1 | /* Function hypot 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 | * HIGH LEVEL OVERVIEW |
23 | * |
24 | * Calculate z = (x*x+y*y) |
25 | * Calculate reciplicle sqrt (z) |
26 | * Calculate error = z*(rsqrt(z)*rsqrt(z)) - 1 |
27 | * Calculate fixing part p with polynom |
28 | * Fix answer with sqrt(z) = z * rsqrt(z) + error * p * z |
29 | * |
30 | * ALGORITHM DETAILS |
31 | * |
32 | * Multiprecision branch for _HA_ only |
33 | * Remove sigm from both arguments |
34 | * Find maximum (_x) and minimum (_y) (by abs value) between arguments |
35 | * Split _x int _a and _b for multiprecision |
36 | * If _x >> _y we will we will not split _y for multiprecision |
37 | * all _y will be put into lower part (_d) and higher part (_c = 0) |
38 | * Fixing _hilo_mask for the case _x >> _y |
39 | * Split _y into _c and _d for multiprecision with fixed mask |
40 | * |
41 | * compute Hi and Lo parts of _z = _x*_x + _y*_y |
42 | * |
43 | * _zHi = _a*_a + _c*_c |
44 | * _zLo = (_x + _a)*_b + _d*_y + _d*_c |
45 | * _z = _zHi + _zLo |
46 | * |
47 | * No multiprecision branch for _LA_ and _EP_ |
48 | * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2 |
49 | * |
50 | * Check _z exponent to be within borders [3BC ; 441] else goto Callout |
51 | * |
52 | * _s ~ 1.0/sqrt(_z) |
53 | * _s2 ~ 1.0/(sqrt(_z)*sqrt(_z)) ~ 1.0/_z = (1.0/_z + O) |
54 | * _e[rror] = (1.0/_z + O) * _z - 1.0 |
55 | * calculate fixing part _p |
56 | * _p = (((_POLY_C5*_e + _POLY_C4)*_e +_POLY_C3)*_e +_POLY_C2)*_e + _POLY_C1 |
57 | * some parts of polynom are skipped for lower flav |
58 | * |
59 | * result = _z * (1.0/sqrt(_z) + O) + _p * _e[rror] * _z |
60 | * |
61 | * |
62 | */ |
63 | |
64 | /* Offsets for data table __svml_dhypot_data_internal |
65 | */ |
66 | #define _dHiLoMask 0 |
67 | #define _dAbsMask 16 |
68 | #define _dOne 32 |
69 | #define _POLY_C5 48 |
70 | #define _POLY_C4 64 |
71 | #define _POLY_C3 80 |
72 | #define _POLY_C2 96 |
73 | #define _POLY_C1 112 |
74 | #define _LowBoundary 128 |
75 | #define _HighBoundary 144 |
76 | |
77 | #include <sysdep.h> |
78 | |
79 | .section .text.sse4, "ax" , @progbits |
80 | ENTRY(_ZGVbN2vv_hypot_sse4) |
81 | subq $88, %rsp |
82 | cfi_def_cfa_offset(96) |
83 | |
84 | /* |
85 | * Defines |
86 | * Implementation |
87 | * Multiprecision branch for _HA_ only |
88 | * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2 |
89 | */ |
90 | movaps %xmm0, %xmm10 |
91 | movaps %xmm1, %xmm2 |
92 | mulpd %xmm0, %xmm10 |
93 | mulpd %xmm1, %xmm2 |
94 | addpd %xmm2, %xmm10 |
95 | |
96 | /* |
97 | * _s ~ 1.0/sqrt(_z) |
98 | * _s2 ~ 1.0/(sqrt(_z)*sqrt(_z)) ~ 1.0/_z |
99 | */ |
100 | cvtpd2ps %xmm10, %xmm7 |
101 | movlhps %xmm7, %xmm7 |
102 | rsqrtps %xmm7, %xmm8 |
103 | cvtps2pd %xmm8, %xmm11 |
104 | movaps %xmm11, %xmm2 |
105 | mulpd %xmm11, %xmm2 |
