1 | /* Function expm1 vectorized with AVX-512. |
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 | * After computing exp(x) in high-low parts, an accurate computation is performed to obtain exp(x)-1 |
22 | * Typical exp() implementation, except that: |
23 | * - tables are small (16 elements), allowing for fast gathers |
24 | * - all arguments processed in the main path |
25 | * - final VSCALEF assists branch-free design (correct overflow/underflow and special case responses) |
26 | * - a VAND is used to ensure the reduced argument |R|<2, even for large inputs |
27 | * - RZ mode used to avoid overflow to +/-Inf for x*log2(e); helps with special case handling |
28 | * |
29 | * |
30 | */ |
31 | |
32 | /* Offsets for data table __svml_dexpm1_data_internal_avx512 |
33 | */ |
34 | #define Exp_tbl_H 0 |
35 | #define Exp_tbl_L 128 |
36 | #define L2E 256 |
37 | #define Shifter 320 |
38 | #define Threshold 384 |
39 | #define SgnMask 448 |
40 | #define L2H 512 |
41 | #define L2L 576 |
42 | #define ZThres 640 |
43 | #define EMask 704 |
44 | #define poly_coeff7 768 |
45 | #define poly_coeff6 832 |
46 | #define poly_coeff5 896 |
47 | #define poly_coeff4 960 |
48 | #define poly_coeff3 1024 |
49 | #define poly_coeff2 1088 |
50 | #define One 1152 |
51 | |
52 | #include <sysdep.h> |
53 | |
54 | .section .text.evex512, "ax" , @progbits |
55 | ENTRY(_ZGVeN8v_expm1_skx) |
56 | pushq %rbp |
57 | cfi_def_cfa_offset(16) |
58 | movq %rsp, %rbp |
59 | cfi_def_cfa(6, 16) |
60 | cfi_offset(6, -16) |
61 | andq $-64, %rsp |
62 | subq $192, %rsp |
63 | vmovups L2E+__svml_dexpm1_data_internal_avx512(%rip), %zmm6 |
64 | vmovups Shifter+__svml_dexpm1_data_internal_avx512(%rip), %zmm4 |
65 | vmovups L2H+__svml_dexpm1_data_internal_avx512(%rip), %zmm11 |
66 | vmovups L2L+__svml_dexpm1_data_internal_avx512(%rip), %zmm5 |
67 | vmovups Threshold+__svml_dexpm1_data_internal_avx512(%rip), %zmm3 |
68 | vmovups poly_coeff5+__svml_dexpm1_data_internal_avx512(%rip), %zmm13 |
69 | vmovups poly_coeff4+__svml_dexpm1_data_internal_avx512(%rip), %zmm15 |
70 | |
71 | /* polynomial */ |
72 | vmovups poly_coeff7+__svml_dexpm1_data_internal_avx512(%rip), %zmm12 |
73 | |
74 | /* set Z0=max(Z0, -128.0) */ |
75 | vmovups ZThres+__svml_dexpm1_data_internal_avx512(%rip), %zmm8 |
76 | vmovups poly_coeff3+__svml_dexpm1_data_internal_avx512(%rip), %zmm14 |
77 | vmovups __svml_dexpm1_data_internal_avx512(%rip), %zmm9 |
78 | vmovaps %zmm0, %zmm2 |
79 | |
80 | /* 2^(52-4)*1.5 + x * log2(e) */ |
81 | vfmadd213pd {rn-sae}, %zmm4, %zmm2, %zmm6 |
82 | vmovups Exp_tbl_L+__svml_dexpm1_data_internal_avx512(%rip), %zmm0 |
83 | vcmppd $21, {sae}, %zmm3, %zmm2, %k0 |
84 | |
85 | /* Z0 ~ x*log2(e), rounded to 4 fractional bits */ |
86 | vsubpd {rn-sae}, %zmm4, %zmm6, %zmm7 |
87 | vpermt2pd Exp_tbl_H+64+__svml_dexpm1_data_internal_avx512(%rip), %zmm6, %zmm9 |
