1 | /* Function exp10f 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 | * 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 144 |
49 | #define _sInvLg2_10hi 160 |
50 | #define _sInvLg2_10lo 176 |
51 | #define _sPC0 192 |
52 | #define _sPC1 208 |
53 | #define _sPC2 224 |
54 | #define _iIndexMask 240 |
55 | #define _iAbsMask 256 |
56 | #define _iDomainRange 272 |
57 | |
58 | #include <sysdep.h> |
59 | |
60 | .section .text.sse4, "ax" , @progbits |
61 | ENTRY(_ZGVbN4v_exp10f_sse4) |
62 | subq $72, %rsp |
63 | cfi_def_cfa_offset(80) |
64 | movaps %xmm0, %xmm4 |
65 | |
66 | /* Load argument */ |
67 | movups _sLg2_10+__svml_sexp10_data_internal(%rip), %xmm2 |
68 | lea __svml_sexp10_data_internal(%rip), %r8 |
69 | mulps %xmm4, %xmm2 |
70 | movups _sShifter+__svml_sexp10_data_internal(%rip), %xmm5 |
71 | |
72 | /* R */ |
73 | movups _sInvLg2_10hi+__svml_sexp10_data_internal(%rip), %xmm14 |
74 | addps %xmm5, %xmm2 |
75 | movaps %xmm2, %xmm1 |
76 | movups _sInvLg2_10lo+__svml_sexp10_data_internal(%rip), %xmm15 |
77 | subps %xmm5, %xmm1 |
78 | mulps %xmm1, %xmm14 |
79 | movaps %xmm4, %xmm5 |
80 | mulps %xmm1, %xmm15 |
81 | subps %xmm14, %xmm5 |
82 | |
83 | /* |
84 | * Polynomial |
85 | * exp10 = 2^N*(Tj+Tj*poly) |
86 | * poly(sN) = {1+later} a0+a1*sR |
87 | */ |
88 | movups _sPC2+__svml_sexp10_data_internal(%rip), %xmm1 |
89 | subps %xmm15, %xmm5 |
90 | mulps %xmm5, %xmm1 |
91 | movdqu _iIndexMask+__svml_sexp10_data_internal(%rip), %xmm3 |
92 | |
93 | /* Index and lookup */ |
94 | movdqa %xmm3, %xmm10 |
95 | |
96 | /* remove index bits */ |
97 | pandn %xmm2, %xmm3 |
98 | pand %xmm2, %xmm10 |
99 | |
100 | /* 2^N */ |
101 | pslld $18, %xmm3 |
102 | |
103 | /* iIndex *= sizeof(S); */ |
104 | pslld $2, %xmm10 |
105 | addps _sPC1+__svml_sexp10_data_internal(%rip), %xmm1 |
106 | movd %xmm10, %edx |
107 | pshufd $1, %xmm10, %xmm7 |
108 | pshufd $2, %xmm10, %xmm9 |
109 | pshufd $3, %xmm10, %xmm11 |
110 | movd %xmm7, %ecx |
111 | movd %xmm9, %esi |
112 | movd %xmm11, %edi |
113 | |
114 | /* Check for overflow\underflow */ |
115 | movdqu _iAbsMask+__svml_sexp10_data_internal(%rip), %xmm6 |
116 | pand %xmm4, %xmm6 |
117 | mulps %xmm1, %xmm5 |
118 | movslq %edx, %rdx |
119 | addps _sPC0+__svml_sexp10_data_internal(%rip), %xmm5 |
120 | movslq %ecx, %rcx |
121 | movslq %esi, %rsi |
122 | movslq %edi, %rdi |
123 | movd (%r8, %rdx), %xmm0 |
124 | movd (%r8, %rcx), %xmm8 |
125 | movd (%r8, %rsi), %xmm13 |
126 | movd (%r8, %rdi), %xmm12 |
127 | punpckldq %xmm8, %xmm0 |
128 | punpckldq %xmm12, %xmm13 |
129 | punpcklqdq %xmm13, %xmm0 |
130 | |
131 | /* Tj_l+Tj_h*poly */ |
132 | mulps %xmm0, %xmm5 |
133 | pcmpgtd _iDomainRange+__svml_sexp10_data_internal(%rip), %xmm6 |
134 | addps %xmm5, %xmm0 |
135 | movmskps %xmm6, %eax |
136 | |
137 | /* quick mul 2^N */ |
138 | paddd %xmm3, %xmm0 |
139 | |
140 | /* Finish */ |
