1 | /* Function cbrt 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 | * x=2^{3*k+j} * 1.b1 b2 ... b5 b6 ... b52 |
23 | * Let r=(x*2^{-3k-j} - 1.b1 b2 ... b5 1)* rcp[b1 b2 ..b5], |
24 | * where rcp[b1 b2 .. b5]=1/(1.b1 b2 b3 b4 b5 1) in double precision |
25 | * cbrt(2^j * 1. b1 b2 .. b5 1) is approximated as T[j][b1..b5]+D[j][b1..b5] |
26 | * (T stores the high 53 bits, D stores the low order bits) |
27 | * Result=2^k*T+(2^k*T*r)*P+2^k*D |
28 | * where P=p1+p2*r+..+p8*r^7 |
29 | * |
30 | */ |
31 | |
32 | /* Offsets for data table __svml_dcbrt_data_internal |
33 | */ |
34 | #define _dRcp 0 |
35 | #define _dCbrtHiLo 256 |
36 | #define _dA7 1024 |
37 | #define _dA6 1056 |
38 | #define _dA5 1088 |
39 | #define _dA4 1120 |
40 | #define _dA3 1152 |
41 | #define _dA2 1184 |
42 | #define _dA1 1216 |
43 | #define _dNeg65Div64 1248 |
44 | #define _dSgnf6Mask 1280 |
45 | #define _dNegOne 1312 |
46 | #define _dMantissaMask 1344 |
47 | #define _lExpHiMask 1376 |
48 | #define _lExpLoMask 1408 |
49 | #define _l1556 1440 |
50 | #define _iRcpIndexMask 1472 |
51 | #define _iAbsMask 1504 |
52 | #define _iSignMask 1536 |
53 | #define _iBias 1568 |
54 | #define _iSub 1600 |
55 | #define _iCmp 1632 |
56 | |
57 | #include <sysdep.h> |
58 | |
59 | .section .text.avx2, "ax" , @progbits |
60 | ENTRY(_ZGVdN4v_cbrt_avx2) |
61 | pushq %rbp |
62 | cfi_def_cfa_offset(16) |
63 | movq %rsp, %rbp |
64 | cfi_def_cfa(6, 16) |
65 | cfi_offset(6, -16) |
66 | andq $-32, %rsp |
67 | subq $96, %rsp |
68 | |
69 | /* Load 1/(1+iRcpIndex/32+1/64) reciprocal table value */ |
70 | lea __svml_dcbrt_data_internal(%rip), %rax |
71 | vmovapd %ymm0, %ymm5 |
72 | |
73 | /* |
74 | * Declarations |
75 | * Load constants |
76 | * Get iX - high part of argument |
77 | */ |
78 | vextractf128 $1, %ymm5, %xmm6 |
79 | |
80 | /* Calculate CbrtIndex */ |
81 | vpsrlq $52, %ymm5, %ymm15 |
82 | vshufps $221, %xmm6, %xmm5, %xmm4 |
83 | |
84 | /* Calculate Rcp table index */ |
85 | vandps _iRcpIndexMask+__svml_dcbrt_data_internal(%rip), %xmm4, %xmm10 |
86 | vpsrld $12, %xmm10, %xmm3 |
87 | vmovd %xmm3, %ecx |
88 | |
89 | /* If the exponent field is zero - go to callout to process denormals */ |
90 | vandps _iAbsMask+__svml_dcbrt_data_internal(%rip), %xmm4, %xmm7 |
91 | |
92 | /* Compute 2^k */ |
93 | vpsrld $20, %xmm4, %xmm4 |
94 | vpsubd _iSub+__svml_dcbrt_data_internal(%rip), %xmm7, %xmm8 |
95 | vandps _lExpLoMask+__svml_dcbrt_data_internal(%rip), %ymm15, %ymm0 |
96 | vpmuludq _l1556+__svml_dcbrt_data_internal(%rip), %ymm0, %ymm6 |
97 | vpextrd $2, %xmm3, %edi |
98 | movslq %ecx, %rcx |
99 | vpextrd $1, %xmm3, %esi |
100 | movslq %edi, %rdi |
101 | vpextrd $3, %xmm3, %r8d |
102 | movslq %esi, %rsi |
103 | movslq %r8d, %r8 |
104 | vpcmpgtd _iCmp+__svml_dcbrt_data_internal(%rip), %xmm8, %xmm9 |
105 | vmovsd (%rax, %rcx), %xmm11 |
106 | vmovmskps %xmm9, %edx |
107 | vmovsd (%rax, %rdi), %xmm13 |
