1 | /* Function exp2 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 | * exp2(x) = 2^n * T[j] * (1 + P(y)) |
23 | * where |
24 | * x = m*(1/K) + y, y in [-1/K..1/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 exp2(x)-1 |
30 | * on small interval [-1/K..1/K] |
31 | * |
32 | * Special cases: |
33 | * |
34 | * exp2(NaN) = NaN |
35 | * exp2(+INF) = +INF |
36 | * exp2(-INF) = 0 |
37 | * exp2(x) = 1 for subnormals |
38 | * For IEEE double |
39 | * if x >= 1024.0 then exp2(x) overflows |
40 | * if x < -1076.0 then exp2(x) underflows |
41 | * |
42 | */ |
43 | |
44 | /* Offsets for data table __svml_dexp2_data_internal |
45 | */ |
46 | #define _dbT 0 |
47 | #define _dbShifter 1024 |
48 | #define _dPC1 1040 |
49 | #define _dPC2 1056 |
50 | #define _dPC3 1072 |
51 | #define _dPC4 1088 |
52 | #define _lIndexMask 1104 |
53 | #define _iAbsMask 1120 |
54 | #define _iDomainRange 1136 |
55 | |
56 | #include <sysdep.h> |
57 | |
58 | .section .text.sse4, "ax" , @progbits |
59 | ENTRY(_ZGVbN2v_exp2_sse4) |
60 | subq $72, %rsp |
61 | cfi_def_cfa_offset(80) |
62 | |
63 | /* R */ |
64 | movaps %xmm0, %xmm7 |
65 | movups _dbShifter+__svml_dexp2_data_internal(%rip), %xmm1 |
66 | |
67 | /* out, basePtr, iIndex, iBaseOfs, iSize, iGran, iOfs */ |
68 | lea __svml_dexp2_data_internal(%rip), %rsi |
69 | |
70 | /* Load argument */ |
71 | movaps %xmm1, %xmm10 |
72 | addpd %xmm0, %xmm10 |
73 | movaps %xmm10, %xmm6 |
74 | subpd %xmm1, %xmm6 |
75 | subpd %xmm6, %xmm7 |
76 | |
77 | /* |
78 | * Polynomial |
79 | * poly(dN) = a1*dR+...+a4*dR^4 |
80 | */ |
81 | movups _dPC4+__svml_dexp2_data_internal(%rip), %xmm8 |
82 | mulpd %xmm7, %xmm8 |
83 | addpd _dPC3+__svml_dexp2_data_internal(%rip), %xmm8 |
84 | mulpd %xmm7, %xmm8 |
85 | addpd _dPC2+__svml_dexp2_data_internal(%rip), %xmm8 |
86 | movdqu _lIndexMask+__svml_dexp2_data_internal(%rip), %xmm9 |
87 | |
88 | /* Index and lookup */ |
89 | movdqa %xmm9, %xmm5 |
90 | pandn %xmm10, %xmm9 |
91 | pand %xmm10, %xmm5 |
92 | |
93 | /* 2^N */ |
94 | psllq $45, %xmm9 |
95 | movd %xmm5, %eax |
96 | movq _iAbsMask+__svml_dexp2_data_internal(%rip), %xmm2 |
97 | |
98 | /* Check for overflow\underflow */ |
99 | pshufd $221, %xmm0, %xmm4 |
100 | pextrw $4, %xmm5, %ecx |
101 | |
102 | /* a1+...+a4*dR^3 ! */ |
103 | mulpd %xmm7, %xmm8 |
104 | shll $3, %eax |
105 | pand %xmm2, %xmm4 |
106 | shll $3, %ecx |
107 | movq (%rsi, %rax), %xmm1 |
108 | movhpd (%rsi, %rcx), %xmm1 |
109 | |
110 | /* dR=dR*dT */ |
111 | mulpd %xmm1, %xmm7 |
