1 | /* Function acoshf 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 acosh(x) as log(x + sqrt(x*x - 1)) |
23 | * |
24 | * Special cases: |
25 | * |
26 | * acosh(NaN) = quiet NaN, and raise invalid exception |
27 | * acosh(-INF) = NaN |
28 | * acosh(+INF) = +INF |
29 | * acosh(x) = NaN if x < 1 |
30 | * acosh(1) = +0 |
31 | * |
32 | */ |
33 | |
34 | /* Offsets for data table __svml_sacosh_data_internal |
35 | */ |
36 | #define sOne 0 |
37 | #define sPoly 16 |
38 | #define iBrkValue 144 |
39 | #define iOffExpoMask 160 |
40 | #define sBigThreshold 176 |
41 | #define sC2 192 |
42 | #define sC3 208 |
43 | #define sHalf 224 |
44 | #define sLargestFinite 240 |
45 | #define sThirtyOne 256 |
46 | #define sTopMask8 272 |
47 | #define XScale 288 |
48 | #define sLn2 304 |
49 | |
50 | #include <sysdep.h> |
51 | |
52 | .section .text.sse4, "ax" , @progbits |
53 | ENTRY(_ZGVbN4v_acoshf_sse4) |
54 | subq $72, %rsp |
55 | cfi_def_cfa_offset(80) |
56 | |
57 | /* Compute U = X - 1 and V = X + 1, naively first. */ |
58 | movaps %xmm0, %xmm12 |
59 | |
60 | /* Load constants, always including One = 1 */ |
61 | movups sOne+__svml_sacosh_data_internal(%rip), %xmm2 |
62 | |
63 | /* |
64 | * Check that 1 < X < +inf; otherwise go to the callout function. |
65 | * We need the callout for X = 1 to avoid division by zero below. |
66 | * This test ensures that callout handles NaN and either infinity. |
67 | */ |
68 | movaps %xmm0, %xmm4 |
69 | movaps %xmm2, %xmm9 |
70 | |
71 | /* |
72 | * Compute e = -(2 * d + d^2) |
73 | * The first FMR is exact, and the rounding error in the other is acceptable |
74 | * since d and e are ~ 2^-8 |
75 | */ |
76 | movaps %xmm2, %xmm10 |
77 | |
78 | /* Finally, express Y + W = U * V accurately where Y has <= 8 bits */ |
79 | movups sTopMask8+__svml_sacosh_data_internal(%rip), %xmm5 |
80 | |
81 | /* |
82 | * Now we feed into the log1p code, using H in place of _VARG1 and |
83 | * also adding L into Xl. |
84 | * compute 1+x as high, low parts |
85 | */ |
86 | movaps %xmm2, %xmm13 |
87 | movaps %xmm5, %xmm11 |
88 | movaps %xmm2, %xmm3 |
89 | |
90 | /* |
91 | * Now 1 / (1 + d) |
92 | * = 1 / (1 + (sqrt(1 - e) - 1)) |
93 | * = 1 / sqrt(1 - e) |
94 | * = 1 + 1/2 * e + 3/8 * e^2 + 5/16 * e^3 + 35/128 * e^4 + ... |
95 | * So compute the first three nonconstant terms of that, so that |
96 | * we have a relative correction (1 + Corr) to apply to S etc. |
97 | * C1 = 1/2 |
98 | * C2 = 3/8 |
99 | * C3 = 5/16 |
100 | */ |
101 | movups sC3+__svml_sacosh_data_internal(%rip), %xmm8 |
102 | |
103 | /* |
104 | * The following computation can go wrong for very large X, e.g. |
105 | * the X^2 - 1 = U * V can overflow. But for large X we have |
106 | * acosh(X) / log(2 X) - 1 =~= 1/(4 * X^2), so for X >= 2^30 |
107 | * we can just later stick X back into the log and tweak up the exponent. |
108 | * Actually we scale X by 2^-30 and tweak the exponent up by 31, |
109 | * to stay in the safe range for the later log computation. |
110 | * Compute a flag now telling us when to do this. |
111 | */ |
112 | movaps %xmm0, %xmm1 |
