diff options
Diffstat (limited to 'sysdeps/x86_64/fpu/multiarch/svml_s_acoshf4_core_sse4.S')
| -rw-r--r-- | sysdeps/x86_64/fpu/multiarch/svml_s_acoshf4_core_sse4.S | 389 |
1 files changed, 389 insertions, 0 deletions
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_acoshf4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_acoshf4_core_sse4.S new file mode 100644 index 0000000000..e897ea304f --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_acoshf4_core_sse4.S @@ -0,0 +1,389 @@ +/* Function acoshf vectorized with SSE4. + 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 16 +#define iBrkValue 144 +#define iOffExpoMask 160 +#define sBigThreshold 176 +#define sC2 192 +#define sC3 208 +#define sHalf 224 +#define sLargestFinite 240 +#define sThirtyOne 256 +#define sTopMask8 272 +#define XScale 288 +#define sLn2 304 + +#include <sysdep.h> + + .text + .section .text.sse4,"ax",@progbits +ENTRY(_ZGVbN4v_acoshf_sse4) + subq $72, %rsp + cfi_def_cfa_offset(80) + +/* Compute U = X - 1 and V = X + 1, naively first. */ + movaps %xmm0, %xmm12 + +/* Load constants, always including One = 1 */ + movups sOne+__svml_sacosh_data_internal(%rip), %xmm2 + +/* + * 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. + */ + movaps %xmm0, %xmm4 + movaps %xmm2, %xmm9 + +/* + * 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 + */ + movaps %xmm2, %xmm10 + +/* Finally, express Y + W = U * V accurately where Y has <= 8 bits */ + movups sTopMask8+__svml_sacosh_data_internal(%rip), %xmm5 + +/* + * 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 + */ + movaps %xmm2, %xmm13 + movaps %xmm5, %xmm11 + movaps %xmm2, %xmm3 + +/* + * 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 + */ + movups sC3+__svml_sacosh_data_internal(%rip), %xmm8 + +/* + * 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. + */ + movaps %xmm0, %xmm1 + cmpnleps sLargestFinite+__svml_sacosh_data_internal(%rip), %xmm4 + cmpltps sBigThreshold+__svml_sacosh_data_internal(%rip), %xmm1 + cmpnltps %xmm0, %xmm3 + subps %xmm2, %xmm12 + addps %xmm0, %xmm9 + +/* For low-accuracy versions, naivety is harmless */ + mulps %xmm12, %xmm9 + orps %xmm3, %xmm4 + movmskps %xmm4, %edx + andps %xmm9, %xmm11 + movaps %xmm1, %xmm3 + +/* + * 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. + */ + rsqrtps %xmm11, %xmm7 + subps %xmm11, %xmm9 + andps %xmm5, %xmm7 + movaps %xmm2, %xmm4 + +/* + * 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. + */ + mulps %xmm7, %xmm11 + movaps %xmm7, %xmm6 + mulps %xmm7, %xmm9 + mulps %xmm11, %xmm6 + mulps %xmm9, %xmm7 + +/* + * For low-accuracy versions, the computation can be done + * just as U + ((S + T) + (S + T) * Corr) + */ + addps %xmm9, %xmm11 + subps %xmm6, %xmm10 + movaps %xmm2, %xmm9 + subps %xmm7, %xmm10 + mulps %xmm10, %xmm8 + +/* Now multiplex to the case X = 2^-30 * input, Xl = 0 in the "big" case. */ + movups XScale+__svml_sacosh_data_internal(%rip), %xmm14 + mulps %xmm0, %xmm14 + addps sC2+__svml_sacosh_data_internal(%rip), %xmm8 + mulps %xmm10, %xmm8 + andnps %xmm14, %xmm3 + +/* + * Now resume the main code. + * reduction: compute r,n + */ + movdqu iBrkValue+__svml_sacosh_data_internal(%rip), %xmm14 + movdqu iOffExpoMask+__svml_sacosh_data_internal(%rip), %xmm5 + +/* Add 31 to the exponent in the "large" case to get log(2 * input) */ + movups sThirtyOne+__svml_sacosh_data_internal(%rip), %xmm6 + addps sHalf+__svml_sacosh_data_internal(%rip), %xmm8 + mulps %xmm8, %xmm10 + movaps %xmm1, %xmm8 + mulps %xmm11, %xmm10 + addps %xmm10, %xmm11 + addps %xmm11, %xmm12 + maxps %xmm12, %xmm13 + minps %xmm12, %xmm9 + movaps %xmm13, %xmm15 + addps %xmm9, %xmm15 + subps %xmm15, %xmm13 + andps %xmm1, %xmm15 + orps %xmm15, %xmm3 + addps %xmm13, %xmm9 + psubd %xmm14, %xmm3 + andps %xmm1, %xmm9 + pand %xmm3, %xmm5 + psrad $23, %xmm3 + cvtdq2ps %xmm3, %xmm7 + pslld $23, %xmm3 + paddd %xmm14, %xmm5 + psubd %xmm3, %xmm4 + +/* polynomial evaluation */ + subps %xmm2, %xmm5 + mulps %xmm4, %xmm9 + addps %xmm7, %xmm6 + movups sPoly+112+__svml_sacosh_data_internal(%rip), %xmm2 + andnps %xmm6, %xmm8 + andps %xmm1, %xmm7 + addps %xmm5, %xmm9 + mulps %xmm9, %xmm2 + orps %xmm7, %xmm8 + +/* final reconstruction */ + mulps sLn2+__svml_sacosh_data_internal(%rip), %xmm8 + addps sPoly+96+__svml_sacosh_data_internal(%rip), %xmm2 + mulps %xmm9, %xmm2 + addps sPoly+80+__svml_sacosh_data_internal(%rip), %xmm2 + mulps %xmm9, %xmm2 + addps sPoly+64+__svml_sacosh_data_internal(%rip), %xmm2 + mulps %xmm9, %xmm2 + addps sPoly+48+__svml_sacosh_data_internal(%rip), %xmm2 + mulps %xmm9, %xmm2 + addps sPoly+32+__svml_sacosh_data_internal(%rip), %xmm2 + mulps %xmm9, %xmm2 + addps sPoly+16+__svml_sacosh_data_internal(%rip), %xmm2 + mulps %xmm9, %xmm2 + addps sPoly+__svml_sacosh_data_internal(%rip), %xmm2 + mulps %xmm9, %xmm2 + mulps %xmm9, %xmm2 + addps %xmm2, %xmm9 + addps %xmm8, %xmm9 + testl %edx, %edx + +/* Go to special inputs processing branch */ + jne L(SPECIAL_VALUES_BRANCH) + # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm9 + +/* Restore registers + * and exit the function + */ + +L(EXIT): + movaps %xmm9, %xmm0 + addq $72, %rsp + cfi_def_cfa_offset(8) + ret + cfi_def_cfa_offset(80) + +/* Branch to process + * special inputs + */ + +L(SPECIAL_VALUES_BRANCH): + movups %xmm0, 32(%rsp) + movups %xmm9, 48(%rsp) + # LOE rbx rbp r12 r13 r14 r15 edx + + xorl %eax, %eax + movq %r12, 16(%rsp) + cfi_offset(12, -64) + movl %eax, %r12d + movq %r13, 8(%rsp) + cfi_offset(13, -72) + movl %edx, %r13d + movq %r14, (%rsp) + cfi_offset(14, -80) + # LOE rbx rbp r15 r12d r13d + +/* Range mask + * bits check + */ + +L(RANGEMASK_CHECK): + btl %r12d, %r13d + +/* Call scalar math function */ + jc L(SCALAR_MATH_CALL) + # LOE rbx rbp r15 r12d r13d + +/* Special inputs + * processing loop + */ + +L(SPECIAL_VALUES_LOOP): + incl %r12d + cmpl $4, %r12d + +/* Check bits in range mask */ + jl L(RANGEMASK_CHECK) + # LOE rbx rbp r15 r12d r13d + + movq 16(%rsp), %r12 + cfi_restore(12) + movq 8(%rsp), %r13 + cfi_restore(13) + movq (%rsp), %r14 + cfi_restore(14) + movups 48(%rsp), %xmm9 + +/* Go to exit */ + jmp L(EXIT) + cfi_offset(12, -64) + cfi_offset(13, -72) + cfi_offset(14, -80) + # LOE rbx rbp r12 r13 r14 r15 xmm9 + +/* 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 rbp r14 r15 r12d r13d xmm0 + + movss %xmm0, 48(%rsp,%r14,4) + +/* Process special inputs in loop */ + jmp L(SPECIAL_VALUES_LOOP) + # LOE rbx rbp r15 r12d r13d +END(_ZGVbN4v_acoshf_sse4) + + .section .rodata, "a" + .align 16 + +#ifdef __svml_sacosh_data_internal_typedef +typedef unsigned int VUINT32; +typedef struct { + __declspec(align(16)) VUINT32 sOne[4][1]; + __declspec(align(16)) VUINT32 sPoly[8][4][1]; + __declspec(align(16)) VUINT32 iBrkValue[4][1]; + __declspec(align(16)) VUINT32 iOffExpoMask[4][1]; + __declspec(align(16)) VUINT32 sBigThreshold[4][1]; + __declspec(align(16)) VUINT32 sC2[4][1]; + __declspec(align(16)) VUINT32 sC3[4][1]; + __declspec(align(16)) VUINT32 sHalf[4][1]; + __declspec(align(16)) VUINT32 sLargestFinite[4][1]; + __declspec(align(16)) VUINT32 sThirtyOne[4][1]; + __declspec(align(16)) VUINT32 sTopMask8[4][1]; + __declspec(align(16)) VUINT32 XScale[4][1]; + __declspec(align(16)) VUINT32 sLn2[4][1]; +} __svml_sacosh_data_internal; +#endif +__svml_sacosh_data_internal: + /*== sOne = SP 1.0 ==*/ + .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 + /*== sPoly[] = SP polynomial ==*/ + .align 16 + .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */ + .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */ + .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */ + .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */ + .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */ + .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */ + .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */ + .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */ + /*== iBrkValue = SP 2/3 ==*/ + .align 16 + .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab + /*== iOffExpoMask = SP significand mask ==*/ + .align 16 + .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff + /*== sBigThreshold ==*/ + .align 16 + .long 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000 + /*== sC2 ==*/ + .align 16 + .long 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000 + /*== sC3 ==*/ + .align 16 + .long 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000 + /*== sHalf ==*/ + .align 16 + .long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000 + /*== sLargestFinite ==*/ + .align 16 + .long 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF + /*== sThirtyOne ==*/ + .align 16 + .long 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000 + /*== sTopMask8 ==*/ + .align 16 + .long 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000 + /*== XScale ==*/ + .align 16 + .long 0x30800000, 0x30800000, 0x30800000, 0x30800000 + /*== sLn2 = SP ln(2) ==*/ + .align 16 + .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 + .align 16 + .type __svml_sacosh_data_internal,@object + .size __svml_sacosh_data_internal,.-__svml_sacosh_data_internal |