112 | addpd _dPC1+__svml_dexp2_data_internal(%rip), %xmm8 |
113 | |
114 | /* |
115 | * Reconstruction |
116 | * exp2 = {2^N later}*(Tj+Tj*poly) |
117 | * dN = dT+dT*dR*(a1+...+a4*dR^3) |
118 | */ |
119 | mulpd %xmm7, %xmm8 |
120 | addpd %xmm8, %xmm1 |
121 | movq _iDomainRange+__svml_dexp2_data_internal(%rip), %xmm3 |
122 | pcmpgtd %xmm3, %xmm4 |
123 | movmskps %xmm4, %edx |
124 | |
125 | /* quick 2^N */ |
126 | paddq %xmm9, %xmm1 |
127 | andl $3, %edx |
128 | |
129 | /* Finish */ |
130 | |
131 | /* Go to special inputs processing branch */ |
132 | jne L(SPECIAL_VALUES_BRANCH) |
133 | # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1 |
134 | |
135 | /* Restore registers |
136 | * and exit the function |
137 | */ |
138 | |
139 | L(EXIT): |
140 | movaps %xmm1, %xmm0 |
141 | addq $72, %rsp |
142 | cfi_def_cfa_offset(8) |
143 | ret |
144 | cfi_def_cfa_offset(80) |
145 | |
146 | /* Branch to process |
147 | * special inputs |
148 | */ |
149 | |
150 | L(SPECIAL_VALUES_BRANCH): |
151 | movups %xmm0, 32(%rsp) |
152 | movups %xmm1, 48(%rsp) |
153 | # LOE rbx rbp r12 r13 r14 r15 edx xmm1 |
154 | |
155 | xorl %eax, %eax |
156 | movq %r12, 16(%rsp) |
157 | cfi_offset(12, -64) |
158 | movl %eax, %r12d |
159 | movq %r13, 8(%rsp) |
160 | cfi_offset(13, -72) |
161 | movl %edx, %r13d |
162 | movq %r14, (%rsp) |
163 | cfi_offset(14, -80) |
164 | # LOE rbx rbp r15 r12d r13d |
165 | |
166 | /* Range mask |
167 | * bits check |
168 | */ |
169 | |
170 | L(RANGEMASK_CHECK): |
171 | btl %r12d, %r13d |
172 | |
173 | /* Call scalar math function */ |
174 | jc L(SCALAR_MATH_CALL) |
175 | # LOE rbx rbp r15 r12d r13d |
176 | |
177 | /* Special inputs |
178 | * processing loop |
179 | */ |
180 | |
181 | L(SPECIAL_VALUES_LOOP): |
182 | incl %r12d |
183 | cmpl $2, %r12d |
184 | |
185 | /* Check bits in range mask */ |
186 | jl L(RANGEMASK_CHECK) |
187 | # LOE rbx rbp r15 r12d r13d |
188 | |
189 | movq 16(%rsp), %r12 |
190 | cfi_restore(12) |
191 | movq 8(%rsp), %r13 |
192 | cfi_restore(13) |
193 | movq (%rsp), %r14 |
194 | cfi_restore(14) |
195 | movups 48(%rsp), %xmm1 |
196 | |
197 | /* Go to exit */ |
198 | jmp L(EXIT) |
199 | cfi_offset(12, -64) |
200 | cfi_offset(13, -72) |
201 | cfi_offset(14, -80) |
202 | # LOE rbx rbp r12 r13 r14 r15 xmm1 |
203 | |
204 | /* Scalar math function call |
205 | * to process special input |
206 | */ |
207 | |
208 | L(SCALAR_MATH_CALL): |
209 | movl %r12d, %r14d |
210 | movsd 32(%rsp, %r14, 8), %xmm0 |
211 | call exp2@PLT |
