/* Function coshf vectorized with AVX-512. Copyright (C) 2021-2023 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: * * Compute cosh(x) as (exp(x)+exp(-x))/2, * where exp is calculated as * exp(M*ln2 + ln2*(j/2^k) + r) = 2^M * 2^(j/2^k) * exp(r) * * Special cases: * * cosh(NaN) = quiet NaN, and raise invalid exception * cosh(INF) = that INF * cosh(0) = 1 * cosh(x) overflows for big x and returns MAXLOG+log(2) * */ /* Offsets for data table __svml_scosh_data_internal */ #define _sExp_tbl_PH 0 #define _sExp_tbl_NH 128 #define _sShifter_UISA 256 #define _iDomainRange_UISA 320 #define _sPC1_UISA 384 #define _sPC2_UISA 448 #define _sPC3_UISA 512 #define _sInvLn2 576 #define _sLn2hi 640 #define _sLn2lo 704 #define _sSign 768 #define _iExpMask 832 #define _sShifter 896 #define _iDomainRange 960 #define _sPC1 1024 #define _sPC2 1088 #define _sPC3 1152 #include .section .text.evex512, "ax", @progbits ENTRY(_ZGVeN16v_coshf_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 _sSign+__svml_scosh_data_internal(%rip), %zmm4 vmovups _sShifter_UISA+__svml_scosh_data_internal(%rip), %zmm6 /* * Load argument * dM = x/log(2) + RShifter */ vmovups _sInvLn2+__svml_scosh_data_internal(%rip), %zmm10 vmovups _sLn2hi+__svml_scosh_data_internal(%rip), %zmm7 vmovups _sLn2lo+__svml_scosh_data_internal(%rip), %zmm9 /* */ vmovups _sPC3_UISA+__svml_scosh_data_internal(%rip), %zmm2 /* x^2 */ vmovups _sPC2_UISA+__svml_scosh_data_internal(%rip), %zmm3 /* G1, G2 2^N, 2^(-N) */ vmovups __svml_scosh_data_internal(%rip), %zmm12 vmovups _sExp_tbl_NH+__svml_scosh_data_internal(%rip), %zmm13 /* * Implementation * Abs argument */ vandnps %zmm0, %zmm4, %zmm1 /* Check for overflow\underflow */ vpternlogd $255, %zmm5, %zmm5, %zmm5 vfmadd213ps {rn-sae}, %zmm6, %zmm1, %zmm10 vpcmpd $1, _iDomainRange_UISA+__svml_scosh_data_internal(%rip), %zmm1, %k1 /* iM now is an EXP(2^N) */ vpslld $18, %zmm10, %zmm11 /* * R * sN = sM - RShifter */ vsubps {rn-sae}, %zmm6, %zmm10, %zmm8 vpermt2ps _sExp_tbl_PH+64+__svml_scosh_data_internal(%rip), %zmm10, %zmm12 vpermt2ps _sExp_tbl_NH+64+__svml_scosh_data_internal(%rip), %zmm10, %zmm13 vpandnd %zmm1, %zmm1, %zmm5{%k1} /* sR = sX - sN*Log2_hi */ vfnmadd231ps {rn-sae}, %zmm7, %zmm8, %zmm1 vptestmd %zmm5, %zmm5, %k0 /* sR = (sX - sN*Log2_hi) - sN*Log2_lo */ vfnmadd231ps {rn-sae}, %zmm9, %zmm8, %zmm1 kmovw %k0, %edx vmulps {rn-sae}, %zmm1, %zmm1, %zmm4 vmulps {rn-sae}, %zmm4, %zmm2, %zmm2 /* sSinh_r = r + r*(r^2*(a3)) */ vfmadd213ps {rn-sae}, %zmm1, %zmm1, %zmm2 /* sOut = r^2*(a2) */ vmulps {rn-sae}, %zmm4, %zmm3, %zmm1 vpandd _iExpMask+__svml_scosh_data_internal(%rip), %zmm11, %zmm14 vpaddd %zmm14, %zmm12, %zmm15 vpsubd %zmm14, %zmm13, %zmm10 /* sG2 = 2^N*Th + 2^(-N)*T_h */ vaddps {rn-sae}, %zmm10, %zmm15, %zmm5 /* sG1 = 2^N*Th - 2^(-N)*T_h */ vsubps {rn-sae}, %zmm10, %zmm15, %zmm6 /* res = sG1*(r + r*(r^2*(a3))) + sG2*(1+r^2*(a2)) */ vfmadd213ps {rn-sae}, %zmm5, %zmm5, %zmm1 vfmadd213ps {rn-sae}, %zmm1, %zmm2, %zmm6 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): vmovaps %zmm6, %zmm0 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 %zmm0, 64(%rsp) vmovups %zmm6, 128(%rsp) # LOE rbx r12 r13 r14 r15 edx zmm6 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 $16, %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), %zmm6 /* 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 zmm6 /* Scalar math fucntion call * to process special input */ L(SCALAR_MATH_CALL): movl %r12d, %r14d vmovss 64(%rsp, %r14, 4), %xmm0 call coshf@PLT # LOE rbx r14 r15 r12d r13d xmm0 vmovss %xmm0, 128(%rsp, %r14, 4) /* Process