sysdeps/x86_64/fpu/multiarch/svml_d_asin2_core_sse4.S

   1 /* Function asin vectorized with SSE4.
   2    Copyright (C) 2021 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  *      SelMask = (|x| >= 0.5) ? 1 : 0;
  23  *      R = SelMask ? sqrt(0.5 - 0.5*|x|) : |x|
  24  *      asin(x) = (SelMask ? (Pi/2 - 2*Poly(R)) : Poly(R))*(-1)^sign(x)
  25  *
  26  */
  27
  28 /* Offsets for data table __svml_dasin_data_internal
  29  */
  30 #define AbsMask                         0
  31 #define OneHalf                         16
  32 #define SmallNorm                       32
  33 #define One                             48
  34 #define Two                             64
  35 #define sqrt_coeff                      80
  36 #define poly_coeff                      144
  37 #define Pi2H                            336
  38
  39 #include <sysdep.h>
  40
  41         .text
  42         .section .text.sse4,"ax",@progbits
  43 ENTRY(_ZGVbN2v_asin_sse4)
  44         subq      $72, %rsp
  45         cfi_def_cfa_offset(80)
  46         movaps    %xmm0, %xmm5
  47         movups    __svml_dasin_data_internal(%rip), %xmm3
  48         movups    OneHalf+__svml_dasin_data_internal(%rip), %xmm8
  49
  50 /* x = |arg| */
  51         movaps    %xmm3, %xmm4
  52         andps     %xmm5, %xmm4
  53
  54 /* Y = 0.5 - 0.5*x */
  55         movaps    %xmm8, %xmm6
  56         mulpd     %xmm4, %xmm6
  57         movaps    %xmm8, %xmm14
  58
  59 /* x^2 */
  60         movaps    %xmm4, %xmm2
  61         subpd     %xmm6, %xmm14
  62         mulpd     %xmm4, %xmm2
  63
  64 /* S ~ -2*sqrt(Y) */
  65         cvtpd2ps  %xmm14, %xmm9
  66         minpd     %xmm14, %xmm2
  67         movlhps   %xmm9, %xmm9
  68         movaps    %xmm14, %xmm15
  69         rsqrtps   %xmm9, %xmm10
  70         cmpltpd   SmallNorm+__svml_dasin_data_internal(%rip), %xmm15
  71         addpd     %xmm14, %xmm14
  72         cvtps2pd  %xmm10, %xmm11
  73         andnps    %xmm11, %xmm15
  74         movaps    %xmm4, %xmm1
  75         movaps    %xmm15, %xmm12
  76         andnps    %xmm5, %xmm3
  77         mulpd     %xmm15, %xmm12
  78         mulpd     %xmm14, %xmm15
  79         mulpd     %xmm12, %xmm14
  80         cmpnltpd  %xmm8, %xmm1
  81         subpd     Two+__svml_dasin_data_internal(%rip), %xmm14
  82
  83 /* polynomial */
  84         movups    poly_coeff+__svml_dasin_data_internal(%rip), %xmm6
  85         movaps    %xmm2, %xmm12
  86         mulpd     %xmm2, %xmm6
  87         mulpd     %xmm2, %xmm12
  88         addpd     poly_coeff+16+__svml_dasin_data_internal(%rip), %xmm6
  89         movups    One+__svml_dasin_data_internal(%rip), %xmm7
  90         movaps    %xmm12, %xmm8
  91         cmpltpd   %xmm4, %xmm7
  92         mulpd     %xmm12, %xmm6
  93         movmskpd  %xmm7, %edx
  94         movups    poly_coeff+32+__svml_dasin_data_internal(%rip), %xmm9
  95         movaps    %xmm14, %xmm0
  96         movups    poly_coeff+64+__svml_dasin_data_internal(%rip), %xmm7
  97         mulpd     %xmm2, %xmm9
  98         mulpd     %xmm2, %xmm7
  99         addpd     poly_coeff+48+__svml_dasin_data_internal(%rip), %xmm9
 100         addpd     poly_coeff+80+__svml_dasin_data_internal(%rip), %xmm7
 101         mulpd     %xmm12, %xmm8
 102         mulpd     %xmm12, %xmm7
 103         addpd     %xmm6, %xmm9
 104         mulpd     %xmm15, %xmm0
 105         mulpd     %xmm8, %xmm9
 106         movups    poly_coeff+96+__svml_dasin_data_internal(%rip), %xmm10
 107         mulpd     %xmm2, %xmm10