88 | vpermt2pd Exp_tbl_L+64+__svml_dexpm1_data_internal_avx512(%rip), %zmm6, %zmm0 |
89 | vandpd SgnMask+__svml_dexpm1_data_internal_avx512(%rip), %zmm2, %zmm1 |
90 | |
91 | /* R = x - Z0*log(2) */ |
92 | vfnmadd213pd {rn-sae}, %zmm2, %zmm7, %zmm11 |
93 | vmaxpd {sae}, %zmm8, %zmm7, %zmm10 |
94 | vfnmadd231pd {rn-sae}, %zmm7, %zmm5, %zmm11 |
95 | kmovw %k0, %edx |
96 | |
97 | /* ensure |R|<2 even for special cases */ |
98 | vandpd EMask+__svml_dexpm1_data_internal_avx512(%rip), %zmm11, %zmm3 |
99 | vmovups poly_coeff6+__svml_dexpm1_data_internal_avx512(%rip), %zmm11 |
100 | |
101 | /* scale Th */ |
102 | vscalefpd {rn-sae}, %zmm10, %zmm9, %zmm4 |
103 | vfmadd231pd {rn-sae}, %zmm3, %zmm13, %zmm15 |
104 | vfmadd231pd {rn-sae}, %zmm3, %zmm12, %zmm11 |
105 | vmovups poly_coeff2+__svml_dexpm1_data_internal_avx512(%rip), %zmm12 |
106 | vmulpd {rn-sae}, %zmm3, %zmm3, %zmm13 |
107 | vfmadd231pd {rn-sae}, %zmm3, %zmm14, %zmm12 |
108 | vfmadd213pd {rn-sae}, %zmm15, %zmm13, %zmm11 |
109 | vfmadd213pd {rn-sae}, %zmm12, %zmm13, %zmm11 |
110 | |
111 | /* Tlr + R+ R*Poly */ |
112 | vfmadd213pd {rn-sae}, %zmm0, %zmm13, %zmm11 |
113 | |
114 | /* Th - 1 */ |
115 | vmovups One+__svml_dexpm1_data_internal_avx512(%rip), %zmm0 |
116 | vaddpd {rn-sae}, %zmm3, %zmm11, %zmm14 |
117 | vsubpd {rn-sae}, %zmm0, %zmm4, %zmm15 |
118 | |
119 | /* (Th-1)+Th*(Tlr + R+ R*Poly) */ |
120 | vfmadd213pd {rn-sae}, %zmm15, %zmm14, %zmm4 |
121 | vorpd %zmm1, %zmm4, %zmm0 |
122 | testl %edx, %edx |
123 | |
124 | /* Go to special inputs processing branch */ |
125 | jne L(SPECIAL_VALUES_BRANCH) |
126 | # LOE rbx r12 r13 r14 r15 edx zmm0 zmm2 |
127 | |
128 | /* Restore registers |
129 | * and exit the function |
130 | */ |
131 | |
132 | L(EXIT): |
133 | movq %rbp, %rsp |
134 | popq %rbp |
135 | cfi_def_cfa(7, 8) |
136 | cfi_restore(6) |
137 | ret |
138 | cfi_def_cfa(6, 16) |
139 | cfi_offset(6, -16) |
140 | |
141 | /* Branch to process |
142 | * special inputs |
143 | */ |
144 | |
145 | L(SPECIAL_VALUES_BRANCH): |
146 | vmovups %zmm2, 64(%rsp) |
147 | vmovups %zmm0, 128(%rsp) |
148 | # LOE rbx r12 r13 r14 r15 edx zmm0 |
149 | |
150 | xorl %eax, %eax |
151 | # LOE rbx r12 r13 r14 r15 eax edx |
152 | |
153 | vzeroupper |
154 | movq %r12, 16(%rsp) |
155 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */ |
156 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22 |
157 | movl %eax, %r12d |
158 | movq %r13, 8(%rsp) |
159 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */ |
160 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22 |
161 | movl %edx, %r13d |
162 | movq %r14, (%rsp) |
163 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */ |
164 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22 |
165 | # LOE rbx r15 r12d r13d |
166 | |
167 | /* Range mask |
168 | * bits check |
169 | */ |
170 | |
171 | L(RANGEMASK_CHECK): |
172 | btl %r12d, %r13d |
173 | |
174 | /* Call scalar math function */ |
