1 | /* Function acoshf vectorized with AVX2. |
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 32 |
38 | #define iBrkValue 288 |
39 | #define iOffExpoMask 320 |
40 | #define sBigThreshold 352 |
41 | #define sC2 384 |
42 | #define sC3 416 |
43 | #define sHalf 448 |
44 | #define sLargestFinite 480 |
45 | #define sThirtyOne 512 |
46 | #define sTopMask8 544 |
47 | #define XScale 576 |
48 | #define sLn2 608 |
49 | |
50 | #include <sysdep.h> |
51 | |
52 | .section .text.avx2, "ax" , @progbits |
53 | ENTRY(_ZGVdN8v_acoshf_avx2) |
54 | pushq %rbp |
55 | cfi_def_cfa_offset(16) |
56 | movq %rsp, %rbp |
57 | cfi_def_cfa(6, 16) |
58 | cfi_offset(6, -16) |
59 | andq $-32, %rsp |
60 | subq $96, %rsp |
61 | |
62 | /* Load constants, always including One = 1 */ |
63 | vmovups sOne+__svml_sacosh_data_internal(%rip), %ymm2 |
64 | |
65 | /* Finally, express Y + W = U * V accurately where Y has <= 8 bits */ |
66 | vmovups sTopMask8+__svml_sacosh_data_internal(%rip), %ymm9 |
67 | |
68 | /* |
69 | * Now 1 / (1 + d) |
70 | * = 1 / (1 + (sqrt(1 - e) - 1)) |
71 | * = 1 / sqrt(1 - e) |
72 | * = 1 + 1/2 * e + 3/8 * e^2 + 5/16 * e^3 + 35/128 * e^4 + ... |
73 | * So compute the first three nonconstant terms of that, so that |
74 | * we have a relative correction (1 + Corr) to apply to S etc. |
75 | * C1 = 1/2 |
76 | * C2 = 3/8 |
77 | * C3 = 5/16 |
78 | */ |
79 | vmovups sC3+__svml_sacosh_data_internal(%rip), %ymm14 |
80 | vmovaps %ymm0, %ymm3 |
81 | vmovaps %ymm2, %ymm7 |
82 | vfmsub231ps %ymm3, %ymm3, %ymm7 |
83 | |
84 | /* |
85 | * Check that 1 < X < +inf; otherwise go to the callout function. |
86 | * We need the callout for X = 1 to avoid division by zero below. |
87 | * This test ensures that callout handles NaN and either infinity. |
88 | */ |
89 | vcmpnle_uqps sLargestFinite+__svml_sacosh_data_internal(%rip), %ymm3, %ymm4 |
90 | vcmpngt_uqps %ymm2, %ymm3, %ymm5 |
91 | |
92 | /* |
93 | * The following computation can go wrong for very large X, e.g. |
94 | * the X^2 - 1 = U * V can overflow. But for large X we have |
95 | * acosh(X) / log(2 X) - 1 =~= 1/(4 * X^2), so for X >= 2^30 |
96 | * we can just later stick X back into the log and tweak up the exponent. |
97 | * Actually we scale X by 2^-30 and tweak the exponent up by 31, |
98 | * to stay in the safe range for the later log computation. |
99 | * Compute a flag now telling us when to do this. |
100 | */ |
101 | vcmplt_oqps sBigThreshold+__svml_sacosh_data_internal(%rip), %ymm3, %ymm1 |
102 | vandps %ymm9, %ymm7, %ymm10 |
103 | |
104 | /* |
105 | * Compute R = 1/sqrt(Y + W) * (1 + d) |
106 | * Force R to <= 8 significant bits. |
107 | * This means that R * Y and R^2 * Y are exactly representable. |
108 | */ |
109 | vrsqrtps %ymm10, %ymm8 |
110 | vsubps %ymm10, %ymm7, %ymm11 |
111 | vandps %ymm9, %ymm8, %ymm12 |
112 | |
113 | /* |
114 | * Compute S = (Y/sqrt(Y + W)) * (1 + d) |
115 | * and T = (W/sqrt(Y + W)) * (1 + d) |
116 | * so that S + T = sqrt(Y + W) * (1 + d) |
117 | * S is exact, and the rounding error in T is OK. |
118 | */ |
119 | vmulps %ymm12, %ymm10, %ymm15 |
120 | vmulps %ymm11, %ymm12, %ymm0 |
121 | |
122 | /* Now multiplex to the case X = 2^-30 * input, Xl = 0 in the "big" case. */ |
123 | vmulps XScale+__svml_sacosh_data_internal(%rip), %ymm3, %ymm11 |
124 | |
125 | /* |
126 | * Compute e = -(2 * d + d^2) |
127 | * The first FMR is exact, and the rounding error in the other is acceptable |
128 | * since d and e are ~ 2^-8 |
129 | */ |
130 | vmovaps %ymm2, %ymm13 |
131 | vfnmadd231ps %ymm15, %ymm12, %ymm13 |
132 | vfnmadd231ps %ymm0, %ymm12, %ymm13 |
133 | vfmadd213ps sC2+__svml_sacosh_data_internal(%rip), %ymm13, %ymm14 |
134 | vfmadd213ps sHalf+__svml_sacosh_data_internal(%rip), %ymm13, %ymm14 |
135 | vmulps %ymm14, %ymm13, %ymm7 |
136 | vorps %ymm5, %ymm4, %ymm6 |
137 | |
138 | /* |
139 | * For low-accuracy versions, the computation can be done |
140 | * just as U + ((S + T) + (S + T) * Corr) |
141 | */ |
142 | vaddps %ymm0, %ymm15, %ymm5 |
143 | |
144 | /* sU is needed later on */ |
145 | vsubps %ymm2, %ymm3, %ymm4 |
