1/* Function asinhf vectorized with SSE4.
2 Copyright (C) 2021-2024 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/*
20 * ALGORITHM DESCRIPTION:
21 *
22 * Compute asinh(x) as log(x + sqrt(x*x + 1))
23 *
24 * Special cases:
25 *
26 * asinh(NaN) = quiet NaN, and raise invalid exception
27 * asinh(INF) = that INF
28 * asinh(0) = that 0
29 *
30 */
31
32/* Offsets for data table __svml_sasinh_data_internal
33 */
34#define SgnMask 0
35#define sOne 16
36#define sPoly 32
37#define iBrkValue 160
38#define iOffExpoMask 176
39#define sBigThreshold 192
40#define sC2 208
41#define sC3 224
42#define sHalf 240
43#define sLargestFinite 256
44#define sLittleThreshold 272
45#define sSign 288
46#define sThirtyOne 304
47#define sTopMask11 320
48#define sTopMask8 336
49#define XScale 352
50#define sLn2 368
51
52#include <sysdep.h>
53
54 .section .text.sse4, "ax", @progbits
55ENTRY(_ZGVbN4v_asinhf_sse4)
56 subq $72, %rsp
57 cfi_def_cfa_offset(80)
58 movaps %xmm0, %xmm8
59
60 /*
61 * Split X into high and low parts, XHi (<= 11 bits) and XLo (<= 13 bits)
62 * We could use either X or |X| here, but it doesn't seem to matter
63 */
64 movups sTopMask11+__svml_sasinh_data_internal(%rip), %xmm10
65 movaps %xmm8, %xmm2
66 andps %xmm8, %xmm10
67
68 /*
69 * Compute X^2 = (XHi + XLo)^2 = XHi^2 + XLo * (X + XHi)
70 * The two parts are shifted off by around 11 bits. So even though
71 * the low bit will not in general be exact, it's near enough
72 */
73 movaps %xmm10, %xmm3
74 subps %xmm10, %xmm2
75 mulps %xmm10, %xmm3
76 addps %xmm8, %xmm10
77
78 /* Load the constant 1 and a sign mask */
79 movups sOne+__svml_sasinh_data_internal(%rip), %xmm7
80
81 /*
82 * Finally, express Y + W = X^2 + 1 accurately where Y has <= 8 bits.
83 * If |X| <= 1 then |XHi| <= 1 and so |X2Hi| <= 1, so we can treat 1
84 * as the dominant component in the compensated summation. Otherwise,
85 * if |X| >= 1, then since X2Hi only has 22 significant bits, the basic
86 * addition will be exact anyway until we get to |X| >= 2^24. But by
87 * that time the log function is well-conditioned enough that the
88 * rounding error doesn't matter. Hence we can treat 1 as dominant even
89 * if it literally isn't.
90 */
91 movaps %xmm7, %xmm11
92 movaps %xmm7, %xmm4
93 movups sTopMask8+__svml_sasinh_data_internal(%rip), %xmm12
94 addps %xmm3, %xmm11
95 mulps %xmm10, %xmm2
96 subps %xmm11, %xmm4
97 movaps %xmm12, %xmm0
98 addps %xmm3, %xmm4
99
100 /*
101 * Unfortunately, we can still be in trouble if |X| <= 2^-5, since
102 * the absolute error 2^-(7+24)-ish in sqrt(1 + X^2) gets scaled up
103 * by 1/X and comes close to our threshold. Hence if |X| <= 2^-4,
104 * perform an alternative computation
105 * sqrt(1 + X^2) - 1 = X^2/2 - X^4/8 + X^6/16
106 * X2 = X^2
107 */
108 addps %xmm2, %xmm3
109 addps %xmm2, %xmm4
110 andps %xmm11, %xmm0
111
112 /*
113 * Compute R = 1/sqrt(Y + W) * (1 + d)
114 * Force R to <= 8 significant bits.
