| /* ix87 specific implementation of pow function. |
| Copyright (C) 1996, 1997, 1998, 1999, 2001, 2004, 2007 |
| 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, write to the Free |
| Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA |
| 02111-1307 USA. */ |
| |
| #include <machine/asm.h> |
| |
| #ifdef __ELF__ |
| .section .rodata |
| #else |
| .text |
| #endif |
| |
| .align ALIGNARG(4) |
| 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) |
| 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) |
| |
| #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 $4500,%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 // <empty> |
| 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 // <empty> |
| 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 // <empty> |
| 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) |