 108         movups    sqrt_coeff+__svml_dasin_data_internal(%rip), %xmm13
 109         mulpd     %xmm14, %xmm13
 110         addpd     poly_coeff+112+__svml_dasin_data_internal(%rip), %xmm10
 111         addpd     sqrt_coeff+16+__svml_dasin_data_internal(%rip), %xmm13
 112         addpd     %xmm7, %xmm10
 113         mulpd     %xmm14, %xmm13
 114         addpd     %xmm9, %xmm10
 115         addpd     sqrt_coeff+32+__svml_dasin_data_internal(%rip), %xmm13
 116         mulpd     %xmm12, %xmm10
 117         mulpd     %xmm13, %xmm14
 118         movups    poly_coeff+128+__svml_dasin_data_internal(%rip), %xmm11
 119         mulpd     %xmm2, %xmm11
 120         addpd     sqrt_coeff+48+__svml_dasin_data_internal(%rip), %xmm14
 121         addpd     poly_coeff+144+__svml_dasin_data_internal(%rip), %xmm11
 122         mulpd     %xmm14, %xmm0
 123         addpd     %xmm10, %xmm11
 124         subpd     %xmm15, %xmm0
 125         mulpd     %xmm11, %xmm12
 126         movups    poly_coeff+160+__svml_dasin_data_internal(%rip), %xmm13
 127         movaps    %xmm1, %xmm14
 128         mulpd     %xmm2, %xmm13
 129         addpd     poly_coeff+176+__svml_dasin_data_internal(%rip), %xmm13
 130         addpd     %xmm12, %xmm13
 131         mulpd     %xmm13, %xmm2
 132         andnps    %xmm4, %xmm14
 133         andps     %xmm1, %xmm0
 134         orps      %xmm0, %xmm14
 135         mulpd     %xmm14, %xmm2
 136         addpd     %xmm2, %xmm14
 137         movups    Pi2H+__svml_dasin_data_internal(%rip), %xmm0
 138         andps     %xmm1, %xmm0
 139         addpd     %xmm14, %xmm0
 140         pxor      %xmm3, %xmm0
 141         testl     %edx, %edx
 142
 143 /* Go to special inputs processing branch */
 144         jne       L(SPECIAL_VALUES_BRANCH)
 145                                 # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm5
 146
 147 /* Restore registers
 148  * and exit the function
 149  */
 150
 151 L(EXIT):
 152         addq      $72, %rsp
 153         cfi_def_cfa_offset(8)
 154         ret
 155         cfi_def_cfa_offset(80)
 156
 157 /* Branch to process
 158  * special inputs
 159  */
 160
 161 L(SPECIAL_VALUES_BRANCH):
 162         movups    %xmm5, 32(%rsp)
 163         movups    %xmm0, 48(%rsp)
 164                                 # LOE rbx rbp r12 r13 r14 r15 edx
 165
 166         xorl      %eax, %eax
 167         movq      %r12, 16(%rsp)
 168         cfi_offset(12, -64)
 169         movl      %eax, %r12d
 170         movq      %r13, 8(%rsp)
 171         cfi_offset(13, -72)
 172         movl      %edx, %r13d
 173         movq      %r14, (%rsp)
 174         cfi_offset(14, -80)
 175                                 # LOE rbx rbp r15 r12d r13d
 176
 177 /* Range mask
 178  * bits check
 179  */
 180
 181 L(RANGEMASK_CHECK):
 182         btl       %r12d, %r13d
 183
 184 /* Call scalar math function */
 185         jc        L(SCALAR_MATH_CALL)
 186                                 # LOE rbx rbp r15 r12d r13d
 187
 188 /* Special inputs
 189  * processing loop
 190  */
 191
 192 L(SPECIAL_VALUES_LOOP):
 193         incl      %r12d
 194         cmpl      $2, %r12d
 195
 196 /* Check bits in range mask */
 197         jl        L(RANGEMASK_CHECK)
 198                                 # LOE rbx rbp r15 r12d r13d
 199
 200         movq      16(%rsp), %r12
 201         cfi_restore(12)
 202         movq      8(%rsp), %r13
 203         cfi_restore(13)
 204         movq      (%rsp), %r14
 205         cfi_restore(14)
 206         movups    48(%rsp), %xmm0