115 * This means that R * Y and R^2 * Y are exactly representable.
116 */
117 rsqrtps %xmm0, %xmm14
118 subps %xmm0, %xmm11
119 andps %xmm12, %xmm14
120 addps %xmm11, %xmm4
121
122 /*
123 * Compute S = (Y/sqrt(Y + W)) * (1 + d)
124 * and T = (W/sqrt(Y + W)) * (1 + d)
125 * so that S + T = sqrt(Y + W) * (1 + d)
126 * S is exact, and the rounding error in T is OK.
127 */
128 mulps %xmm14, %xmm0
129 mulps %xmm14, %xmm4
130
131 /*
132 * Get the absolute value of the input, since we will exploit antisymmetry
133 * and mostly assume X >= 0 in the core computation
134 */
135 movups SgnMask+__svml_sasinh_data_internal(%rip), %xmm6
136
137 /*
138 * Compute e = -(2 * d + d^2)
139 * The first FMR is exact, and the rounding error in the other is acceptable
140 * since d and e are ~ 2^-8
141 */
142 movaps %xmm14, %xmm13
143 andps %xmm8, %xmm6
144
145 /*
146 * Obtain sqrt(1 + X^2) - 1 in two pieces
147 * sqrt(1 + X^2) - 1
148 * = sqrt(Y + W) - 1
149 * = (S + T) * (1 + Corr) - 1
150 * = [S - 1] + [T + (S + T) * Corr]
151 * We need a compensated summation for the last part. We treat S - 1
152 * as the larger part; it certainly is until about X < 2^-4, and in that
153 * case, the error is affordable since X dominates over sqrt(1 + X^2) - 1
154 * Final sum is dTmp5 (hi) + dTmp7 (lo)
155 */
156 movaps %xmm0, %xmm1
157
158 /*
159 * Check whether the input is finite, by checking |X| <= MaxFloat
160 * Otherwise set the rangemask so that the callout will get used.
161 * Note that this will also use the callout for NaNs since not(NaN <= MaxFloat)
162 */
163 movaps %xmm6, %xmm9
164
165 /*
166 * The following computation can go wrong for very large X, basically
167 * because X^2 overflows. But for large X we have
168 * asinh(X) / log(2 X) - 1 =~= 1/(4 * X^2), so for X >= 2^30
169 * we can just later stick X back into the log and tweak up the exponent.
170 * Actually we scale X by 2^-30 and tweak the exponent up by 31,
171 * to stay in the safe range for the later log computation.
172 * Compute a flag now telling us when do do this.
173 */
174 movaps %xmm6, %xmm5
175 cmpnleps sLargestFinite+__svml_sasinh_data_internal(%rip), %xmm9
176 cmpltps sBigThreshold+__svml_sasinh_data_internal(%rip), %xmm5
177 mulps %xmm0, %xmm13
178 addps %xmm4, %xmm1
179 subps %xmm7, %xmm0
180 mulps %xmm4, %xmm14
181 movmskps %xmm9, %edx
182 movaps %xmm7, %xmm9
183
184 /*
185 * Now 1 / (1 + d)
186 * = 1 / (1 + (sqrt(1 - e) - 1))
187 * = 1 / sqrt(1 - e)
188 * = 1 + 1/2 * e + 3/8 * e^2 + 5/16 * e^3 + 35/128 * e^4 + ...
189 * So compute the first three nonconstant terms of that, so that
190 * we have a relative correction (1 + Corr) to apply to S etc.
191 * C1 = 1/2
192 * C2 = 3/8
193 * C3 = 5/16
194 */
195 movups sC3+__svml_sasinh_data_internal(%rip), %xmm15
196 subps %xmm13, %xmm9
197 movups sHalf+__svml_sasinh_data_internal(%rip), %xmm10
198 subps %xmm14, %xmm9
199
200 /* sX2over2 = X^2/2 */
201 mulps %xmm10, %xmm3
202 mulps %xmm9, %xmm15
203
204 /* sX46 = -X^4/4 + X^6/8 */
205 movaps %xmm3, %xmm2
206 movaps %xmm3, %xmm12
207
208 /*
209 * Now do another compensated sum to add |X| + [sqrt(1 + X^2) - 1].