113 | cmpnleps sLargestFinite+__svml_sacosh_data_internal(%rip), %xmm4 |
114 | cmpltps sBigThreshold+__svml_sacosh_data_internal(%rip), %xmm1 |
115 | cmpnltps %xmm0, %xmm3 |
116 | subps %xmm2, %xmm12 |
117 | addps %xmm0, %xmm9 |
118 | |
119 | /* For low-accuracy versions, naivety is harmless */ |
120 | mulps %xmm12, %xmm9 |
121 | orps %xmm3, %xmm4 |
122 | movmskps %xmm4, %edx |
123 | andps %xmm9, %xmm11 |
124 | movaps %xmm1, %xmm3 |
125 | |
126 | /* |
127 | * Compute R = 1/sqrt(Y + W) * (1 + d) |
128 | * Force R to <= 8 significant bits. |
129 | * This means that R * Y and R^2 * Y are exactly representable. |
130 | */ |
131 | rsqrtps %xmm11, %xmm7 |
132 | subps %xmm11, %xmm9 |
133 | andps %xmm5, %xmm7 |
134 | movaps %xmm2, %xmm4 |
135 | |
136 | /* |
137 | * Compute S = (Y/sqrt(Y + W)) * (1 + d) |
138 | * and T = (W/sqrt(Y + W)) * (1 + d) |
139 | * so that S + T = sqrt(Y + W) * (1 + d) |
140 | * S is exact, and the rounding error in T is OK. |
141 | */ |
142 | mulps %xmm7, %xmm11 |
143 | movaps %xmm7, %xmm6 |
144 | mulps %xmm7, %xmm9 |
145 | mulps %xmm11, %xmm6 |
146 | mulps %xmm9, %xmm7 |
147 | |
148 | /* |
149 | * For low-accuracy versions, the computation can be done |
150 | * just as U + ((S + T) + (S + T) * Corr) |
151 | */ |
152 | addps %xmm9, %xmm11 |
153 | subps %xmm6, %xmm10 |
154 | movaps %xmm2, %xmm9 |
155 | subps %xmm7, %xmm10 |
156 | mulps %xmm10, %xmm8 |
157 | |
158 | /* Now multiplex to the case X = 2^-30 * input, Xl = 0 in the "big" case. */ |
159 | movups XScale+__svml_sacosh_data_internal(%rip), %xmm14 |
160 | mulps %xmm0, %xmm14 |
161 | addps sC2+__svml_sacosh_data_internal(%rip), %xmm8 |
162 | mulps %xmm10, %xmm8 |
163 | andnps %xmm14, %xmm3 |
164 | |
165 | /* |
166 | * Now resume the main code. |
167 | * reduction: compute r, n |
168 | */ |
169 | movdqu iBrkValue+__svml_sacosh_data_internal(%rip), %xmm14 |
170 | movdqu iOffExpoMask+__svml_sacosh_data_internal(%rip), %xmm5 |
171 | |
172 | /* Add 31 to the exponent in the "large" case to get log(2 * input) */ |
173 | movups sThirtyOne+__svml_sacosh_data_internal(%rip), %xmm6 |
174 | addps sHalf+__svml_sacosh_data_internal(%rip), %xmm8 |
175 | mulps %xmm8, %xmm10 |
176 | movaps %xmm1, %xmm8 |
177 | mulps %xmm11, %xmm10 |
178 | addps %xmm10, %xmm11 |
179 | addps %xmm11, %xmm12 |
180 | maxps %xmm12, %xmm13 |
181 | minps %xmm12, %xmm9 |
182 | movaps %xmm13, %xmm15 |
183 | addps %xmm9, %xmm15 |
184 | subps %xmm15, %xmm13 |
185 | andps %xmm1, %xmm15 |
186 | orps %xmm15, %xmm3 |
187 | addps %xmm13, %xmm9 |
188 | psubd %xmm14, %xmm3 |
189 | andps %xmm1, %xmm9 |
190 | pand %xmm3, %xmm5 |
191 | psrad $23, %xmm3 |
192 | cvtdq2ps %xmm3, %xmm7 |
193 | pslld $23, %xmm3 |
194 | paddd %xmm14, %xmm5 |
195 | psubd %xmm3, %xmm4 |
196 | |
197 | /* polynomial evaluation */ |
198 | subps %xmm2, %xmm5 |
199 | mulps %xmm4, %xmm9 |
200 | addps %xmm7, %xmm6 |
201 | movups sPoly+112+__svml_sacosh_data_internal(%rip), %xmm2 |
202 | andnps %xmm6, %xmm8 |
203 | andps %xmm1, %xmm7 |
204 | addps %xmm5, %xmm9 |
205 | mulps %xmm9, %xmm2 |
206 | orps %xmm7, %xmm8 |
