1 | /* Function expm1f 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 (32 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_sexpm1_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 EMask 640 |
43 | #define poly_coeff3 704 |
44 | #define poly_coeff2 768 |
45 | #define One 832 |
46 | |
47 | #include <sysdep.h> |
48 | |
49 | .section .text.evex512, "ax" , @progbits |
50 | ENTRY(_ZGVeN16v_expm1f_skx) |
51 | pushq %rbp |
52 | cfi_def_cfa_offset(16) |
53 | movq %rsp, %rbp |
54 | cfi_def_cfa(6, 16) |
55 | cfi_offset(6, -16) |
56 | andq $-64, %rsp |
57 | subq $192, %rsp |
58 | vmovups L2E+__svml_sexpm1_data_internal_avx512(%rip), %zmm5 |
59 | vmovups Shifter+__svml_sexpm1_data_internal_avx512(%rip), %zmm3 |
60 | vmovups L2H+__svml_sexpm1_data_internal_avx512(%rip), %zmm8 |
61 | vmovups L2L+__svml_sexpm1_data_internal_avx512(%rip), %zmm4 |
62 | vmovups __svml_sexpm1_data_internal_avx512(%rip), %zmm6 |
63 | |
64 | /* polynomial */ |
65 | vmovups poly_coeff3+__svml_sexpm1_data_internal_avx512(%rip), %zmm9 |
66 | vmovups poly_coeff2+__svml_sexpm1_data_internal_avx512(%rip), %zmm12 |
67 | vmovups Exp_tbl_L+__svml_sexpm1_data_internal_avx512(%rip), %zmm11 |
68 | vmovups Threshold+__svml_sexpm1_data_internal_avx512(%rip), %zmm2 |
69 | |
70 | /* Th - 1 */ |
71 | vmovups One+__svml_sexpm1_data_internal_avx512(%rip), %zmm14 |
72 | vmovaps %zmm0, %zmm1 |
73 | |
74 | /* 2^(52-5)*1.5 + x * log2(e) */ |
75 | vfmadd213ps {rn-sae}, %zmm3, %zmm1, %zmm5 |
76 | vcmpps $29, {sae}, %zmm2, %zmm1, %k0 |
77 | |
78 | /* Z0 ~ x*log2(e), rounded to 5 fractional bits */ |
79 | vsubps {rn-sae}, %zmm3, %zmm5, %zmm7 |
80 | vpermt2ps Exp_tbl_H+64+__svml_sexpm1_data_internal_avx512(%rip), %zmm5, %zmm6 |
81 | vpermt2ps Exp_tbl_L+64+__svml_sexpm1_data_internal_avx512(%rip), %zmm5, %zmm11 |
82 | vandps SgnMask+__svml_sexpm1_data_internal_avx512(%rip), %zmm1, %zmm0 |
83 | |
84 | /* R = x - Z0*log(2) */ |
85 | vfnmadd213ps {rn-sae}, %zmm1, %zmm7, %zmm8 |
86 | |
87 | /* scale Th */ |
88 | vscalefps {rn-sae}, %zmm7, %zmm6, %zmm2 |
89 | vfnmadd231ps {rn-sae}, %zmm7, %zmm4, %zmm8 |
90 | kmovw %k0, %edx |
91 | |
92 | /* ensure |R|<2 even for special cases */ |
93 | vandps EMask+__svml_sexpm1_data_internal_avx512(%rip), %zmm8, %zmm13 |
94 | vsubps {rn-sae}, %zmm14, %zmm2, %zmm8 |
95 | vmulps {rn-sae}, %zmm13, %zmm13, %zmm10 |
96 | vfmadd231ps {rn-sae}, %zmm13, %zmm9, %zmm12 |
97 | |
98 | /* Tlr + R+ R2*Poly */ |
99 | vfmadd213ps {rn-sae}, %zmm11, %zmm10, %zmm12 |
100 | vaddps {rn-sae}, %zmm13, %zmm12, %zmm15 |
101 | |
102 | /* (Th-1)+Th*(Tlr + R+ R*Poly) */ |
103 | vfmadd213ps {rn-sae}, %zmm8, %zmm15, %zmm2 |
104 | vorps %zmm0, %zmm2, %zmm0 |
105 | testl %edx, %edx |
106 | |
107 | /* Go to special inputs processing branch */ |
108 | jne L(SPECIAL_VALUES_BRANCH) |
109 | # LOE rbx r12 r13 r14 r15 edx zmm0 zmm1 |
110 | |
111 | /* Restore registers |
112 | * and exit the function |
113 | */ |
114 | |
115 | L(EXIT): |
116 | movq %rbp, %rsp |