106 | |
107 | /* _e[rror] ~ (1.0/_z + O) * _z - 1.0 */ |
108 | mulpd %xmm10, %xmm2 |
109 | subpd _dOne+__svml_dhypot_data_internal(%rip), %xmm2 |
110 | |
111 | /* |
112 | * calculate fixing part _p |
113 | * _p = (((_POLY_C5*_e + _POLY_C4)*_e +_POLY_C3)*_e +_POLY_C2)*_e + _POLY_C1 |
114 | * some parts of polynom are skipped for lower flav |
115 | */ |
116 | movups _POLY_C4+__svml_dhypot_data_internal(%rip), %xmm9 |
117 | mulpd %xmm2, %xmm9 |
118 | addpd _POLY_C3+__svml_dhypot_data_internal(%rip), %xmm9 |
119 | mulpd %xmm2, %xmm9 |
120 | addpd _POLY_C2+__svml_dhypot_data_internal(%rip), %xmm9 |
121 | mulpd %xmm2, %xmm9 |
122 | addpd _POLY_C1+__svml_dhypot_data_internal(%rip), %xmm9 |
123 | |
124 | /* result = _z * (1.0/sqrt(_z) + O) + _p * _e[rror] * _z */ |
125 | mulpd %xmm9, %xmm2 |
126 | mulpd %xmm11, %xmm2 |
127 | mulpd %xmm10, %xmm11 |
128 | mulpd %xmm10, %xmm2 |
129 | |
130 | /* Check _z exponent to be within borders [3BC ; 441] else goto Callout */ |
131 | movq _LowBoundary+__svml_dhypot_data_internal(%rip), %xmm5 |
132 | movq _HighBoundary+__svml_dhypot_data_internal(%rip), %xmm3 |
133 | pshufd $221, %xmm10, %xmm4 |
134 | pcmpgtd %xmm4, %xmm5 |
135 | pcmpgtd %xmm3, %xmm4 |
136 | por %xmm4, %xmm5 |
137 | pshufd $80, %xmm5, %xmm6 |
138 | movmskpd %xmm6, %edx |
139 | addpd %xmm11, %xmm2 |
140 | |
141 | /* The end of implementation */ |
142 | testl %edx, %edx |
143 | |
144 | /* Go to special inputs processing branch */ |
145 | jne L(SPECIAL_VALUES_BRANCH) |
146 | # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1 xmm2 |
147 | |
148 | /* Restore registers |
149 | * and exit the function |
150 | */ |
151 | |
152 | L(EXIT): |
153 | movaps %xmm2, %xmm0 |
154 | addq $88, %rsp |
155 | cfi_def_cfa_offset(8) |
156 | ret |
157 | cfi_def_cfa_offset(96) |
158 | |
159 | /* Branch to process |
160 | * special inputs |
161 | */ |
162 | |
163 | L(SPECIAL_VALUES_BRANCH): |
164 | movups %xmm0, 32(%rsp) |
165 | movups %xmm1, 48(%rsp) |
166 | movups %xmm2, 64(%rsp) |
167 | # LOE rbx rbp r12 r13 r14 r15 edx |
168 | |
169 | xorl %eax, %eax |
170 | movq %r12, 16(%rsp) |
171 | cfi_offset(12, -80) |
172 | movl %eax, %r12d |
173 | movq %r13, 8(%rsp) |
174 | cfi_offset(13, -88) |
175 | movl %edx, %r13d |
176 | movq %r14, (%rsp) |
177 | cfi_offset(14, -96) |
178 | # LOE rbx rbp r15 r12d r13d |
179 | |
180 | /* Range mask |
181 | * bits check |
182 | */ |
183 | |
184 | L(RANGEMASK_CHECK): |
185 | btl %r12d, %r13d |
186 | |
187 | /* Call scalar math function */ |
188 | jc L(SCALAR_MATH_CALL) |
189 | # LOE rbx rbp r15 r12d r13d |
190 | |
191 | /* Special inputs |
192 | * processing loop |
193 | */ |
194 | |
195 | L(SPECIAL_VALUES_LOOP): |
196 | incl %r12d |
197 | cmpl $2, %r12d |
198 | |
199 | /* Check bits in range mask */ |
200 | jl L(RANGEMASK_CHECK) |
