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aa95fc13 1/* Optimized sinf(). PowerPC64/POWER8 version.
bfff8b1b 2 Copyright (C) 2016-2017 Free Software Foundation, Inc.
aa95fc13
AB		 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 <http://www.gnu.org/licenses/>. */
18
19#include <sysdep.h>
20#define _ERRNO_H 1
21#include <bits/errno.h>
22
23#define FRAMESIZE (FRAME_MIN_SIZE+16)
24
25#define FLOAT_EXPONENT_SHIFT 23
26#define FLOAT_EXPONENT_BIAS 127
27#define INTEGER_BITS 3
28
29#define PI_4 0x3f490fdb /* PI/4 */
30#define NINEPI_4 0x40e231d6 /* 9 * PI/4 */
31#define TWO_PN5 0x3d000000 /* 2^-5 */
32#define TWO_PN27 0x32000000 /* 2^-27 */
33#define INFINITY 0x7f800000
34#define TWO_P23 0x4b000000 /* 2^27 */
35#define FX_FRACTION_1_28 0x9249250 /* 0x100000000 / 28 + 1 */
36
37 /* Implements the function
38
39 float [fp1] sinf (float [fp1] x) */
40
41 .machine power8
42EALIGN(__sinf, 4, 0)
43 addis r9,r2,L(anchor)@toc@ha
44 addi r9,r9,L(anchor)@toc@l
45
46 lis r4,PI_4@h
47 ori r4,r4,PI_4@l
48
49 xscvdpspn v0,v1
50 mfvsrd r8,v0
51 rldicl r3,r8,32,33 /* Remove sign bit. */
52
53 cmpw r3,r4
54 bge L(greater_or_equal_pio4)
55
56 lis r4,TWO_PN5@h
57 ori r4,r4,TWO_PN5@l
58
59 cmpw r3,r4
60 blt L(less_2pn5)
61
62 /* Chebyshev polynomial of the form:
63 * x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
64
65 lfd fp9,(L(S0)-L(anchor))(r9)
66 lfd fp10,(L(S1)-L(anchor))(r9)
67 lfd fp11,(L(S2)-L(anchor))(r9)
68 lfd fp12,(L(S3)-L(anchor))(r9)
69 lfd fp13,(L(S4)-L(anchor))(r9)
70
71 fmul fp2,fp1,fp1 /* x^2 */
72 fmul fp3,fp2,fp1 /* x^3 */
73
74 fmadd fp4,fp2,fp13,fp12 /* S3+x^2*S4 */
75 fmadd fp4,fp2,fp4,fp11 /* S2+x^2*(S3+x^2*S4) */
76 fmadd fp4,fp2,fp4,fp10 /* S1+x^2*(S2+x^2*(S3+x^2*S4)) */
77 fmadd fp4,fp2,fp4,fp9 /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))) */
78 fmadd fp1,fp3,fp4,fp1 /* x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))) */
79 frsp fp1,fp1 /* Round to single precision. */
80
81 blr
82
83 .balign 16
84L(greater_or_equal_pio4):
85 lis r4,NINEPI_4@h
86 ori r4,r4,NINEPI_4@l
87 cmpw r3,r4
88 bge L(greater_or_equal_9pio4)
89
90 /* Calculate quotient of |x|/(PI/4). */
91 lfd fp2,(L(invpio4)-L(anchor))(r9)
92 fabs fp1,fp1 /* |x| */
93 fmul fp2,fp1,fp2 /* |x|/(PI/4) */
94 fctiduz fp2,fp2
95 mfvsrd r3,v2 /* n = |x| mod PI/4 */
96
97 /* Now use that quotient to find |x| mod (PI/2). */
98 addi r7,r3,1
99 rldicr r5,r7,2,60 /* ((n+1) >> 1) << 3 */
100 addi r6,r9,(L(pio2_table)-L(anchor))
101 lfdx fp4,r5,r6
102 fsub fp1,fp1,fp4
103
104 .balign 16
105L(reduced):
106 /* Now we are in the range -PI/4 to PI/4. */
107
108 /* Work out if we are in a positive or negative primary interval. */
109 rldicl r4,r7,62,63 /* ((n+1) >> 2) & 1 */
