1/* Function hypotf vectorized with AVX-512.
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 _sAbsMask 0
78#define _sHalf 64
79#define _iExpBound 128
80
81#include <sysdep.h>
82
83 .section .text.evex512, "ax", @progbits
84ENTRY(_ZGVeN16vv_hypotf_skx)
85 pushq %rbp
86 cfi_def_cfa_offset(16)
87 movq %rsp, %rbp
88 cfi_def_cfa(6, 16)
89 cfi_offset(6, -16)
90 andq $-64, %rsp
91 subq $256, %rsp
92 vgetexpps {sae}, %zmm0, %zmm2
93 vgetexpps {sae}, %zmm1, %zmm3
94 vmovups _sHalf+__svml_shypot_data_internal(%rip), %zmm6
95 vmaxps {sae}, %zmm3, %zmm2, %zmm4
96 vmulps {rn-sae}, %zmm0, %zmm0, %zmm2
97 vandps _sAbsMask+__svml_shypot_data_internal(%rip), %zmm4, %zmm5
98 vfmadd231ps {rn-sae}, %zmm1, %zmm1, %zmm2
99 vpcmpd $5, _iExpBound+__svml_shypot_data_internal(%rip), %zmm5, %k0
100 vrsqrt14ps %zmm2, %zmm7
101 kmovw %k0, %edx
102 vmulps {rn-sae}, %zmm7, %zmm2, %zmm9
103 vmulps {rn-sae}, %zmm7, %zmm6, %zmm8
104 vfnmadd231ps {rn-sae}, %zmm9, %zmm9, %zmm2
105 vfmadd213ps {rn-sae}, %zmm9, %zmm8, %zmm2
106
107 /*
108 * VSCALEF( S, _VRES1, _VRES1, sExp );
109 * The end of implementation
110 */
111 testl %edx, %edx
112
113 /* Go to special inputs processing branch */
114 jne L(SPECIAL_VALUES_BRANCH)
115 # LOE rbx r12 r13 r14 r15 edx zmm0 zmm1 zmm2
116
117 /* Restore registers
118 * and exit the function
119 */
120
121L(EXIT):
122 vmovaps %zmm2, %zmm0
123 movq %rbp, %rsp
124 popq %rbp
125 cfi_def_cfa(7, 8)
126 cfi_restore(6)
127 ret
128 cfi_def_cfa(6, 16)
129 cfi_offset(6, -16)
130
131 /* Branch to process
132 * special inputs
133 */
134
135L(SPECIAL_VALUES_BRANCH):
136 vmovups %zmm0, 64(%rsp)
137 vmovups %zmm1, 128(%rsp)
138 vmovups %zmm2, 192(%rsp)
139 # LOE rbx r12 r13 r14 r15 edx zmm2
140
141 xorl %eax, %eax
142 # LOE rbx r12 r13 r14 r15 eax edx
143
144 vzeroupper
145 movq %r12, 16(%rsp)
146 /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -240; DW_OP_plus) */
147 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x10, 0xff, 0xff, 0xff, 0x22
148 movl %eax, %r12d
149 movq %r13, 8(%rsp)
150 /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -248; DW_OP_plus) */
151 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x08, 0xff, 0xff, 0xff, 0x22
152 movl %edx, %r13d
153 movq %r14, (%rsp)
154 /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -256; DW_OP_plus) */
155 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x00, 0xff, 0xff, 0xff, 0x22
156 # LOE rbx r15 r12d r13d
157
158 /* Range mask
159 * bits check
160 */
161
162L(RANGEMASK_CHECK):
163 btl %r12d, %r13d
164
165 /* Call scalar math function */
166 jc L(SCALAR_MATH_CALL)
167 # LOE rbx r15 r12d r13d
168
169 /* Special inputs
170 * processing loop
171 */
172
173L(SPECIAL_VALUES_LOOP):
174 incl %r12d
175 cmpl $16, %r12d
176
177 /* Check bits in range mask */
178 jl L(RANGEMASK_CHECK)
179 # LOE rbx r15 r12d r13d
180
181 movq 16(%rsp), %r12
182 cfi_restore(12)
183 movq 8(%rsp), %r13
184 cfi_restore(13)
185 movq (%rsp), %r14
186 cfi_restore(14)
187 vmovups 192(%rsp), %zmm2
188
189 /* Go to exit */
190 jmp L(EXIT)
191 /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -240; DW_OP_plus) */
192 .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x10, 0xff, 0xff, 0xff, 0x22
193 /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -248; DW_OP_plus) */
194 .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x08, 0xff, 0xff, 0xff, 0x22
195 /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -256; DW_OP_plus) */
196 .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x00, 0xff, 0xff, 0xff, 0x22
197 # LOE rbx r12 r13 r14 r15 zmm2
198
199 /* Scalar math function call
200 * to process special input
201 */
202
203L(SCALAR_MATH_CALL):
204 movl %r12d, %r14d
205 vmovss 64(%rsp, %r14, 4), %xmm0
206 vmovss 128(%rsp, %r14, 4), %xmm1
207 call hypotf@PLT
208 # LOE rbx r14 r15 r12d r13d xmm0
209
210 vmovss %xmm0, 192(%rsp, %r14, 4)
211
212 /* Process special inputs in loop */
213 jmp L(SPECIAL_VALUES_LOOP)
214 # LOE rbx r15 r12d r13d
215END(_ZGVeN16vv_hypotf_skx)
216
217 .section .rodata, "a"
218 .align 64
219
220#ifdef __svml_shypot_data_internal_typedef
221typedef unsigned int VUINT32;
222typedef struct {
223 __declspec(align(64)) VUINT32 _sAbsMask[16][1];
224 __declspec(align(64)) VUINT32 _sHalf[16][1];
225 __declspec(align(64)) VUINT32 _iExpBound[16][1];
226} __svml_shypot_data_internal;
227#endif
228__svml_shypot_data_internal:
229 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _sAbsMask */
230 .align 64
231 .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _sHalf */
232 /* fma based algorithm*/
233 .align 64
234 .long 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000, 0x427C0000 /* _iExpBound */
235 .align 64
236 .type __svml_shypot_data_internal, @object
237 .size __svml_shypot_data_internal, .-__svml_shypot_data_internal
238

source code of glibc/sysdeps/x86_64/fpu/multiarch/svml_s_hypotf16_core_avx512.S