1/* ix87 specific implementation of pow function.
2 Copyright (C) 1996-2022 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <https://www.gnu.org/licenses/>. */
18
19#include <machine/asm.h>
20#include <i386-math-asm.h>
21#include <libm-alias-finite.h>
22
23 .section .rodata.cst8,"aM",@progbits,8
24
25 .p2align 3
26 .type one,@object
27one: .double 1.0
28 ASM_SIZE_DIRECTIVE(one)
29 .type p2,@object
30p2: .byte 0, 0, 0, 0, 0, 0, 0x10, 0x40
31 ASM_SIZE_DIRECTIVE(p2)
32 .type p63,@object
33p63: .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
34 ASM_SIZE_DIRECTIVE(p63)
35 .type p64,@object
36p64: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43
37 ASM_SIZE_DIRECTIVE(p64)
38 .type p78,@object
39p78: .byte 0, 0, 0, 0, 0, 0, 0xd0, 0x44
40 ASM_SIZE_DIRECTIVE(p78)
41 .type pm79,@object
42pm79: .byte 0, 0, 0, 0, 0, 0, 0, 0x3b
43 ASM_SIZE_DIRECTIVE(pm79)
44
45 .section .rodata.cst16,"aM",@progbits,16
46
47 .p2align 3
48 .type infinity,@object
49inf_zero:
50infinity:
51 .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x7f
52 ASM_SIZE_DIRECTIVE(infinity)
53 .type zero,@object
54zero: .double 0.0
55 ASM_SIZE_DIRECTIVE(zero)
56 .type minf_mzero,@object
57minf_mzero:
58minfinity:
59 .byte 0, 0, 0, 0, 0, 0, 0xf0, 0xff
60mzero:
61 .byte 0, 0, 0, 0, 0, 0, 0, 0x80
62 ASM_SIZE_DIRECTIVE(minf_mzero)
63DEFINE_LDBL_MIN
64
65#ifdef PIC
66# define MO(op) op##@GOTOFF(%ecx)
67# define MOX(op,x,f) op##@GOTOFF(%ecx,x,f)
68#else
69# define MO(op) op
70# define MOX(op,x,f) op(,x,f)
71#endif
72
73 .text
74ENTRY(__ieee754_powl)
75 fldt 16(%esp) // y
76 fxam
77
78#ifdef PIC
79 LOAD_PIC_REG (cx)
80#endif
81
82 fnstsw
83 movb %ah, %dl
84 andb $0x45, %ah
85 cmpb $0x40, %ah // is y == 0 ?
86 je 11f
87
88 cmpb $0x05, %ah // is y == ±inf ?
89 je 12f
90
91 cmpb $0x01, %ah // is y == NaN ?
92 je 30f
93
94 fldt 4(%esp) // x : y
95
96 subl $8,%esp
97 cfi_adjust_cfa_offset (8)
98
99 fxam
100 fnstsw
101 movb %ah, %dh
102 andb $0x45, %ah
103 cmpb $0x40, %ah
104 je 20f // x is ±0
105
106 cmpb $0x05, %ah
107 je 15f // x is ±inf
108
109 cmpb $0x01, %ah
110 je 32f // x is NaN
111
112 fxch // y : x
113
114 /* fistpll raises invalid exception for |y| >= 1L<<63. */
115 fld %st // y : y : x
116 fabs // |y| : y : x
117 fcompl MO(p63) // y : x
118 fnstsw
119 sahf
120 jnc 2f
121
122 /* First see whether `y' is a natural number. In this case we
123 can use a more precise algorithm. */
124 fld %st // y : y : x
125 fistpll (%esp) // y : x
126 fildll (%esp) // int(y) : y : x
127 fucomp %st(1) // y : x
128 fnstsw
129 sahf
130 je 9f
131
132 // If y has absolute value at most 0x1p-79, then any finite
133 // nonzero x will result in 1. Saturate y to those bounds to
134 // avoid underflow in the calculation of y*log2(x).