108 | vmovhpd (%rax, %rsi), %xmm11, %xmm12 |
109 | vmovhpd (%rax, %r8), %xmm13, %xmm14 |
110 | vextractf128 $1, %ymm6, %xmm7 |
111 | vshufps $136, %xmm7, %xmm6, %xmm8 |
112 | vmovups __VUNPACK_ODD_ind1.613.0.1(%rip), %ymm7 |
113 | vextractf128 $1, %ymm0, %xmm1 |
114 | vshufps $136, %xmm1, %xmm0, %xmm9 |
115 | vpsrld $14, %xmm8, %xmm1 |
116 | vpsubd %xmm1, %xmm9, %xmm10 |
117 | vpaddd %xmm1, %xmm1, %xmm11 |
118 | |
119 | /* |
120 | * VAND( L, l2k, = l2k, lExpHiMask ); |
121 | * Argument reduction Z |
122 | */ |
123 | vandpd _dMantissaMask+__svml_dcbrt_data_internal(%rip), %ymm5, %ymm9 |
124 | vinsertf128 $1, %xmm14, %ymm12, %ymm2 |
125 | vpsubd %xmm11, %xmm10, %xmm12 |
126 | vpslld $8, %xmm12, %xmm13 |
127 | vpaddd %xmm13, %xmm3, %xmm15 |
128 | |
129 | /* Load cbrt(2^j*(1+iRcpIndex/32+1/64)) Hi & Lo values */ |
130 | vmovd %xmm15, %r9d |
131 | vpextrd $2, %xmm15, %r11d |
132 | movslq %r9d, %r9 |
133 | vpextrd $1, %xmm15, %r10d |
134 | movslq %r11d, %r11 |
135 | vpextrd $3, %xmm15, %ecx |
136 | movslq %r10d, %r10 |
137 | movslq %ecx, %rcx |
138 | vmovsd 256(%rax, %r9), %xmm3 |
139 | vmovsd 256(%rax, %r11), %xmm0 |
140 | vandpd _dSgnf6Mask+__svml_dcbrt_data_internal(%rip), %ymm5, %ymm10 |
141 | vmovhpd 256(%rax, %r10), %xmm3, %xmm14 |
142 | vmovhpd 256(%rax, %rcx), %xmm0, %xmm3 |
143 | vorpd _dNegOne+__svml_dcbrt_data_internal(%rip), %ymm9, %ymm11 |
144 | vorpd _dNeg65Div64+__svml_dcbrt_data_internal(%rip), %ymm10, %ymm12 |
145 | vsubpd %ymm12, %ymm11, %ymm13 |
146 | vmulpd %ymm13, %ymm2, %ymm2 |
147 | vinsertf128 $1, %xmm3, %ymm14, %ymm0 |
148 | vpand _iSignMask+__svml_dcbrt_data_internal(%rip), %xmm4, %xmm3 |
149 | vpor _iBias+__svml_dcbrt_data_internal(%rip), %xmm3, %xmm4 |
150 | vpaddd %xmm1, %xmm4, %xmm1 |
151 | vpslld $20, %xmm1, %xmm6 |
152 | |
153 | /* Polynomial */ |
154 | vmovupd _dA7+__svml_dcbrt_data_internal(%rip), %ymm1 |
155 | vfmadd213pd _dA6+__svml_dcbrt_data_internal(%rip), %ymm2, %ymm1 |
156 | vfmadd213pd _dA5+__svml_dcbrt_data_internal(%rip), %ymm2, %ymm1 |
157 | vfmadd213pd _dA4+__svml_dcbrt_data_internal(%rip), %ymm2, %ymm1 |
158 | vfmadd213pd _dA3+__svml_dcbrt_data_internal(%rip), %ymm2, %ymm1 |
159 | vfmadd213pd _dA2+__svml_dcbrt_data_internal(%rip), %ymm2, %ymm1 |
160 | vfmadd213pd _dA1+__svml_dcbrt_data_internal(%rip), %ymm2, %ymm1 |
161 | vpermps %ymm6, %ymm7, %ymm8 |
162 | vandps __VUNPACK_ODD_mask.613.0.1(%rip), %ymm8, %ymm14 |
163 | |
164 | /* THi*2^k, TLo*2^k */ |
165 | vmulpd %ymm14, %ymm0, %ymm0 |
166 | |
167 | /* THi*2^k*Z */ |
168 | vmulpd %ymm0, %ymm2, %ymm2 |
169 | |
170 | /* Final reconstruction */ |
171 | vmulpd %ymm2, %ymm1, %ymm3 |
172 | vaddpd %ymm3, %ymm0, %ymm0 |
173 | testl %edx, %edx |
174 | |
175 | /* Go to special inputs processing branch */ |
176 | jne L(SPECIAL_VALUES_BRANCH) |
177 | # LOE rbx r12 r13 r14 r15 edx ymm0 ymm5 |
178 | |
179 | /* Restore registers |
