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, see
19 <http://www.gnu.org/licenses/>. */
21 #include <machine/asm.h>
23 .section .rodata.cst8,"aM",@progbits,8
28 ASM_SIZE_DIRECTIVE(one)
31 ASM_SIZE_DIRECTIVE(limit)
33 p63: .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
34 ASM_SIZE_DIRECTIVE(p63)
36 p10: .byte 0, 0, 0, 0, 0, 0, 0x90, 0x40
37 ASM_SIZE_DIRECTIVE(p10)
39 .section .rodata.cst16,"aM",@progbits,16
42 .type infinity,@object
45 .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
46 ASM_SIZE_DIRECTIVE(infinity)
49 ASM_SIZE_DIRECTIVE(zero)
50 .type minf_mzero,@object
53 .byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
55 .byte 0, 0, 0, 0, 0, 0, 0, 0x80
56 ASM_SIZE_DIRECTIVE(minf_mzero)
59 # define MO(op) op##@GOTOFF(%ecx)
60 # define MOX(op,x,f) op##@GOTOFF(%ecx,x,f)
63 # define MOX(op,x,f) op(,x,f)
78 cmpb $0x40, %ah // is y == 0 ?
81 cmpb $0x05, %ah // is y == ±inf ?
84 cmpb $0x01, %ah // is y == NaN ?
90 cfi_adjust_cfa_offset (8)
104 /* fistpll raises invalid exception for |y| >= 1L<<63. */
107 fcompl MO(p63) // y : x
112 /* First see whether `y' is a natural number. In this case we
113 can use a more precise algorithm. */
115 fistpll (%esp) // y : x
116 fildll (%esp) // int(y) : y : x
117 fucomp %st(1) // y : x
122 /* OK, we have an integer value for y. If large enough that
123 errors may propagate out of the 11 bits excess precision, use
124 the algorithm for real exponent instead. */
127 fcompl MO(p10) // y : x
132 cfi_adjust_cfa_offset (-4)
134 cfi_adjust_cfa_offset (-4)
137 jns 4f // y >= 0, jump
138 fdivrl MO(one) // 1/x (now referred to as x)
142 4: fldl MO(one) // 1 : x
145 6: shrdl $1, %edx, %eax
148 fmul %st(1) // x : ST*x
150 5: fmul %st(0), %st // x*x : ST*x
159 30: fldl 4(%esp) // x : y
160 fldl MO(one) // 1.0 : x : y
161 fucomp %st(1) // x : y
169 cfi_adjust_cfa_offset (8)
171 2: // y is a large integer (absolute value at least 1L<<10), but
172 // may be odd unless at least 1L<<64. So it may be necessary
173 // to adjust the sign of a negative result afterwards.
178 3: /* y is a real number. */
180 fldl MO(one) // 1.0 : x : y
181 fldl MO(limit) // 0.29 : 1.0 : x : y
182 fld %st(2) // x : 0.29 : 1.0 : x : y
183 fsub %st(2) // x-1 : 0.29 : 1.0 : x : y
184 fabs // |x-1| : 0.29 : 1.0 : x : y
185 fucompp // 1.0 : x : y
190 fsub %st(1) // x-1 : 1.0 : y
191 fyl2xp1 // log2(x) : y
194 7: fyl2x // log2(x) : y
195 8: fmul %st(1) // y*log2(x) : y
196 fst %st(1) // y*log2(x) : y*log2(x)
197 frndint // int(y*log2(x)) : y*log2(x)
198 fsubr %st, %st(1) // int(y*log2(x)) : fract(y*log2(x))
199 fxch // fract(y*log2(x)) : int(y*log2(x))
200 f2xm1 // 2^fract(y*log2(x))-1 : int(y*log2(x))
201 faddl MO(one) // 2^fract(y*log2(x)) : int(y*log2(x))
202 fscale // 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
203 fstp %st(1) // 2^fract(y*log2(x))*2^int(y*log2(x))
206 // x is negative. If y is an odd integer, negate the result.
207 fldl 20(%esp) // y : abs(result)
208 fld %st // y : y : abs(result)
209 fabs // |y| : y : abs(result)
210 fcompl MO(p63) // y : abs(result)
215 // We must find out whether y is an odd integer.
216 fld %st // y : y : abs(result)
217 fistpll (%esp) // y : abs(result)
218 fildll (%esp) // int(y) : y : abs(result)
219 fucompp // abs(result)
224 // OK, the value is an integer, but is it odd?
226 cfi_adjust_cfa_offset (-4)
228 cfi_adjust_cfa_offset (-4)
230 jz 290f // jump if not odd
231 // It's an odd integer.
234 cfi_adjust_cfa_offset (8)
235 291: fstp %st(0) // abs(result)
237 cfi_adjust_cfa_offset (-8)
243 11: fstp %st(0) // pop y
249 12: fstp %st(0) // pop y
251 fldl 4(%esp) // x : 1
253 fucompp // < 1, == 1, or > 1
257 je 13f // jump if x is NaN
260 je 14f // jump if |x| == 1
265 fldl MOX(inf_zero, %edx, 4)
273 13: fldl 4(%esp) // load x == NaN
276 cfi_adjust_cfa_offset (8)
281 jz 16f // jump if x == +inf
283 // fistpll raises invalid exception for |y| >= 1L<<63, so test
284 // that (in which case y is certainly even) before testing
293 // We must find out whether y is an odd integer.
296 fildll (%esp) // int(y) : y
302 // OK, the value is an integer.
304 cfi_adjust_cfa_offset (-4)
306 cfi_adjust_cfa_offset (-4)
308 jz 18f // jump if not odd
309 // It's an odd integer.
311 fldl MOX(minf_mzero, %edx, 8)
314 cfi_adjust_cfa_offset (8)
318 cfi_adjust_cfa_offset (-8)
322 fldl MOX(inf_zero, %eax, 1)
325 cfi_adjust_cfa_offset (8)
327 17: shll $30, %edx // sign bit for y in right position
329 cfi_adjust_cfa_offset (-8)
331 fldl MOX(inf_zero, %edx, 8)
334 cfi_adjust_cfa_offset (8)
341 // x is ±0 and y is < 0. We must find out whether y is an odd integer.
345 // fistpll raises invalid exception for |y| >= 1L<<63, so test
346 // that (in which case y is certainly even) before testing
357 fildll (%esp) // int(y) : y
363 // OK, the value is an integer.
365 cfi_adjust_cfa_offset (-4)
367 cfi_adjust_cfa_offset (-4)
369 jz 27f // jump if not odd
370 // It's an odd integer.
371 // Raise divide-by-zero exception and get minus infinity value.
377 cfi_adjust_cfa_offset (8)
380 cfi_adjust_cfa_offset (-8)
381 27: // Raise divide-by-zero exception and get infinity value.
386 cfi_adjust_cfa_offset (8)
388 // x is ±0 and y is > 0. We must find out whether y is an odd integer.
392 // fistpll raises invalid exception for |y| >= 1L<<63, so test
393 // that (in which case y is certainly even) before testing
402 fildll (%esp) // int(y) : y
408 // OK, the value is an integer.
410 cfi_adjust_cfa_offset (-4)
412 cfi_adjust_cfa_offset (-4)
414 jz 24f // jump if not odd
415 // It's an odd integer.
419 cfi_adjust_cfa_offset (8)
421 23: addl $8, %esp // Don't use 2 x pop
422 cfi_adjust_cfa_offset (-8)
427 strong_alias (__ieee754_pow, __pow_finite)