210 * It's always safe to assume |X| is larger.
211 * This is the final 2-part argument to the log1p function
212 */
213 movaps %xmm6, %xmm14
214 addps sC2+__svml_sasinh_data_internal(%rip), %xmm15
215 mulps %xmm9, %xmm15
216 addps %xmm10, %xmm15
217 mulps %xmm15, %xmm9
218 mulps %xmm1, %xmm9
219
220 /* Now multiplex to the case X = 2^-30 * input, Xl = sL = 0 in the "big" case. */
221 movups XScale+__svml_sasinh_data_internal(%rip), %xmm15
222 addps %xmm9, %xmm4
223 movaps %xmm4, %xmm11
224 addps %xmm0, %xmm11
225 subps %xmm11, %xmm0
226 addps %xmm0, %xmm4
227
228 /* sX4over4 = X^4/4 */
229 movaps %xmm3, %xmm0
230 mulps %xmm3, %xmm0
231 mulps %xmm0, %xmm2
232 subps %xmm0, %xmm2
233
234 /*
235 * Now we feed into the log1p code, using H in place of _VARG1 and
236 * also adding L into Xl.
237 * compute 1+x as high, low parts
238 */
239 movaps %xmm7, %xmm0
240
241 /* sX46over2 = -X^4/8 + x^6/16 */
242 mulps %xmm2, %xmm10
243 movaps %xmm7, %xmm2
244 addps %xmm10, %xmm12
245 subps %xmm12, %xmm3
246 addps %xmm3, %xmm10
247
248 /* Now multiplex the two possible computations */
249 movaps %xmm6, %xmm3
250 cmpleps sLittleThreshold+__svml_sasinh_data_internal(%rip), %xmm3
251 movaps %xmm3, %xmm13
252 andps %xmm3, %xmm12
253 andnps %xmm11, %xmm13
254 movaps %xmm3, %xmm1
255 orps %xmm12, %xmm13
256 andnps %xmm4, %xmm1
257 andps %xmm3, %xmm10
258 movaps %xmm6, %xmm4
259 orps %xmm10, %xmm1
260 addps %xmm13, %xmm14
261 mulps %xmm15, %xmm6
262 maxps %xmm14, %xmm0
263 minps %xmm14, %xmm2
264 subps %xmm14, %xmm4
265 movaps %xmm0, %xmm3
266 addps %xmm4, %xmm13
267 addps %xmm2, %xmm3
268 addps %xmm13, %xmm1
269 subps %xmm3, %xmm0
270 movaps %xmm5, %xmm4
271 andps %xmm5, %xmm3
272 andnps %xmm6, %xmm4
273 addps %xmm0, %xmm2
274
275 /*
276 * Now resume the main code.
