/* Function asin vectorized with AVX-512. Copyright (C) 2021 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, see https://www.gnu.org/licenses/. */ /* * ALGORITHM DESCRIPTION: * * SelMask = (|x| >= 0.5) ? 1 : 0; * R = SelMask ? sqrt(0.5 - 0.5*|x|) : |x| * asin(x) = (SelMask ? (Pi/2 - 2*Poly(R)) : Poly(R))*(-1)^sign(x) * */ /* Offsets for data table __svml_dasin_data_internal */ #define AbsMask 0 #define OneHalf 64 #define SmallNorm 128 #define One 192 #define Two 256 #define sqrt_coeff_1 320 #define sqrt_coeff_2 384 #define sqrt_coeff_3 448 #define sqrt_coeff_4 512 #define poly_coeff_1 576 #define poly_coeff_2 640 #define poly_coeff_3 704 #define poly_coeff_4 768 #define poly_coeff_5 832 #define poly_coeff_6 896 #define poly_coeff_7 960 #define poly_coeff_8 1024 #define poly_coeff_9 1088 #define poly_coeff_10 1152 #define poly_coeff_11 1216 #define poly_coeff_12 1280 #define Pi2H 1344 #include .text .section .text.evex512,"ax",@progbits ENTRY(_ZGVeN8v_asin_skx) pushq %rbp cfi_def_cfa_offset(16) movq %rsp, %rbp cfi_def_cfa(6, 16) cfi_offset(6, -16) andq $-64, %rsp subq $192, %rsp vmovups OneHalf+__svml_dasin_data_internal(%rip), %zmm8 /* S ~ -2*sqrt(Y) */ vmovups SmallNorm+__svml_dasin_data_internal(%rip), %zmm10 vmovups Two+__svml_dasin_data_internal(%rip), %zmm14 vmovups sqrt_coeff_1+__svml_dasin_data_internal(%rip), %zmm15 vmovups sqrt_coeff_2+__svml_dasin_data_internal(%rip), %zmm2 vmovups sqrt_coeff_3+__svml_dasin_data_internal(%rip), %zmm1 vmovups One+__svml_dasin_data_internal(%rip), %zmm9 vmovaps %zmm0, %zmm6 /* x = |arg| */ vandpd __svml_dasin_data_internal(%rip), %zmm6, %zmm4 /* Y = 0.5 - 0.5*x */ vmovaps %zmm8, %zmm11 vfnmadd231pd {rn-sae}, %zmm4, %zmm8, %zmm11 /* x^2 */ vmulpd {rn-sae}, %zmm4, %zmm4, %zmm7 vrsqrt14pd %zmm11, %zmm12 vcmppd $17, {sae}, %zmm10, %zmm11, %k1 vcmppd $21, {sae}, %zmm8, %zmm4, %k2 vcmppd $17, {sae}, %zmm4, %zmm9, %k0 vmovups poly_coeff_5+__svml_dasin_data_internal(%rip), %zmm10 /* polynomial */ vmovups poly_coeff_1+__svml_dasin_data_internal(%rip), %zmm8 vmovups poly_coeff_3+__svml_dasin_data_internal(%rip), %zmm9 vminpd {sae}, %zmm11, %zmm7, %zmm3 vxorpd %zmm12, %zmm12, %zmm12{%k1} vaddpd {rn-sae}, %zmm11, %zmm11, %zmm0 vxorpd %zmm6, %zmm4, %zmm5 vmulpd {rn-sae}, %zmm12, %zmm12, %zmm13 vmulpd {rn-sae}, %zmm12, %zmm0, %zmm7 vmovups poly_coeff_7+__svml_dasin_data_internal(%rip), %zmm11 vmovups poly_coeff_4+__svml_dasin_data_internal(%rip), %zmm12 vfmsub213pd {rn-sae}, %zmm14, %zmm13, %zmm0 vmovups sqrt_coeff_4+__svml_dasin_data_internal(%rip), %zmm13 vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm12 vmovups poly_coeff_11+__svml_dasin_data_internal(%rip), %zmm9 vfmadd231pd {rn-sae}, %zmm0, %zmm15, %zmm2 vmovups poly_coeff_9+__svml_dasin_data_internal(%rip), %zmm15 vmulpd {rn-sae}, %zmm0, %zmm7, %zmm14 vfmadd213pd {rn-sae}, %zmm1, %zmm0, %zmm2 vmovups poly_coeff_2+__svml_dasin_data_internal(%rip), %zmm1 kmovw %k0, %edx vfmadd213pd {rn-sae}, %zmm13, %zmm0, %zmm2 vfmadd231pd {rn-sae}, %zmm3, %zmm8, %zmm1 vmovups poly_coeff_10+__svml_dasin_data_internal(%rip), %zmm8 vmulpd {rn-sae}, %zmm3, %zmm3, %zmm0 vfmsub213pd {rn-sae}, %zmm7, %zmm14, %zmm2 vmovups poly_coeff_6+__svml_dasin_data_internal(%rip), %zmm7 vfmadd231pd {rn-sae}, %zmm3, %zmm15, %zmm8 vfmadd213pd {rn-sae}, %zmm12, %zmm0, %zmm1 vblendmpd %zmm2, %zmm4, %zmm2{%k2} vfmadd231pd {rn-sae}, %zmm3, %zmm10, %zmm7 vmovups poly_coeff_8+__svml_dasin_data_internal(%rip), %zmm10 vmovups Pi2H+__svml_dasin_data_internal(%rip), %zmm4 vfmadd231pd {rn-sae}, %zmm3, %zmm11, %zmm10 vmovups poly_coeff_12+__svml_dasin_data_internal(%rip), %zmm11 vfmadd213pd {rn-sae}, %zmm10, %zmm0, %zmm7 vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm11 vmulpd {rn-sae}, %zmm0, %zmm0, %zmm10 vfmadd213pd {rn-sae}, %zmm7, %zmm10, %zmm1 vfmadd213pd {rn-sae}, %zmm8, %zmm0, %zmm1 vfmadd213pd {rn-sae}, %zmm11, %zmm0, %zmm1 vmulpd {rn-sae}, %zmm3, %zmm1, %zmm3 vfmadd213pd {rn-sae}, %zmm2, %zmm2, %zmm3 vaddpd {rn-sae}, %zmm4, %zmm3, %zmm3{%k2} vxorpd %zmm5, %zmm3, %zmm0 testl %edx, %edx /* Go to special inputs processing branch */ jne L(SPECIAL_VALUES_BRANCH) # LOE rbx r12 r13 r14 r15 edx zmm0 zmm6 /* Restore registers * and exit the function */ L(EXIT): movq %rbp, %rsp popq %rbp cfi_def_cfa(7, 8) cfi_restore(6) ret cfi_def_cfa(6, 16) cfi_offset(6, -16) /* Branch to process * special inputs */ L(SPECIAL_VALUES_BRANCH): vmovups %zmm6, 64(%rsp) vmovups %zmm0, 128(%rsp) # LOE rbx r12 r13 r14 r15 edx zmm0 xorl %eax, %eax # LOE rbx r12 r13 r14 r15 eax edx vzeroupper movq %r12, 16(%rsp) /* 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) */ .