141 | testl %eax, %eax |
142 | |
143 | /* Go to special inputs processing branch */ |
144 | jne L(SPECIAL_VALUES_BRANCH) |
145 | # LOE rbx rbp r12 r13 r14 r15 eax xmm0 xmm4 |
146 | |
147 | /* Restore registers |
148 | * and exit the function |
149 | */ |
150 | |
151 | L(EXIT): |
152 | addq $72, %rsp |
153 | cfi_def_cfa_offset(8) |
154 | ret |
155 | cfi_def_cfa_offset(80) |
156 | |
157 | /* Branch to process |
158 | * special inputs |
159 | */ |
160 | |
161 | L(SPECIAL_VALUES_BRANCH): |
162 | movups %xmm4, 32(%rsp) |
163 | movups %xmm0, 48(%rsp) |
164 | # LOE rbx rbp r12 r13 r14 r15 eax |
165 | |
166 | xorl %edx, %edx |
167 | movq %r12, 16(%rsp) |
168 | cfi_offset(12, -64) |
169 | movl %edx, %r12d |
170 | movq %r13, 8(%rsp) |
171 | cfi_offset(13, -72) |
172 | movl %eax, %r13d |
173 | movq %r14, (%rsp) |
174 | cfi_offset(14, -80) |
175 | # LOE rbx rbp r15 r12d r13d |
176 | |
177 | /* Range mask |
178 | * bits check |
179 | */ |
180 | |
181 | L(RANGEMASK_CHECK): |
182 | btl %r12d, %r13d |
183 | |
184 | /* Call scalar math function */ |
185 | jc L(SCALAR_MATH_CALL) |
186 | # LOE rbx rbp r15 r12d r13d |
187 | |
188 | /* Special inputs |
189 | * processing loop |
190 | */ |
191 | |
192 | L(SPECIAL_VALUES_LOOP): |
193 | incl %r12d |
194 | cmpl $4, %r12d |
195 | |
196 | /* Check bits in range mask */ |
197 | jl L(RANGEMASK_CHECK) |
198 | # LOE rbx rbp r15 r12d r13d |
199 | |
200 | movq 16(%rsp), %r12 |
201 | cfi_restore(12) |
202 | movq 8(%rsp), %r13 |
203 | cfi_restore(13) |
204 | movq (%rsp), %r14 |
205 | cfi_restore(14) |
206 | movups 48(%rsp), %xmm0 |
207 | |
208 | /* Go to exit */ |
209 | jmp L(EXIT) |
210 | cfi_offset(12, -64) |
211 | cfi_offset(13, -72) |
212 | cfi_offset(14, -80) |
213 | # LOE rbx rbp r12 r13 r14 r15 xmm0 |
214 | |
215 | /* Scalar math function call |
216 | * to process special input |
217 | */ |
218 | |
219 | L(SCALAR_MATH_CALL): |
220 | movl %r12d, %r14d |
221 | movss 32(%rsp, %r14, 4), %xmm0 |
222 | call exp10f@PLT |
223 | # LOE rbx rbp r14 r15 r12d r13d xmm0 |
224 | |
225 | movss %xmm0, 48(%rsp, %r14, 4) |
226 | |
227 | /* Process special inputs in loop */ |
228 | jmp L(SPECIAL_VALUES_LOOP) |
229 | # LOE rbx rbp r15 r12d r13d |
230 | END(_ZGVbN4v_exp10f_sse4) |
231 | |
232 | .section .rodata, "a" |
233 | .align 16 |
234 | |
235 | #ifdef __svml_sexp10_data_internal_typedef |
236 | typedef unsigned int VUINT32; |
237 | typedef struct { |
238 | __declspec(align(16)) VUINT32 _sT[(1<<5)][1]; |
239 | __declspec(align(16)) VUINT32 _sLg2_10[4][1]; |
240 | __declspec(align(16)) VUINT32 _sShifter[4][1]; |
241 | __declspec(align(16)) VUINT32 _sInvLg2_10hi[4][1]; |
242 | __declspec(align(16)) VUINT32 _sInvLg2_10lo[4][1]; |
243 | __declspec(align(16)) VUINT32 _sPC0[4][1]; |
244 | __declspec(align(16)) VUINT32 _sPC1[4][1]; |
245 | __declspec(align(16)) VUINT32 _sPC2[4][1]; |
246 | __declspec(align(16)) VUINT32 _iIndexMask[4][1]; |
