/* 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 limit,@object limit: .double 0.29 ASM_SIZE_DIRECTIVE(limit) .type p63,@object p63: .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43 ASM_SIZE_DIRECTIVE(p63) .type p10,@object p10: .byte 0, 0, 0, 0, 0, 0, 0x90, 0x40 ASM_SIZE_DIRECTIVE(p10) .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_DBL_MIN #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_pow) fldl 12(%esp) // y fxam #ifdef PIC LOAD_PIC_REG (cx) #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 fldl 4(%esp) // x : y subl $8,%esp cfi_adjust_cfa_offset (8) 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 32f // x is NaN fxch // y : x /* fistpll raises invalid exception for |y| >= 1L<<63. */ fld %st // y : y : x fabs // |y| : y : x fcompl MO(p63) // y : x fnstsw sahf 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 (%esp) // y : x fildll (%esp) // int(y) : y : x fucomp %st(1) // y : x fnstsw sahf jne 3f /* OK, we have an integer value for y. If large enough that errors may propagate out of the 11 bits excess precision, use the algorithm for real exponent instead. */ fld %st // y : y : x fabs // |y| : y : x fcompl MO(p10) // y : x fnstsw sahf jnc 2f popl %eax cfi_adjust_cfa_offset (-4) popl %edx cfi_adjust_cfa_offset (-4) 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 #ifdef PIC LOAD_PIC_REG (cx) #endif DBL_NARROW_EVAL_UFLOW_NONNAN ret /* y is ±NAN */ 30: fldl 4(%esp) // x : y fldl MO(one) // 1.0 : x : y fucomp %st(1) // x : y fnstsw sahf je 31f fxch // y : x 31: fstp %st(1) ret cfi_adjust_cfa_offset (8) 32: addl $8, %esp cfi_adjust_cfa_offset (-8) fstp %st(1) ret cfi_adjust_cfa_offset (8) .align ALIGNARG(4) 2: // y is a large integer (absolute value at least 1L<<10), but // may be odd unless at least 1L<<64. So it may be necessary // to adjust the sign of a negative result afterwards. fxch // x : y fabs // |x| : y fxch // y : x .align ALIGNARG(4) 3: /* 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 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)) // Before scaling, we must negate if x is negative and y is an // odd integer. testb $2, %dh jz 291f // x is negative. If y is an odd integer, negate the result. fldl 20(%esp) // y : 2^fract(y*log2(x)) : int(y*log2(x)) fld %st // y : y : 2^fract(y*log2(x)) : int(y*log2(x)) fabs // |y| : y : 2^fract(y*log2(x)) : int(y*log2(x)) fcompl MO(p63) // y : 2^fract(y*log2(x)) : int(y*log2(x)) fnstsw sahf jnc 290f // We must find out whether y is an odd integer. fld %st // y : y : 2^fract(y*log2(x)) : int(y*log2(x)) fistpll (%esp) // y : 2^fract(y*log2(x)) : int(y*log2(x)) fildll (%esp) // int(y) : y : 2^fract(y*log2(x)) : int(y*log2(x)) fucompp // 2^fract(y*log2(x)) : int(y*log2(x)) fnstsw sahf jne 291f // OK, the value is an integer, but is it odd? popl %eax cfi_adjust_cfa_offset (-4) popl %edx cfi_adjust_cfa_offset (-4) andb $1, %al jz 292f // jump if not odd // It's an odd integer. fchs jmp 292f cfi_adjust_cfa_offset (8) 290: fstp %st(0) // 2^fract(y*log2(x)) : int(y*log2(x)) 291: addl $8, %esp cfi_adjust_cfa_offset (-8) 292: 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)) DBL_NARROW_EVAL_UFLOW_NONNAN 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 fldl 4(%esp) // 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 fldl MOX(inf_zero, %edx, 4) ret .align ALIGNARG(4) 14: fldl MO(one) ret .align ALIGNARG(4) 13: fldl 4(%esp) // load x == NaN ret cfi_adjust_cfa_offset (8) .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, so test // that (in which case y is certainly even) before testing // whether y is odd. fld %st // y : y fabs // |y| : y fcompl MO(p63) // y fnstsw sahf jnc 16f // We must find out whether y is an odd integer. fld %st // y : y fistpll (%esp) // y fildll (%esp) // int(y) : y fucompp // fnstsw sahf jne 17f // OK, the value is an integer. popl %eax cfi_adjust_cfa_offset (-4) popl %edx cfi_adjust_cfa_offset (-4) andb $1, %al jz 18f // jump if not odd // It's an odd integer. shrl $31, %edx fldl MOX(minf_mzero, %edx, 8) ret cfi_adjust_cfa_offset (8) .align ALIGNARG(4) 16: fcompl MO(zero) addl $8, %esp cfi_adjust_cfa_offset (-8) fnstsw shrl $5, %eax andl $8, %eax fldl MOX(inf_zero, %eax, 1) ret cfi_adjust_cfa_offset (8) .align ALIGNARG(4) 17: shll $30, %edx // sign bit for y in right position addl $8, %esp cfi_adjust_cfa_offset (-8) 18: shrl $31, %edx fldl MOX(inf_zero, %edx, 8) ret cfi_adjust_cfa_offset (8) .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, so test // that (in which case y is certainly even) before testing // whether y is odd. fld %st // y : y fabs // |y| : y fcompl MO(p63) // y fnstsw sahf jnc 25f fld %st // y : y fistpll (%esp) // y fildll (%esp) // int(y) : y fucompp // fnstsw sahf jne 26f // OK, the value is an integer. popl %eax cfi_adjust_cfa_offset (-4) popl %edx cfi_adjust_cfa_offset (-4) 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 cfi_adjust_cfa_offset (8) 25: fstp %st(0) 26: addl $8, %esp cfi_adjust_cfa_offset (-8) 27: // Raise divide-by-zero exception and get infinity value. fldl MO(one) fdivl MO(zero) ret cfi_adjust_cfa_offset (8) .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, so test // that (in which case y is certainly even) before testing // whether y is odd. fcoml MO(p63) // y fnstsw sahf jnc 22f fld %st // y : y fistpll (%esp) // y fildll (%esp) // int(y) : y fucompp // fnstsw sahf jne 23f // OK, the value is an integer. popl %eax cfi_adjust_cfa_offset (-4) popl %edx cfi_adjust_cfa_offset (-4) andb $1, %al jz 24f // jump if not odd // It's an odd integer. fldl MO(mzero) ret cfi_adjust_cfa_offset (8) 22: fstp %st(0) 23: addl $8, %esp // Don't use 2 x pop cfi_adjust_cfa_offset (-8) 24: fldl MO(zero) ret END(__ieee754_pow) strong_alias (__ieee754_pow, __pow_finite)