1/* Function hypotf 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 make two NR iterations
27 *
28 * ALGORITHM DETAILS
29 *
30 * Multiprecision branch for _HA_ only
31 * Remove sigm from both arguments
32 * Find maximum (_x) and minimum (_y) (by abs value) between arguments
33 * Split _x int _a and _b for multiprecision
34 * If _x >> _y we will we will not split _y for multiprecision
35 * all _y will be put into lower part (_d) and higher part (_c = 0)
36 * Fixing _hilo_mask for the case _x >> _y
37 * Split _y into _c and _d for multiprecision with fixed mask
38 *
39 * compute Hi and Lo parts of _z = _x*_x + _y*_y
40 *
41 * _zHi = _a*_a + _c*_c
42 * _zLo = (_x + _a)*_b + _d*_y + _d*_c
43 * _z = _zHi + _zLo
44 *
45 * No multiprecision branch for _LA_ and _EP_
46 * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2
47 *
48 * Check _z exponent to be within borders [1E3 ; 60A] else goto Callout
49 *
50 * Compute resciplicle sqrt s0 ~ 1.0/sqrt(_z),
51 * that multiplied by _z, is final result for _EP_ version.
52 *
53 * First iteration (or zero iteration):
54 * s = z * s0
55 * h = .5 * s0
56 * d = s * h - .5
57 *
58 * Second iteration:
59 * h = d * h + h
60 * s = s * d + s
61 * d = s * s - z (in multiprecision for _HA_)
62 *
63 * result = s - h * d
64 *
65 * EP version of the function can be implemented as y[i]=sqrt(a[i]^2+b[i]^2)
66 * with all intermediate operations done in target precision for i=1, .., n.
67 * It can return result y[i]=0 in case a[i]^2 and b[i]^2 underflow in target
68 * precision (for some i). It can return result y[i]=NAN in case
69 * a[i]^2+b[i]^2 overflow in target precision, for some i. It can return
70 * result y[i]=NAN in case a[i] or b[i] is infinite, for some i.
71 *
72 *
73 */
74
75/* Offsets for data table __svml_shypot_data_internal
76 */
77#define _sHiLoMask 0
78#define _sAbsMask 32
79#define _sHalf 64
80#define _LowBoundary 96
81#define _HighBoundary 128
82
83#include <sysdep.h>
84
85 .section .text.avx2, "ax", @progbits
86ENTRY(_ZGVdN8vv_hypotf_avx2)
87 pushq %rbp
88 cfi_def_cfa_offset(16)
89 movq %rsp, %rbp
90 cfi_def_cfa(6, 16)
91 cfi_offset(6, -16)
92 andq $-32, %rsp
93 subq $128, %rsp
94
95 /*
96 * Implementation
97 * Multiprecision branch for _HA_ only
98 * No multiprecision branch for _LA_
99 * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2
100 */
101 vmulps %ymm0, %ymm0, %ymm8
102
103 /*
104 * Variables
105 * Defines
106 * Constants loading
107 */
108 vmovups _sHalf+__svml_shypot_data_internal(%rip), %ymm7
109
110 /* Check _z exponent to be within borders [1E3 ; 60A] else goto Callout */
111 vmovups _LowBoundary+__svml_shypot_data_internal(%rip), %ymm2
112 vfmadd231ps %ymm1, %ymm1, %ymm8
113
114 /* _s0 ~ 1.0/sqrt(_z) */
115 vrsqrtps %ymm8, %ymm6
116 vpcmpgtd %ymm8, %ymm2, %ymm3
117
118 /* First iteration */
119 vmulps %ymm8, %ymm6, %ymm9
120 vmulps %ymm7, %ymm6, %ymm2
121 vfnmadd231ps %ymm9, %ymm2, %ymm7
122 vfmadd213ps %ymm9, %ymm7, %ymm9
123
124 /* Second iteration */
125 vfmadd132ps %ymm7, %ymm2, %ymm2
126 vpcmpgtd _HighBoundary+__svml_shypot_data_internal(%rip), %ymm8, %ymm4
127 vpor %ymm4, %ymm3, %ymm5
128
129 /* Finish second iteration in native precision for _LA_ */
130 vfmsub231ps %ymm9, %ymm9, %ymm8
131 vmovmskps %ymm5, %edx
132 vfnmadd213ps %ymm9, %ymm8, %ymm2
133
134 /* The end of implementation */
135 testl %edx, %edx
136
137 /* Go to special inputs processing branch */
138 jne L(SPECIAL_VALUES_BRANCH)
139 # LOE rbx r12 r13 r14 r15 edx ymm0 ymm1 ymm2
140
141 /* Restore registers
142 * and exit the function
143 */
144
145L(EXIT):
