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1663be05 | 1 | /* Function expf vectorized with SSE4. |
2b778ceb | 2 | Copyright (C) 2014-2021 Free Software Foundation, Inc. |
1663be05 AS |
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 | |
5a82c748 | 17 | <https://www.gnu.org/licenses/>. */ |
1663be05 AS |
18 | |
19 | #include <sysdep.h> | |
20 | #include "svml_s_expf_data.h" | |
21 | ||
22 | .text | |
23 | ENTRY (_ZGVbN4v_expf_sse4) | |
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 $320, %rsp | |
52 | movaps %xmm0, %xmm5 | |
53 | movq __svml_sexp_data@GOTPCREL(%rip), %rax | |
54 | movups __sInvLn2(%rax), %xmm0 | |
55 | ||
56 | /* m = x*2^k/ln2 + shifter */ | |
57 | mulps %xmm5, %xmm0 | |
58 | movups __sShifter(%rax), %xmm6 | |
59 | movups __sLn2hi(%rax), %xmm4 | |
60 | addps %xmm6, %xmm0 | |
61 | ||
62 | /* n = m - shifter = rint(x*2^k/ln2) */ | |
63 | movaps %xmm0, %xmm2 | |
64 | ||
65 | /* remove sign of x by "and" operation */ | |
66 | movdqu __iAbsMask(%rax), %xmm7 | |
67 | subps %xmm6, %xmm2 | |
68 | ||
69 | /* r = x-n*ln2_hi/2^k */ | |
70 | mulps %xmm2, %xmm4 | |
71 | pand %xmm5, %xmm7 | |
72 | ||
73 | /* compare against threshold */ | |
74 | pcmpgtd __iDomainRange(%rax), %xmm7 | |
75 | movups __sLn2lo(%rax), %xmm1 | |
76 | ||
77 | /* set mask for overflow/underflow */ | |
78 | movmskps %xmm7, %ecx | |
79 | movaps %xmm5, %xmm7 | |
80 | movups __sPC5(%rax), %xmm3 | |
81 | subps %xmm4, %xmm7 | |
82 | ||
83 | /* r = r-n*ln2_lo/2^k = x - n*ln2/2^k */ | |
84 | mulps %xmm1, %xmm2 | |
85 | ||
86 | /* compute 2^N with "shift" */ | |
87 | movdqu __iBias(%rax), %xmm6 | |
88 | subps %xmm2, %xmm7 | |
89 | ||
90 | /* c5*r+c4 */ | |
91 | mulps %xmm7, %xmm3 | |
92 | paddd %xmm6, %xmm0 | |
93 | pslld $23, %xmm0 | |
94 | addps __sPC4(%rax), %xmm3 | |
95 | ||
96 | /* (c5*r+c4)*r+c3 */ | |
97 | mulps %xmm7, %xmm3 | |
98 | addps __sPC3(%rax), %xmm3 | |
99 | ||
100 | /* ((c5*r+c4)*r+c3)*r+c2 */ | |
101 | mulps %xmm7, %xmm3 | |
102 | addps __sPC2(%rax), %xmm3 | |
103 | ||
104 | /* (((c5*r+c4)*r+c3)*r+c2)*r+c1 */ | |
105 | mulps %xmm7, %xmm3 | |
106 | addps __sPC1(%rax), %xmm3 | |
107 | ||
108 | /* exp(r) = ((((c5*r+c4)*r+c3)*r+c2)*r+c1)*r+c0 */ | |
109 | mulps %xmm3, %xmm7 | |
110 | addps __sPC0(%rax), %xmm7 | |
111 | ||
112 | /* 2^N*exp(r) */ | |
113 | mulps %xmm7, %xmm0 | |
114 | testl %ecx, %ecx | |
115 | jne .LBL_1_3 | |
116 | ||
117 | .LBL_1_2: | |
118 | cfi_remember_state | |
119 | movq %rbp, %rsp | |
120 | cfi_def_cfa_register (%rsp) | |
