/* Function acoshf vectorized with AVX2. 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: * * Compute acosh(x) as log(x + sqrt(x*x - 1)) * * Special cases: * * acosh(NaN) = quiet NaN, and raise invalid exception * acosh(-INF) = NaN * acosh(+INF) = +INF * acosh(x) = NaN if x < 1 * acosh(1) = +0 * */ /* Offsets for data table __svml_sacosh_data_internal */ #define sOne 0 #define sPoly 32 #define iBrkValue 288 #define iOffExpoMask 320 #define sBigThreshold 352 #define sC2 384 #define sC3 416 #define sHalf 448 #define sLargestFinite 480 #define sThirtyOne 512 #define sTopMask8 544 #define XScale 576 #define sLn2 608 #include .text .section .text.avx2,"ax",@progbits ENTRY(_ZGVdN8v_acoshf_avx2) pushq %rbp cfi_def_cfa_offset(16) movq %rsp, %rbp cfi_def_cfa(6, 16) cfi_offset(6, -16) andq $-32, %rsp subq $96, %rsp /* Load constants, always including One = 1 */ vmovups sOne+__svml_sacosh_data_internal(%rip), %ymm2 /* Finally, express Y + W = U * V accurately where Y has <= 8 bits */ vmovups sTopMask8+__svml_sacosh_data_internal(%rip), %ymm9 /* * Now 1 / (1 + d) * = 1 / (1 + (sqrt(1 - e) - 1)) * = 1 / sqrt(1 - e) * = 1 + 1/2 * e + 3/8 * e^2 + 5/16 * e^3 + 35/128 * e^4 + ... * So compute the first three nonconstant terms of that, so that * we have a relative correction (1 + Corr) to apply to S etc. * C1 = 1/2 * C2 = 3/8 * C3 = 5/16 */ vmovups sC3+__svml_sacosh_data_internal(%rip), %ymm14 vmovaps %ymm0, %ymm3 vmovaps %ymm2, %ymm7 vfmsub231ps %ymm3, %ymm3, %ymm7 /* * Check that 1 < X < +inf; otherwise go to the callout function. * We need the callout for X = 1 to avoid division by zero below. * This test ensures that callout handles NaN and either infinity. */ vcmpnle_uqps sLargestFinite+__svml_sacosh_data_internal(%rip), %ymm3, %ymm4 vcmpngt_uqps %ymm2, %ymm3, %ymm5 /* * The following computation can go wrong for very large X, e.g. * the X^2 - 1 = U * V can overflow. But for large X we have * acosh(X) / log(2 X) - 1 =~= 1/(4 * X^2), so for X >= 2^30 * we can just later stick X back into the log and tweak up the exponent. * Actually we scale X by 2^-30 and tweak the exponent up by 31, * to stay in the safe range for the later log computation. * Compute a flag now telling us when to do this. */ vcmplt_oqps sBigThreshold+__svml_sacosh_data_internal(%rip), %ymm3, %ymm1 vandps %ymm9, %ymm7, %ymm10 /* * Compute R = 1/sqrt(Y + W) * (1 + d) * Force R to <= 8 significant bits. * This means that R * Y and R^2 * Y are exactly representable. */ vrsqrtps %ymm10, %ymm8 vsubps %ymm10, %ymm7, %ymm11 vandps %ymm9, %ymm8, %ymm12 /* * Compute S = (Y/sqrt(Y + W)) * (1 + d) * and T = (W/sqrt(Y + W)) * (1 + d) * so that S + T = sqrt(Y + W) * (1 + d) * S is exact, and the rounding error in T is OK. */ vmulps %ymm12, %ymm10, %ymm15 vmulps %ymm11, %ymm12, %ymm0 /* Now multiplex to the case X = 2^-30 * input, Xl = 0 in the "big" case. */ vmulps XScale+__svml_sacosh_data_internal(%rip), %ymm3, %ymm11 /* * Compute e = -(2 * d + d^2) * The first FMR is exact, and the rounding error in the other is acceptable * since d and e are ~ 2^-8 */ vmovaps %ymm2, %ymm13 vfnmadd231ps %ymm15, %ymm12, %ymm13 vfnmadd231ps %ymm0, %ymm12, %ymm13 vfmadd213ps sC2+__svml_sacosh_data_internal(%rip), %ymm13, %ymm14 vfmadd213ps sHalf+__svml_sacosh_data_internal(%rip), %ymm13, %ymm14 vmulps %ymm14, %ymm13, %ymm7 vorps %ymm5, %ymm4, %ymm6 /* * For low-accuracy versions, the computation can be done * just as U + ((S + T) + (S + T) * Corr) */ vaddps %ymm0, %ymm15, %ymm5 /* sU is needed later on */ vsubps %ymm2, %ymm3, %ymm4 vfmadd213ps %ymm5, %ymm7, %ymm5 vmovmskps %ymm6, %edx vaddps %ymm5, %ymm4, %ymm6 /* * Now resume the main code. * reduction: compute r,n */ vmovups iBrkValue+__svml_sacosh_data_internal(%rip), %ymm4 /* * Now we feed into the log1p code, using H in place of _VARG1 and * also adding L into Xl. * compute 1+x as high, low parts */ vmaxps %ymm6, %ymm2, %ymm8 vminps %ymm6, %ymm2, %ymm9 vaddps %ymm9, %ymm8, %ymm12 vblendvps %ymm1, %ymm12, %ymm11, %ymm14 vsubps %ymm12, %ymm8, %ymm10 vpsubd %ymm4, %ymm14, %ymm15 vaddps %ymm10, %ymm9, %ymm13 vpand iOffExpoMask+__svml_sacosh_data_internal(%rip), %ymm15, %ymm14 vpsrad $23, %ymm15, %ymm15 vpaddd %ymm4, %ymm14, %ymm8 vpslld $23, %ymm15, %ymm5 vmovups sPoly+224+__svml_sacosh_data_internal(%rip), %ymm4 vcvtdq2ps %ymm15, %ymm0 vpsubd %ymm5, %ymm2, %ymm7 /* polynomial evaluation */ vsubps %ymm2, %ymm8, %ymm2 /* Add 31 to the exponent in the "large" case to get log(2 * input) */ vaddps sThirtyOne+__svml_sacosh_data_internal(%rip), %ymm0, %ymm5 vandps %ymm1, %ymm13, %ymm6 vmulps %ymm7, %ymm6, %ymm9 vblendvps %ymm1, %ymm0, %ymm5, %ymm0 vaddps %ymm2, %ymm9, %ymm2 vfmadd213ps sPoly+192+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 