sysdeps/x86_64/fpu/multiarch/svml_d_acos4_core_avx2.S

   1 /* Function acos vectorized with AVX2.
   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  *      acos(|x|) = SelMask ? 2*Poly(R) : (Pi/2 - Poly(R))
  25  *      acos(x) = sign(x) ? (Pi - acos(|x|)) : acos(|x|)
  26  *
  27  */
  28
  29 /* Offsets for data table __svml_dacos_data_internal
  30  */
  31 #define SgnBit                          0
  32 #define OneHalf                         32
  33 #define SmallNorm                       64
  34 #define MOne                            96
  35 #define Two                             128
  36 #define sqrt_coeff                      160
  37 #define poly_coeff                      288
  38 #define PiH                             672
  39 #define Pi2H                            704
  40
  41 #include <sysdep.h>
  42
  43         .text
  44         .section .text.avx2,"ax",@progbits
  45 ENTRY(_ZGVdN4v_acos_avx2)
  46         pushq     %rbp
  47         cfi_def_cfa_offset(16)
  48         movq      %rsp, %rbp
  49         cfi_def_cfa(6, 16)
  50         cfi_offset(6, -16)
  51         andq      $-32, %rsp
  52         subq      $96, %rsp
  53         vmovupd   __svml_dacos_data_internal(%rip), %ymm6
  54         vmovupd   OneHalf+__svml_dacos_data_internal(%rip), %ymm7
  55         vmovapd   %ymm0, %ymm5
  56
  57 /* x = -|arg| */
  58         vorpd     %ymm5, %ymm6, %ymm4
  59
  60 /* Y = 0.5 + 0.5*(-x) */
  61         vfmadd231pd %ymm4, %ymm7, %ymm7
  62
  63 /* x^2 */
  64         vmulpd    %ymm4, %ymm4, %ymm8
  65
  66 /* S ~ 2*sqrt(Y) */
  67         vmovupd   sqrt_coeff+__svml_dacos_data_internal(%rip), %ymm0
  68         vcmplt_oqpd SmallNorm+__svml_dacos_data_internal(%rip), %ymm7, %ymm12
  69         vminpd    %ymm7, %ymm8, %ymm2
  70
  71 /* NaN processed in special branch (so wind test passed) */
  72         vcmpnge_uqpd MOne+__svml_dacos_data_internal(%rip), %ymm4, %ymm9
  73         vcvtpd2ps %ymm7, %xmm10
  74         vmovupd   poly_coeff+64+__svml_dacos_data_internal(%rip), %ymm8
  75         vcmpnlt_uqpd %ymm7, %ymm2, %ymm1
  76         vrsqrtps  %xmm10, %xmm11
  77         vfmadd213pd poly_coeff+96+__svml_dacos_data_internal(%rip), %ymm2, %ymm8
  78         vcvtps2pd %xmm11, %ymm13
  79         vmovupd   poly_coeff+128+__svml_dacos_data_internal(%rip), %ymm11
  80         vandnpd   %ymm13, %ymm12, %ymm14
  81         vmulpd    %ymm14, %ymm14, %ymm15
  82         vfmadd213pd poly_coeff+160+__svml_dacos_data_internal(%rip), %ymm2, %ymm11
  83         vmulpd    %ymm2, %ymm2, %ymm13
  84         vmovupd   poly_coeff+256+__svml_dacos_data_internal(%rip), %ymm12
  85         vmulpd    %ymm13, %ymm13, %ymm10
  86         vfmadd213pd poly_coeff+288+__svml_dacos_data_internal(%rip), %ymm2, %ymm12
  87         vandpd    %ymm5, %ymm6, %ymm3
  88         vaddpd    %ymm7, %ymm7, %ymm6
  89         vmulpd    %ymm6, %ymm14, %ymm7
  90         vfmsub213pd Two+__svml_dacos_data_internal(%rip), %ymm15, %ymm6
  91         vmovupd   poly_coeff+320+__svml_dacos_data_internal(%rip), %ymm14
  92         vfmadd213pd sqrt_coeff+32+__svml_dacos_data_internal(%rip), %ymm6, %ymm0
  93         vmulpd    %ymm6, %ymm7, %ymm15
  94         vfmadd213pd poly_coeff+352+__svml_dacos_data_internal(%rip), %ymm2, %ymm14
  95         vfmadd213pd sqrt_coeff+64+__svml_dacos_data_internal(%rip), %ymm6, %ymm0
  96         vfmadd213pd sqrt_coeff+96+__svml_dacos_data_internal(%rip), %ymm6, %ymm0
  97
  98 /* polynomial */
  99         vmovupd   poly_coeff+__svml_dacos_data_internal(%rip), %ymm6
 100         vfnmadd213pd %ymm7, %ymm15, %ymm0
 101         vfmadd213pd poly_coeff+32+__svml_dacos_data_internal(%rip), %ymm2, %ymm6
 102         vblendvpd %ymm1, %ymm0, %ymm4, %ymm0