135 fld %st // y : y : x
136 fabs // |y| : y : x
137 fcompl MO(pm79) // y : x
138 fnstsw
139 sahf
140 jnc 3f
141 fstp %st(0) // pop y
142 fldl MO(pm79) // 0x1p-79 : x
143 testb $2, %dl
144 jnz 3f // y > 0
145 fchs // -0x1p-79 : x
146 jmp 3f
147
1489: /* OK, we have an integer value for y. Unless very small
149 (we use < 4), use the algorithm for real exponent to avoid
150 accumulation of errors. */
151 fld %st // y : y : x
152 fabs // |y| : y : x
153 fcompl MO(p2) // y : x
154 fnstsw
155 sahf
156 jnc 3f
157 popl %eax
158 cfi_adjust_cfa_offset (-4)
159 popl %edx
160 cfi_adjust_cfa_offset (-4)
161 orl $0, %edx
162 fstp %st(0) // x
163 jns 4f // y >= 0, jump
164 fdivrl MO(one) // 1/x (now referred to as x)
165 negl %eax
166 adcl $0, %edx
167 negl %edx
1684: fldl MO(one) // 1 : x
169 fxch
170
171 /* If y is even, take the absolute value of x. Otherwise,
172 ensure all intermediate values that might overflow have the
173 sign of x. */
174 testb $1, %al
175 jnz 6f
176 fabs
177
1786: shrdl $1, %edx, %eax
179 jnc 5f
180 fxch
181 fabs
182 fmul %st(1) // x : ST*x
183 fxch
1845: fld %st // x : x : ST*x
185 fabs // |x| : x : ST*x
186 fmulp // |x|*x : ST*x
187 shrl $1, %edx
188 movl %eax, %ecx
189 orl %edx, %ecx
190 jnz 6b
191 fstp %st(0) // ST*x
192#ifdef PIC
193 LOAD_PIC_REG (cx)
194#endif
195 LDBL_CHECK_FORCE_UFLOW_NONNAN
196 ret
197
198 /* y is ±NAN */
19930: fldt 4(%esp) // x : y
200 fldl MO(one) // 1.0 : x : y
201 fucomp %st(1) // x : y
202 fnstsw
203 sahf
204 je 33f
20531: /* At least one argument NaN, and result should be NaN. */
206 faddp
207 ret
20833: jp 31b
209 /* pow (1, NaN); check if the NaN signaling. */
210 testb $0x40, 23(%esp)
211 jz 31b
212 fstp %st(1)
213 ret
214
215 cfi_adjust_cfa_offset (8)
21632: addl $8, %esp
217 cfi_adjust_cfa_offset (-8)
218 faddp
219 ret
220
221 cfi_adjust_cfa_offset (8)
222 .align ALIGNARG(4)
2232: // y is a large integer (absolute value at least 1L<<63).
224 // If y has absolute value at least 1L<<78, then any finite
225 // nonzero x will result in 0 (underflow), 1 or infinity (overflow).
226 // Saturate y to those bounds to avoid overflow in the calculation
227 // of y*log2(x).
228 fld %st // y : y : x
229 fabs // |y| : y : x
230 fcompl MO(p78) // y : x
231 fnstsw
232 sahf
233 jc 3f
234 fstp %st(0) // pop y
235 fldl MO(p78) // 1L<<78 : x
236 testb $2, %dl
237 jz 3f // y > 0
238 fchs // -(1L<<78) : x
239 .align ALIGNARG(4)
2403: /* y is a real number. */
241 subl $28, %esp
242 cfi_adjust_cfa_offset (28)
243 fstpt 12(%esp) // x
244 fstpt (%esp) // <empty>
245 call HIDDEN_JUMPTARGET (__powl_helper) // <result>
246 addl $36, %esp
247 cfi_adjust_cfa_offset (-36)
248 ret
249
250 // pow(x,±0) = 1, unless x is sNaN
251 .align ALIGNARG(4)
25211: fstp %st(0) // pop y
253 fldt 4(%esp) // x
254 fxam
255 fnstsw
256 andb $0x45, %ah
257 cmpb $0x01, %ah
258 je 112f // x is NaN
259111: fstp %st(0)
260 fldl MO(one)
261 ret
262
263112: testb $0x40, 11(%esp)
264 jnz 111b
265 fadd %st(0)
266 ret
267
268 // y == ±inf
269 .align ALIGNARG(4)
27012: fstp %st(0) // pop y
271 fldl MO(one) // 1
272 fldt 4(%esp) // x : 1
273 fabs // abs(x) : 1
274 fucompp // < 1, == 1, or > 1
275 fnstsw
276 andb $0x45, %ah
277 cmpb $0x45, %ah
278 je 13f // jump if x is NaN
279
280 cmpb $0x40, %ah
281 je 14f // jump if |x| == 1
282
283 shlb $1, %ah
284 xorb %ah, %dl
285 andl $2, %edx
286 fldl MOX(inf_zero, %edx, 4)
287 ret
288
289 .align ALIGNARG(4)
29014: fldl MO(one)
291 ret
292
293 .align ALIGNARG(4)
29413: fldt 4(%esp) // load x == NaN
295 fadd %st(0)
296 ret
297
298 cfi_adjust_cfa_offset (8)
299 .align ALIGNARG(4)
300 // x is ±inf
30115: fstp %st(0) // y
302 testb $2, %dh
303 jz 16f // jump if x == +inf
304
305 // fistpll raises invalid exception for |y| >= 1L<<63, but y
306 // may be odd unless we know |y| >= 1L<<64.