110
111 /* We are operating on |x|, so we need to add back the original
112 sign. */
113 rldicl r8,r8,33,63 /* (x >> 31) & 1, ie the sign bit. */
114 xor r4,r4,r8 /* 0 if result should be positive,
115 1 if negative. */
116
117 /* Load a 1.0 or -1.0. */
118 addi r5,r9,(L(ones)-L(anchor))
119 sldi r4,r4,3
120 lfdx fp0,r4,r5
121
122 /* Are we in the primary interval of sin or cos? */
123 andi. r4,r7,0x2
124 bne L(cos)
125
126 /* Chebyshev polynomial of the form:
127 x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
128
129 lfd fp9,(L(S0)-L(anchor))(r9)
130 lfd fp10,(L(S1)-L(anchor))(r9)
131 lfd fp11,(L(S2)-L(anchor))(r9)
132 lfd fp12,(L(S3)-L(anchor))(r9)
133 lfd fp13,(L(S4)-L(anchor))(r9)
134
135 fmul fp2,fp1,fp1 /* x^2 */
136 fmul fp3,fp2,fp1 /* x^3 */
137
138 fmadd fp4,fp2,fp13,fp12 /* S3+x^2*S4 */
139 fmadd fp4,fp2,fp4,fp11 /* S2+x^2*(S3+x^2*S4) */
140 fmadd fp4,fp2,fp4,fp10 /* S1+x^2*(S2+x^2*(S3+x^2*S4)) */
141 fmadd fp4,fp2,fp4,fp9 /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))) */
142 fmadd fp4,fp3,fp4,fp1 /* x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))) */
143 fmul fp4,fp4,fp0 /* Add in the sign. */
144 frsp fp1,fp4 /* Round to single precision. */
145
146 blr
147
148 .balign 16
149L(cos):
150 /* Chebyshev polynomial of the form:
151 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
152
153 lfd fp9,(L(C0)-L(anchor))(r9)
154 lfd fp10,(L(C1)-L(anchor))(r9)
155 lfd fp11,(L(C2)-L(anchor))(r9)
156 lfd fp12,(L(C3)-L(anchor))(r9)
157 lfd fp13,(L(C4)-L(anchor))(r9)
158
159 fmul fp2,fp1,fp1 /* x^2 */
160 lfd fp3,(L(DPone)-L(anchor))(r9)
161
162 fmadd fp4,fp2,fp13,fp12 /* C3+x^2*C4 */
163 fmadd fp4,fp2,fp4,fp11 /* C2+x^2*(C3+x^2*C4) */
164 fmadd fp4,fp2,fp4,fp10 /* C1+x^2*(C2+x^2*(C3+x^2*C4)) */
165 fmadd fp4,fp2,fp4,fp9 /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))) */
166 fmadd fp4,fp2,fp4,fp3 /* 1.0 + x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))) */
167 fmul fp4,fp4,fp0 /* Add in the sign. */
168 frsp fp1,fp4 /* Round to single precision. */
169
170 blr
171
172 .balign 16
173L(greater_or_equal_9pio4):
174 lis r4,INFINITY@h
175 ori r4,r4,INFINITY@l
176 cmpw r3,r4
177 bge L(inf_or_nan)
178
179 lis r4,TWO_P23@h
180 ori r4,r4,TWO_P23@l
181 cmpw r3,r4
182 bge L(greater_or_equal_2p23)
183
184 fabs fp1,fp1 /* |x| */
185
186 /* Calculate quotient of |x|/(PI/4). */
187 lfd fp2,(L(invpio4)-L(anchor))(r9)
188
189 lfd fp3,(L(DPone)-L(anchor))(r9)
190 lfd fp4,(L(DPhalf)-L(anchor))(r9)
191 fmul fp2,fp1,fp2 /* |x|/(PI/4) */
192 friz fp2,fp2 /* n = floor(|x|/(PI/4)) */
193
194 /* Calculate (n + 1) / 2. */
195 fadd fp2,fp2,fp3 /* n + 1 */
196 fmul fp3,fp2,fp4 /* (n + 1) / 2 */
197 friz fp3,fp3
198