175 | jc L(SCALAR_MATH_CALL) |
176 | # LOE rbx r15 r12d r13d |
177 | |
178 | /* Special inputs |
179 | * processing loop |
180 | */ |
181 | |
182 | L(SPECIAL_VALUES_LOOP): |
183 | incl %r12d |
184 | cmpl $8, %r12d |
185 | |
186 | /* Check bits in range mask */ |
187 | jl L(RANGEMASK_CHECK) |
188 | # LOE rbx r15 r12d r13d |
189 | |
190 | movq 16(%rsp), %r12 |
191 | cfi_restore(12) |
192 | movq 8(%rsp), %r13 |
193 | cfi_restore(13) |
194 | movq (%rsp), %r14 |
195 | cfi_restore(14) |
196 | vmovups 128(%rsp), %zmm0 |
197 | |
198 | /* Go to exit */ |
199 | jmp L(EXIT) |
200 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */ |
201 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22 |
202 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */ |
203 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22 |
204 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */ |
205 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22 |
206 | # LOE rbx r12 r13 r14 r15 zmm0 |
207 | |
208 | /* Scalar math function call |
209 | * to process special input |
210 | */ |
211 | |
212 | L(SCALAR_MATH_CALL): |
213 | movl %r12d, %r14d |
214 | vmovsd 64(%rsp, %r14, 8), %xmm0 |
215 | call expm1@PLT |
216 | # LOE rbx r14 r15 r12d r13d xmm0 |
217 | |
218 | vmovsd %xmm0, 128(%rsp, %r14, 8) |
219 | |
220 | /* Process special inputs in loop */ |
221 | jmp L(SPECIAL_VALUES_LOOP) |
222 | # LOE rbx r15 r12d r13d |
223 | END(_ZGVeN8v_expm1_skx) |
224 | |
225 | .section .rodata, "a" |
226 | .align 64 |
227 | |
228 | #ifdef __svml_dexpm1_data_internal_avx512_typedef |
229 | typedef unsigned int VUINT32; |
230 | typedef struct { |
231 | __declspec(align(64)) VUINT32 Exp_tbl_H[16][2]; |
232 | __declspec(align(64)) VUINT32 Exp_tbl_L[16][2]; |
233 | __declspec(align(64)) VUINT32 L2E[8][2]; |
234 | __declspec(align(64)) VUINT32 Shifter[8][2]; |
235 | __declspec(align(64)) VUINT32 Threshold[8][2]; |
236 | __declspec(align(64)) VUINT32 SgnMask[8][2]; |
237 | __declspec(align(64)) VUINT32 L2H[8][2]; |
238 | __declspec(align(64)) VUINT32 L2L[8][2]; |
239 | __declspec(align(64)) VUINT32 ZThres[8][2]; |
240 | __declspec(align(64)) VUINT32 EMask[8][2]; |
241 | __declspec(align(64)) VUINT32 poly_coeff7[8][2]; |
242 | __declspec(align(64)) VUINT32 poly_coeff6[8][2]; |
243 | __declspec(align(64)) VUINT32 poly_coeff5[8][2]; |
244 | __declspec(align(64)) VUINT32 poly_coeff4[8][2]; |
245 | __declspec(align(64)) VUINT32 poly_coeff3[8][2]; |
246 | __declspec(align(64)) VUINT32 poly_coeff2[8][2]; |
247 | __declspec(align(64)) VUINT32 One[8][2]; |
248 | } __svml_dexpm1_data_internal_avx512; |
249 | #endif |
250 | __svml_dexpm1_data_internal_avx512: |
251 | /* Exp_tbl_H */ |
252 | .quad 0x3ff0000000000000 |
253 | .quad 0x3ff0b5586cf9890f |
254 | .quad 0x3ff172b83c7d517b |
255 | .quad 0x3ff2387a6e756238 |
256 | .quad 0x3ff306fe0a31b715 |
257 | .quad 0x3ff3dea64c123422 |