vfmadd213ps sPoly+160+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 vfmadd213ps sPoly+128+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 vfmadd213ps sPoly+96+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 vfmadd213ps sPoly+64+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 vfmadd213ps sPoly+32+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 vfmadd213ps sPoly+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4 vmulps %ymm4, %ymm2, %ymm6 vfmadd213ps %ymm2, %ymm2, %ymm6 /* final reconstruction */ vfmadd132ps sLn2+__svml_sacosh_data_internal(%rip), %ymm6, %ymm0 testl %edx, %edx /* Go to special inputs processing branch */ jne L(SPECIAL_VALUES_BRANCH) # LOE rbx r12 r13 r14 r15 edx ymm0 ymm3 /* 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 %ymm3, 32(%rsp) vmovups %ymm0, 64(%rsp) # LOE rbx r12 r13 r14 r15 edx ymm0 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: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */ .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 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: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */ .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 movl %edx, %r13d movq %r14, (%rsp) /* 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) */ .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 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 64(%rsp), %ymm0 /* Go to exit */ jmp L(EXIT) /* 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) */ .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22 /* 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) */ .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22 /* 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) */ .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22 # LOE rbx r12 r13 r14 r15 ymm0 /* Scalar math fucntion call * to process special input */ L(SCALAR_MATH_CALL): movl %r12d, %r14d movss 32(%rsp,%r14,4), %xmm0 call acoshf@PLT # LOE rbx r14 r15 r12d r13d xmm0 movss %xmm0, 64(%rsp,%r14,4) /* Process special inputs in loop */ jmp L(SPECIAL_VALUES_LOOP) # LOE rbx r15 r12d r13d END(_ZGVdN8v_acoshf_avx2) .section .rodata, "a" .align 32 #ifdef __svml_sacosh_data_internal_typedef typedef unsigned int VUINT32; typedef struct { __declspec(align(32)) VUINT32 sOne[8][1]; __declspec(align(32)) VUINT32 sPoly[8][8][1]; __declspec(align(32)) VUINT32 iBrkValue[8][1]; __declspec(align(32)) VUINT32 iOffExpoMask[8][1]; __declspec(align(32)) VUINT32 sBigThreshold[8][1]; __declspec(align(32)) VUINT32 sC2[8][1]; __declspec(align(32)) VUINT32 sC3[8][1]; __declspec(align(32)) VUINT32 sHalf[8][1]; __declspec(align(32)) VUINT32 sLargestFinite[8][1]; __declspec(align(32)) VUINT32 sThirtyOne[8][1]; __declspec(align(32)) VUINT32 sTopMask8[8][1]; __declspec(align(32)) VUINT32 XScale[8][1]; __declspec(align(32)) VUINT32 sLn2[8][1]; } __svml_sacosh_data_internal; #endif __svml_sacosh_data_internal: /*== sOne = SP 1.0 ==*/ .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 /*== sPoly[] = SP polynomial ==*/ .align 32 .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */ .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */ .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */ .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */ .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */ .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */ .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */ .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */ /*== iBrkValue = SP 2/3 ==*/ .align 32 .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab /*== iOffExpoMask = SP significand mask ==*/ .align 32 .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff /*== sBigThreshold ==*/ .align 32 .long 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000 /*== sC2 ==*/ .align 32 .long 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000 /*== sC3 ==*/ .align 32 .long 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000 /*== sHalf ==*/ .align 32 .long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000 /*== sLargestFinite ==*/ .align 32 .long 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF /*== sThirtyOne ==*/ .align 32 .long 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000 /*== sTopMask8 ==*/ .align 32 .long 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000 /*== XScale ==*/ .align 32 .long 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000 /*== sLn2 = SP ln(2) ==*/ .align 32 .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 .align 32 .type __svml_sacosh_data_internal,@object .size __svml_sacosh_data_internal,.-__svml_sacosh_data_internal