146 | vfmadd213ps %ymm5, %ymm7, %ymm5 |
147 | vmovmskps %ymm6, %edx |
148 | vaddps %ymm5, %ymm4, %ymm6 |
149 | |
150 | /* |
151 | * Now resume the main code. |
152 | * reduction: compute r, n |
153 | */ |
154 | vmovups iBrkValue+__svml_sacosh_data_internal(%rip), %ymm4 |
155 | |
156 | /* |
157 | * Now we feed into the log1p code, using H in place of _VARG1 and |
158 | * also adding L into Xl. |
159 | * compute 1+x as high, low parts |
160 | */ |
161 | vmaxps %ymm6, %ymm2, %ymm8 |
162 | vminps %ymm6, %ymm2, %ymm9 |
163 | vaddps %ymm9, %ymm8, %ymm12 |
164 | vblendvps %ymm1, %ymm12, %ymm11, %ymm14 |
165 | vsubps %ymm12, %ymm8, %ymm10 |
166 | vpsubd %ymm4, %ymm14, %ymm15 |
167 | vaddps %ymm10, %ymm9, %ymm13 |
168 | vpand iOffExpoMask+__svml_sacosh_data_internal(%rip), %ymm15, %ymm14 |
169 | vpsrad $23, %ymm15, %ymm15 |
170 | vpaddd %ymm4, %ymm14, %ymm8 |
171 | vpslld $23, %ymm15, %ymm5 |
172 | vmovups sPoly+224+__svml_sacosh_data_internal(%rip), %ymm4 |
173 | vcvtdq2ps %ymm15, %ymm0 |
174 | vpsubd %ymm5, %ymm2, %ymm7 |
175 | |
176 | /* polynomial evaluation */ |
177 | vsubps %ymm2, %ymm8, %ymm2 |
178 | |
179 | /* Add 31 to the exponent in the "large" case to get log(2 * input) */ |
180 | vaddps sThirtyOne+__svml_sacosh_data_internal(%rip), %ymm0, %ymm5 |
181 | vandps %ymm1, %ymm13, %ymm6 |
182 | vmulps %ymm7, %ymm6, %ymm9 |
183 | vblendvps %ymm1, %ymm0, %ymm5, %ymm0 |
184 | vaddps %ymm2, %ymm9, %ymm2 |
185 | vfmadd213ps sPoly+192+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 |
186 | vfmadd213ps sPoly+160+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 |
187 | vfmadd213ps sPoly+128+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 |
188 | vfmadd213ps sPoly+96+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 |
189 | vfmadd213ps sPoly+64+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 |
190 | vfmadd213ps sPoly+32+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 |
191 | vfmadd213ps sPoly+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 |
192 | vmulps %ymm4, %ymm2, %ymm6 |
193 | vfmadd213ps %ymm2, %ymm2, %ymm6 |
194 | |
195 | /* final reconstruction */ |
196 | vfmadd132ps sLn2+__svml_sacosh_data_internal(%rip), %ymm6, %ymm0 |
197 | testl %edx, %edx |
198 | |
199 | /* Go to special inputs processing branch */ |
200 | jne L(SPECIAL_VALUES_BRANCH) |
201 | # LOE rbx r12 r13 r14 r15 edx ymm0 ymm3 |
202 | |
203 | /* Restore registers |
204 | * and exit the function |
205 | */ |
206 | |
207 | L(EXIT): |
208 | movq %rbp, %rsp |
209 | popq %rbp |
210 | cfi_def_cfa(7, 8) |
211 | cfi_restore(6) |
212 | ret |
213 | cfi_def_cfa(6, 16) |
214 | cfi_offset(6, -16) |
215 | |
216 | /* Branch to process |
217 | * special inputs |
218 | */ |
219 | |
220 | L(SPECIAL_VALUES_BRANCH): |
221 | vmovups %ymm3, 32(%rsp) |
222 | vmovups %ymm0, 64(%rsp) |
223 | # LOE rbx r12 r13 r14 r15 edx ymm0 |
224 | |
225 | xorl %eax, %eax |
226 | # LOE rbx r12 r13 r14 r15 eax edx |
227 | |
228 | vzeroupper |
229 | movq %r12, 16(%rsp) |
230 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */ |
231 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 |
232 | movl %eax, %r12d |
233 | movq %r13, 8(%rsp) |
234 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */ |
235 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 |
236 | movl %edx, %r13d |
237 | movq %r14, (%rsp) |
238 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */ |
239 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 |
240 | # LOE rbx r15 r12d r13d |
241 | |
242 | /* Range mask |
243 | * bits check |
244 | */ |
245 | |
246 | L(RANGEMASK_CHECK): |
247 | btl %r12d, %r13d |
248 | |
249 | /* Call scalar math function */ |
250 | jc L(SCALAR_MATH_CALL) |
251 | # LOE rbx r15 r12d r13d |
252 | |
253 | /* Special inputs |
254 | * processing loop |
255 | */ |
256 | |
257 | L(SPECIAL_VALUES_LOOP): |
258 | incl %r12d |
259 | cmpl $8, %r12d |
260 | |
261 | /* Check bits in range mask */ |
262 | jl L(RANGEMASK_CHECK) |
263 | # LOE rbx r15 r12d r13d |
264 | |
265 | movq 16(%rsp), %r12 |
266 | cfi_restore(12) |
267 | movq 8(%rsp), %r13 |