180 | * and exit the function |
181 | */ |
182 | |
183 | L(EXIT): |
184 | movq %rbp, %rsp |
185 | popq %rbp |
186 | cfi_def_cfa(7, 8) |
187 | cfi_restore(6) |
188 | ret |
189 | cfi_def_cfa(6, 16) |
190 | cfi_offset(6, -16) |
191 | |
192 | /* Branch to process |
193 | * special inputs |
194 | */ |
195 | |
196 | L(SPECIAL_VALUES_BRANCH): |
197 | vmovupd %ymm5, 32(%rsp) |
198 | vmovupd %ymm0, 64(%rsp) |
199 | # LOE rbx r12 r13 r14 r15 edx ymm0 |
200 | |
201 | xorl %eax, %eax |
202 | # LOE rbx r12 r13 r14 r15 eax edx |
203 | |
204 | vzeroupper |
205 | movq %r12, 16(%rsp) |
206 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */ |
207 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 |
208 | movl %eax, %r12d |
209 | movq %r13, 8(%rsp) |
210 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */ |
211 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 |
212 | movl %edx, %r13d |
213 | movq %r14, (%rsp) |
214 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */ |
215 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 |
216 | # LOE rbx r15 r12d r13d |
217 | |
218 | /* Range mask |
219 | * bits check |
220 | */ |
221 | |
222 | L(RANGEMASK_CHECK): |
223 | btl %r12d, %r13d |
224 | |
225 | /* Call scalar math function */ |
226 | jc L(SCALAR_MATH_CALL) |
227 | # LOE rbx r15 r12d r13d |
228 | |
229 | /* Special inputs |
230 | * processing loop |
231 | */ |
232 | |
233 | L(SPECIAL_VALUES_LOOP): |
234 | incl %r12d |
235 | cmpl $4, %r12d |
236 | |
237 | /* Check bits in range mask */ |
238 | jl L(RANGEMASK_CHECK) |
239 | # LOE rbx r15 r12d r13d |
240 | |
241 | movq 16(%rsp), %r12 |
242 | cfi_restore(12) |
243 | movq 8(%rsp), %r13 |
244 | cfi_restore(13) |
245 | movq (%rsp), %r14 |
246 | cfi_restore(14) |
247 | vmovupd 64(%rsp), %ymm0 |
248 | |
249 | /* Go to exit */ |
250 | jmp L(EXIT) |
251 | /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */ |
252 | .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 |
253 | /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */ |
254 | .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 |
255 | /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */ |
256 | .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 |
257 | # LOE rbx r12 r13 r14 r15 ymm0 |
258 | |
259 | /* Scalar math function call |
260 | * to process special input |
261 | */ |
262 | |
263 | L(SCALAR_MATH_CALL): |
264 | movl %r12d, %r14d |
265 | vmovsd 32(%rsp, %r14, 8), %xmm0 |
266 | call cbrt@PLT |
267 | # LOE rbx r14 r15 r12d r13d xmm0 |
268 | |
269 | vmovsd %xmm0, 64(%rsp, %r14, 8) |
270 | |
271 | /* Process special inputs in loop */ |
272 | jmp L(SPECIAL_VALUES_LOOP) |
273 | # LOE rbx r15 r12d r13d |
274 | END(_ZGVdN4v_cbrt_avx2) |
275 | .section .rodata, "a" |
276 | .align 32 |
277 | |
278 | __VUNPACK_ODD_ind1.613.0.1: |
279 | .rept 3 |
280 | .long 0 |
281 | .endr |
282 | .long 1 |
283 | .long 0 |
284 | .long 2 |