207 | |
208 | /* final reconstruction */ |
209 | mulps sLn2+__svml_sacosh_data_internal(%rip), %xmm8 |
210 | addps sPoly+96+__svml_sacosh_data_internal(%rip), %xmm2 |
211 | mulps %xmm9, %xmm2 |
212 | addps sPoly+80+__svml_sacosh_data_internal(%rip), %xmm2 |
213 | mulps %xmm9, %xmm2 |
214 | addps sPoly+64+__svml_sacosh_data_internal(%rip), %xmm2 |
215 | mulps %xmm9, %xmm2 |
216 | addps sPoly+48+__svml_sacosh_data_internal(%rip), %xmm2 |
217 | mulps %xmm9, %xmm2 |
218 | addps sPoly+32+__svml_sacosh_data_internal(%rip), %xmm2 |
219 | mulps %xmm9, %xmm2 |
220 | addps sPoly+16+__svml_sacosh_data_internal(%rip), %xmm2 |
221 | mulps %xmm9, %xmm2 |
222 | addps sPoly+__svml_sacosh_data_internal(%rip), %xmm2 |
223 | mulps %xmm9, %xmm2 |
224 | mulps %xmm9, %xmm2 |
225 | addps %xmm2, %xmm9 |
226 | addps %xmm8, %xmm9 |
227 | testl %edx, %edx |
228 | |
229 | /* Go to special inputs processing branch */ |
230 | jne L(SPECIAL_VALUES_BRANCH) |
231 | # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm9 |
232 | |
233 | /* Restore registers |
234 | * and exit the function |
235 | */ |
236 | |
237 | L(EXIT): |
238 | movaps %xmm9, %xmm0 |
239 | addq $72, %rsp |
240 | cfi_def_cfa_offset(8) |
241 | ret |
242 | cfi_def_cfa_offset(80) |
243 | |
244 | /* Branch to process |
245 | * special inputs |
246 | */ |
247 | |
248 | L(SPECIAL_VALUES_BRANCH): |
249 | movups %xmm0, 32(%rsp) |
250 | movups %xmm9, 48(%rsp) |
251 | # LOE rbx rbp r12 r13 r14 r15 edx |
252 | |
253 | xorl %eax, %eax |
254 | movq %r12, 16(%rsp) |
255 | cfi_offset(12, -64) |
256 | movl %eax, %r12d |
257 | movq %r13, 8(%rsp) |
258 | cfi_offset(13, -72) |
259 | movl %edx, %r13d |
260 | movq %r14, (%rsp) |
261 | cfi_offset(14, -80) |
262 | # LOE rbx rbp r15 r12d r13d |
263 | |
264 | /* Range mask |
265 | * bits check |
266 | */ |
267 | |
268 | L(RANGEMASK_CHECK): |
269 | btl %r12d, %r13d |
270 | |
271 | /* Call scalar math function */ |
272 | jc L(SCALAR_MATH_CALL) |
273 | # LOE rbx rbp r15 r12d r13d |
274 | |
275 | /* Special inputs |
276 | * processing loop |
277 | */ |
278 | |
279 | L(SPECIAL_VALUES_LOOP): |
280 | incl %r12d |
281 | cmpl $4, %r12d |
282 | |
283 | /* Check bits in range mask */ |
284 | jl L(RANGEMASK_CHECK) |
285 | # LOE rbx rbp r15 r12d r13d |
286 | |
287 | movq 16(%rsp), %r12 |
288 | cfi_restore(12) |
289 | movq 8(%rsp), %r13 |
290 | cfi_restore(13) |
291 | movq (%rsp), %r14 |
292 | cfi_restore(14) |
293 | movups 48(%rsp), %xmm9 |
294 | |
295 | /* Go to exit */ |
296 | jmp L(EXIT) |
297 | cfi_offset(12, -64) |
298 | cfi_offset(13, -72) |
299 | cfi_offset(14, -80) |
300 | # LOE rbx rbp r12 r13 r14 r15 xmm9 |
301 | |
302 | /* Scalar math function call |
303 | * to process special input |
304 | */ |
305 | |
306 | L(SCALAR_MATH_CALL): |
307 | movl %r12d, %r14d |
308 | movss 32(%rsp, %r14, 4), %xmm0 |
309 | call acoshf@PLT |
310 | # LOE rbx rbp r14 r15 r12d r13d xmm0 |
311 | |
312 | movss %xmm0, 48(%rsp, %r14, 4) |
313 | |
314 | /* Process special inputs in loop */ |
315 | jmp L(SPECIAL_VALUES_LOOP) |
316 | # LOE rbx rbp r15 r12d r13d |