307 fld %st // y : y
308 fabs // |y| : y
309 fcompl MO(p64) // y
310 fnstsw
311 sahf
312 jnc 16f
313 fldl MO(p63) // p63 : y
314 fxch // y : p63
315 fprem // y%p63 : p63
316 fstp %st(1) // y%p63
317
318 // We must find out whether y is an odd integer.
319 fld %st // y : y
320 fistpll (%esp) // y
321 fildll (%esp) // int(y) : y
322 fucompp // <empty>
323 fnstsw
324 sahf
325 jne 17f
326
327 // OK, the value is an integer, but is it odd?
328 popl %eax
329 cfi_adjust_cfa_offset (-4)
330 popl %edx
331 cfi_adjust_cfa_offset (-4)
332 andb $1, %al
333 jz 18f // jump if not odd
334 // It's an odd integer.
335 shrl $31, %edx
336 fldl MOX(minf_mzero, %edx, 8)
337 ret
338
339 cfi_adjust_cfa_offset (8)
340 .align ALIGNARG(4)
34116: fcompl MO(zero)
342 addl $8, %esp
343 cfi_adjust_cfa_offset (-8)
344 fnstsw
345 shrl $5, %eax
346 andl $8, %eax
347 fldl MOX(inf_zero, %eax, 1)
348 ret
349
350 cfi_adjust_cfa_offset (8)
351 .align ALIGNARG(4)
35217: shll $30, %edx // sign bit for y in right position
353 addl $8, %esp
354 cfi_adjust_cfa_offset (-8)
35518: shrl $31, %edx
356 fldl MOX(inf_zero, %edx, 8)
357 ret
358
359 cfi_adjust_cfa_offset (8)
360 .align ALIGNARG(4)
361 // x is ±0
36220: fstp %st(0) // y
363 testb $2, %dl
364 jz 21f // y > 0
365
366 // x is ±0 and y is < 0. We must find out whether y is an odd integer.
367 testb $2, %dh
368 jz 25f
369
370 // fistpll raises invalid exception for |y| >= 1L<<63, but y
371 // may be odd unless we know |y| >= 1L<<64.
372 fld %st // y : y
373 fabs // |y| : y
374 fcompl MO(p64) // y
375 fnstsw
376 sahf
377 jnc 25f
378 fldl MO(p63) // p63 : y
379 fxch // y : p63
380 fprem // y%p63 : p63
381 fstp %st(1) // y%p63
382
383 fld %st // y : y
384 fistpll (%esp) // y
385 fildll (%esp) // int(y) : y
386 fucompp // <empty>
387 fnstsw
388 sahf
389 jne 26f
390
391 // OK, the value is an integer, but is it odd?
392 popl %eax
393 cfi_adjust_cfa_offset (-4)
394 popl %edx
395 cfi_adjust_cfa_offset (-4)
396 andb $1, %al
397 jz 27f // jump if not odd
398 // It's an odd integer.
399 // Raise divide-by-zero exception and get minus infinity value.
400 fldl MO(one)
401 fdivl MO(zero)
402 fchs
403 ret
404
405 cfi_adjust_cfa_offset (8)
40625: fstp %st(0)
40726: addl $8, %esp
408 cfi_adjust_cfa_offset (-8)
40927: // Raise divide-by-zero exception and get infinity value.
410 fldl MO(one)
411 fdivl MO(zero)
412 ret
413
414 cfi_adjust_cfa_offset (8)
415 .align ALIGNARG(4)
416 // x is ±0 and y is > 0. We must find out whether y is an odd integer.
41721: testb $2, %dh
418 jz 22f
419
420 // fistpll raises invalid exception for |y| >= 1L<<63, but y
421 // may be odd unless we know |y| >= 1L<<64.
422 fld %st // y : y
423 fcompl MO(p64) // y
424 fnstsw
425 sahf
426 jnc 22f
427 fldl MO(p63) // p63 : y
428 fxch // y : p63
429 fprem // y%p63 : p63
430 fstp %st(1) // y%p63
431
432 fld %st // y : y
433 fistpll (%esp) // y
434 fildll (%esp) // int(y) : y
435 fucompp // <empty>
436 fnstsw
437 sahf
438 jne 23f
439
440 // OK, the value is an integer, but is it odd?
441 popl %eax
442 cfi_adjust_cfa_offset (-4)
443 popl %edx
444 cfi_adjust_cfa_offset (-4)
445 andb $1, %al
446 jz 24f // jump if not odd
447 // It's an odd integer.
448 fldl MO(mzero)
449 ret
450
451 cfi_adjust_cfa_offset (8)
45222: fstp %st(0)
45323: addl $8, %esp // Don't use 2 x pop
454 cfi_adjust_cfa_offset (-8)
45524: fldl MO(zero)
456 ret
457
458END(__ieee754_powl)
459libm_alias_finite (__ieee754_powl, __powl)
460

source code of glibc/sysdeps/i386/fpu/e_powl.S