117 | popq %rbp |
118 | cfi_def_cfa(7, 8) |
119 | cfi_restore(6) |
120 | ret |
121 | cfi_def_cfa(6, 16) |
122 | cfi_offset(6, -16) |
123 | |
124 | /* Branch to process |
125 | * special inputs |
126 | */ |
127 | |
128 | L(SPECIAL_VALUES_BRANCH): |
129 | vmovups %zmm1, 64(%rsp) |
130 | vmovups %zmm0, 128(%rsp) |
131 | # LOE rbx r12 r13 r14 r15 edx zmm0 |
132 | |
133 | xorl %eax, %eax |
134 | # LOE rbx r12 r13 r14 r15 eax edx |
135 | |
136 | vzeroupper |
137 | movq %r12, 16(%rsp) |
138 | /* 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) */ |
139 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22 |
140 | movl %eax, %r12d |
141 | movq %r13, 8(%rsp) |
142 | /* 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) */ |
143 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22 |
144 | movl %edx, %r13d |
145 | movq %r14, (%rsp) |
146 | /* 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) */ |
147 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22 |
148 | # LOE rbx r15 r12d r13d |
149 | |
150 | /* Range mask |
151 | * bits check |
152 | */ |
153 | |
154 | L(RANGEMASK_CHECK): |
155 | btl %r12d, %r13d |
156 | |
157 | /* Call scalar math function */ |
158 | jc L(SCALAR_MATH_CALL) |
159 | # LOE rbx r15 r12d r13d |
160 | |
161 | /* Special inputs |
162 | * processing loop |
163 | */ |
164 | |
165 | L(SPECIAL_VALUES_LOOP): |
166 | incl %r12d |
167 | cmpl $16, %r12d |
168 | |
169 | /* Check bits in range mask */ |
170 | jl L(RANGEMASK_CHECK) |
171 | # LOE rbx r15 r12d r13d |
172 | |
173 | movq 16(%rsp), %r12 |
174 | cfi_restore(12) |
175 | movq 8(%rsp), %r13 |
176 | cfi_restore(13) |
177 | movq (%rsp), %r14 |
178 | cfi_restore(14) |
179 | vmovups 128(%rsp), %zmm0 |
180 | |
181 | /* Go to exit */ |
182 | jmp L(EXIT) |
183 | /* 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) */ |
184 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22 |
185 | /* 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) */ |
186 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22 |
187 | /* 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) */ |
188 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22 |
189 | # LOE rbx r12 r13 r14 r15 zmm0 |
190 | |
191 | /* Scalar math function call |
192 | * to process special input |
193 | */ |
194 | |
195 | L(SCALAR_MATH_CALL): |
196 | movl %r12d, %r14d |
197 | vmovss 64(%rsp, %r14, 4), %xmm0 |
198 | call expm1f@PLT |
199 | # LOE rbx r14 r15 r12d r13d xmm0 |
200 | |
201 | vmovss %xmm0, 128(%rsp, %r14, 4) |
202 | |
203 | /* Process special inputs in loop */ |
204 | jmp L(SPECIAL_VALUES_LOOP) |
205 | # LOE rbx r15 r12d r13d |
206 | END(_ZGVeN16v_expm1f_skx) |
207 | |
208 | .section .rodata, "a" |
209 | .align 64 |
210 | |
211 | #ifdef __svml_sexpm1_data_internal_avx512_typedef |
212 | typedef unsigned int VUINT32; |
213 | typedef struct { |
214 | __declspec(align(64)) VUINT32 Exp_tbl_H[32][1]; |
215 | __declspec(align(64)) VUINT32 Exp_tbl_L[32][1]; |