special inputs in loop */ jmp L(SPECIAL_VALUES_LOOP) # LOE rbx r15 r12d r13d END(_ZGVeN16v_coshf_skx) .section .rodata, "a" .align 64 #ifdef __svml_scosh_data_internal_typedef typedef unsigned int VUINT32; typedef struct { __declspec(align(64)) VUINT32 _sExp_tbl_PH[32][1]; __declspec(align(64)) VUINT32 _sExp_tbl_NH[32][1]; __declspec(align(64)) VUINT32 _sShifter_UISA[16][1]; __declspec(align(64)) VUINT32 _iDomainRange_UISA[16][1]; __declspec(align(64)) VUINT32 _sPC1_UISA[16][1]; __declspec(align(64)) VUINT32 _sPC2_UISA[16][1]; __declspec(align(64)) VUINT32 _sPC3_UISA[16][1]; __declspec(align(64)) VUINT32 _sInvLn2[16][1]; __declspec(align(64)) VUINT32 _sLn2hi[16][1]; __declspec(align(64)) VUINT32 _sLn2lo[16][1]; __declspec(align(64)) VUINT32 _sSign[16][1]; __declspec(align(64)) VUINT32 _iExpMask[16][1]; __declspec(align(64)) VUINT32 _sShifter[16][1]; __declspec(align(64)) VUINT32 _iDomainRange[16][1]; __declspec(align(64)) VUINT32 _sPC1[16][1]; __declspec(align(64)) VUINT32 _sPC2[16][1]; __declspec(align(64)) VUINT32 _sPC3[16][1]; } __svml_scosh_data_internal; #endif __svml_scosh_data_internal: /* _sExp_tbl_PH 2^(i/32-1), i=0..31 */ .long 0x3f000000, 0x3f02cd87, 0x3f05aac3, 0x3f08980f .long 0x3f0b95c2, 0x3f0ea43a, 0x3f11c3d3, 0x3f14f4f0 .long 0x3f1837f0, 0x3f1b8d3a, 0x3f1ef532, 0x3f227043 .long 0x3f25fed7, 0x3f29a15b, 0x3f2d583f, 0x3f3123f6 .long 0x3f3504f3, 0x3f38fbaf, 0x3f3d08a4, 0x3f412c4d .long 0x3f45672a, 0x3f49b9be, 0x3f4e248c, 0x3f52a81e .long 0x3f5744fd, 0x3f5bfbb8, 0x3f60ccdf, 0x3f65b907 .long 0x3f6ac0c7, 0x3f6fe4ba, 0x3f75257d, 0x3f7a83b3 /* _sExp_tbl_NH 2^(-i/32-1), i=0..31 */ .align 64 .long 0x3f000000, 0x3efa83b3, 0x3ef5257d, 0x3eefe4ba .long 0x3eeac0c7, 0x3ee5b907, 0x3ee0ccdf, 0x3edbfbb8 .long 0x3ed744fd, 0x3ed2a81e, 0x3ece248c, 0x3ec9b9be .long 0x3ec5672a, 0x3ec12c4d, 0x3ebd08a4, 0x3eb8fbaf .long 0x3eb504f3, 0x3eb123f6, 0x3ead583f, 0x3ea9a15b .long 0x3ea5fed7, 0x3ea27043, 0x3e9ef532, 0x3e9b8d3a .long 0x3e9837f0, 0x3e94f4f0, 0x3e91c3d3, 0x3e8ea43a .long 0x3e8b95c2, 0x3e88980f, 0x3e85aac3, 0x3e82cd87 .align 64 .long 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000 /* 1.5*2^18 _sShifter_UISA */ .align 64 .long 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E /* _iDomainRange_UISA */ .align 64 .long 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000 /* _sPC1_UISA=1 */ .align 64 .long 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f, 0x3f00010f /* _sPC2_UISA */ .align 64 .long 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd, 0x3e2aaacd /* _sPC3_UISA */ .align 64 .long 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B, 0x3FB8AA3B /* _sInvLn2 */ // k=0 .align 64 .long 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000, 0x3F317000 /* _sLn2hi */ .align 64 .long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4 /* _sLn2lo */ .align 64 .long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000 /* _sSign */ .align 64 .long 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000, 0x7f800000 /* _iExpMask */ .align 64 .long 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000 /* _sShifter */ .align 64 .long 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E, 0x42AEAC4E /* _iDomainRange */ .align 64 .long 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000 /* _sPC1=1 */ .align 64 .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 /* _sPC2 */ .align 64 .long 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57, 0x3e2aaa57 /* _sPC3 */ .align 64 .type __svml_scosh_data_internal, @object .size __svml_scosh_data_internal, .-__svml_scosh_data_internal