277 * reduction: compute r, n
278 */
279 movdqu iBrkValue+__svml_sasinh_data_internal(%rip), %xmm6
280 orps %xmm3, %xmm4
281 psubd %xmm6, %xmm4
282 movaps %xmm7, %xmm0
283 addps %xmm2, %xmm1
284 movdqu iOffExpoMask+__svml_sasinh_data_internal(%rip), %xmm2
285 pand %xmm4, %xmm2
286 psrad $23, %xmm4
287 cvtdq2ps %xmm4, %xmm3
288 pslld $23, %xmm4
289 andps %xmm5, %xmm1
290 paddd %xmm6, %xmm2
291 psubd %xmm4, %xmm0
292 mulps %xmm0, %xmm1
293
294 /* polynomial evaluation */
295 subps %xmm7, %xmm2
296 movups sPoly+112+__svml_sasinh_data_internal(%rip), %xmm7
297 addps %xmm2, %xmm1
298 mulps %xmm1, %xmm7
299 movaps %xmm5, %xmm2
300
301 /* Add 31 to the exponent in the "large" case to get log(2 * input) */
302 movups sThirtyOne+__svml_sasinh_data_internal(%rip), %xmm0
303 addps sPoly+96+__svml_sasinh_data_internal(%rip), %xmm7
304 addps %xmm3, %xmm0
305 mulps %xmm1, %xmm7
306 andnps %xmm0, %xmm2
307 andps %xmm5, %xmm3
308 orps %xmm3, %xmm2
309 addps sPoly+80+__svml_sasinh_data_internal(%rip), %xmm7
310
311 /* final reconstruction */
312 mulps sLn2+__svml_sasinh_data_internal(%rip), %xmm2
313 mulps %xmm1, %xmm7
314
315 /* Finally, reincorporate the original sign. */
316 movups sSign+__svml_sasinh_data_internal(%rip), %xmm0
317 andps %xmm8, %xmm0
318 addps sPoly+64+__svml_sasinh_data_internal(%rip), %xmm7
319 mulps %xmm1, %xmm7
320 addps sPoly+48+__svml_sasinh_data_internal(%rip), %xmm7
321 mulps %xmm1, %xmm7
322 addps sPoly+32+__svml_sasinh_data_internal(%rip), %xmm7
323 mulps %xmm1, %xmm7
324 addps sPoly+16+__svml_sasinh_data_internal(%rip), %xmm7
325 mulps %xmm1, %xmm7
326 addps sPoly+__svml_sasinh_data_internal(%rip), %xmm7
327 mulps %xmm1, %xmm7
328 mulps %xmm1, %xmm7
329 addps %xmm7, %xmm1
330 addps %xmm2, %xmm1
331 pxor %xmm1, %xmm0
332 testl %edx, %edx
333
334 /* Go to special inputs processing branch */
335 jne L(SPECIAL_VALUES_BRANCH)
336 # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm8
337
338 /* Restore registers
339 * and exit the function
340 */
341
342L(EXIT):
343 addq $72, %rsp
344 cfi_def_cfa_offset(8)
345 ret
346 cfi_def_cfa_offset(80)
347
348 /* Branch to process
349 * special inputs
350 */
351
352L(SPECIAL_VALUES_BRANCH):
353 movups %xmm8, 32(%rsp)
354 movups %xmm0, 48(%rsp)
355 # LOE rbx rbp r12 r13 r14 r15 edx
356
357 xorl %eax, %eax
358 movq %r12, 16(%rsp)
359 cfi_offset(12, -64)
360 movl %eax, %r12d
361 movq %r13, 8(%rsp)
362 cfi_offset(13, -72)
363 movl %edx, %r13d
364 movq %r14, (%rsp)
365 cfi_offset(14, -80)
366 # LOE rbx rbp r15 r12d r13d
367
368 /* Range mask
369 * bits check
370 */
371
372L(RANGEMASK_CHECK):
373 btl %r12d, %r13d
374
375 /* Call scalar math function */
376 jc L(SCALAR_MATH_CALL)
377 # LOE rbx rbp r15 r12d r13d
378
379 /* Special inputs
380 * processing loop
381 */
382
383L(SPECIAL_VALUES_LOOP):
384 incl %r12d
385 cmpl $4, %r12d
386
387 /* Check bits in range mask */
388 jl L(RANGEMASK_CHECK)
389 # LOE rbx rbp r15 r12d r13d
390
391 movq 16(%rsp), %r12
392 cfi_restore(12)
393 movq 8(%rsp), %r13
394 cfi_restore(13)
395 movq (%rsp), %r14
396 cfi_restore(14)
397 movups 48(%rsp), %xmm0
398
399 /* Go to exit */
400 jmp L(EXIT)
401 cfi_offset(12, -64)
402 cfi_offset(13, -72)
403 cfi_offset(14, -80)
404 # LOE rbx rbp r12 r13 r14 r15 xmm0
405
406 /* Scalar math function call
407 * to process special input
408 */
409
410L(SCALAR_MATH_CALL):
411 movl %r12d, %r14d
412 movss 32(%rsp, %r14, 4), %xmm0
413 call asinhf@PLT
414 # LOE rbx rbp r14 r15 r12d r13d xmm0
415
416 movss %xmm0, 48(%rsp, %r14, 4)
417