 103         vfmadd213pd %ymm8, %ymm13, %ymm6
 104         vmovmskpd %ymm9, %edx
 105         vmovupd   poly_coeff+192+__svml_dacos_data_internal(%rip), %ymm9
 106         vfmadd213pd poly_coeff+224+__svml_dacos_data_internal(%rip), %ymm2, %ymm9
 107         vfmadd213pd %ymm9, %ymm13, %ymm11
 108         vfmadd213pd %ymm11, %ymm10, %ymm6
 109         vfmadd213pd %ymm12, %ymm13, %ymm6
 110         vfmadd213pd %ymm14, %ymm13, %ymm6
 111         vmulpd    %ymm6, %ymm2, %ymm9
 112
 113 /* X<X^2 iff X<0 */
 114         vcmplt_oqpd %ymm2, %ymm5, %ymm6
 115         vandpd    PiH+__svml_dacos_data_internal(%rip), %ymm1, %ymm2
 116         vandnpd   Pi2H+__svml_dacos_data_internal(%rip), %ymm1, %ymm7
 117         vxorpd    %ymm3, %ymm0, %ymm1
 118         vfmadd213pd %ymm1, %ymm1, %ymm9
 119         vandpd    %ymm6, %ymm2, %ymm2
 120         vaddpd    %ymm7, %ymm2, %ymm8
 121         vaddpd    %ymm9, %ymm8, %ymm0
 122         testl     %edx, %edx
 123
 124 /* Go to special inputs processing branch */
 125         jne       L(SPECIAL_VALUES_BRANCH)
 126                                 # LOE rbx r12 r13 r14 r15 edx ymm0 ymm5
 127
 128 /* Restore registers
 129  * and exit the function
 130  */
 131
 132 L(EXIT):
 133         movq      %rbp, %rsp
 134         popq      %rbp
 135         cfi_def_cfa(7, 8)
 136         cfi_restore(6)
 137         ret
 138         cfi_def_cfa(6, 16)
 139         cfi_offset(6, -16)
 140
 141 /* Branch to process
 142  * special inputs
 143  */
 144
 145 L(SPECIAL_VALUES_BRANCH):
 146         vmovupd   %ymm5, 32(%rsp)
 147         vmovupd   %ymm0, 64(%rsp)
 148                                 # LOE rbx r12 r13 r14 r15 edx ymm0
 149
 150         xorl      %eax, %eax
 151                                 # LOE rbx r12 r13 r14 r15 eax edx
 152
 153         vzeroupper
 154         movq      %r12, 16(%rsp)
 155         /*  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)  */
 156         .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
 157         movl      %eax, %r12d
 158         movq      %r13, 8(%rsp)
 159         /*  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)  */
 160         .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
 161         movl      %edx, %r13d
 162         movq      %r14, (%rsp)
 163         /*  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)  */
 164         .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
 165                                 # LOE rbx r15 r12d r13d
 166
 167 /* Range mask
 168  * bits check
 169  */
 170
 171 L(RANGEMASK_CHECK):
 172         btl       %r12d, %r13d
 173
 174 /* Call scalar math function */
 175         jc        L(SCALAR_MATH_CALL)
 176                                 # LOE rbx r15 r12d r13d
 177
 178 /* Special inputs
 179  * processing loop
 180  */
 181
 182 L(SPECIAL_VALUES_LOOP):
 183         incl      %r12d
 184         cmpl      $4, %r12d
 185
 186 /* Check bits in range mask */
 187         jl        L(RANGEMASK_CHECK)
 188                                 # LOE rbx r15 r12d r13d
 189
 190         movq      16(%rsp), %r12
 191         cfi_restore(12)
 192         movq      8(%rsp), %r13
 193         cfi_restore(13)
 194         movq      (%rsp), %r14
 195         cfi_restore(14)
 196         vmovupd   64(%rsp), %ymm0
 197
 198 /* Go to exit */
 199         jmp       L(EXIT)
 200         /*  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)  */
 201         .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
 202         /*  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)  */
 203         .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
 204         /*  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)  */