 207
 208 /* Go to exit */
 209         jmp       L(EXIT)
 210         cfi_offset(12, -64)
 211         cfi_offset(13, -72)
 212         cfi_offset(14, -80)
 213                                 # LOE rbx rbp r12 r13 r14 r15 xmm0
 214
 215 /* Scalar math fucntion call
 216  * to process special input
 217  */
 218
 219 L(SCALAR_MATH_CALL):
 220         movl      %r12d, %r14d
 221         movsd     32(%rsp,%r14,8), %xmm0
 222         call      asin@PLT
 223                                 # LOE rbx rbp r14 r15 r12d r13d xmm0
 224
 225         movsd     %xmm0, 48(%rsp,%r14,8)
 226
 227 /* Process special inputs in loop */
 228         jmp       L(SPECIAL_VALUES_LOOP)
 229                                 # LOE rbx rbp r15 r12d r13d
 230 END(_ZGVbN2v_asin_sse4)
 231
 232         .section .rodata, "a"
 233         .align 16
 234
 235 #ifdef __svml_dasin_data_internal_typedef
 236 typedef unsigned int VUINT32;
 237 typedef struct {
 238         __declspec(align(16)) VUINT32 AbsMask[2][2];
 239         __declspec(align(16)) VUINT32 OneHalf[2][2];
 240         __declspec(align(16)) VUINT32 SmallNorm[2][2];
 241         __declspec(align(16)) VUINT32 One[2][2];
 242         __declspec(align(16)) VUINT32 Two[2][2];
 243         __declspec(align(16)) VUINT32 sqrt_coeff[4][2][2];
 244         __declspec(align(16)) VUINT32 poly_coeff[12][2][2];
 245         __declspec(align(16)) VUINT32 Pi2H[2][2];
 246 } __svml_dasin_data_internal;
 247 #endif
 248 __svml_dasin_data_internal:
 249         /*== AbsMask ==*/
 250         .quad 0x7fffffffffffffff, 0x7fffffffffffffff
 251         /*== OneHalf ==*/
 252         .align 16
 253         .quad 0x3fe0000000000000, 0x3fe0000000000000
 254         /*== SmallNorm ==*/
 255         .align 16
 256         .quad 0x3000000000000000, 0x3000000000000000
 257         /*== One ==*/
 258         .align 16
 259         .quad 0x3ff0000000000000, 0x3ff0000000000000
 260         /*== Two ==*/
 261         .align 16
 262         .quad 0x4000000000000000, 0x4000000000000000
 263         /*== sqrt_coeff[4] ==*/
 264         .align 16
 265         .quad 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
 266         .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
 267         .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
 268         .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
 269         /*== poly_coeff[12] ==*/
 270         .align 16
 271         .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
 272         .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
 273         .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
 274         .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
 275         .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
 276         .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
 277         .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
 278         .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
 279         .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
 280         .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
 281         .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
 282         .quad 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
 283         /*== Pi2H ==*/
 284         .align 16
 285         .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18
 286         .align 16
 287         .type   __svml_dasin_data_internal,@object
 288         .size   __svml_dasin_data_internal,.-__svml_dasin_data_internal