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22 movl %eax, %r12d movq %r13, 8(%rsp) /* 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) */ .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22 movl %edx, %r13d movq %r14, (%rsp) /* 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) */ .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22 # LOE rbx r15 r12d r13d /* Range mask * bits check */ L(RANGEMASK_CHECK): btl %r12d, %r13d /* Call scalar math function */ jc L(SCALAR_MATH_CALL) # LOE rbx r15 r12d r13d /* Special inputs * processing loop */ L(SPECIAL_VALUES_LOOP): incl %r12d cmpl $8, %r12d /* Check bits in range mask */ jl L(RANGEMASK_CHECK) # LOE rbx r15 r12d r13d movq 16(%rsp), %r12 cfi_restore(12) movq 8(%rsp), %r13 cfi_restore(13) movq (%rsp), %r14 cfi_restore(14) vmovups 128(%rsp), %zmm0 /* Go to exit */ jmp L(EXIT) /* 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) */ .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22 /* 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) */ .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22 /* 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) */ .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22 # LOE rbx r12 r13 r14 r15 zmm0 /* Scalar math fucntion call * to process special input */ L(SCALAR_MATH_CALL): movl %r12d, %r14d movsd 64(%rsp,%r14,8), %xmm0 call asin@PLT # LOE rbx r14 r15 r12d r13d xmm0 movsd %xmm0, 128(%rsp,%r14,8) /* Process special inputs in loop */ jmp L(SPECIAL_VALUES_LOOP) # LOE rbx r15 r12d r13d END(_ZGVeN8v_asin_skx) .section .rodata, "a" .align 64 #ifdef __svml_dasin_data_internal_typedef typedef unsigned int VUINT32; typedef struct { __declspec(align(64)) VUINT32 AbsMask[8][2]; __declspec(align(64)) VUINT32 OneHalf[8][2]; __declspec(align(64)) VUINT32 SmallNorm[8][2]; __declspec(align(64)) VUINT32 One[8][2]; __declspec(align(64)) VUINT32 Two[8][2]; __declspec(align(64)) VUINT32 sqrt_coeff[4][8][2]; __declspec(align(64)) VUINT32 poly_coeff[12][8][2]; __declspec(align(64)) VUINT32 Pi2H[8][2]; } __svml_dasin_data_internal; #endif __svml_dasin_data_internal: /*== AbsMask ==*/ .quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff /*== OneHalf ==*/ .align 64 .quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000 /*== SmallNorm ==*/ .align 64 .quad 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000 /*== One ==*/ .align 64 .quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000 /*== Two ==*/ .align 64 .quad 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000 /*== sqrt_coeff[4] ==*/ .align 64 .quad 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */ .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */ .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */ .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */ /*== poly_coeff[12] ==*/ .align 64 .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */ .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */ .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */ .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */ .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */ .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */ .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */ .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */ .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */ .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */ .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */ .quad 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */ /*== Pi2H ==*/ .align 64 .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18 .align 64 .type __svml_dasin_data_internal,@object .size __svml_dasin_data_internal,.-__svml_dasin_data_internal