andb $0x45, %ah cmpb $0x05, %ah // is y*log2(x) == ±inf ? je 28f fst %st(1) // y*log2(x) : y*log2(x) frndint // int(y*log2(x)) : y*log2(x) fsubr %st, %st(1) // int(y*log2(x)) : fract(y*log2(x)) fxch // fract(y*log2(x)) : int(y*log2(x)) f2xm1 // 2^fract(y*log2(x))-1 : int(y*log2(x)) faddl MO(one) // 2^fract(y*log2(x)) : int(y*log2(x)) fscale // 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x)) fstp %st(1) // 2^fract(y*log2(x))*2^int(y*log2(x)) ret 28: fstp %st(1) // y*log2(x) fldl MO(one) // 1 : y*log2(x) fscale // 2^(y*log2(x)) : y*log2(x) fstp %st(1) // 2^(y*log2(x)) ret // pow(x,±0) = 1 .align ALIGNARG(4) 11: fstp %st(0) // pop y fldl MO(one) ret // y == ±inf .align ALIGNARG(4) 12: fstp %st(0) // pop y fldl MO(one) // 1 fldt 8(%rsp) // x : 1 fabs // abs(x) : 1 fucompp // < 1, == 1, or > 1 fnstsw andb $0x45, %ah cmpb $0x45, %ah je 13f // jump if x is NaN cmpb $0x40, %ah je 14f // jump if |x| == 1 shlb $1, %ah xorb %ah, %dl andl $2, %edx #ifdef PIC lea inf_zero(%rip),%rcx fldl (%rcx, %rdx, 4) #else fldl inf_zero(,%rdx, 4) #endif ret .align ALIGNARG(4) 14: fldl MO(one) ret .align ALIGNARG(4) 13: fldt 8(%rsp) // load x == NaN ret .align ALIGNARG(4) // x is ±inf 15: fstp %st(0) // y testb $2, %dh jz 16f // jump if x == +inf // We must find out whether y is an odd integer. fld %st // y : y fistpll -8(%rsp) // y fildll -8(%rsp) // int(y) : y fucomip %st(1),%st ffreep %st // jne 17f // OK, the value is an integer, but is it odd? mov -8(%rsp), %eax mov -4(%rsp), %edx andb $1, %al jz 18f // jump if not odd // It's an odd integer. shrl $31, %edx #ifdef PIC lea minf_mzero(%rip),%rcx fldl (%rcx, %rdx, 8) #else fldl minf_mzero(,%rdx, 8) #endif ret .align ALIGNARG(4) 16: fcompl MO(zero) fnstsw shrl $5, %eax andl $8, %eax #ifdef PIC lea inf_zero(%rip),%rcx fldl (%rcx, %rax, 1) #else fldl inf_zero(,%rax, 1) #endif ret .align ALIGNARG(4) 17: shll $30, %edx // sign bit for y in right position 18: shrl $31, %edx #ifdef PIC lea inf_zero(%rip),%rcx fldl (%rcx, %rdx, 8) #else fldl inf_zero(,%rdx, 8) #endif ret .align ALIGNARG(4) // x is ±0 20: fstp %st(0) // y testb $2, %dl jz 21f // y > 0 // x is ±0 and y is < 0. We must find out whether y is an odd integer. testb $2, %dh jz 25f fld %st // y : y fistpll -8(%rsp) // y fildll -8(%rsp) // int(y) : y fucomip %st(1),%st ffreep %st // jne 26f // OK, the value is an integer, but is it odd? mov -8(%rsp),%eax mov -4(%rsp),%edx andb $1, %al jz 27f // jump if not odd // It's an odd integer. // Raise divide-by-zero exception and get minus infinity value. fldl MO(one) fdivl MO(zero) fchs ret 25: fstp %st(0) 26: 27: // Raise divide-by-zero exception and get infinity value. fldl MO(one) fdivl MO(zero) ret .align ALIGNARG(4) // x is ±0 and y is > 0. We must find out whether y is an odd integer. 21: testb $2, %dh jz 22f fld %st // y : y fistpll -8(%rsp) // y fildll -8(%rsp) // int(y) : y fucomip %st(1),%st ffreep %st // jne 23f // OK, the value is an integer, but is it odd? mov -8(%rsp),%eax mov -4(%rsp),%edx andb $1, %al jz 24f // jump if not odd // It's an odd integer. fldl MO(mzero) ret 22: fstp %st(0) 23: 24: fldl MO(zero) ret END(__ieee754_powl) strong_alias (__ieee754_powl, __powl_finite)