sysdeps/x86_64/fpu/multiarch/svml_d_asin8_core_avx512.S

   1 /* Function asin vectorized with AVX-512.
   2    Copyright (C) 2021-2023 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                         64
  32 #define SmallNorm                       128
  33 #define One                             192
  34 #define Two                             256
  35 #define sqrt_coeff_1                    320
  36 #define sqrt_coeff_2                    384
  37 #define sqrt_coeff_3                    448
  38 #define sqrt_coeff_4                    512
  39 #define poly_coeff_1                    576
  40 #define poly_coeff_2                    640
  41 #define poly_coeff_3                    704
  42 #define poly_coeff_4                    768
  43 #define poly_coeff_5                    832
  44 #define poly_coeff_6                    896
  45 #define poly_coeff_7                    960
  46 #define poly_coeff_8                    1024
  47 #define poly_coeff_9                    1088
  48 #define poly_coeff_10                   1152
  49 #define poly_coeff_11                   1216
  50 #define poly_coeff_12                   1280
  51 #define Pi2H                            1344
  52
  53 #include <sysdep.h>
  54
  55         .section .text.evex512, "ax", @progbits
  56 ENTRY(_ZGVeN8v_asin_skx)
  57         pushq   %rbp
  58         cfi_def_cfa_offset(16)
  59         movq    %rsp, %rbp
  60         cfi_def_cfa(6, 16)
  61         cfi_offset(6, -16)
  62         andq    $-64, %rsp
  63         subq    $192, %rsp
  64         vmovups OneHalf+__svml_dasin_data_internal(%rip), %zmm8
  65
  66         /* S ~ -2*sqrt(Y) */
  67         vmovups SmallNorm+__svml_dasin_data_internal(%rip), %zmm10
  68         vmovups Two+__svml_dasin_data_internal(%rip), %zmm14
  69         vmovups sqrt_coeff_1+__svml_dasin_data_internal(%rip), %zmm15
  70         vmovups sqrt_coeff_2+__svml_dasin_data_internal(%rip), %zmm2
  71         vmovups sqrt_coeff_3+__svml_dasin_data_internal(%rip), %zmm1
  72         vmovups One+__svml_dasin_data_internal(%rip), %zmm9
  73         vmovaps %zmm0, %zmm6
  74
  75         /* x = |arg| */
  76         vandpd  __svml_dasin_data_internal(%rip), %zmm6, %zmm4
  77
  78         /* Y = 0.5 - 0.5*x */
  79         vmovaps %zmm8, %zmm11
  80         vfnmadd231pd {rn-sae}, %zmm4, %zmm8, %zmm11
  81
  82         /* x^2 */
  83         vmulpd  {rn-sae}, %zmm4, %zmm4, %zmm7
  84         vrsqrt14pd %zmm11, %zmm12
  85         vcmppd  $17, {sae}, %zmm10, %zmm11, %k1
  86         vcmppd  $21, {sae}, %zmm8, %zmm4, %k2
  87         vcmppd  $17, {sae}, %zmm4, %zmm9, %k0
  88         vmovups poly_coeff_5+__svml_dasin_data_internal(%rip), %zmm10
  89
  90         /* polynomial */
  91         vmovups poly_coeff_1+__svml_dasin_data_internal(%rip), %zmm8
  92         vmovups poly_coeff_3+__svml_dasin_data_internal(%rip), %zmm9
  93         vminpd  {sae}, %zmm11, %zmm7, %zmm3
  94         vxorpd  %zmm12, %zmm12, %zmm12{%k1}
  95         vaddpd  {rn-sae}, %zmm11, %zmm11, %zmm0
  96         vxorpd  %zmm6, %zmm4, %zmm5
  97         vmulpd  {rn-sae}, %zmm12, %zmm12, %zmm13
  98         vmulpd  {rn-sae}, %zmm12, %zmm0, %zmm7
  99         vmovups poly_coeff_7+__svml_dasin_data_internal(%rip), %zmm11
 100         vmovups poly_coeff_4+__svml_dasin_data_internal(%rip), %zmm12
 101         vfmsub213pd {rn-sae}, %zmm14, %zmm13, %zmm0
 102         vmovups sqrt_coeff_4+__svml_dasin_data_internal(%rip), %zmm13
 103         vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm12
 104         vmovups poly_coeff_11+__svml_dasin_data_internal(%rip), %zmm9
 105         vfmadd231pd {rn-sae}, %zmm0, %zmm15, %zmm2
 106         vmovups poly_coeff_9+__svml_dasin_data_internal(%rip), %zmm15
 107         vmulpd  {rn-sae}, %zmm0, %zmm7, %zmm14
 108         vfmadd213pd {rn-sae}, %zmm1, %zmm0, %zmm2
 109         vmovups poly_coeff_2+__svml_dasin_data_internal(%rip), %zmm1