212 | # LOE rbx rbp r14 r15 r12d r13d xmm0 |
213 | |
214 | movsd %xmm0, 48(%rsp, %r14, 8) |
215 | |
216 | /* Process special inputs in loop */ |
217 | jmp L(SPECIAL_VALUES_LOOP) |
218 | # LOE rbx rbp r15 r12d r13d |
219 | END(_ZGVbN2v_exp2_sse4) |
220 | |
221 | .section .rodata, "a" |
222 | .align 16 |
223 | |
224 | #ifdef __svml_dexp2_data_internal_typedef |
225 | typedef unsigned int VUINT32; |
226 | typedef struct { |
227 | __declspec(align(16)) VUINT32 _dbT[(1<<7)][2]; |
228 | __declspec(align(16)) VUINT32 _dbShifter[2][2]; |
229 | __declspec(align(16)) VUINT32 _dPC1[2][2]; |
230 | __declspec(align(16)) VUINT32 _dPC2[2][2]; |
231 | __declspec(align(16)) VUINT32 _dPC3[2][2]; |
232 | __declspec(align(16)) VUINT32 _dPC4[2][2]; |
233 | __declspec(align(16)) VUINT32 _lIndexMask[2][2]; |
234 | __declspec(align(16)) VUINT32 _iAbsMask[4][1]; |
235 | __declspec(align(16)) VUINT32 _iDomainRange[4][1]; |
236 | } __svml_dexp2_data_internal; |
237 | #endif |
238 | __svml_dexp2_data_internal: |
239 | /* _dbT */ |
240 | .quad 0x3ff0000000000000, 0x3ff0163da9fb3335 /* 2^( 0 /128), 2^( 1 /128) */ |
241 | .quad 0x3ff02c9a3e778061, 0x3ff04315e86e7f85 /* 2^( 2 /128), 2^( 3 /128) */ |
242 | .quad 0x3ff059b0d3158574, 0x3ff0706b29ddf6de /* 2^( 4 /128), 2^( 5 /128) */ |
243 | .quad 0x3ff0874518759bc8, 0x3ff09e3ecac6f383 /* 2^( 6 /128), 2^( 7 /128) */ |
244 | .quad 0x3ff0b5586cf9890f, 0x3ff0cc922b7247f7 /* 2^( 8 /128), 2^( 9 /128) */ |
245 | .quad 0x3ff0e3ec32d3d1a2, 0x3ff0fb66affed31b /* 2^( 10 /128), 2^( 11 /128) */ |
246 | .quad 0x3ff11301d0125b51, 0x3ff12abdc06c31cc /* 2^( 12 /128), 2^( 13 /128) */ |
247 | .quad 0x3ff1429aaea92de0, 0x3ff15a98c8a58e51 /* 2^( 14 /128), 2^( 15 /128) */ |
248 | .quad 0x3ff172b83c7d517b, 0x3ff18af9388c8dea /* 2^( 16 /128), 2^( 17 /128) */ |
249 | .quad 0x3ff1a35beb6fcb75, 0x3ff1bbe084045cd4 /* 2^( 18 /128), 2^( 19 /128) */ |
250 | .quad 0x3ff1d4873168b9aa, 0x3ff1ed5022fcd91d /* 2^( 20 /128), 2^( 21 /128) */ |
251 | .quad 0x3ff2063b88628cd6, 0x3ff21f49917ddc96 /* 2^( 22 /128), 2^( 23 /128) */ |
252 | .quad 0x3ff2387a6e756238, 0x3ff251ce4fb2a63f /* 2^( 24 /128), 2^( 25 /128) */ |
253 | .quad 0x3ff26b4565e27cdd, 0x3ff284dfe1f56381 /* 2^( 26 /128), 2^( 27 /128) */ |
254 | .quad 0x3ff29e9df51fdee1, 0x3ff2b87fd0dad990 /* 2^( 28 /128), 2^( 29 /128) */ |
255 | .quad 0x3ff2d285a6e4030b, 0x3ff2ecafa93e2f56 /* 2^( 30 /128), 2^( 31 /128) */ |
256 | .quad 0x3ff306fe0a31b715, 0x3ff32170fc4cd831 /* 2^( 32 /128), 2^( 33 /128) */ |
