/* ix87 specific implementation of pow function. Copyright (C) 1996, 1997 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 Library General Public License as published by the Free Software Foundation; either version 2 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 Library General Public License for more details. You should have received a copy of the GNU Library General Public License along with the GNU C Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include #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(nan,@object) nan: .byte 0, 0, 0, 0, 0, 0, 0xff, 0x7f ASM_SIZE_DIRECTIVE(nan) #ifdef PIC #define MO(op) op##@GOTOFF(%ecx) #define MOX(op,x,f) op##@GOTOFF(%ecx,x,f) #else #define MO(op) op #define MOX(op,x,f) op(,x,f) #endif .text ENTRY(__ieee754_powf) flds 8(%esp) // y fxam #ifdef PIC call 1f 1: popl %ecx addl $_GLOBAL_OFFSET_TABLE_+[.-1b], %ecx #endif 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 flds 4(%esp) // x : y subl $4, %esp 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 /* First see whether `y' is a natural number. In this case we can use a more precise algorithm. */ fld %st // y : y : x fistpl (%esp) // y : x fildl (%esp) // int(y) : y : x fucomp %st(1) // y : x fnstsw sahf jne 2f /* OK, we have an integer value for y. */ popl %edx orl $0, %edx fstp %st(0) // x jns 4f // y >= 0, jump fdivrl MO(one) // 1/x (now referred to as x) negl %edx 4: fldl MO(one) // 1 : x fxch 6: shrl $1, %edx jnc 5f fxch fmul %st(1) // x : ST*x fxch 5: fmul %st(0), %st // x*x : ST*x testl %edx, %edx jnz 6b fstp %st(0) // ST*x 30: ret .align ALIGNARG(4) 2: /* y is a real number. */ fxch // x : y fldl MO(one) // 1.0 : x : y fld %st(1) // x : 1.0 : x : y fsub %st(1) // x-1 : 1.0 : x : y fabs // |x-1| : 1.0 : x : y fcompl MO(limit) // 1.0 : x : y fnstsw fxch // x : 1.0 : y sahf ja 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 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)) addl $4, %esp fstp %st(1) // 2^fract(y*log2(x))*2^int(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 flds 4(%esp) // x fabs fcompl MO(one) // < 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 fldl MOX(inf_zero, %edx, 4) ret .align ALIGNARG(4) 14: fldl MO(nan) faddl MO(zero) // raise invalid exception ret .align ALIGNARG(4) 13: flds 4(%esp) // 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 fistpl (%esp) // y fildl (%esp) // int(y) : y fucompp // fnstsw sahf jne 17f // OK, the value is an integer, but is the number of bits small // enough so that all are coming from the mantissa? popl %edx testb $1, %dl jz 18f // jump if not odd movl %edx, %eax orl %edx, %edx jns 155f negl %eax 155: cmpl $0x01000000, %eax ja 18f // does not fit in mantissa bits // It's an odd integer. shrl $31, %edx fldl MOX(minf_mzero, %edx, 8) ret .align ALIGNARG(4) 16: fcompl MO(zero) addl $4, %esp fnstsw shrl $5, %eax andl $8, %eax fldl MOX(inf_zero, %eax, 1) ret .align ALIGNARG(4) 17: shll $30, %edx // sign bit for y in right position addl $4, %esp 18: shrl $31, %edx fldl MOX(inf_zero, %edx, 8) 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 fistpl (%esp) // y fildl (%esp) // int(y) : y fucompp // fnstsw sahf jne 26f // OK, the value is an integer, but is the number of bits small // enough so that all are coming from the mantissa? popl %edx testb $1, %dl jz 27f // jump if not odd cmpl $0xff000000, %edx jbe 27f // does not fit in mantissa bits // 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: popl %eax 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 fistpl (%esp) // y fildl (%esp) // int(y) : y fucompp // fnstsw sahf jne 23f // OK, the value is an integer, but is the number of bits small // enough so that all are coming from the mantissa? popl %edx testb $1, %dl jz 24f // jump if not odd cmpl $0xff000000, %edx jbe 24f // does not fit in mantissa bits // It's an odd integer. fldl MO(mzero) ret 22: fstp %st(0) 23: popl %eax 24: fldl MO(zero) ret END(__ieee754_powf)