258 | .quad 0x3ff4bfdad5362a27 |
259 | .quad 0x3ff5ab07dd485429 |
260 | .quad 0x3ff6a09e667f3bcd |
261 | .quad 0x3ff7a11473eb0187 |
262 | .quad 0x3ff8ace5422aa0db |
263 | .quad 0x3ff9c49182a3f090 |
264 | .quad 0x3ffae89f995ad3ad |
265 | .quad 0x3ffc199bdd85529c |
266 | .quad 0x3ffd5818dcfba487 |
267 | .quad 0x3ffea4afa2a490da |
268 | /* Exp_tbl_L */ |
269 | .align 64 |
270 | .quad 0x0000000000000000 |
271 | .quad 0x3c979aa65d837b6d |
272 | .quad 0xbc801b15eaa59348 |
273 | .quad 0x3c968efde3a8a894 |
274 | .quad 0x3c834d754db0abb6 |
275 | .quad 0x3c859f48a72a4c6d |
276 | .quad 0x3c7690cebb7aafb0 |
277 | .quad 0x3c9063e1e21c5409 |
278 | .quad 0xbc93b3efbf5e2228 |
279 | .quad 0xbc7b32dcb94da51d |
280 | .quad 0x3c8db72fc1f0eab4 |
281 | .quad 0x3c71affc2b91ce27 |
282 | .quad 0x3c8c1a7792cb3387 |
283 | .quad 0x3c736eae30af0cb3 |
284 | .quad 0x3c74a385a63d07a7 |
285 | .quad 0xbc8ff7128fd391f0 |
286 | /* log2(e) */ |
287 | .align 64 |
288 | .quad 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE |
289 | /* Shifter=2^(52-4)*1.5 */ |
290 | .align 64 |
291 | .quad 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0 |
292 | /* Threshold */ |
293 | .align 64 |
294 | .quad 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44 |
295 | /* Sgn */ |
296 | .align 64 |
297 | .quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000 |
298 | /* L2H = log(2)_high */ |
299 | .align 64 |
300 | .quad 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef |
301 | /* L2L = log(2)_low */ |
302 | .align 64 |
303 | .quad 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f |
304 | /* ZThres */ |
305 | .align 64 |
306 | .quad 0xc060000000000000, 0xc060000000000000, 0xc060000000000000, 0xc060000000000000, 0xc060000000000000, 0xc060000000000000, 0xc060000000000000, 0xc060000000000000 |
307 | /* EMask */ |
308 | .align 64 |
309 | .quad 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff |
310 | /* poly_coeff7 */ |
311 | .align 64 |
312 | .quad 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a |
313 | /* poly_coeff6 */ |
314 | .align 64 |
315 | .quad 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f |
316 | /* poly_coeff5 */ |
317 | .align 64 |
318 | .quad 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214 |
319 | /* poly_coeff4 */ |
320 | .align 64 |
321 | .quad 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06 |
322 | /* poly_coeff3 */ |
323 | .align 64 |
324 | .quad 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656 |
325 | /* poly_coeff2 */ |
326 | .align 64 |
327 | .quad 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2 |
328 | /* One */ |
329 | .align 64 |
330 | .quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000 |
331 | .align 64 |
332 | .type __svml_dexpm1_data_internal_avx512, @object |
333 | .size __svml_dexpm1_data_internal_avx512, .-__svml_dexpm1_data_internal_avx512 |
334 | |