1/* Function hypotf 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 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 16
79#define _sHalf 32
80#define _LowBoundary 48
81#define _HighBoundary 64
82
83#include <sysdep.h>
84
85 .section .text.sse4, "ax", @progbits
86ENTRY(_ZGVbN4vv_hypotf_sse4)
87 subq $88, %rsp
88 cfi_def_cfa_offset(96)
89
90 /*
91 * Implementation
92 * Multiprecision branch for _HA_ only
93 * No multiprecision branch for _LA_
94 * _z = _VARG1 * _VARG1 + _VARG2 * _VARG2
95 */
96 movaps %xmm0, %xmm8
97 movaps %xmm1, %xmm2
98 mulps %xmm0, %xmm8
99 mulps %xmm1, %xmm2
100
101 /*
102 * Variables
103 * Defines
104 * Constants loading
105 */
106 movups _sHalf+__svml_shypot_data_internal(%rip), %xmm5
107 addps %xmm2, %xmm8
108
109 /* _s0 ~ 1.0/sqrt(_z) */
110 rsqrtps %xmm8, %xmm10
111
112 /* First iteration */
113 movaps %xmm10, %xmm2
114 movaps %xmm8, %xmm3
115 mulps %xmm8, %xmm2
116 mulps %xmm5, %xmm10
117 movaps %xmm2, %xmm6
118 mulps %xmm10, %xmm6
119
120 /* Check _z exponent to be within borders [1E3 ; 60A] else goto Callout */
121 movdqu _LowBoundary+__svml_shypot_data_internal(%rip), %xmm4
122 subps %xmm6, %xmm5
123
124 /* Second iteration */
125 movaps %xmm5, %xmm7
126 pcmpgtd %xmm8, %xmm4
127 mulps %xmm2, %xmm5
128 mulps %xmm10, %xmm7
129 addps %xmm5, %xmm2
130 addps %xmm7, %xmm10
131
132 /* Finish second iteration in native precision for _LA_ */
133 movaps %xmm2, %xmm9
134 mulps %xmm2, %xmm9
135 pcmpgtd _HighBoundary+__svml_shypot_data_internal(%rip), %xmm3
136 subps %xmm8, %xmm9
137 mulps %xmm9, %xmm10
138 por %xmm3, %xmm4
139 movmskps %xmm4, %edx
140 subps %xmm10, %xmm2
141
142 /* The end of implementation */
143 testl %edx, %edx
144
145 /* Go to special inputs processing branch */
146 jne L(SPECIAL_VALUES_BRANCH)
147 # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1 xmm2
148
149 /* Restore registers
150 * and exit the function
151 */
152
153L(EXIT):
154 movaps %xmm2, %xmm0
155 addq $88, %rsp
156 cfi_def_cfa_offset(8)
157 ret
158 cfi_def_cfa_offset(96)
159
160 /* Branch to process
161 * special inputs
162 */
163
164L(SPECIAL_VALUES_BRANCH):
165 movups %xmm0, 32(%rsp)
166 movups %xmm1, 48(%rsp)
167 movups %xmm2, 64(%rsp)
168 # LOE rbx rbp r12 r13 r14 r15 edx
169
170 xorl %eax, %eax
171 movq %r12, 16(%rsp)
172 cfi_offset(12, -80)
173 movl %eax, %r12d
174 movq %r13, 8(%rsp)
175 cfi_offset(13, -88)
176 movl %edx, %r13d
177 movq %r14, (%rsp)
178 cfi_offset(14, -96)
179 # LOE rbx rbp r15 r12d r13d
180
181 /* Range mask
182 * bits check
183 */
184
185L(RANGEMASK_CHECK):
186 btl %r12d, %r13d
187
188 /* Call scalar math function */
189 jc L(SCALAR_MATH_CALL)
190 # LOE rbx rbp r15 r12d r13d
191
192 /* Special inputs
193 * processing loop
194 */
195
196L(SPECIAL_VALUES_LOOP):
197 incl %r12d
198 cmpl $4, %r12d
199
200 /* Check bits in range mask */
201 jl L(RANGEMASK_CHECK)
202 # LOE rbx rbp r15 r12d r13d
203
204 movq 16(%rsp), %r12
205 cfi_restore(12)
206 movq 8(%rsp), %r13
207 cfi_restore(13)
208 movq (%rsp), %r14
209 cfi_restore(14)
210 movups 64(%rsp), %xmm2
211
212 /* Go to exit */
213 jmp L(EXIT)
214 cfi_offset(12, -80)
215 cfi_offset(13, -88)
216 cfi_offset(14, -96)
217 # LOE rbx rbp r12 r13 r14 r15 xmm2
218
219 /* Scalar math function call
220 * to process special input
221 */
222
223L(SCALAR_MATH_CALL):
224 movl %r12d, %r14d
225 movss 32(%rsp, %r14, 4), %xmm0
226 movss 48(%rsp, %r14, 4), %xmm1
227 call hypotf@PLT
228 # LOE rbx rbp r14 r15 r12d r13d xmm0
229
230 movss %xmm0, 64(%rsp, %r14, 4)
231
232 /* Process special inputs in loop */
233 jmp L(SPECIAL_VALUES_LOOP)
234 # LOE rbx rbp r15 r12d r13d
235END(_ZGVbN4vv_hypotf_sse4)
236
237 .section .rodata, "a"
238 .align 16
239
240#ifdef __svml_shypot_data_internal_typedef
241typedef unsigned int VUINT32;
242typedef struct {
243 __declspec(align(16)) VUINT32 _sHiLoMask[4][1];
244 __declspec(align(16)) VUINT32 _sAbsMask[4][1];
245 __declspec(align(16)) VUINT32 _sHalf[4][1];
246 __declspec(align(16)) VUINT32 _LowBoundary[4][1];
247 __declspec(align(16)) VUINT32 _HighBoundary[4][1];
248} __svml_shypot_data_internal;
249#endif
250__svml_shypot_data_internal:
251 /* legacy algorithm */
252 .long 0xFFF80000, 0xFFF80000, 0xFFF80000, 0xFFF80000 /* _sHiLoMask */
253 .align 16
254 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _sAbsMask */
255 .align 16
256 .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _sHalf */
257 .align 16
258 .long 0x1E300000, 0x1E300000, 0x1E300000, 0x1E300000 /* _LowBoundary */
259 .align 16
260 .long 0x60A00000, 0x60A00000, 0x60A00000, 0x60A00000 /* _HighBoundary */
261 .align 16
262 .type __svml_shypot_data_internal, @object
263 .size __svml_shypot_data_internal, .-__svml_shypot_data_internal
264

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_s_hypotf4_core_sse4.S