199 lfd fp4,(L(pio2hi)-L(anchor))(r9)
200 lfd fp5,(L(pio2lo)-L(anchor))(r9)
201
202 fmul fp6,fp4,fp3
203 fadd fp6,fp6,fp1
204 fmadd fp1,fp5,fp3,fp6
205
206 fctiduz fp2,fp2
207 mfvsrd r7,v2 /* n + 1 */
208
209 b L(reduced)
210
211 .balign 16
212L(inf_or_nan):
213 bne L(skip_errno_setting) /* Is a NAN? */
214
215 /* We delayed the creation of the stack frame, as well as the saving of
216 the link register, because only at this point, we are sure that
217 doing so is actually needed. */
218
219 stfd fp1,-8(r1)
220
221 /* Save the link register. */
222 mflr r0
223 std r0,16(r1)
224 cfi_offset(lr, 16)
225
226 /* Create the stack frame. */
227 stdu r1,-FRAMESIZE(r1)
228 cfi_adjust_cfa_offset(FRAMESIZE)
229
230 bl JUMPTARGET(__errno_location)
231 nop
232
233 /* Restore the stack frame. */
234 addi r1,r1,FRAMESIZE
235 cfi_adjust_cfa_offset(-FRAMESIZE)
236 /* Restore the link register. */
237 ld r0,16(r1)
238 mtlr r0
239
240 lfd fp1,-8(r1)
241
242 /* errno = EDOM */
243 li r4,EDOM
244 stw r4,0(r3)
245
246L(skip_errno_setting):
247 fsub fp1,fp1,fp1 /* x - x */
248 blr
249
250 .balign 16
251L(greater_or_equal_2p23):
252 fabs fp1,fp1
253
254 srwi r4,r3,FLOAT_EXPONENT_SHIFT
255 subi r4,r4,FLOAT_EXPONENT_BIAS
256
257 /* We reduce the input modulo pi/4, so we need 3 bits of integer
258 to determine where in 2*pi we are. Index into our array
259 accordingly. */
260 addi r4,r4,INTEGER_BITS
261
262 /* To avoid an expensive divide, for the range we care about (0 - 127)
263 we can transform x/28 into:
264
265 x/28 = (x * ((0x100000000 / 28) + 1)) >> 32
266
267 mulhwu returns the top 32 bits of the 64 bit result, doing the
268 shift for us in the same instruction. The top 32 bits are undefined,
269 so we have to mask them. */
270
271 lis r6,FX_FRACTION_1_28@h
272 ori r6,r6,FX_FRACTION_1_28@l
273 mulhwu r5,r4,r6
274 clrldi r5,r5,32
275
276 /* Get our pointer into the invpio4_table array. */
277 sldi r4,r5,3
278 addi r6,r9,(L(invpio4_table)-L(anchor))
279 add r4,r4,r6
280
281 lfd fp2,0(r4)
282 lfd fp3,8(r4)
283 lfd fp4,16(r4)
284 lfd fp5,24(r4)
285
286 fmul fp6,fp2,fp1
287 fmul fp7,fp3,fp1
288 fmul fp8,fp4,fp1
289 fmul fp9,fp5,fp1
290
291 /* Mask off larger integer bits in highest double word that we don't
292 care about to avoid losing precision when combining with smaller
293 values. */
294 fctiduz fp10,fp6
295 mfvsrd r7,v10
296 rldicr r7,r7,0,(63-INTEGER_BITS)
297 mtvsrd v10,r7
298 fcfidu fp10,fp10 /* Integer bits. */
299
300 fsub fp6,fp6,fp10 /* highest -= integer bits */
301
302 /* Work out the integer component, rounded down. Use the top two
303 limbs for this. */
304 fadd fp10,fp6,fp7 /* highest + higher */
305
306 fctiduz fp10,fp10
307 mfvsrd r7,v10
308 andi. r0,r7,1
