1/* Function expf vectorized with AVX2.
2 Copyright (C) 2014-2024 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#include <sysdep.h>
20#include "svml_s_expf_data.h"
21
22 .section .text.avx2, "ax", @progbits
23ENTRY(_ZGVdN8v_expf_avx2)
24/*
25 ALGORITHM DESCRIPTION:
26
27 Argument representation:
28 M = rint(X*2^k/ln2) = 2^k*N+j
29 X = M*ln2/2^k + r = N*ln2 + ln2*(j/2^k) + r
30 then -ln2/2^(k+1) < r < ln2/2^(k+1)
31 Alternatively:
32 M = trunc(X*2^k/ln2)
33 then 0 < r < ln2/2^k
34
35 Result calculation:
36 exp(X) = exp(N*ln2 + ln2*(j/2^k) + r)
37 = 2^N * 2^(j/2^k) * exp(r)
38 2^N is calculated by bit manipulation
39 2^(j/2^k) is computed from table lookup
40 exp(r) is approximated by polynomial
41
42 The table lookup is skipped if k = 0.
43 For low accuracy approximation, exp(r) ~ 1 or 1+r. */
44
45 pushq %rbp
46 cfi_adjust_cfa_offset (8)
47 cfi_rel_offset (%rbp, 0)
48 movq %rsp, %rbp
49 cfi_def_cfa_register (%rbp)
50 andq $-64, %rsp
51 subq $448, %rsp
52 movq __svml_sexp_data@GOTPCREL(%rip), %rax
53 vmovaps %ymm0, %ymm2
54 vmovups __sInvLn2(%rax), %ymm7
55 vmovups __sShifter(%rax), %ymm4
56 vmovups __sLn2hi(%rax), %ymm3
57 vmovups __sPC5(%rax), %ymm1
58
59/* m = x*2^k/ln2 + shifter */
60 vfmadd213ps %ymm4, %ymm2, %ymm7
61
62/* n = m - shifter = rint(x*2^k/ln2) */
63 vsubps %ymm4, %ymm7, %ymm0
64 vpaddd __iBias(%rax), %ymm7, %ymm4
65
66/* remove sign of x by "and" operation */
67 vandps __iAbsMask(%rax), %ymm2, %ymm5
68
69/* compare against threshold */
70 vpcmpgtd __iDomainRange(%rax), %ymm5, %ymm6
71
72/* r = x-n*ln2_hi/2^k */
73 vmovaps %ymm2, %ymm5
74 vfnmadd231ps %ymm0, %ymm3, %ymm5
75
76/* r = r-n*ln2_lo/2^k = x - n*ln2/2^k */
77 vfnmadd132ps __sLn2lo(%rax), %ymm5, %ymm0
78
79/* c5*r+c4 */
80 vfmadd213ps __sPC4(%rax), %ymm0, %ymm1
81
82/* (c5*r+c4)*r+c3 */
83 vfmadd213ps __sPC3(%rax), %ymm0, %ymm1
84
85/* ((c5*r+c4)*r+c3)*r+c2 */
86 vfmadd213ps __sPC2(%rax), %ymm0, %ymm1
87
88/* (((c5*r+c4)*r+c3)*r+c2)*r+c1 */
89 vfmadd213ps __sPC1(%rax), %ymm0, %ymm1
90
91/* exp(r) = ((((c5*r+c4)*r+c3)*r+c2)*r+c1)*r+c0 */
92 vfmadd213ps __sPC0(%rax), %ymm0, %ymm1
93
94/* set mask for overflow/underflow */
95 vmovmskps %ymm6, %ecx
96
97/* compute 2^N with "shift" */
98 vpslld $23, %ymm4, %ymm6
99
100/* 2^N*exp(r) */
101 vmulps %ymm1, %ymm6, %ymm0
102 testl %ecx, %ecx
103 jne .LBL_1_3
104
105.LBL_1_2:
106 cfi_remember_state
107 movq %rbp, %rsp
108 cfi_def_cfa_register (%rsp)
109 popq %rbp
110 cfi_adjust_cfa_offset (-8)
111 cfi_restore (%rbp)
112 ret
113
114.LBL_1_3:
115 cfi_restore_state
116 vmovups %ymm2, 320(%rsp)
117 vmovups %ymm0, 384(%rsp)
118 je .LBL_1_2
119
120 xorb %dl, %dl
121 xorl %eax, %eax
122 vmovups %ymm8, 224(%rsp)
123 vmovups %ymm9, 192(%rsp)
124 vmovups %ymm10, 160(%rsp)
125 vmovups %ymm11, 128(%rsp)
126 vmovups %ymm12, 96(%rsp)
127 vmovups %ymm13, 64(%rsp)
128 vmovups %ymm14, 32(%rsp)
129 vmovups %ymm15, (%rsp)
130 movq %rsi, 264(%rsp)
131 movq %rdi, 256(%rsp)
132 movq %r12, 296(%rsp)
133 cfi_offset_rel_rsp (12, 296)
134 movb %dl, %r12b
135 movq %r13, 288(%rsp)
136 cfi_offset_rel_rsp (13, 288)
137 movl %ecx, %r13d
138 movq %r14, 280(%rsp)
139 cfi_offset_rel_rsp (14, 280)
140 movl %eax, %r14d
141 movq %r15, 272(%rsp)
142 cfi_offset_rel_rsp (15, 272)
143 cfi_remember_state
144
145.LBL_1_6:
146 btl %r14d, %r13d
147 jc .LBL_1_12
148
149.LBL_1_7:
150 lea 1(%r14), %esi
151 btl %esi, %r13d
152 jc .LBL_1_10
153
154.LBL_1_8:
155 incb %r12b
156 addl $2, %r14d
157 cmpb $16, %r12b
158 jb .LBL_1_6
159
160 vmovups 224(%rsp), %ymm8
161 vmovups 192(%rsp), %ymm9
162 vmovups 160(%rsp), %ymm10
163 vmovups 128(%rsp), %ymm11
164 vmovups 96(%rsp), %ymm12
165 vmovups 64(%rsp), %ymm13
166 vmovups 32(%rsp), %ymm14
167 vmovups (%rsp), %ymm15
168 vmovups 384(%rsp), %ymm0
169 movq 264(%rsp), %rsi
170 movq 256(%rsp), %rdi
171 movq 296(%rsp), %r12
172 cfi_restore (%r12)
173 movq 288(%rsp), %r13
174 cfi_restore (%r13)
175 movq 280(%rsp), %r14
176 cfi_restore (%r14)
177 movq 272(%rsp), %r15
178 cfi_restore (%r15)
179 jmp .LBL_1_2
180
181.LBL_1_10:
182 cfi_restore_state
183 movzbl %r12b, %r15d
184 vmovss 324(%rsp,%r15,8), %xmm0
185 vzeroupper
186
187 call JUMPTARGET(expf)
188
189 vmovss %xmm0, 388(%rsp,%r15,8)
190 jmp .LBL_1_8
191
192.LBL_1_12:
193 movzbl %r12b, %r15d
194 vmovss 320(%rsp,%r15,8), %xmm0
195 vzeroupper
196
197 call JUMPTARGET(expf)
198
199 vmovss %xmm0, 384(%rsp,%r15,8)
200 jmp .LBL_1_7
201
202END(_ZGVdN8v_expf_avx2)
203

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_s_expf8_core_avx2.S