 110         kmovw   %k0, %edx
 111         vfmadd213pd {rn-sae}, %zmm13, %zmm0, %zmm2
 112         vfmadd231pd {rn-sae}, %zmm3, %zmm8, %zmm1
 113         vmovups poly_coeff_10+__svml_dasin_data_internal(%rip), %zmm8
 114         vmulpd  {rn-sae}, %zmm3, %zmm3, %zmm0
 115         vfmsub213pd {rn-sae}, %zmm7, %zmm14, %zmm2
 116         vmovups poly_coeff_6+__svml_dasin_data_internal(%rip), %zmm7
 117         vfmadd231pd {rn-sae}, %zmm3, %zmm15, %zmm8
 118         vfmadd213pd {rn-sae}, %zmm12, %zmm0, %zmm1
 119         vblendmpd %zmm2, %zmm4, %zmm2{%k2}
 120         vfmadd231pd {rn-sae}, %zmm3, %zmm10, %zmm7
 121         vmovups poly_coeff_8+__svml_dasin_data_internal(%rip), %zmm10
 122         vmovups Pi2H+__svml_dasin_data_internal(%rip), %zmm4
 123         vfmadd231pd {rn-sae}, %zmm3, %zmm11, %zmm10
 124         vmovups poly_coeff_12+__svml_dasin_data_internal(%rip), %zmm11
 125         vfmadd213pd {rn-sae}, %zmm10, %zmm0, %zmm7
 126         vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm11
 127         vmulpd  {rn-sae}, %zmm0, %zmm0, %zmm10
 128         vfmadd213pd {rn-sae}, %zmm7, %zmm10, %zmm1
 129         vfmadd213pd {rn-sae}, %zmm8, %zmm0, %zmm1
 130         vfmadd213pd {rn-sae}, %zmm11, %zmm0, %zmm1
 131         vmulpd  {rn-sae}, %zmm3, %zmm1, %zmm3
 132         vfmadd213pd {rn-sae}, %zmm2, %zmm2, %zmm3
 133         vaddpd  {rn-sae}, %zmm4, %zmm3, %zmm3{%k2}
 134         vxorpd  %zmm5, %zmm3, %zmm0
 135         testl   %edx, %edx
 136
 137         /* Go to special inputs processing branch */
 138         jne     L(SPECIAL_VALUES_BRANCH)
 139         # LOE rbx r12 r13 r14 r15 edx zmm0 zmm6
 140
 141         /* Restore registers
 142          * and exit the function
 143          */
 144
 145 L(EXIT):
 146         movq    %rbp, %rsp
 147         popq    %rbp
 148         cfi_def_cfa(7, 8)
 149         cfi_restore(6)
 150         ret
 151         cfi_def_cfa(6, 16)
 152         cfi_offset(6, -16)
 153
 154         /* Branch to process
 155          * special inputs
 156          */
 157
 158 L(SPECIAL_VALUES_BRANCH):
 159         vmovups %zmm6, 64(%rsp)
 160         vmovups %zmm0, 128(%rsp)
 161         # LOE rbx r12 r13 r14 r15 edx zmm0
 162
 163         xorl    %eax, %eax
 164         # LOE rbx r12 r13 r14 r15 eax edx
 165
 166         vzeroupper
 167         movq    %r12, 16(%rsp)
 168         /*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus)  */
 169         .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
 170         movl    %eax, %r12d
 171         movq    %r13, 8(%rsp)
 172         /*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus)  */
 173         .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
 174         movl    %edx, %r13d
 175         movq    %r14, (%rsp)
 176         /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus)  */
 177         .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
 178         # LOE rbx r15 r12d r13d
 179
 180         /* Range mask
 181          * bits check
 182          */
 183
 184 L(RANGEMASK_CHECK):
 185         btl     %r12d, %r13d
 186
 187         /* Call scalar math function */
 188         jc      L(SCALAR_MATH_CALL)
 189         # LOE rbx r15 r12d r13d
 190
 191         /* Special inputs
 192          * processing loop
 193          */
 194
 195 L(SPECIAL_VALUES_LOOP):
 196         incl    %r12d
 197         cmpl    $8, %r12d
 198
 199         /* Check bits in range mask */
 200         jl      L(RANGEMASK_CHECK)
 201         # LOE rbx r15 r12d r13d
 202
 203         movq    16(%rsp), %r12
 204         cfi_restore(12)
 205         movq    8(%rsp), %r13
 206         cfi_restore(13)
 207         movq    (%rsp), %r14
 208         cfi_restore(14)
 209         vmovups 128(%rsp), %zmm0
 210
 211         /* Go to exit */
 212         jmp     L(EXIT)
 213         /*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus)  */