216 | __declspec(align(64)) VUINT32 L2E[16][1]; |
217 | __declspec(align(64)) VUINT32 Shifter[16][1]; |
218 | __declspec(align(64)) VUINT32 Threshold[16][1]; |
219 | __declspec(align(64)) VUINT32 SgnMask[16][1]; |
220 | __declspec(align(64)) VUINT32 L2H[16][1]; |
221 | __declspec(align(64)) VUINT32 L2L[16][1]; |
222 | __declspec(align(64)) VUINT32 EMask[16][1]; |
223 | __declspec(align(64)) VUINT32 poly_coeff3[16][1]; |
224 | __declspec(align(64)) VUINT32 poly_coeff2[16][1]; |
225 | __declspec(align(64)) VUINT32 One[16][1]; |
226 | } __svml_sexpm1_data_internal_avx512; |
227 | #endif |
228 | __svml_sexpm1_data_internal_avx512: |
229 | /* Exp_tbl_H */ |
230 | .long 0x3f800000, 0x3f82cd87, 0x3f85aac3, 0x3f88980f |
231 | .long 0x3f8b95c2, 0x3f8ea43a, 0x3f91c3d3, 0x3f94f4f0 |
232 | .long 0x3f9837f0, 0x3f9b8d3a, 0x3f9ef532, 0x3fa27043 |
233 | .long 0x3fa5fed7, 0x3fa9a15b, 0x3fad583f, 0x3fb123f6 |
234 | .long 0x3fb504f3, 0x3fb8fbaf, 0x3fbd08a4, 0x3fc12c4d |
235 | .long 0x3fc5672a, 0x3fc9b9be, 0x3fce248c, 0x3fd2a81e |
236 | .long 0x3fd744fd, 0x3fdbfbb8, 0x3fe0ccdf, 0x3fe5b907 |
237 | .long 0x3feac0c7, 0x3fefe4ba, 0x3ff5257d, 0x3ffa83b3 |
238 | /* Exp_tbl_L */ |
239 | .align 64 |
240 | .long 0x00000000, 0xb34a3a0a, 0x3346cb6a, 0xb36ed17e |
241 | .long 0xb24e0611, 0xb3517dd9, 0x334b2482, 0xb31586de |
242 | .long 0x33092801, 0xb2e6f467, 0x331b85f2, 0x3099b6f1 |
243 | .long 0xb3051aa8, 0xb2e2a0da, 0xb2006c56, 0xb3365942 |
244 | .long 0x329302ae, 0x32c595dc, 0xb302e5a2, 0xb28e10a1 |
245 | .long 0x31b3d0e5, 0xb31a472b, 0x31d1daf2, 0xb305bf64 |
246 | .long 0xb27ce182, 0xb2f26443, 0xb1b4b0da, 0xb1da8a8f |
247 | .long 0xb1d290be, 0xb2d5b899, 0x31b0a147, 0xb2156afc |
248 | /* log2(e) */ |
249 | .align 64 |
250 | .long 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B |
251 | /* Shifter=2^(23-5)*1.5 */ |
252 | .align 64 |
253 | .long 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000 |
254 | /* Threshold */ |
255 | .align 64 |
256 | .long 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B |
257 | /* Sgn */ |
258 | .align 64 |
259 | .long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000 |
260 | /* L2H = log(2)_high */ |
261 | .align 64 |
262 | .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 |
263 | /* L2L = log(2)_low */ |
264 | .align 64 |
265 | .long 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308 |
266 | /* EMask */ |
267 | .align 64 |
268 | .long 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff |
269 | /* poly_coeff3 */ |
270 | .align 64 |
271 | .long 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3 |
272 | /* poly_coeff2 */ |
273 | .align 64 |
274 | .long 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6 |
275 | /* One */ |
276 | .align 64 |
277 | .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 |
278 | .align 64 |
279 | .type __svml_sexpm1_data_internal_avx512, @object |
280 | .size __svml_sexpm1_data_internal_avx512, .-__svml_sexpm1_data_internal_avx512 |
281 | |