247 | __declspec(align(16)) VUINT32 _iAbsMask[4][1]; |
248 | __declspec(align(16)) VUINT32 _iDomainRange[4][1]; |
249 | } __svml_sexp10_data_internal; |
250 | #endif |
251 | __svml_sexp10_data_internal: |
252 | /* _sT */ |
253 | .long 0x3f800000 // 2^( 0 /32 ) |
254 | .long 0x3f82cd87 // 2^( 1 /32 ) |
255 | .long 0x3f85aac3 // 2^( 2 /32 ) |
256 | .long 0x3f88980f // 2^( 3 /32 ) |
257 | .long 0x3f8b95c2 // 2^( 4 /32 ) |
258 | .long 0x3f8ea43a // 2^( 5 /32 ) |
259 | .long 0x3f91c3d3 // 2^( 6 /32 ) |
260 | .long 0x3f94f4f0 // 2^( 7 /32 ) |
261 | .long 0x3f9837f0 // 2^( 8 /32 ) |
262 | .long 0x3f9b8d3a // 2^( 9 /32 ) |
263 | .long 0x3f9ef532 // 2^( 10/32 ) |
264 | .long 0x3fa27043 // 2^( 11/32 ) |
265 | .long 0x3fa5fed7 // 2^( 12/32 ) |
266 | .long 0x3fa9a15b // 2^( 13/32 ) |
267 | .long 0x3fad583f // 2^( 14/32 ) |
268 | .long 0x3fb123f6 // 2^( 15/32 ) |
269 | .long 0x3fb504f3 // 2^( 16/32 ) |
270 | .long 0x3fb8fbaf // 2^( 17/32 ) |
271 | .long 0x3fbd08a4 // 2^( 18/32 ) |
272 | .long 0x3fc12c4d // 2^( 19/32 ) |
273 | .long 0x3fc5672a // 2^( 20/32 ) |
274 | .long 0x3fc9b9be // 2^( 21/32 ) |
275 | .long 0x3fce248c // 2^( 22/32 ) |
276 | .long 0x3fd2a81e // 2^( 23/32 ) |
277 | .long 0x3fd744fd // 2^( 24/32 ) |
278 | .long 0x3fdbfbb8 // 2^( 25/32 ) |
279 | .long 0x3fe0ccdf // 2^( 26/32 ) |
280 | .long 0x3fe5b907 // 2^( 27/32 ) |
281 | .long 0x3feac0c7 // 2^( 28/32 ) |
282 | .long 0x3fefe4ba // 2^( 29/32 ) |
283 | .long 0x3ff5257d // 2^( 30/32 ) |
284 | .long 0x3ffa83b3 // 2^( 31/32 ) |
285 | .align 16 |
286 | .long 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78 /* _sLg2_10*2^K */ |
287 | .align 16 |
288 | .long 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000 /* _sShifter) */ |
289 | .align 16 |
290 | .long 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000 /* _sInvLg2_10hi/2^K hi (24-K-7) bits */ |
291 | .align 16 |
292 | .long 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc /* _sInvLg2_10lo/2^K lo bits */ |
293 | // otherwise exp10(0) won't produce exact 1.0 |
294 | .align 16 |
295 | .long 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868 /* _sPC0 */ |
296 | .align 16 |
297 | .long 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b /* _sPC1 */ |
298 | .align 16 |
299 | .long 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2 /* _sPC2 */ |
300 | .align 16 |
301 | .long 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f /* _iIndexMask =(2^K-1) */ |
302 | //common |
303 | .align 16 |
304 | .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */ |
305 | .align 16 |
306 | .long 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818 /* _iDomainRange=-log10(max_denormal=0x007fffff) RZ */ |
307 | .align 16 |
308 | .type __svml_sexp10_data_internal, @object |
309 | .size __svml_sexp10_data_internal, .-__svml_sexp10_data_internal |
310 | |