 214         .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
 215         /*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus)  */
 216         .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
 217         /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus)  */
 218         .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
 219         # LOE rbx r12 r13 r14 r15 zmm0
 220
 221         /* Scalar math fucntion call
 222          * to process special input
 223          */
 224
 225 L(SCALAR_MATH_CALL):
 226         movl    %r12d, %r14d
 227         vmovsd  64(%rsp, %r14, 8), %xmm0
 228         call    asin@PLT
 229         # LOE rbx r14 r15 r12d r13d xmm0
 230
 231         vmovsd  %xmm0, 128(%rsp, %r14, 8)
 232
 233         /* Process special inputs in loop */
 234         jmp     L(SPECIAL_VALUES_LOOP)
 235         # LOE rbx r15 r12d r13d
 236 END(_ZGVeN8v_asin_skx)
 237
 238         .section .rodata, "a"
 239         .align  64
 240
 241 #ifdef __svml_dasin_data_internal_typedef
 242 typedef unsigned int VUINT32;
 243 typedef struct {
 244         __declspec(align(64)) VUINT32 AbsMask[8][2];
 245         __declspec(align(64)) VUINT32 OneHalf[8][2];
 246         __declspec(align(64)) VUINT32 SmallNorm[8][2];
 247         __declspec(align(64)) VUINT32 One[8][2];
 248         __declspec(align(64)) VUINT32 Two[8][2];
 249         __declspec(align(64)) VUINT32 sqrt_coeff[4][8][2];
 250         __declspec(align(64)) VUINT32 poly_coeff[12][8][2];
 251         __declspec(align(64)) VUINT32 Pi2H[8][2];
 252 } __svml_dasin_data_internal;
 253 #endif
 254 __svml_dasin_data_internal:
 255         /* AbsMask */
 256         .quad   0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff
 257         /* OneHalf */
 258         .align  64
 259         .quad   0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000
 260         /* SmallNorm */
 261         .align  64
 262         .quad   0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000
 263         /* One */
 264         .align  64
 265         .quad   0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000
 266         /* Two */
 267         .align  64
 268         .quad   0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000
 269         /* sqrt_coeff[4] */
 270         .align  64
 271         .quad   0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
 272         .quad   0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
 273         .quad   0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
 274         .quad   0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
 275         /* poly_coeff[12] */
 276         .align  64
 277         .quad   0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
 278         .quad   0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
 279         .quad   0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
 280         .quad   0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
 281         .quad   0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
 282         .quad   0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
 283         .quad   0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
 284         .quad   0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
 285         .quad   0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
 286         .quad   0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
 287         .quad   0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
 288         .quad   0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
 289         /* Pi2H */
 290         .align  64
 291         .quad   0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18
 292         .align  64
 293         .type   __svml_dasin_data_internal, @object
 294         .size   __svml_dasin_data_internal, .-__svml_dasin_data_internal