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 |
86 | ENTRY(_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 | |
153 | L(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 | |
164 | L(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 | |
185 | L(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 | |
196 | L(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 | |
223 | L(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 |
235 | END(_ZGVbN4vv_hypotf_sse4) |
236 | |
237 | .section .rodata, "a" |
238 | .align 16 |
239 | |
240 | #ifdef __svml_shypot_data_internal_typedef |
241 | typedef unsigned int VUINT32; |
242 | typedef 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 | |