268 | cfi_restore(13) |
269 | movq (%rsp), %r14 |
270 | cfi_restore(14) |
271 | vmovups 64(%rsp), %ymm0 |
272 | |
273 | /* Go to exit */ |
274 | jmp L(EXIT) |
275 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */ |
276 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 |
277 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */ |
278 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 |
279 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */ |
280 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 |
281 | # LOE rbx r12 r13 r14 r15 ymm0 |
282 | |
283 | /* Scalar math function call |
284 | * to process special input |
285 | */ |
286 | |
287 | L(SCALAR_MATH_CALL): |
288 | movl %r12d, %r14d |
289 | vmovss 32(%rsp, %r14, 4), %xmm0 |
290 | call acoshf@PLT |
291 | # LOE rbx r14 r15 r12d r13d xmm0 |
292 | |
293 | vmovss %xmm0, 64(%rsp, %r14, 4) |
294 | |
295 | /* Process special inputs in loop */ |
296 | jmp L(SPECIAL_VALUES_LOOP) |
297 | # LOE rbx r15 r12d r13d |
298 | END(_ZGVdN8v_acoshf_avx2) |
299 | |
300 | .section .rodata, "a" |
301 | .align 32 |
302 | |
303 | #ifdef __svml_sacosh_data_internal_typedef |
304 | typedef unsigned int VUINT32; |
305 | typedef struct { |
306 | __declspec(align(32)) VUINT32 sOne[8][1]; |
307 | __declspec(align(32)) VUINT32 sPoly[8][8][1]; |
308 | __declspec(align(32)) VUINT32 iBrkValue[8][1]; |
309 | __declspec(align(32)) VUINT32 iOffExpoMask[8][1]; |
310 | __declspec(align(32)) VUINT32 sBigThreshold[8][1]; |
311 | __declspec(align(32)) VUINT32 sC2[8][1]; |
312 | __declspec(align(32)) VUINT32 sC3[8][1]; |
313 | __declspec(align(32)) VUINT32 sHalf[8][1]; |
314 | __declspec(align(32)) VUINT32 sLargestFinite[8][1]; |
315 | __declspec(align(32)) VUINT32 sThirtyOne[8][1]; |
316 | __declspec(align(32)) VUINT32 sTopMask8[8][1]; |
317 | __declspec(align(32)) VUINT32 XScale[8][1]; |
318 | __declspec(align(32)) VUINT32 sLn2[8][1]; |
319 | } __svml_sacosh_data_internal; |
320 | #endif |
321 | __svml_sacosh_data_internal: |
322 | /* sOne = SP 1.0 */ |
323 | .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 |
324 | /* sPoly[] = SP polynomial */ |
325 | .align 32 |
326 | .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */ |
327 | .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */ |
328 | .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */ |
329 | .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */ |
330 | .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */ |
331 | .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */ |
332 | .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */ |
333 | .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */ |
334 | /* iBrkValue = SP 2/3 */ |
335 | .align 32 |
336 | .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab |
337 | /* iOffExpoMask = SP significand mask */ |
338 | .align 32 |
339 | .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff |
340 | /* sBigThreshold */ |
341 | .align 32 |
342 | .long 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000 |
343 | /* sC2 */ |
344 | .align 32 |
345 | .long 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000 |
346 | /* sC3 */ |
347 | .align 32 |
348 | .long 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000 |
349 | /* sHalf */ |
350 | .align 32 |
351 | .long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000 |
352 | /* sLargestFinite */ |
353 | .align 32 |
354 | .long 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF |
355 | /* sThirtyOne */ |
356 | .align 32 |
357 | .long 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000 |
358 | /* sTopMask8 */ |
359 | .align 32 |
360 | .long 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000 |
361 | /* XScale */ |
362 | .align 32 |
363 | .long 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000 |
364 | /* sLn2 = SP ln(2) */ |
365 | .align 32 |
366 | .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 |
367 | .align 32 |
368 | .type __svml_sacosh_data_internal, @object |
369 | .size __svml_sacosh_data_internal, .-__svml_sacosh_data_internal |
370 | |