309 fcfidu fp10,fp10
310
311 /* Subtract integer component from highest limb. */
312 fsub fp12,fp6,fp10
313
314 beq L(even_integer)
315
316 /* Our integer component is odd, so we are in the -PI/4 to 0 primary
317 region. We need to shift our result down by PI/4, and to do this
318 in the mod (4/PI) space we simply subtract 1. */
319 lfd fp11,(L(DPone)-L(anchor))(r9)
320 fsub fp12,fp12,fp11
321
322 /* Now add up all the limbs in order. */
323 fadd fp12,fp12,fp7
324 fadd fp12,fp12,fp8
325 fadd fp12,fp12,fp9
326
327 /* And finally multiply by pi/4. */
328 lfd fp13,(L(pio4)-L(anchor))(r9)
329 fmul fp1,fp12,fp13
330
331 addi r7,r7,1
332 b L(reduced)
333
334L(even_integer):
335 lfd fp11,(L(DPone)-L(anchor))(r9)
336
337 /* Now add up all the limbs in order. */
338 fadd fp12,fp12,fp7
339 fadd fp12,r12,fp8
340 fadd fp12,r12,fp9
341
342 /* We need to check if the addition of all the limbs resulted in us
343 overflowing 1.0. */
344 fcmpu 0,fp12,fp11
345 bgt L(greater_than_one)
346
347 /* And finally multiply by pi/4. */
348 lfd fp13,(L(pio4)-L(anchor))(r9)
349 fmul fp1,fp12,fp13
350
351 addi r7,r7,1
352 b L(reduced)
353
354L(greater_than_one):
355 /* We did overflow 1.0 when adding up all the limbs. Add 1.0 to our
356 integer, and subtract 1.0 from our result. Since that makes the
357 integer component odd, we need to subtract another 1.0 as
358 explained above. */
359 addi r7,r7,1
360
361 lfd fp11,(L(DPtwo)-L(anchor))(r9)
362 fsub fp12,fp12,fp11
363
364 /* And finally multiply by pi/4. */
365 lfd fp13,(L(pio4)-L(anchor))(r9)
366 fmul fp1,fp12,fp13
367
368 addi r7,r7,1
369 b L(reduced)
370
371 .balign 16
372L(less_2pn5):
373 lis r4,TWO_PN27@h
374 ori r4,r4,TWO_PN27@l
375
376 cmpw r3,r4
377 blt L(less_2pn27)
378
379 /* A simpler Chebyshev approximation is close enough for this range:
380 x+x^3*(SS0+x^2*SS1). */
381
382 lfd fp10,(L(SS0)-L(anchor))(r9)
383 lfd fp11,(L(SS1)-L(anchor))(r9)
384
385 fmul fp2,fp1,fp1 /* x^2 */
386 fmul fp3,fp2,fp1 /* x^3 */
387
388 fmadd fp4,fp2,fp11,fp10 /* SS0+x^2*SS1 */
389 fmadd fp1,fp3,fp4,fp1 /* x+x^3*(SS0+x^2*SS1) */
390
391 frsp fp1,fp1 /* Round to single precision. */
392
393 blr
394
395 .balign 16
396L(less_2pn27):
397 cmpwi r3,0
398 beq L(zero)
399
400 /* Handle some special cases:
401
402 sinf(subnormal) raises inexact/underflow
403 sinf(min_normalized) raises inexact/underflow
404 sinf(normalized) raises inexact. */
405
406 lfd fp2,(L(small)-L(anchor))(r9)
407
408 fmul fp2,fp1,fp2 /* x * small */
409 fsub fp1,fp1,fp2 /* x - x * small */
410
411 frsp fp1,fp1
412
413 blr
414
415 .balign 16
416L(zero):
417 blr
418
419END (__sinf)
420
421 .section .rodata, "a"
422
423 .balign 8
424
425L(anchor):
426
427 /* Chebyshev constants for sin, range -PI/4 - PI/4. */