146 vmovaps %ymm2, %ymm0
147 movq %rbp, %rsp
148 popq %rbp
149 cfi_def_cfa(7, 8)
150 cfi_restore(6)
151 ret
152 cfi_def_cfa(6, 16)
153 cfi_offset(6, -16)
154
155 /* Branch to process
156 * special inputs
157 */
158
159L(SPECIAL_VALUES_BRANCH):
160 vmovups %ymm0, 32(%rsp)
161 vmovups %ymm1, 64(%rsp)
162 vmovups %ymm2, 96(%rsp)
163 # LOE rbx r12 r13 r14 r15 edx ymm2
164
165 xorl %eax, %eax
166 # LOE rbx r12 r13 r14 r15 eax edx
167
168 vzeroupper
169 movq %r12, 16(%rsp)
170 /* 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) */
171 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22
172 movl %eax, %r12d
173 movq %r13, 8(%rsp)
174 /* 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) */
175 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22
176 movl %edx, %r13d
177 movq %r14, (%rsp)
178 /* 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) */
179 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22
180 # LOE rbx r15 r12d r13d
181
182 /* Range mask
183 * bits check
184 */
185
186L(RANGEMASK_CHECK):
187 btl %r12d, %r13d
188
189 /* Call scalar math function */
190 jc L(SCALAR_MATH_CALL)
191 # LOE rbx r15 r12d r13d
192
193 /* Special inputs
194 * processing loop
195 */
196
197L(SPECIAL_VALUES_LOOP):
198 incl %r12d
199 cmpl $8, %r12d
200
201 /* Check bits in range mask */
202 jl L(RANGEMASK_CHECK)
203 # LOE rbx r15 r12d r13d
204
205 movq 16(%rsp), %r12
206 cfi_restore(12)
207 movq 8(%rsp), %r13
208 cfi_restore(13)
209 movq (%rsp), %r14
210 cfi_restore(14)
211 vmovups 96(%rsp), %ymm2
212
213 /* Go to exit */
214 jmp L(EXIT)
215 /* 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) */
216 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22
217 /* 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) */
218 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22
219 /* 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) */
220 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22
221 # LOE rbx r12 r13 r14 r15 ymm2
222
223 /* Scalar math function call
224 * to process special input
225 */
226
227L(SCALAR_MATH_CALL):
228 movl %r12d, %r14d
229 vmovss 32(%rsp, %r14, 4), %xmm0
230 vmovss 64(%rsp, %r14, 4), %xmm1
231 call hypotf@PLT
232 # LOE rbx r14 r15 r12d r13d xmm0
233
234 vmovss %xmm0, 96(%rsp, %r14, 4)
235
236 /* Process special inputs in loop */
237 jmp L(SPECIAL_VALUES_LOOP)
238 # LOE rbx r15 r12d r13d
239END(_ZGVdN8vv_hypotf_avx2)
240
241 .section .rodata, "a"
242 .align 32
243
244#ifdef __svml_shypot_data_internal_typedef
245typedef unsigned int VUINT32;
246typedef struct {
247 __declspec(align(32)) VUINT32 _sHiLoMask[8][1];
248 __declspec(align(32)) VUINT32 _sAbsMask[8][1];
249 __declspec(align(32)) VUINT32 _sHalf[8][1];
250 __declspec(align(32)) VUINT32 _LowBoundary[8][1];
251 __declspec(align(32)) VUINT32 _HighBoundary[8][1];
252} __svml_shypot_data_internal;
253#endif
254__svml_shypot_data_internal:
255 /* legacy algorithm */
256 .long 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000 /* _sHiLoMask */
257 .align 32
258 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _sAbsMask */
259 .align 32
260 .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _sHalf */
261 .align 32
262 .long 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000 /* _LowBoundary */
263 .align 32
264 .long 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000 /* _HighBoundary */
265 .align 32
266 .type __svml_shypot_data_internal, @object
267 .size __svml_shypot_data_internal, .-__svml_shypot_data_internal
268

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_s_hypotf8_core_avx2.S