418 /* Process special inputs in loop */
419 jmp L(SPECIAL_VALUES_LOOP)
420 # LOE rbx rbp r15 r12d r13d
421END(_ZGVbN4v_asinhf_sse4)
422
423 .section .rodata, "a"
424 .align 16
425
426#ifdef __svml_sasinh_data_internal_typedef
427typedef unsigned int VUINT32;
428typedef struct {
429 __declspec(align(16)) VUINT32 SgnMask[4][1];
430 __declspec(align(16)) VUINT32 sOne[4][1];
431 __declspec(align(16)) VUINT32 sPoly[8][4][1];
432 __declspec(align(16)) VUINT32 iBrkValue[4][1];
433 __declspec(align(16)) VUINT32 iOffExpoMask[4][1];
434 __declspec(align(16)) VUINT32 sBigThreshold[4][1];
435 __declspec(align(16)) VUINT32 sC2[4][1];
436 __declspec(align(16)) VUINT32 sC3[4][1];
437 __declspec(align(16)) VUINT32 sHalf[4][1];
438 __declspec(align(16)) VUINT32 sLargestFinite[4][1];
439 __declspec(align(16)) VUINT32 sLittleThreshold[4][1];
440 __declspec(align(16)) VUINT32 sSign[4][1];
441 __declspec(align(16)) VUINT32 sThirtyOne[4][1];
442 __declspec(align(16)) VUINT32 sTopMask11[4][1];
443 __declspec(align(16)) VUINT32 sTopMask8[4][1];
444 __declspec(align(16)) VUINT32 XScale[4][1];
445 __declspec(align(16)) VUINT32 sLn2[4][1];
446} __svml_sasinh_data_internal;
447#endif
448__svml_sasinh_data_internal:
449 /* SgnMask */
450 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
451 /* sOne = SP 1.0 */
452 .align 16
453 .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
454 /* sPoly[] = SP polynomial */
455 .align 16
456 .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
457 .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
458 .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
459 .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
460 .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
461 .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
462 .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
463 .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
464 /* iBrkValue = SP 2/3 */
465 .align 16
466 .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
467 /* iOffExpoMask = SP significand mask */
468 .align 16
469 .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
470 /* sBigThreshold */
471 .align 16
472 .long 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000
473 /* sC2 */
474 .align 16
475 .long 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000
476 /* sC3 */
477 .align 16
478 .long 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000
479 /* sHalf */
480 .align 16
481 .long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
482 /* sLargestFinite */
483 .align 16
484 .long 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF
485 /* sLittleThreshold */
486 .align 16
487 .long 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000
488 /* sSign */
489 .align 16
490 .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
491 /* sThirtyOne */
492 .align 16
493 .long 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000
494 /* sTopMask11 */
495 .align 16
496 .long 0xFFFFE000, 0xFFFFE000, 0xFFFFE000, 0xFFFFE000
497 /* sTopMask8 */
498 .align 16
499 .long 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000
500 /* XScale */
501 .align 16
502 .long 0x30800000, 0x30800000, 0x30800000, 0x30800000
503 /* sLn2 = SP ln(2) */
504 .align 16
505 .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
506 .align 16
507 .type __svml_sasinh_data_internal, @object
508 .size __svml_sasinh_data_internal, .-__svml_sasinh_data_internal
509

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_s_asinhf4_core_sse4.S