1/* Function exp10f 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 * exp10(x) = 2^x/log10(2) = 2^n * (1 + T[j]) * (1 + P(y))
23 * where
24 * x = m*log10(2)/K + y, y in [-log10(2)/K..log10(2)/K]
25 * m = n*K + j, m, n,j - signed integer, j in [-K/2..K/2]
26 *
27 * values of 2^j/K are tabulated
28 *
29 * P(y) is a minimax polynomial approximation of exp10(x)-1
30 * on small interval [-log10(2)/K..log10(2)/K]
31 *
32 * Special cases:
33 *
34 * exp10(NaN) = NaN
35 * exp10(+INF) = +INF
36 * exp10(-INF) = 0
37 * exp10(x) = 1 for subnormals
38 * For IEEE float
39 * if x > 38.5318412780761720 then exp10f(x) overflow
40 * if x < -45.4555282592773440 then exp10f(x) underflow
41 *
42 */
43
44/* Offsets for data table __svml_sexp10_data_internal
45 */
46#define _sT 0
47#define _sLg2_10 128
48#define _sShifter 160
49#define _sInvLg2_10hi 192
50#define _sInvLg2_10lo 224
51#define _sPC0 256
52#define _sPC1 288
53#define _sPC2 320
54#define _iIndexMask 352
55#define _iAbsMask 384
56#define _iDomainRange 416
57
58#include <sysdep.h>
59
60 .section .text.avx2, "ax", @progbits
61ENTRY(_ZGVdN8v_exp10f_avx2)
62 pushq %rbp
63 cfi_def_cfa_offset(16)
64 movq %rsp, %rbp
65 cfi_def_cfa(6, 16)
66 cfi_offset(6, -16)
67 andq $-32, %rsp
68 subq $96, %rsp
69 lea __svml_sexp10_data_internal(%rip), %rax
70 vmovups _sShifter+__svml_sexp10_data_internal(%rip), %ymm4
71
72 /* Load argument */
73 vmovups _sLg2_10+__svml_sexp10_data_internal(%rip), %ymm1
74 vmovups _iIndexMask+__svml_sexp10_data_internal(%rip), %ymm2
75 vmovaps %ymm0, %ymm3
76 vfmadd213ps %ymm4, %ymm3, %ymm1
77
78 /* Index and lookup */
79 vandps %ymm2, %ymm1, %ymm7
80
81 /* iIndex *= sizeof(S); */
82 vpslld $2, %ymm7, %ymm10
83 vsubps %ymm4, %ymm1, %ymm0
84
85 /* Check for overflow\underflow */
86 vandps _iAbsMask+__svml_sexp10_data_internal(%rip), %ymm3, %ymm5
87 vpcmpgtd _iDomainRange+__svml_sexp10_data_internal(%rip), %ymm5, %ymm6
88 vmovmskps %ymm6, %edx
89 vmovd %xmm10, %ecx
90 vextractf128 $1, %ymm10, %xmm6
91 vpextrd $1, %xmm10, %esi
92 vpextrd $2, %xmm10, %edi
93 vpextrd $3, %xmm10, %r8d
94 movslq %ecx, %rcx
95 movslq %esi, %rsi
96 movslq %edi, %rdi
97 movslq %r8d, %r8
98 vmovd (%rax, %rcx), %xmm8
99 vmovd (%rax, %rsi), %xmm9
100 vmovd (%rax, %rdi), %xmm11
101 vmovd (%rax, %r8), %xmm12
102 vpunpckldq %xmm9, %xmm8, %xmm13
103 vpunpckldq %xmm12, %xmm11, %xmm14
104 vpunpcklqdq %xmm14, %xmm13, %xmm15
105
106 /* R */
107 vmovups _sInvLg2_10hi+__svml_sexp10_data_internal(%rip), %ymm13
108 vmovd %xmm6, %r9d
109 vfnmadd213ps %ymm3, %ymm0, %ymm13
110 vpextrd $1, %xmm6, %r10d
111 movslq %r9d, %r9
112 movslq %r10d, %r10
113 vfnmadd132ps _sInvLg2_10lo+__svml_sexp10_data_internal(%rip), %ymm13, %ymm0
114 vmovd (%rax, %r9), %xmm4
115 vmovd (%rax, %r10), %xmm5
116 vpunpckldq %xmm5, %xmm4, %xmm9
117
118 /*
119 * Polynomial
120 * exp10 = 2^N*(Tj+Tj*poly)
121 * poly(sN) = {1+later} a0+a1*sR
122 */
123 vmovups _sPC2+__svml_sexp10_data_internal(%rip), %ymm4
124 vfmadd213ps _sPC1+__svml_sexp10_data_internal(%rip), %ymm0, %ymm4
125 vpextrd $2, %xmm6, %r11d
126 vpextrd $3, %xmm6, %ecx
127 movslq %r11d, %r11
128 movslq %ecx, %rcx
