/* ix87 specific implementation of pow function. Copyright (C) 1996-2016 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, see . */ #include #include .section .rodata.cst8,"aM",@progbits,8 .p2align 3 .type one,@object one: .double 1.0 ASM_SIZE_DIRECTIVE(one) .type p3,@object p3: .byte 0, 0, 0, 0, 0, 0, 0x20, 0x40 ASM_SIZE_DIRECTIVE(p3) .type p63,@object p63: .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43 ASM_SIZE_DIRECTIVE(p63) .type p64,@object p64: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43 ASM_SIZE_DIRECTIVE(p64) .type p78,@object p78: .byte 0, 0, 0, 0, 0, 0, 0xd0, 0x44 ASM_SIZE_DIRECTIVE(p78) .type pm79,@object pm79: .byte 0, 0, 0, 0, 0, 0, 0, 0x3b ASM_SIZE_DIRECTIVE(pm79) .section .rodata.cst16,"aM",@progbits,16 .p2align 3 .type infinity,@object inf_zero: infinity: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f ASM_SIZE_DIRECTIVE(infinity) .type zero,@object zero: .double 0.0 ASM_SIZE_DIRECTIVE(zero) .type 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) DEFINE_LDBL_MIN #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 cmpb $0x01, %ah je 31f // x is NaN 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 je 9f // If y has absolute value at most 0x1p-79, then any finite // nonzero x will result in 1. Saturate y to those bounds to // avoid underflow in the calculation of y*log2(x). fldl MO(pm79) // 0x1p-79 : y : x fld %st(1) // y : 0x1p-79 : y : x fabs // |y| : 0x1p-79 : y : x fcomip %st(1), %st // 0x1p-79 : y : x fstp %st(0) // y : x jnc 3f fstp %st(0) // pop y fldl MO(pm79) // 0x1p-79 : x testb $2, %dl jnz 3f // y > 0 fchs // -0x1p-79 : x jmp 3f 9: /* OK, we have an integer value for y. Unless very small (we use < 8), use the algorithm for real exponent to avoid accumulation of errors. */ fldl MO(p3) // 8 : y : x fld %st(1) // y : 8 : y : x fabs // |y| : 8 : y : x fcomip %st(1), %st // 8 : y : x fstp %st(0) // y : x jnc 3f 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 /* If y is even, take the absolute value of x. Otherwise, ensure all intermediate values that might overflow have the sign of x. */ testb $1, %al jnz 6f fabs 6: shrdl $1, %edx, %eax jnc 5f fxch fabs fmul %st(1) // x : ST*x fxch 5: fld %st // x : x : ST*x fabs // |x| : x : ST*x fmulp // |x|*x : ST*x shrl $1, %edx movl %eax, %ecx orl %edx, %ecx jnz 6b fstp %st(0) // ST*x LDBL_CHECK_FORCE_UFLOW_NONNAN 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 large integer (absolute value at least 1L<<63). // If y has absolute value at least 1L<<78, then any finite // nonzero x will result in 0 (underflow), 1 or infinity (overflow). // Saturate y to those bounds to avoid overflow in the calculation // of y*log2(x). fldl MO(p78) // 1L<<78 : y : x fld %st(1) // y : 1L<<78 : y : x fabs // |y| : 1L<<78 : y : x fcomip %st(1), %st // 1L<<78 : y : x fstp %st(0) // y : x jc 3f fstp %st(0) // pop y fldl MO(p78) // 1L<<78 : x testb $2, %dl jz 3f // y > 0 fchs // -(1L<<78) : x .align ALIGNARG(4) 3: /* y is a real number. */ subq $40, %rsp cfi_adjust_cfa_offset (40) fstpt 16(%rsp) // x fstpt (%rsp) // call HIDDEN_JUMPTARGET (__powl_helper) // addq $40, %rsp cfi_adjust_cfa_offset (-40) 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 // fistpll raises invalid exception for |y| >= 1L<<63, but y // may be odd unless we know |y| >= 1L<<64. fldl MO(p64) // 1L<<64 : y fld %st(1) // y : 1L<<64 : y fabs // |y| : 1L<<64 : y fcomip %st(1), %st // 1L<<64 : y fstp %st(0) // y jnc 16f fldl MO(p63) // p63 : y fxch // y : p63 fprem // y%p63 : p63 fstp %st(1) // y%p63 // 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 // fistpll raises invalid exception for |y| >= 1L<<63, but y // may be odd unless we know |y| >= 1L<<64. fldl MO(p64) // 1L<<64 : y fld %st(1) // y : 1L<<64 : y fabs // |y| : 1L<<64 : y fcomip %st(1), %st // 1L<<64 : y fstp %st(0) // y jnc 25f fldl MO(p63) // p63 : y fxch // y : p63 fprem // y%p63 : p63 fstp %st(1) // y%p63 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 // fistpll raises invalid exception for |y| >= 1L<<63, but y // may be odd unless we know |y| >= 1L<<64. fldl MO(p64) // 1L<<64 : y fxch // y : 1L<<64 fcomi %st(1), %st // y : 1L<<64 fstp %st(1) // y jnc 22f fldl MO(p63) // p63 : y fxch // y : p63 fprem // y%p63 : p63 fstp %st(1) // y%p63 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)