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
59ENTRY(_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
139L(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
150L(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
170L(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
181L(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
208L(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
219END(_ZGVbN2v_exp2_sse4)
220
221 .section .rodata, "a"
222 .align 16
223
224#ifdef __svml_dexp2_data_internal_typedef
225typedef unsigned int VUINT32;
226typedef 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

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_d_exp22_core_sse4.S