 205         .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
 206                                 # LOE rbx r12 r13 r14 r15 ymm0
 207
 208 /* Scalar math fucntion call
 209  * to process special input
 210  */
 211
 212 L(SCALAR_MATH_CALL):
 213         movl      %r12d, %r14d
 214         movsd     32(%rsp,%r14,8), %xmm0
 215         call      acos@PLT
 216                                 # LOE rbx r14 r15 r12d r13d xmm0
 217
 218         movsd     %xmm0, 64(%rsp,%r14,8)
 219
 220 /* Process special inputs in loop */
 221         jmp       L(SPECIAL_VALUES_LOOP)
 222                                 # LOE rbx r15 r12d r13d
 223 END(_ZGVdN4v_acos_avx2)
 224
 225         .section .rodata, "a"
 226         .align 32
 227
 228 #ifdef __svml_dacos_data_internal_typedef
 229 typedef unsigned int VUINT32;
 230 typedef struct {
 231         __declspec(align(32)) VUINT32 SgnBit[4][2];
 232         __declspec(align(32)) VUINT32 OneHalf[4][2];
 233         __declspec(align(32)) VUINT32 SmallNorm[4][2];
 234         __declspec(align(32)) VUINT32 MOne[4][2];
 235         __declspec(align(32)) VUINT32 Two[4][2];
 236         __declspec(align(32)) VUINT32 sqrt_coeff[4][4][2];
 237         __declspec(align(32)) VUINT32 poly_coeff[12][4][2];
 238         __declspec(align(32)) VUINT32 PiH[4][2];
 239         __declspec(align(32)) VUINT32 Pi2H[4][2];
 240 } __svml_dacos_data_internal;
 241 #endif
 242 __svml_dacos_data_internal:
 243         /*== SgnBit ==*/
 244         .quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000
 245         /*== OneHalf ==*/
 246         .align 32
 247         .quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000
 248         /*== SmallNorm ==*/
 249         .align 32
 250         .quad 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000
 251         /*== MOne ==*/
 252         .align 32
 253         .quad 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000
 254         /*== Two ==*/
 255         .align 32
 256         .quad 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000
 257         /*== sqrt_coeff[4] ==*/
 258         .align 32
 259         .quad 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
 260         .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
 261         .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
 262         .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
 263         /*== poly_coeff[12] ==*/
 264         .align 32
 265         .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
 266         .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
 267         .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
 268         .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
 269         .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
 270         .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
 271         .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
 272         .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
 273         .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
 274         .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
 275         .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
 276         .quad 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
 277         /*== PiH ==*/
 278         .align 32
 279         .quad 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18
 280         /*== Pi2H ==*/
 281         .align 32
 282         .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18
 283         .align 32
 284         .type   __svml_dacos_data_internal,@object
 285         .size   __svml_dacos_data_internal,.-__svml_dacos_data_internal