1 | /* Function hypot vectorized with AVX2. |
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 32 |
68 | #define _dOne 64 |
69 | #define _POLY_C5 96 |
70 | #define _POLY_C4 128 |
71 | #define _POLY_C3 160 |
72 | #define _POLY_C2 192 |
73 | #define _POLY_C1 224 |
74 | #define _LowBoundary 256 |
75 | #define _HighBoundary 288 |
76 | |
77 | #include <sysdep.h> |
78 | |
79 | .section .text.avx2, "ax" , @progbits |
80 | ENTRY(_ZGVdN4vv_hypot_avx2) |
81 | pushq %rbp |
82 | cfi_def_cfa_offset(16) |
83 | movq %rsp, %rbp |
84 | cfi_def_cfa(6, 16) |
85 | cfi_offset(6, -16) |
86 | andq $-32, %rsp |
87 | subq $128, %rsp |
88 | vmovapd %ymm1, %ymm2 |
89 | vmovapd %ymm0, %ymm1 |
90 | |
91 | /* |
92 | * Defines |
93 | * Implementation |
94 | * Multiprecision branch for _HA_ only |
95 | * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2 |
96 | */ |
97 | vmulpd %ymm1, %ymm1, %ymm0 |
98 | |
99 | /* |
100 | * calculate fixing part _p |
101 | * _p = (((_POLY_C5*_e + _POLY_C4)*_e +_POLY_C3)*_e +_POLY_C2)*_e + _POLY_C1 |
102 | * some parts of polynom are skipped for lower flav |
103 | */ |
104 | vmovupd _POLY_C4+__svml_dhypot_data_internal(%rip), %ymm15 |
105 | vmovups _LowBoundary+__svml_dhypot_data_internal(%rip), %xmm4 |
106 | vfmadd231pd %ymm2, %ymm2, %ymm0 |
107 | |
108 | /* |
109 | * _s ~ 1.0/sqrt(_z) |
110 | * _s2 ~ 1.0/(sqrt(_z)*sqrt(_z)) ~ 1.0/_z |
111 | */ |
112 | vcvtpd2ps %ymm0, %xmm12 |
113 | |
114 | /* Check _z exponent to be within borders [3BC ; 441] else goto Callout */ |
115 | vextractf128 $1, %ymm0, %xmm3 |
116 | vrsqrtps %xmm12, %xmm13 |
117 | vshufps $221, %xmm3, %xmm0, %xmm5 |
118 | vcvtps2pd %xmm13, %ymm3 |
119 | vpcmpgtd %xmm5, %xmm4, %xmm6 |
120 | vpcmpgtd _HighBoundary+__svml_dhypot_data_internal(%rip), %xmm5, %xmm7 |
121 | vpor %xmm7, %xmm6, %xmm9 |
122 | vpshufd $80, %xmm9, %xmm8 |
123 | vmulpd %ymm3, %ymm3, %ymm14 |
124 | vpshufd $250, %xmm9, %xmm10 |
125 | |
126 | /* _e[rror] ~ (1.0/_z + O) * _z - 1.0 */ |
127 | vfmsub213pd _dOne+__svml_dhypot_data_internal(%rip), %ymm0, %ymm14 |
128 | vfmadd213pd _POLY_C3+__svml_dhypot_data_internal(%rip), %ymm14, %ymm15 |
129 | vfmadd213pd _POLY_C2+__svml_dhypot_data_internal(%rip), %ymm14, %ymm15 |
130 | vfmadd213pd _POLY_C1+__svml_dhypot_data_internal(%rip), %ymm14, %ymm15 |
131 | |
132 | /* result = _z * (1.0/sqrt(_z) + O) + _p * _e[rror] * _z */ |
133 | vmulpd %ymm15, %ymm14, %ymm14 |
134 | vmulpd %ymm14, %ymm3, %ymm15 |
135 | vmulpd %ymm15, %ymm0, %ymm4 |
136 | vfmadd213pd %ymm4, %ymm3, %ymm0 |
137 | vinsertf128 $1, %xmm10, %ymm8, %ymm11 |
138 | vmovmskpd %ymm11, %edx |
139 | |
140 | /* The end of implementation */ |
141 | testl %edx, %edx |
142 | |
143 | /* Go to special inputs processing branch */ |
144 | jne L(SPECIAL_VALUES_BRANCH) |
145 | # LOE rbx r12 r13 r14 r15 edx ymm0 ymm1 ymm2 |
146 | |
147 | /* Restore registers |
148 | * and exit the function |
149 | */ |
150 | |
151 | L(EXIT): |
152 | movq %rbp, %rsp |
153 | popq %rbp |
154 | cfi_def_cfa(7, 8) |
155 | cfi_restore(6) |
156 | ret |
157 | cfi_def_cfa(6, 16) |
158 | cfi_offset(6, -16) |
159 | |
160 | /* Branch to process |
161 | * special inputs |
162 | */ |
163 | |
164 | L(SPECIAL_VALUES_BRANCH): |
165 | vmovupd %ymm1, 32(%rsp) |
166 | vmovupd %ymm2, 64(%rsp) |
167 | vmovupd %ymm0, 96(%rsp) |
168 | # LOE rbx r12 r13 r14 r15 edx ymm0 |
169 | |
170 | xorl %eax, %eax |
171 | # LOE rbx r12 r13 r14 r15 eax edx |
172 | |
173 | vzeroupper |
174 | movq %r12, 16(%rsp) |
175 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -112; DW_OP_plus) */ |
176 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22 |
177 | movl %eax, %r12d |
178 | movq %r13, 8(%rsp) |
179 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -120; DW_OP_plus) */ |
180 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22 |
181 | movl %edx, %r13d |
182 | movq %r14, (%rsp) |
183 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -128; DW_OP_plus) */ |
184 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22 |