317 | END(_ZGVbN4v_acoshf_sse4) |
318 | |
319 | .section .rodata, "a" |
320 | .align 16 |
321 | |
322 | #ifdef __svml_sacosh_data_internal_typedef |
323 | typedef unsigned int VUINT32; |
324 | typedef struct { |
325 | __declspec(align(16)) VUINT32 sOne[4][1]; |
326 | __declspec(align(16)) VUINT32 sPoly[8][4][1]; |
327 | __declspec(align(16)) VUINT32 iBrkValue[4][1]; |
328 | __declspec(align(16)) VUINT32 iOffExpoMask[4][1]; |
329 | __declspec(align(16)) VUINT32 sBigThreshold[4][1]; |
330 | __declspec(align(16)) VUINT32 sC2[4][1]; |
331 | __declspec(align(16)) VUINT32 sC3[4][1]; |
332 | __declspec(align(16)) VUINT32 sHalf[4][1]; |
333 | __declspec(align(16)) VUINT32 sLargestFinite[4][1]; |
334 | __declspec(align(16)) VUINT32 sThirtyOne[4][1]; |
335 | __declspec(align(16)) VUINT32 sTopMask8[4][1]; |
336 | __declspec(align(16)) VUINT32 XScale[4][1]; |
337 | __declspec(align(16)) VUINT32 sLn2[4][1]; |
338 | } __svml_sacosh_data_internal; |
339 | #endif |
340 | __svml_sacosh_data_internal: |
341 | /* sOne = SP 1.0 */ |
342 | .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 |
343 | /* sPoly[] = SP polynomial */ |
344 | .align 16 |
345 | .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */ |
346 | .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */ |
347 | .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */ |
348 | .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */ |
349 | .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */ |
350 | .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */ |
351 | .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */ |
352 | .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */ |
353 | /* iBrkValue = SP 2/3 */ |
354 | .align 16 |
355 | .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab |
356 | /* iOffExpoMask = SP significand mask */ |
357 | .align 16 |
358 | .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff |
359 | /* sBigThreshold */ |
360 | .align 16 |
361 | .long 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000 |
362 | /* sC2 */ |
363 | .align 16 |
364 | .long 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000 |
365 | /* sC3 */ |
366 | .align 16 |
367 | .long 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000 |
368 | /* sHalf */ |
369 | .align 16 |
370 | .long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000 |
371 | /* sLargestFinite */ |
372 | .align 16 |
373 | .long 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF |
374 | /* sThirtyOne */ |
375 | .align 16 |
376 | .long 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000 |
377 | /* sTopMask8 */ |
378 | .align 16 |
379 | .long 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000 |
380 | /* XScale */ |
381 | .align 16 |
382 | .long 0x30800000, 0x30800000, 0x30800000, 0x30800000 |
383 | /* sLn2 = SP ln(2) */ |
384 | .align 16 |
385 | .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 |
386 | .align 16 |
387 | .type __svml_sacosh_data_internal, @object |
388 | .size __svml_sacosh_data_internal, .-__svml_sacosh_data_internal |
389 | |