129 vfmadd213ps _sPC0+__svml_sexp10_data_internal(%rip), %ymm0, %ymm4
130 vmovd (%rax, %r11), %xmm7
131 vmovd (%rax, %rcx), %xmm8
132 vpunpckldq %xmm8, %xmm7, %xmm11
133
134 /* remove index bits */
135 vpandn %ymm1, %ymm2, %ymm0
136 vpunpcklqdq %xmm11, %xmm9, %xmm12
137
138 /* 2^N */
139 vpslld $18, %ymm0, %ymm1
140 vinsertf128 $1, %xmm12, %ymm15, %ymm14
141
142 /* Tj_l+Tj_h*poly */
143 vfmadd213ps %ymm14, %ymm14, %ymm4
144
145 /* quick mul 2^N */
146 vpaddd %ymm1, %ymm4, %ymm0
147
148 /* Finish */
149 testl %edx, %edx
150
151 /* Go to special inputs processing branch */
152 jne L(SPECIAL_VALUES_BRANCH)
153 # LOE rbx r12 r13 r14 r15 edx ymm0 ymm3
154
155 /* Restore registers
156 * and exit the function
157 */
158
159L(EXIT):
160 movq %rbp, %rsp
161 popq %rbp
162 cfi_def_cfa(7, 8)
163 cfi_restore(6)
164 ret
165 cfi_def_cfa(6, 16)
166 cfi_offset(6, -16)
167
168 /* Branch to process
169 * special inputs
170 */
171
172L(SPECIAL_VALUES_BRANCH):
173 vmovups %ymm3, 32(%rsp)
174 vmovups %ymm0, 64(%rsp)
175 # LOE rbx r12 r13 r14 r15 edx ymm0
176
177 xorl %eax, %eax
178 # LOE rbx r12 r13 r14 r15 eax edx
179
180 vzeroupper
181 movq %r12, 16(%rsp)
182 /* 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) */
183 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
184 movl %eax, %r12d
185 movq %r13, 8(%rsp)
186 /* 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) */
187 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
188 movl %edx, %r13d
189 movq %r14, (%rsp)
190 /* 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) */
191 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
192 # LOE rbx r15 r12d r13d
193
194 /* Range mask
195 * bits check
196 */
197
198L(RANGEMASK_CHECK):
199 btl %r12d, %r13d
200
201 /* Call scalar math function */
202 jc L(SCALAR_MATH_CALL)
203 # LOE rbx r15 r12d r13d
204
205 /* Special inputs
206 * processing loop
207 */
208
209L(SPECIAL_VALUES_LOOP):
210 incl %r12d
211 cmpl $8, %r12d
212
213 /* Check bits in range mask */
214 jl L(RANGEMASK_CHECK)
215 # LOE rbx r15 r12d r13d
216
217 movq 16(%rsp), %r12
218 cfi_restore(12)
219 movq 8(%rsp), %r13
220 cfi_restore(13)
221 movq (%rsp), %r14
222 cfi_restore(14)
223 vmovups 64(%rsp), %ymm0
224
225 /* Go to exit */
226 jmp L(EXIT)
227 /* 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) */
228 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
229 /* 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) */
230 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
231 /* 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) */
232 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
233 # LOE rbx r12 r13 r14 r15 ymm0
234
235 /* Scalar math function call
236 * to process special input
237 */
238
239L(SCALAR_MATH_CALL):
240 movl %r12d, %r14d
241 vmovss 32(%rsp, %r14, 4), %xmm0
242 call exp10f@PLT
243 # LOE rbx r14 r15 r12d r13d xmm0
244
245 vmovss %xmm0, 64(%rsp, %r14, 4)
246
247 /* Process special inputs in loop */
248 jmp L(SPECIAL_VALUES_LOOP)
249 # LOE rbx r15 r12d r13d
250END(_ZGVdN8v_exp10f_avx2)
251
252 .section .rodata, "a"
253 .align 32
254
255#ifdef __svml_sexp10_data_internal_typedef
256typedef unsigned int VUINT32;