185 | # LOE rbx r15 r12d r13d |
186 | |
187 | /* Range mask |
188 | * bits check |
189 | */ |
190 | |
191 | L(RANGEMASK_CHECK): |
192 | btl %r12d, %r13d |
193 | |
194 | /* Call scalar math function */ |
195 | jc L(SCALAR_MATH_CALL) |
196 | # LOE rbx r15 r12d r13d |
197 | |
198 | /* Special inputs |
199 | * processing loop |
200 | */ |
201 | |
202 | L(SPECIAL_VALUES_LOOP): |
203 | incl %r12d |
204 | cmpl $4, %r12d |
205 | |
206 | /* Check bits in range mask */ |
207 | jl L(RANGEMASK_CHECK) |
208 | # LOE rbx r15 r12d r13d |
209 | |
210 | movq 16(%rsp), %r12 |
211 | cfi_restore(12) |
212 | movq 8(%rsp), %r13 |
213 | cfi_restore(13) |
214 | movq (%rsp), %r14 |
215 | cfi_restore(14) |
216 | vmovupd 96(%rsp), %ymm0 |
217 | |
218 | /* Go to exit */ |
219 | jmp L(EXIT) |
220 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -112; DW_OP_plus) */ |
221 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22 |
222 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -120; DW_OP_plus) */ |
223 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22 |
224 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -128; DW_OP_plus) */ |
225 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22 |
226 | # LOE rbx r12 r13 r14 r15 ymm0 |
227 | |
228 | /* Scalar math function call |
229 | * to process special input |
230 | */ |
231 | |
232 | L(SCALAR_MATH_CALL): |
233 | movl %r12d, %r14d |
234 | vmovsd 32(%rsp, %r14, 8), %xmm0 |
235 | vmovsd 64(%rsp, %r14, 8), %xmm1 |
236 | call hypot@PLT |
237 | # LOE rbx r14 r15 r12d r13d xmm0 |
238 | |
239 | vmovsd %xmm0, 96(%rsp, %r14, 8) |
240 | |
241 | /* Process special inputs in loop */ |
242 | jmp L(SPECIAL_VALUES_LOOP) |
243 | # LOE rbx r15 r12d r13d |
244 | END(_ZGVdN4vv_hypot_avx2) |
245 | |
246 | .section .rodata, "a" |
247 | .align 32 |
248 | |
249 | #ifdef __svml_dhypot_data_internal_typedef |
250 | typedef unsigned int VUINT32; |
251 | typedef struct { |
252 | __declspec(align(32)) VUINT32 _dHiLoMask[4][2]; |
253 | __declspec(align(32)) VUINT32 _dAbsMask[4][2]; |
254 | __declspec(align(32)) VUINT32 _dOne[4][2]; |
255 | __declspec(align(32)) VUINT32 _POLY_C5[4][2]; |
256 | __declspec(align(32)) VUINT32 _POLY_C4[4][2]; |
257 | __declspec(align(32)) VUINT32 _POLY_C3[4][2]; |
258 | __declspec(align(32)) VUINT32 _POLY_C2[4][2]; |
259 | __declspec(align(32)) VUINT32 _POLY_C1[4][2]; |
260 | __declspec(align(32)) VUINT32 _LowBoundary[8][1]; |
261 | __declspec(align(32)) VUINT32 _HighBoundary[8][1]; |
262 | } __svml_dhypot_data_internal; |
263 | #endif |
264 | __svml_dhypot_data_internal: |
265 | /* legacy algorithm */ |
266 | .quad 0xffffc00000000000, 0xffffc00000000000, 0xffffc00000000000, 0xffffc00000000000 /* _dHiLoMask */ |
267 | .align 32 |
268 | .quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff /* _dAbsMask */ |
269 | .align 32 |
270 | .quad 0x3FF0000000000000, 0x3FF0000000000000, 0x3FF0000000000000, 0x3FF0000000000000 /* _dOne */ |
271 | .align 32 |
272 | .quad 0xBFCF800000000000, 0xBFCF800000000000, 0xBFCF800000000000, 0xBFCF800000000000 /* _POLY_C5 */ |
273 | .align 32 |
274 | .quad 0x3FD1800000000000, 0x3FD1800000000000, 0x3FD1800000000000, 0x3FD1800000000000 /* _POLY_C4 */ |
275 | .align 32 |
276 | .quad 0xBFD4000000000000, 0xBFD4000000000000, 0xBFD4000000000000, 0xBFD4000000000000 /* _POLY_C3 */ |
277 | .align 32 |
278 | .quad 0x3FD8000000000000, 0x3FD8000000000000, 0x3FD8000000000000, 0x3FD8000000000000 /* _POLY_C2 */ |
279 | .align 32 |
280 | .quad 0xBFE0000000000000, 0xBFE0000000000000, 0xBFE0000000000000, 0xBFE0000000000000 /* _POLY_C1 */ |
281 | .align 32 |
282 | .long 0x3BC00000, 0x3BC00000, 0x3BC00000, 0x3BC00000, 0x3BC00000, 0x3BC00000, 0x3BC00000, 0x3BC00000 /* _LowBoundary */ |
283 | .align 32 |
284 | .long 0x44100000, 0x44100000, 0x44100000, 0x44100000, 0x44100000, 0x44100000, 0x44100000, 0x44100000 /* _HighBoundary */ |
285 | .align 32 |
286 | .type __svml_dhypot_data_internal, @object |
287 | .size __svml_dhypot_data_internal, .-__svml_dhypot_data_internal |
288 | |