285 | .long 0 |
286 | .long 3 |
287 | .align 32 |
288 | |
289 | __VUNPACK_ODD_mask.613.0.1: |
290 | .long 0 |
291 | .long -1 |
292 | .long 0 |
293 | .long -1 |
294 | .long 0 |
295 | .long -1 |
296 | .long 0 |
297 | .long -1 |
298 | |
299 | .section .rodata, "a" |
300 | .align 32 |
301 | |
302 | #ifdef __svml_dcbrt_data_internal_typedef |
303 | typedef unsigned int VUINT32; |
304 | typedef struct { |
305 | __declspec(align(32)) VUINT32 _dRcp[32][2]; |
306 | __declspec(align(32)) VUINT32 _dCbrtHiLo[96][2]; |
307 | __declspec(align(32)) VUINT32 _dA7[4][2]; |
308 | __declspec(align(32)) VUINT32 _dA6[4][2]; |
309 | __declspec(align(32)) VUINT32 _dA5[4][2]; |
310 | __declspec(align(32)) VUINT32 _dA4[4][2]; |
311 | __declspec(align(32)) VUINT32 _dA3[4][2]; |
312 | __declspec(align(32)) VUINT32 _dA2[4][2]; |
313 | __declspec(align(32)) VUINT32 _dA1[4][2]; |
314 | __declspec(align(32)) VUINT32 _dNeg65Div64[4][2]; |
315 | __declspec(align(32)) VUINT32 _dSgnf6Mask[4][2]; |
316 | __declspec(align(32)) VUINT32 _dNegOne[4][2]; |
317 | __declspec(align(32)) VUINT32 _dMantissaMask[4][2]; |
318 | __declspec(align(32)) VUINT32 _lExpHiMask[4][2]; |
319 | __declspec(align(32)) VUINT32 _lExpLoMask[4][2]; |
320 | __declspec(align(32)) VUINT32 _l1556[4][2]; |
321 | __declspec(align(32)) VUINT32 _iRcpIndexMask[8][1]; |
322 | __declspec(align(32)) VUINT32 _iAbsMask[8][1]; |
323 | __declspec(align(32)) VUINT32 _iSignMask[8][1]; |
324 | __declspec(align(32)) VUINT32 _iBias[8][1]; |
325 | __declspec(align(32)) VUINT32 _iSub[8][1]; |
326 | __declspec(align(32)) VUINT32 _iCmp[8][1]; |
327 | } __svml_dcbrt_data_internal; |
328 | #endif |
329 | __svml_dcbrt_data_internal: |
330 | /* _dRcp */ |
331 | .quad 0xBFEF81F81F81F820 /* (1/(1+0/32+1/64)) = -.984615 */ |
332 | .quad 0xBFEE9131ABF0B767 /* (1/(1+1/32+1/64)) = -.955224 */ |
333 | .quad 0xBFEDAE6076B981DB /* (1/(1+2/32+1/64)) = -.927536 */ |
334 | .quad 0xBFECD85689039B0B /* (1/(1+3/32+1/64)) = -.901408 */ |
335 | .quad 0xBFEC0E070381C0E0 /* (1/(1+4/32+1/64)) = -.876712 */ |
336 | .quad 0xBFEB4E81B4E81B4F /* (1/(1+5/32+1/64)) = -.853333 */ |
337 | .quad 0xBFEA98EF606A63BE /* (1/(1+6/32+1/64)) = -.831169 */ |
338 | .quad 0xBFE9EC8E951033D9 /* (1/(1+7/32+1/64)) = -.810127 */ |
339 | .quad 0xBFE948B0FCD6E9E0 /* (1/(1+8/32+1/64)) = -.790123 */ |
340 | .quad 0xBFE8ACB90F6BF3AA /* (1/(1+9/32+1/64)) = -.771084 */ |
341 | .quad 0xBFE8181818181818 /* (1/(1+10/32+1/64)) = -.752941 */ |
342 | .quad 0xBFE78A4C8178A4C8 /* (1/(1+11/32+1/64)) = -.735632 */ |
343 | .quad 0xBFE702E05C0B8170 /* (1/(1+12/32+1/64)) = -.719101 */ |
344 | .quad 0xBFE6816816816817 /* (1/(1+13/32+1/64)) = -.703297 */ |
345 | .quad 0xBFE6058160581606 /* (1/(1+14/32+1/64)) = -.688172 */ |
346 | .quad 0xBFE58ED2308158ED /* (1/(1+15/32+1/64)) = -.673684 */ |
347 | .quad 0xBFE51D07EAE2F815 /* (1/(1+16/32+1/64)) = -.659794 */ |