257 | .quad 0x3ff33c08b26416ff, 0x3ff356c55f929ff1 /* 2^( 34 /128), 2^( 35 /128) */ |
258 | .quad 0x3ff371a7373aa9cb, 0x3ff38cae6d05d866 /* 2^( 36 /128), 2^( 37 /128) */ |
259 | .quad 0x3ff3a7db34e59ff7, 0x3ff3c32dc313a8e5 /* 2^( 38 /128), 2^( 39 /128) */ |
260 | .quad 0x3ff3dea64c123422, 0x3ff3fa4504ac801c /* 2^( 40 /128), 2^( 41 /128) */ |
261 | .quad 0x3ff4160a21f72e2a, 0x3ff431f5d950a897 /* 2^( 42 /128), 2^( 43 /128) */ |
262 | .quad 0x3ff44e086061892d, 0x3ff46a41ed1d0057 /* 2^( 44 /128), 2^( 45 /128) */ |
263 | .quad 0x3ff486a2b5c13cd0, 0x3ff4a32af0d7d3de /* 2^( 46 /128), 2^( 47 /128) */ |
264 | .quad 0x3ff4bfdad5362a27, 0x3ff4dcb299fddd0d /* 2^( 48 /128), 2^( 49 /128) */ |
265 | .quad 0x3ff4f9b2769d2ca7, 0x3ff516daa2cf6642 /* 2^( 50 /128), 2^( 51 /128) */ |
266 | .quad 0x3ff5342b569d4f82, 0x3ff551a4ca5d920f /* 2^( 52 /128), 2^( 53 /128) */ |
267 | .quad 0x3ff56f4736b527da, 0x3ff58d12d497c7fd /* 2^( 54 /128), 2^( 55 /128) */ |
268 | .quad 0x3ff5ab07dd485429, 0x3ff5c9268a5946b7 /* 2^( 56 /128), 2^( 57 /128) */ |
269 | .quad 0x3ff5e76f15ad2148, 0x3ff605e1b976dc09 /* 2^( 58 /128), 2^( 59 /128) */ |
270 | .quad 0x3ff6247eb03a5585, 0x3ff6434634ccc320 /* 2^( 60 /128), 2^( 61 /128) */ |
271 | .quad 0x3ff6623882552225, 0x3ff68155d44ca973 /* 2^( 62 /128), 2^( 63 /128) */ |
272 | .quad 0x3ff6a09e667f3bcd, 0x3ff6c012750bdabf /* 2^( 64 /128), 2^( 65 /128) */ |
273 | .quad 0x3ff6dfb23c651a2f, 0x3ff6ff7df9519484 /* 2^( 66 /128), 2^( 67 /128) */ |
274 | .quad 0x3ff71f75e8ec5f74, 0x3ff73f9a48a58174 /* 2^( 68 /128), 2^( 69 /128) */ |
275 | .quad 0x3ff75feb564267c9, 0x3ff780694fde5d3f /* 2^( 70 /128), 2^( 71 /128) */ |
276 | .quad 0x3ff7a11473eb0187, 0x3ff7c1ed0130c132 /* 2^( 72 /128), 2^( 73 /128) */ |
277 | .quad 0x3ff7e2f336cf4e62, 0x3ff80427543e1a12 /* 2^( 74 /128), 2^( 75 /128) */ |
278 | .quad 0x3ff82589994cce13, 0x3ff8471a4623c7ad /* 2^( 76 /128), 2^( 77 /128) */ |
279 | .quad 0x3ff868d99b4492ed, 0x3ff88ac7d98a6699 /* 2^( 78 /128), 2^( 79 /128) */ |
280 | .quad 0x3ff8ace5422aa0db, 0x3ff8cf3216b5448c /* 2^( 80 /128), 2^( 81 /128) */ |
281 | .quad 0x3ff8f1ae99157736, 0x3ff9145b0b91ffc6 /* 2^( 82 /128), 2^( 83 /128) */ |
282 | .quad 0x3ff93737b0cdc5e5, 0x3ff95a44cbc8520f /* 2^( 84 /128), 2^( 85 /128) */ |
283 | .quad 0x3ff97d829fde4e50, 0x3ff9a0f170ca07ba /* 2^( 86 /128), 2^( 87 /128) */ |
284 | .quad 0x3ff9c49182a3f090, 0x3ff9e86319e32323 /* 2^( 88 /128), 2^( 89 /128) */ |
285 | .quad 0x3ffa0c667b5de565, 0x3ffa309bec4a2d33 /* 2^( 90 /128), 2^( 91 /128) */ |