121 | popq %rbp | |
122 | cfi_adjust_cfa_offset (-8) | |
123 | cfi_restore (%rbp) | |
124 | ret | |
125 | ||
126 | .LBL_1_3: | |
127 | cfi_restore_state | |
128 | movups %xmm5, 192(%rsp) | |
129 | movups %xmm0, 256(%rsp) | |
130 | je .LBL_1_2 | |
131 | ||
132 | xorb %dl, %dl | |
133 | xorl %eax, %eax | |
134 | movups %xmm8, 112(%rsp) | |
135 | movups %xmm9, 96(%rsp) | |
136 | movups %xmm10, 80(%rsp) | |
137 | movups %xmm11, 64(%rsp) | |
138 | movups %xmm12, 48(%rsp) | |
139 | movups %xmm13, 32(%rsp) | |
140 | movups %xmm14, 16(%rsp) | |
141 | movups %xmm15, (%rsp) | |
142 | movq %rsi, 136(%rsp) | |
143 | movq %rdi, 128(%rsp) | |
144 | movq %r12, 168(%rsp) | |
145 | cfi_offset_rel_rsp (12, 168) | |
146 | movb %dl, %r12b | |
147 | movq %r13, 160(%rsp) | |
148 | cfi_offset_rel_rsp (13, 160) | |
149 | movl %ecx, %r13d | |
150 | movq %r14, 152(%rsp) | |
151 | cfi_offset_rel_rsp (14, 152) | |
152 | movl %eax, %r14d | |
153 | movq %r15, 144(%rsp) | |
154 | cfi_offset_rel_rsp (15, 144) | |
155 | cfi_remember_state | |
156 | ||
157 | .LBL_1_6: | |
158 | btl %r14d, %r13d | |
159 | jc .LBL_1_12 | |
160 | ||
161 | .LBL_1_7: | |
162 | lea 1(%r14), %esi | |
163 | btl %esi, %r13d | |
164 | jc .LBL_1_10 | |
165 | ||
166 | .LBL_1_8: | |
167 | incb %r12b | |
168 | addl $2, %r14d | |
169 | cmpb $16, %r12b | |
170 | jb .LBL_1_6 | |
171 | ||
172 | movups 112(%rsp), %xmm8 | |
173 | movups 96(%rsp), %xmm9 | |
174 | movups 80(%rsp), %xmm10 | |
175 | movups 64(%rsp), %xmm11 | |
176 | movups 48(%rsp), %xmm12 | |
177 | movups 32(%rsp), %xmm13 | |
178 | movups 16(%rsp), %xmm14 | |
179 | movups (%rsp), %xmm15 | |
180 | movq 136(%rsp), %rsi | |
181 | movq 128(%rsp), %rdi | |
182 | movq 168(%rsp), %r12 | |
183 | cfi_restore (%r12) | |
184 | movq 160(%rsp), %r13 | |
185 | cfi_restore (%r13) | |
186 | movq 152(%rsp), %r14 | |
187 | cfi_restore (%r14) | |
188 | movq 144(%rsp), %r15 | |
189 | cfi_restore (%r15) | |
190 | movups 256(%rsp), %xmm0 | |
191 | jmp .LBL_1_2 | |
192 | ||
193 | .LBL_1_10: | |
194 | cfi_restore_state | |
195 | movzbl %r12b, %r15d | |
196 | movss 196(%rsp,%r15,8), %xmm0 | |
197 | ||
d0007dc5 | 198 | call JUMPTARGET(expf) |
1663be05 AS |
199 | |
200 | movss %xmm0, 260(%rsp,%r15,8) | |
201 | jmp .LBL_1_8 | |
202 | ||
203 | .LBL_1_12: | |
204 | movzbl %r12b, %r15d | |
205 | movss 192(%rsp,%r15,8), %xmm0 | |
206 | ||
d0007dc5 | 207 | call JUMPTARGET(expf) |
1663be05 AS |
208 | |
209 | movss %xmm0, 256(%rsp,%r15,8) | |
210 | jmp .LBL_1_7 | |
211 | ||
212 | END (_ZGVbN4v_expf_sse4) |