348 | .quad 0xBFE4AFD6A052BF5B /* (1/(1+17/32+1/64)) = -.646465 */ |
349 | .quad 0xBFE446F86562D9FB /* (1/(1+18/32+1/64)) = -.633663 */ |
350 | .quad 0xBFE3E22CBCE4A902 /* (1/(1+19/32+1/64)) = -.621359 */ |
351 | .quad 0xBFE3813813813814 /* (1/(1+20/32+1/64)) = -.609524 */ |
352 | .quad 0xBFE323E34A2B10BF /* (1/(1+21/32+1/64)) = -.598131 */ |
353 | .quad 0xBFE2C9FB4D812CA0 /* (1/(1+22/32+1/64)) = -.587156 */ |
354 | .quad 0xBFE27350B8812735 /* (1/(1+23/32+1/64)) = -.576577 */ |
355 | .quad 0xBFE21FB78121FB78 /* (1/(1+24/32+1/64)) = -.566372 */ |
356 | .quad 0xBFE1CF06ADA2811D /* (1/(1+25/32+1/64)) = -.556522 */ |
357 | .quad 0xBFE1811811811812 /* (1/(1+26/32+1/64)) = -.547009 */ |
358 | .quad 0xBFE135C81135C811 /* (1/(1+27/32+1/64)) = -.537815 */ |
359 | .quad 0xBFE0ECF56BE69C90 /* (1/(1+28/32+1/64)) = -.528926 */ |
360 | .quad 0xBFE0A6810A6810A7 /* (1/(1+29/32+1/64)) = -.520325 */ |
361 | .quad 0xBFE0624DD2F1A9FC /* (1/(1+30/32+1/64)) = -.512 */ |
362 | .quad 0xBFE0204081020408 /* (1/(1+31/32+1/64)) = -.503937 */ |
363 | /* _dCbrtHiLo */ |
364 | .align 32 |
365 | .quad 0x3FF01539221D4C97 /* HI((2^0*(1+0/32+1/64))^(1/3)) = 1.005181 */ |
366 | .quad 0x3FF03F06771A2E33 /* HI((2^0*(1+1/32+1/64))^(1/3)) = 1.015387 */ |
367 | .quad 0x3FF06800E629D671 /* HI((2^0*(1+2/32+1/64))^(1/3)) = 1.025391 */ |
368 | .quad 0x3FF090328731DEB2 /* HI((2^0*(1+3/32+1/64))^(1/3)) = 1.035204 */ |
369 | .quad 0x3FF0B7A4B1BD64AC /* HI((2^0*(1+4/32+1/64))^(1/3)) = 1.044835 */ |
370 | .quad 0x3FF0DE601024FB87 /* HI((2^0*(1+5/32+1/64))^(1/3)) = 1.054291 */ |
371 | .quad 0x3FF1046CB0597000 /* HI((2^0*(1+6/32+1/64))^(1/3)) = 1.06358 */ |
372 | .quad 0x3FF129D212A9BA9B /* HI((2^0*(1+7/32+1/64))^(1/3)) = 1.07271 */ |
373 | .quad 0x3FF14E9736CDAF38 /* HI((2^0*(1+8/32+1/64))^(1/3)) = 1.081687 */ |
374 | .quad 0x3FF172C2A772F507 /* HI((2^0*(1+9/32+1/64))^(1/3)) = 1.090518 */ |
375 | .quad 0x3FF1965A848001D3 /* HI((2^0*(1+10/32+1/64))^(1/3)) = 1.099207 */ |
376 | .quad 0x3FF1B9648C38C55D /* HI((2^0*(1+11/32+1/64))^(1/3)) = 1.107762 */ |
377 | .quad 0x3FF1DBE6236A0C45 /* HI((2^0*(1+12/32+1/64))^(1/3)) = 1.116186 */ |
378 | .quad 0x3FF1FDE45CBB1F9F /* HI((2^0*(1+13/32+1/64))^(1/3)) = 1.124485 */ |
379 | .quad 0x3FF21F63FF409042 /* HI((2^0*(1+14/32+1/64))^(1/3)) = 1.132664 */ |
380 | .quad 0x3FF240698C6746E5 /* HI((2^0*(1+15/32+1/64))^(1/3)) = 1.140726 */ |
381 | .quad 0x3FF260F9454BB99B /* HI((2^0*(1+16/32+1/64))^(1/3)) = 1.148675 */ |
382 | .quad 0x3FF281172F8E7073 /* HI((2^0*(1+17/32+1/64))^(1/3)) = 1.156516 */ |
383 | .quad 0x3FF2A0C719B4B6D0 /* HI((2^0*(1+18/32+1/64))^(1/3)) = 1.164252 */ |
384 | .quad 0x3FF2C00C9F2263EC /* HI((2^0*(1+19/32+1/64))^(1/3)) = 1.171887 */ |
385 | .quad 0x3FF2DEEB2BB7FB78 /* HI((2^0*(1+20/32+1/64))^(1/3)) = 1.179423 */ |
386 | .quad 0x3FF2FD65FF1EFBBC /* HI((2^0*(1+21/32+1/64))^(1/3)) = 1.186865 */ |
387 | .quad 0x3FF31B802FCCF6A2 /* HI((2^0*(1+22/32+1/64))^(1/3)) = 1.194214 */ |