257typedef struct {
258 __declspec(align(32)) VUINT32 _sT[(1<<5)][1];
259 __declspec(align(32)) VUINT32 _sLg2_10[8][1];
260 __declspec(align(32)) VUINT32 _sShifter[8][1];
261 __declspec(align(32)) VUINT32 _sInvLg2_10hi[8][1];
262 __declspec(align(32)) VUINT32 _sInvLg2_10lo[8][1];
263 __declspec(align(32)) VUINT32 _sPC0[8][1];
264 __declspec(align(32)) VUINT32 _sPC1[8][1];
265 __declspec(align(32)) VUINT32 _sPC2[8][1];
266 __declspec(align(32)) VUINT32 _iIndexMask[8][1];
267 __declspec(align(32)) VUINT32 _iAbsMask[8][1];
268 __declspec(align(32)) VUINT32 _iDomainRange[8][1];
269} __svml_sexp10_data_internal;
270#endif
271__svml_sexp10_data_internal:
272 /* _sT */
273 .long 0x3f800000 // 2^( 0 /32 )
274 .long 0x3f82cd87 // 2^( 1 /32 )
275 .long 0x3f85aac3 // 2^( 2 /32 )
276 .long 0x3f88980f // 2^( 3 /32 )
277 .long 0x3f8b95c2 // 2^( 4 /32 )
278 .long 0x3f8ea43a // 2^( 5 /32 )
279 .long 0x3f91c3d3 // 2^( 6 /32 )
280 .long 0x3f94f4f0 // 2^( 7 /32 )
281 .long 0x3f9837f0 // 2^( 8 /32 )
282 .long 0x3f9b8d3a // 2^( 9 /32 )
283 .long 0x3f9ef532 // 2^( 10/32 )
284 .long 0x3fa27043 // 2^( 11/32 )
285 .long 0x3fa5fed7 // 2^( 12/32 )
286 .long 0x3fa9a15b // 2^( 13/32 )
287 .long 0x3fad583f // 2^( 14/32 )
288 .long 0x3fb123f6 // 2^( 15/32 )
289 .long 0x3fb504f3 // 2^( 16/32 )
290 .long 0x3fb8fbaf // 2^( 17/32 )
291 .long 0x3fbd08a4 // 2^( 18/32 )
292 .long 0x3fc12c4d // 2^( 19/32 )
293 .long 0x3fc5672a // 2^( 20/32 )
294 .long 0x3fc9b9be // 2^( 21/32 )
295 .long 0x3fce248c // 2^( 22/32 )
296 .long 0x3fd2a81e // 2^( 23/32 )
297 .long 0x3fd744fd // 2^( 24/32 )
298 .long 0x3fdbfbb8 // 2^( 25/32 )
299 .long 0x3fe0ccdf // 2^( 26/32 )
300 .long 0x3fe5b907 // 2^( 27/32 )
301 .long 0x3feac0c7 // 2^( 28/32 )
302 .long 0x3fefe4ba // 2^( 29/32 )
303 .long 0x3ff5257d // 2^( 30/32 )
304 .long 0x3ffa83b3 // 2^( 31/32 )
305 .align 32
306 .long 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78 /* _sLg2_10*2^K */
307 .align 32
308 .long 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000 /* _sShifter) */
309 .align 32
310 .long 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000 /* _sInvLg2_10hi/2^K hi (24-K-7) bits */
311 .align 32
312 .long 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc /* _sInvLg2_10lo/2^K lo bits */
313 // otherwise exp10(0) won't produce exact 1.0
314 .align 32
315 .long 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868 /* _sPC0 */
316 .align 32
317 .long 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b /* _sPC1 */
318 .align 32
319 .long 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2 /* _sPC2 */
320 .align 32
321 .long 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f /* _iIndexMask =(2^K-1) */
322 //common
323 .align 32
324 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */
325 .align 32
326 .long 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818 /* _iDomainRange=-log10(max_denormal=0x007fffff) RZ */
327 .align 32
328 .type __svml_sexp10_data_internal, @object
329 .size __svml_sexp10_data_internal, .-__svml_sexp10_data_internal
330

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_s_exp10f8_core_avx2.S