201 | # LOE rbx rbp r15 r12d r13d |
202 | |
203 | movq 16(%rsp), %r12 |
204 | cfi_restore(12) |
205 | movq 8(%rsp), %r13 |
206 | cfi_restore(13) |
207 | movq (%rsp), %r14 |
208 | cfi_restore(14) |
209 | movups 64(%rsp), %xmm2 |
210 | |
211 | /* Go to exit */ |
212 | jmp L(EXIT) |
213 | cfi_offset(12, -80) |
214 | cfi_offset(13, -88) |
215 | cfi_offset(14, -96) |
216 | # LOE rbx rbp r12 r13 r14 r15 xmm2 |
217 | |
218 | /* Scalar math function call |
219 | * to process special input |
220 | */ |
221 | |
222 | L(SCALAR_MATH_CALL): |
223 | movl %r12d, %r14d |
224 | movsd 32(%rsp, %r14, 8), %xmm0 |
225 | movsd 48(%rsp, %r14, 8), %xmm1 |
226 | call hypot@PLT |
227 | # LOE rbx rbp r14 r15 r12d r13d xmm0 |
228 | |
229 | movsd %xmm0, 64(%rsp, %r14, 8) |
230 | |
231 | /* Process special inputs in loop */ |
232 | jmp L(SPECIAL_VALUES_LOOP) |
233 | # LOE rbx rbp r15 r12d r13d |
234 | END(_ZGVbN2vv_hypot_sse4) |
235 | |
236 | .section .rodata, "a" |
237 | .align 16 |
238 | |
239 | #ifdef __svml_dhypot_data_internal_typedef |
240 | typedef unsigned int VUINT32; |
241 | typedef struct { |
242 | __declspec(align(16)) VUINT32 _dHiLoMask[2][2]; |
243 | __declspec(align(16)) VUINT32 _dAbsMask[2][2]; |
244 | __declspec(align(16)) VUINT32 _dOne[2][2]; |
245 | __declspec(align(16)) VUINT32 _POLY_C5[2][2]; |
246 | __declspec(align(16)) VUINT32 _POLY_C4[2][2]; |
247 | __declspec(align(16)) VUINT32 _POLY_C3[2][2]; |
248 | __declspec(align(16)) VUINT32 _POLY_C2[2][2]; |
249 | __declspec(align(16)) VUINT32 _POLY_C1[2][2]; |
250 | __declspec(align(16)) VUINT32 _LowBoundary[4][1]; |
251 | __declspec(align(16)) VUINT32 _HighBoundary[4][1]; |
252 | } __svml_dhypot_data_internal; |
253 | #endif |
254 | __svml_dhypot_data_internal: |
255 | /* legacy algorithm */ |
256 | .quad 0xffffc00000000000, 0xffffc00000000000 /* _dHiLoMask */ |
257 | .align 16 |
258 | .quad 0x7fffffffffffffff, 0x7fffffffffffffff /* _dAbsMask */ |
259 | .align 16 |
260 | .quad 0x3FF0000000000000, 0x3FF0000000000000 /* _dOne */ |
261 | .align 16 |
262 | .quad 0xBFCF800000000000, 0xBFCF800000000000 /* _POLY_C5 */ |
263 | .align 16 |
264 | .quad 0x3FD1800000000000, 0x3FD1800000000000 /* _POLY_C4 */ |
265 | .align 16 |
266 | .quad 0xBFD4000000000000, 0xBFD4000000000000 /* _POLY_C3 */ |
267 | .align 16 |
268 | .quad 0x3FD8000000000000, 0x3FD8000000000000 /* _POLY_C2 */ |
269 | .align 16 |
270 | .quad 0xBFE0000000000000, 0xBFE0000000000000 /* _POLY_C1 */ |
271 | .align 16 |
272 | .long 0x3BC00000, 0x3BC00000, 0x3BC00000, 0x3BC00000 /* _LowBoundary */ |
273 | .align 16 |
274 | .long 0x44100000, 0x44100000, 0x44100000, 0x44100000 /* _HighBoundary */ |
275 | .align 16 |
276 | .type __svml_dhypot_data_internal, @object |
277 | .size __svml_dhypot_data_internal, .-__svml_dhypot_data_internal |
278 | |