388 | .quad 0x3FF3393CADC50708 /* HI((2^0*(1+23/32+1/64))^(1/3)) = 1.201474 */ |
389 | .quad 0x3FF3569E451E4C2A /* HI((2^0*(1+24/32+1/64))^(1/3)) = 1.208647 */ |
390 | .quad 0x3FF373A7A0554CDE /* HI((2^0*(1+25/32+1/64))^(1/3)) = 1.215736 */ |
391 | .quad 0x3FF3905B4A6D76CE /* HI((2^0*(1+26/32+1/64))^(1/3)) = 1.222743 */ |
392 | .quad 0x3FF3ACBBB0E756B6 /* HI((2^0*(1+27/32+1/64))^(1/3)) = 1.229671 */ |
393 | .quad 0x3FF3C8CB258FA340 /* HI((2^0*(1+28/32+1/64))^(1/3)) = 1.236522 */ |
394 | .quad 0x3FF3E48BE02AC0CE /* HI((2^0*(1+29/32+1/64))^(1/3)) = 1.243297 */ |
395 | .quad 0x3FF4000000000000 /* HI((2^0*(1+30/32+1/64))^(1/3)) = 1.25 */ |
396 | .quad 0x3FF41B298D47800E /* HI((2^0*(1+31/32+1/64))^(1/3)) = 1.256631 */ |
397 | .quad 0x3FF443604B34D9B2 /* HI((2^1*(1+0/32+1/64))^(1/3)) = 1.266449 */ |
398 | .quad 0x3FF4780B20906571 /* HI((2^1*(1+1/32+1/64))^(1/3)) = 1.279307 */ |
399 | .quad 0x3FF4ABAC3EE06706 /* HI((2^1*(1+2/32+1/64))^(1/3)) = 1.291912 */ |
400 | .quad 0x3FF4DE505DA66B8D /* HI((2^1*(1+3/32+1/64))^(1/3)) = 1.304276 */ |
401 | .quad 0x3FF51003420A5C07 /* HI((2^1*(1+4/32+1/64))^(1/3)) = 1.316409 */ |
402 | .quad 0x3FF540CFD6FD11C1 /* HI((2^1*(1+5/32+1/64))^(1/3)) = 1.328323 */ |
403 | .quad 0x3FF570C04260716B /* HI((2^1*(1+6/32+1/64))^(1/3)) = 1.340027 */ |
404 | .quad 0x3FF59FDDF7A45F38 /* HI((2^1*(1+7/32+1/64))^(1/3)) = 1.35153 */ |
405 | .quad 0x3FF5CE31C83539DF /* HI((2^1*(1+8/32+1/64))^(1/3)) = 1.36284 */ |
406 | .quad 0x3FF5FBC3F20966A4 /* HI((2^1*(1+9/32+1/64))^(1/3)) = 1.373966 */ |
407 | .quad 0x3FF6289C2C8F1B70 /* HI((2^1*(1+10/32+1/64))^(1/3)) = 1.384915 */ |
408 | .quad 0x3FF654C1B4316DCF /* HI((2^1*(1+11/32+1/64))^(1/3)) = 1.395693 */ |
409 | .quad 0x3FF6803B54A34E44 /* HI((2^1*(1+12/32+1/64))^(1/3)) = 1.406307 */ |
410 | .quad 0x3FF6AB0F72182659 /* HI((2^1*(1+13/32+1/64))^(1/3)) = 1.416763 */ |
411 | .quad 0x3FF6D544118C08BC /* HI((2^1*(1+14/32+1/64))^(1/3)) = 1.427067 */ |
412 | .quad 0x3FF6FEDEE0388D4A /* HI((2^1*(1+15/32+1/64))^(1/3)) = 1.437224 */ |
413 | .quad 0x3FF727E53A4F645E /* HI((2^1*(1+16/32+1/64))^(1/3)) = 1.44724 */ |
414 | .quad 0x3FF7505C31104114 /* HI((2^1*(1+17/32+1/64))^(1/3)) = 1.457119 */ |
415 | .quad 0x3FF77848904CD549 /* HI((2^1*(1+18/32+1/64))^(1/3)) = 1.466866 */ |
416 | .quad 0x3FF79FAEE36B2534 /* HI((2^1*(1+19/32+1/64))^(1/3)) = 1.476485 */ |
417 | .quad 0x3FF7C69379F4605B /* HI((2^1*(1+20/32+1/64))^(1/3)) = 1.48598 */ |
418 | .quad 0x3FF7ECFA6BBCA391 /* HI((2^1*(1+21/32+1/64))^(1/3)) = 1.495356 */ |
419 | .quad 0x3FF812E79CAE7EB9 /* HI((2^1*(1+22/32+1/64))^(1/3)) = 1.504615 */ |
420 | .quad 0x3FF8385EC043C71D /* HI((2^1*(1+23/32+1/64))^(1/3)) = 1.513762 */ |
421 | .quad 0x3FF85D635CB41B9D /* HI((2^1*(1+24/32+1/64))^(1/3)) = 1.5228 */ |
422 | .quad 0x3FF881F8CDE083DB /* HI((2^1*(1+25/32+1/64))^(1/3)) = 1.531731 */ |
