1 /* ix87 specific implementation of pow function.
2 Copyright (C) 1996-1999, 2001, 2004-2005, 2007, 2011-2012
3 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
5 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
7 The GNU C Library is free software; you can redistribute it and/or
8 modify it under the terms of the GNU Lesser General Public
9 License as published by the Free Software Foundation; either
10 version 2.1 of the License, or (at your option) any later version.
12 The GNU C Library is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 Lesser General Public License for more details.
17 You should have received a copy of the GNU Lesser General Public
18 License along with the GNU C Library; if not, write to the Free
19 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
22 #include <machine/asm.h>
24 .section .rodata.cst8,"aM",@progbits,8
27 ASM_TYPE_DIRECTIVE(one,@object)
29 ASM_SIZE_DIRECTIVE(one)
30 ASM_TYPE_DIRECTIVE(limit,@object)
32 ASM_SIZE_DIRECTIVE(limit)
33 ASM_TYPE_DIRECTIVE(p63,@object)
34 p63: .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
35 ASM_SIZE_DIRECTIVE(p63)
37 .section .rodata.cst16,"aM",@progbits,16
40 ASM_TYPE_DIRECTIVE(infinity,@object)
43 .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
44 ASM_SIZE_DIRECTIVE(infinity)
45 ASM_TYPE_DIRECTIVE(zero,@object)
47 ASM_SIZE_DIRECTIVE(zero)
48 ASM_TYPE_DIRECTIVE(minf_mzero,@object)
51 .byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
53 .byte 0, 0, 0, 0, 0, 0, 0, 0x80
54 ASM_SIZE_DIRECTIVE(minf_mzero)
57 # define MO(op) op##@GOTOFF(%ecx)
58 # define MOX(op,x,f) op##@GOTOFF(%ecx,x,f)
61 # define MOX(op,x,f) op(,x,f)
76 cmpb $0x40, %ah // is y == 0 ?
79 cmpb $0x05, %ah // is y == ±inf ?
82 cmpb $0x01, %ah // is y == NaN ?
88 cfi_adjust_cfa_offset (8)
102 /* fistpll raises invalid exception for |y| >= 1L<<63. */
105 fcompl MO(p63) // y : x
110 /* First see whether `y' is a natural number. In this case we
111 can use a more precise algorithm. */
113 fistpll (%esp) // y : x
114 fildll (%esp) // int(y) : y : x
115 fucomp %st(1) // y : x
120 /* OK, we have an integer value for y. */
122 cfi_adjust_cfa_offset (-4)
124 cfi_adjust_cfa_offset (-4)
127 jns 4f // y >= 0, jump
128 fdivrl MO(one) // 1/x (now referred to as x)
132 4: fldl MO(one) // 1 : x
135 6: shrdl $1, %edx, %eax
138 fmul %st(1) // x : ST*x
140 5: fmul %st(0), %st // x*x : ST*x
149 30: fldl 4(%esp) // x : y
150 fldl MO(one) // 1.0 : x : y
151 fucomp %st(1) // x : y
159 cfi_adjust_cfa_offset (8)
161 2: /* y is a real number. */
163 fldl MO(one) // 1.0 : x : y
164 fldl MO(limit) // 0.29 : 1.0 : x : y
165 fld %st(2) // x : 0.29 : 1.0 : x : y
166 fsub %st(2) // x-1 : 0.29 : 1.0 : x : y
167 fabs // |x-1| : 0.29 : 1.0 : x : y
168 fucompp // 1.0 : x : y
173 fsub %st(1) // x-1 : 1.0 : y
174 fyl2xp1 // log2(x) : y
177 7: fyl2x // log2(x) : y
178 8: fmul %st(1) // y*log2(x) : y
179 fst %st(1) // y*log2(x) : y*log2(x)
180 frndint // int(y*log2(x)) : y*log2(x)
181 fsubr %st, %st(1) // int(y*log2(x)) : fract(y*log2(x))
182 fxch // fract(y*log2(x)) : int(y*log2(x))
183 f2xm1 // 2^fract(y*log2(x))-1 : int(y*log2(x))
184 faddl MO(one) // 2^fract(y*log2(x)) : int(y*log2(x))
185 fscale // 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
187 cfi_adjust_cfa_offset (-8)
188 fstp %st(1) // 2^fract(y*log2(x))*2^int(y*log2(x))
194 11: fstp %st(0) // pop y
200 12: fstp %st(0) // pop y
202 fldl 4(%esp) // x : 1
204 fucompp // < 1, == 1, or > 1
208 je 13f // jump if x is NaN
211 je 14f // jump if |x| == 1
216 fldl MOX(inf_zero, %edx, 4)
224 13: fldl 4(%esp) // load x == NaN
227 cfi_adjust_cfa_offset (8)
232 jz 16f // jump if x == +inf
234 // We must find out whether y is an odd integer.
237 fildll (%esp) // int(y) : y
243 // OK, the value is an integer, but is the number of bits small
244 // enough so that all are coming from the mantissa?
246 cfi_adjust_cfa_offset (-4)
248 cfi_adjust_cfa_offset (-4)
250 jz 18f // jump if not odd
255 155: cmpl $0x00200000, %eax
256 ja 18f // does not fit in mantissa bits
257 // It's an odd integer.
259 fldl MOX(minf_mzero, %edx, 8)
262 cfi_adjust_cfa_offset (8)
266 cfi_adjust_cfa_offset (-8)
270 fldl MOX(inf_zero, %eax, 1)
273 cfi_adjust_cfa_offset (8)
275 17: shll $30, %edx // sign bit for y in right position
277 cfi_adjust_cfa_offset (-8)
279 fldl MOX(inf_zero, %edx, 8)
282 cfi_adjust_cfa_offset (8)
289 // x is ±0 and y is < 0. We must find out whether y is an odd integer.
295 fildll (%esp) // int(y) : y
301 // OK, the value is an integer, but is the number of bits small
302 // enough so that all are coming from the mantissa?
304 cfi_adjust_cfa_offset (-4)
306 cfi_adjust_cfa_offset (-4)
308 jz 27f // jump if not odd
309 cmpl $0xffe00000, %edx
310 jbe 27f // does not fit in mantissa bits
311 // It's an odd integer.
312 // Raise divide-by-zero exception and get minus infinity value.
318 cfi_adjust_cfa_offset (8)
321 cfi_adjust_cfa_offset (-8)
322 27: // Raise divide-by-zero exception and get infinity value.
327 cfi_adjust_cfa_offset (8)
329 // x is ±0 and y is > 0. We must find out whether y is an odd integer.
335 fildll (%esp) // int(y) : y
341 // OK, the value is an integer, but is the number of bits small
342 // enough so that all are coming from the mantissa?
344 cfi_adjust_cfa_offset (-4)
346 cfi_adjust_cfa_offset (-4)
348 jz 24f // jump if not odd
349 cmpl $0xffe00000, %edx
350 jae 24f // does not fit in mantissa bits
351 // It's an odd integer.
355 cfi_adjust_cfa_offset (8)
357 23: addl $8, %esp // Don't use 2 x pop
358 cfi_adjust_cfa_offset (-8)
363 strong_alias (__ieee754_pow, __pow_finite)