286 | .quad 0x3ffa5503b23e255d, 0x3ffa799e1330b358 /* 2^( 92 /128), 2^( 93 /128) */ |
287 | .quad 0x3ffa9e6b5579fdbf, 0x3ffac36bbfd3f37a /* 2^( 94 /128), 2^( 95 /128) */ |
288 | .quad 0x3ffae89f995ad3ad, 0x3ffb0e07298db666 /* 2^( 96 /128), 2^( 97 /128) */ |
289 | .quad 0x3ffb33a2b84f15fb, 0x3ffb59728de5593a /* 2^( 98 /128), 2^( 99 /128) */ |
290 | .quad 0x3ffb7f76f2fb5e47, 0x3ffba5b030a1064a /* 2^( 100 /128), 2^( 101 /128) */ |
291 | .quad 0x3ffbcc1e904bc1d2, 0x3ffbf2c25bd71e09 /* 2^( 102 /128), 2^( 103 /128) */ |
292 | .quad 0x3ffc199bdd85529c, 0x3ffc40ab5fffd07a /* 2^( 104 /128), 2^( 105 /128) */ |
293 | .quad 0x3ffc67f12e57d14b, 0x3ffc8f6d9406e7b5 /* 2^( 106 /128), 2^( 107 /128) */ |
294 | .quad 0x3ffcb720dcef9069, 0x3ffcdf0b555dc3fa /* 2^( 108 /128), 2^( 109 /128) */ |
295 | .quad 0x3ffd072d4a07897c, 0x3ffd2f87080d89f2 /* 2^( 110 /128), 2^( 111 /128) */ |
296 | .quad 0x3ffd5818dcfba487, 0x3ffd80e316c98398 /* 2^( 112 /128), 2^( 113 /128) */ |
297 | .quad 0x3ffda9e603db3285, 0x3ffdd321f301b460 /* 2^( 114 /128), 2^( 115 /128) */ |
298 | .quad 0x3ffdfc97337b9b5f, 0x3ffe264614f5a129 /* 2^( 116 /128), 2^( 117 /128) */ |
299 | .quad 0x3ffe502ee78b3ff6, 0x3ffe7a51fbc74c83 /* 2^( 118 /128), 2^( 119 /128) */ |
300 | .quad 0x3ffea4afa2a490da, 0x3ffecf482d8e67f1 /* 2^( 120 /128), 2^( 121 /128) */ |
301 | .quad 0x3ffefa1bee615a27, 0x3fff252b376bba97 /* 2^( 122 /128), 2^( 123 /128) */ |
302 | .quad 0x3fff50765b6e4540, 0x3fff7bfdad9cbe14 /* 2^( 124 /128), 2^( 125 /128) */ |
303 | .quad 0x3fffa7c1819e90d8, 0x3fffd3c22b8f71f1 /* 2^( 126 /128), 2^( 127 /128) */ |
304 | .align 16 |
305 | .quad 0x42c8000000000000, 0x42c8000000000000 /* _dbShifter - 0x433-7=0x42c shifted right on K! */ |
306 | //log2(relerr) = -53.547756365162 |
307 | .align 16 |
308 | .quad 0x3fe62e42fefa3685, 0x3fe62e42fefa3685 /* _dPC1 */ |
309 | .align 16 |
310 | .quad 0x3fcebfbdff82ca48, 0x3fcebfbdff82ca48 /* _dPC2 */ |
311 | .align 16 |
312 | .quad 0x3fac6b09b180f045, 0x3fac6b09b180f045 /* _dPC3 */ |
313 | .align 16 |
314 | .quad 0x3f83b2ab5bb1268f, 0x3f83b2ab5bb1268f /* _dPC4 */ |
315 | .align 16 |
316 | .quad 0x000000000000007f, 0x000000000000007f /* _lIndexMask =(2^K-1) */ |
317 | .align 16 |
318 | .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */ |
319 | .align 16 |
320 | .long 0x408fefff, 0x408fefff, 0x408fefff, 0x408fefff /* _iDomainRange */ |
321 | .align 16 |
322 | .type __svml_dexp2_data_internal, @object |
323 | .size __svml_dexp2_data_internal, .-__svml_dexp2_data_internal |
324 | |