423 | .quad 0x3FF8A6224802B8A8 /* HI((2^1*(1+26/32+1/64))^(1/3)) = 1.54056 */ |
424 | .quad 0x3FF8C9E2DA25E5E4 /* HI((2^1*(1+27/32+1/64))^(1/3)) = 1.549289 */ |
425 | .quad 0x3FF8ED3D706E1010 /* HI((2^1*(1+28/32+1/64))^(1/3)) = 1.55792 */ |
426 | .quad 0x3FF91034D632B6DF /* HI((2^1*(1+29/32+1/64))^(1/3)) = 1.566457 */ |
427 | .quad 0x3FF932CBB7F0CF2D /* HI((2^1*(1+30/32+1/64))^(1/3)) = 1.574901 */ |
428 | .quad 0x3FF95504A517BF3A /* HI((2^1*(1+31/32+1/64))^(1/3)) = 1.583256 */ |
429 | .quad 0x3FF987AF34F8BB19 /* HI((2^2*(1+0/32+1/64))^(1/3)) = 1.595626 */ |
430 | .quad 0x3FF9CA0A8337B317 /* HI((2^2*(1+1/32+1/64))^(1/3)) = 1.611826 */ |
431 | .quad 0x3FFA0B1709CC13D5 /* HI((2^2*(1+2/32+1/64))^(1/3)) = 1.627708 */ |
432 | .quad 0x3FFA4AE4CE6419ED /* HI((2^2*(1+3/32+1/64))^(1/3)) = 1.643285 */ |
433 | .quad 0x3FFA8982A5567031 /* HI((2^2*(1+4/32+1/64))^(1/3)) = 1.658572 */ |
434 | .quad 0x3FFAC6FE500AB570 /* HI((2^2*(1+5/32+1/64))^(1/3)) = 1.673582 */ |
435 | .quad 0x3FFB036497A15A17 /* HI((2^2*(1+6/32+1/64))^(1/3)) = 1.688328 */ |
436 | .quad 0x3FFB3EC164671755 /* HI((2^2*(1+7/32+1/64))^(1/3)) = 1.702821 */ |
437 | .quad 0x3FFB791FD288C46F /* HI((2^2*(1+8/32+1/64))^(1/3)) = 1.717071 */ |
438 | .quad 0x3FFBB28A44693BE4 /* HI((2^2*(1+9/32+1/64))^(1/3)) = 1.731089 */ |
439 | .quad 0x3FFBEB0A72EB6E31 /* HI((2^2*(1+10/32+1/64))^(1/3)) = 1.744883 */ |
440 | .quad 0x3FFC22A97BF5F697 /* HI((2^2*(1+11/32+1/64))^(1/3)) = 1.758462 */ |
441 | .quad 0x3FFC596FEF6AF983 /* HI((2^2*(1+12/32+1/64))^(1/3)) = 1.771835 */ |
442 | .quad 0x3FFC8F65DAC655A3 /* HI((2^2*(1+13/32+1/64))^(1/3)) = 1.785009 */ |
443 | .quad 0x3FFCC492D38CE8D9 /* HI((2^2*(1+14/32+1/64))^(1/3)) = 1.797992 */ |
444 | .quad 0x3FFCF8FE00B19367 /* HI((2^2*(1+15/32+1/64))^(1/3)) = 1.810789 */ |
445 | .quad 0x3FFD2CAE230F8709 /* HI((2^2*(1+16/32+1/64))^(1/3)) = 1.823408 */ |
446 | .quad 0x3FFD5FA99D15208F /* HI((2^2*(1+17/32+1/64))^(1/3)) = 1.835855 */ |
447 | .quad 0x3FFD91F679B6E505 /* HI((2^2*(1+18/32+1/64))^(1/3)) = 1.848135 */ |
448 | .quad 0x3FFDC39A72BF2302 /* HI((2^2*(1+19/32+1/64))^(1/3)) = 1.860255 */ |
449 | .quad 0x3FFDF49AF68C1570 /* HI((2^2*(1+20/32+1/64))^(1/3)) = 1.872218 */ |
450 | .quad 0x3FFE24FD2D4C23B8 /* HI((2^2*(1+21/32+1/64))^(1/3)) = 1.884031 */ |
451 | .quad 0x3FFE54C5FDC5EC73 /* HI((2^2*(1+22/32+1/64))^(1/3)) = 1.895697 */ |
452 | .quad 0x3FFE83FA11B81DBB /* HI((2^2*(1+23/32+1/64))^(1/3)) = 1.907221 */ |
453 | .quad 0x3FFEB29DD9DBAF25 /* HI((2^2*(1+24/32+1/64))^(1/3)) = 1.918608 */ |
454 | .quad 0x3FFEE0B59191D374 /* HI((2^2*(1+25/32+1/64))^(1/3)) = 1.929861 */ |
455 | .quad 0x3FFF0E454245E4BF /* HI((2^2*(1+26/32+1/64))^(1/3)) = 1.940984 */ |
456 | .quad 0x3FFF3B50C68A9DD3 /* HI((2^2*(1+27/32+1/64))^(1/3)) = 1.951981 */ |
457 | .quad 0x3FFF67DBCCF922DC /* HI((2^2*(1+28/32+1/64))^(1/3)) = 1.962856 */ |
458 | .quad 0x3FFF93E9DAD7A4A6 /* HI((2^2*(1+29/32+1/64))^(1/3)) = 1.973612 */ |