428L(S0): .8byte 0xbfc5555555551cd9
429L(S1): .8byte 0x3f81111110c2688b
430L(S2): .8byte 0xbf2a019f8b4bd1f9
431L(S3): .8byte 0x3ec71d7264e6b5b4
432L(S4): .8byte 0xbe5a947e1674b58a
433
434 /* Chebyshev constants for sin, range 2^-27 - 2^-5. */
435L(SS0): .8byte 0xbfc555555543d49d
436L(SS1): .8byte 0x3f8110f475cec8c5
437
438 /* Chebyshev constants for cos, range -PI/4 - PI/4. */
439L(C0): .8byte 0xbfdffffffffe98ae
440L(C1): .8byte 0x3fa55555545c50c7
441L(C2): .8byte 0xbf56c16b348b6874
442L(C3): .8byte 0x3efa00eb9ac43cc0
443L(C4): .8byte 0xbe923c97dd8844d7
444
445L(invpio2):
446 .8byte 0x3fe45f306dc9c883 /* 2/PI */
447
448L(invpio4):
449 .8byte 0x3ff45f306dc9c883 /* 4/PI */
450
451L(invpio4_table):
452 .8byte 0x0000000000000000
453 .8byte 0x3ff45f306c000000
454 .8byte 0x3e3c9c882a000000
455 .8byte 0x3c54fe13a8000000
456 .8byte 0x3aaf47d4d0000000
457 .8byte 0x38fbb81b6c000000
458 .8byte 0x3714acc9e0000000
459 .8byte 0x3560e4107c000000
460 .8byte 0x33bca2c756000000
461 .8byte 0x31fbd778ac000000
462 .8byte 0x300b7246e0000000
463 .8byte 0x2e5d2126e8000000
464 .8byte 0x2c97003248000000
465 .8byte 0x2ad77504e8000000
466 .8byte 0x290921cfe0000000
467 .8byte 0x274deb1cb0000000
468 .8byte 0x25829a73e0000000
469 .8byte 0x23fd1046be000000
470 .8byte 0x2224baed10000000
471 .8byte 0x20709d338e000000
472 .8byte 0x1e535a2f80000000
473 .8byte 0x1cef904e64000000
474 .8byte 0x1b0d639830000000
475 .8byte 0x1964ce7d24000000
476 .8byte 0x17b908bf16000000
477
478L(pio4):
479 .8byte 0x3fe921fb54442d18 /* PI/4 */
480
481/* PI/2 as a sum of two doubles. We only use 32 bits of the upper limb
482 to avoid losing significant bits when multiplying with up to
483 (2^22)/(pi/2). */
484L(pio2hi):
485 .8byte 0xbff921fb54400000
486
487L(pio2lo):
488 .8byte 0xbdd0b4611a626332
489
490L(pio2_table):
491 .8byte 0
492 .8byte 0x3ff921fb54442d18 /* 1 * PI/2 */
493 .8byte 0x400921fb54442d18 /* 2 * PI/2 */
494 .8byte 0x4012d97c7f3321d2 /* 3 * PI/2 */
495 .8byte 0x401921fb54442d18 /* 4 * PI/2 */
496 .8byte 0x401f6a7a2955385e /* 5 * PI/2 */
497 .8byte 0x4022d97c7f3321d2 /* 6 * PI/2 */
498 .8byte 0x4025fdbbe9bba775 /* 7 * PI/2 */
499 .8byte 0x402921fb54442d18 /* 8 * PI/2 */
500 .8byte 0x402c463abeccb2bb /* 9 * PI/2 */
501 .8byte 0x402f6a7a2955385e /* 10 * PI/2 */
502
503L(small):
504 .8byte 0x3cd0000000000000 /* 2^-50 */
505
506L(ones):
507 .8byte 0x3ff0000000000000 /* +1.0 */
508 .8byte 0xbff0000000000000 /* -1.0 */
509
510L(DPhalf):
511 .8byte 0x3fe0000000000000 /* 0.5 */
512
513L(DPone):
514 .8byte 0x3ff0000000000000 /* 1.0 */
515
516L(DPtwo):
517 .8byte 0x4000000000000000 /* 2.0 */
518
519weak_alias(__sinf, sinf)
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