459 | .quad 0x3FFFBF7E4E8CC9CB /* HI((2^2*(1+30/32+1/64))^(1/3)) = 1.984251 */ |
460 | .quad 0x3FFFEA9C61E47CD3 /* HI((2^2*(1+31/32+1/64))^(1/3)) = 1.994778 */ |
461 | .align 32 |
462 | .quad 0x3F93750AD588F115, 0x3F93750AD588F115, 0x3F93750AD588F115, 0x3F93750AD588F115 /* _dA7 */ |
463 | .align 32 |
464 | .quad 0xBF98090D6221A247, 0xBF98090D6221A247, 0xBF98090D6221A247, 0xBF98090D6221A247 /* _dA6 */ |
465 | .align 32 |
466 | .quad 0x3F9EE7113506AC12, 0x3F9EE7113506AC12, 0x3F9EE7113506AC12, 0x3F9EE7113506AC12 /* _dA5 */ |
467 | .align 32 |
468 | .quad 0xBFA511E8D2B3183B, 0xBFA511E8D2B3183B, 0xBFA511E8D2B3183B, 0xBFA511E8D2B3183B /* _dA4 */ |
469 | .align 32 |
470 | .quad 0x3FAF9ADD3C0CA458, 0x3FAF9ADD3C0CA458, 0x3FAF9ADD3C0CA458, 0x3FAF9ADD3C0CA458 /* _dA3 */ |
471 | .align 32 |
472 | .quad 0xBFBC71C71C71C71C, 0xBFBC71C71C71C71C, 0xBFBC71C71C71C71C, 0xBFBC71C71C71C71C /* _dA2 */ |
473 | .align 32 |
474 | .quad 0x3FD5555555555555, 0x3FD5555555555555, 0x3FD5555555555555, 0x3FD5555555555555 /* _dA1 */ |
475 | .align 32 |
476 | .quad 0xBFF0400000000000, 0xBFF0400000000000, 0xBFF0400000000000, 0xBFF0400000000000 /* _dNeg65Div64 */ |
477 | .align 32 |
478 | .quad 0x000FC00000000000, 0x000FC00000000000, 0x000FC00000000000, 0x000FC00000000000 /* _dSgnf6Mask */ |
479 | .align 32 |
480 | .quad 0xBFF0000000000000, 0xBFF0000000000000, 0xBFF0000000000000, 0xBFF0000000000000 /* _dNegOne */ |
481 | .align 32 |
482 | .quad 0x000FFFFFFFFFFFFF, 0x000FFFFFFFFFFFFF, 0x000FFFFFFFFFFFFF, 0x000FFFFFFFFFFFFF /* _dMantissaMask */ |
483 | .align 32 |
484 | .quad 0xFFF0000000000000, 0xFFF0000000000000, 0xFFF0000000000000, 0xFFF0000000000000 /* _lExpHiMask */ |
485 | .align 32 |
486 | .quad 0x00000000000007FF, 0x00000000000007FF, 0x00000000000007FF, 0x00000000000007FF /* _lExpLoMask */ |
487 | .align 32 |
488 | .quad 0x0000000000001556, 0x0000000000001556, 0x0000000000001556, 0x0000000000001556 /* _l1556 */ |
489 | .align 32 |
490 | .long 0x000F8000, 0x000F8000, 0x000F8000, 0x000F8000, 0x000F8000, 0x000F8000, 0x000F8000, 0x000F8000 /* _iRcpIndexMask */ |
491 | .align 32 |
492 | .long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF /* _iAbsMask */ |
493 | .align 32 |
494 | .long 0x00000800, 0x00000800, 0x00000800, 0x00000800, 0x00000800, 0x00000800, 0x00000800, 0x00000800 /* _iSignMask */ |
495 | .align 32 |
496 | .long 0x000002AA, 0x000002AA, 0x000002AA, 0x000002AA, 0x000002AA, 0x000002AA, 0x000002AA, 0x000002AA /* _iBias */ |
497 | .align 32 |
498 | .long 0x80100000, 0x80100000, 0x80100000, 0x80100000, 0x80100000, 0x80100000, 0x80100000, 0x80100000 /* _iSub */ |
499 | .align 32 |
500 | .long 0xffdfffff, 0xffdfffff, 0xffdfffff, 0xffdfffff, 0xffdfffff, 0xffdfffff, 0xffdfffff, 0xffdfffff /* _iCmp */ |
501 | .align 32 |
502 | .type __svml_dcbrt_data_internal, @object |
503 | .size __svml_dcbrt_data_internal, .-__svml_dcbrt_data_internal |
504 | |