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Diffstat (limited to 'sysdeps/x86_64/fpu/multiarch/svml_s_asinhf4_core_sse4.S')
| -rw-r--r-- | sysdeps/x86_64/fpu/multiarch/svml_s_asinhf4_core_sse4.S | 509 |
1 files changed, 509 insertions, 0 deletions
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_asinhf4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_asinhf4_core_sse4.S new file mode 100644 index 0000000000..1eeeb4f5af --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_asinhf4_core_sse4.S @@ -0,0 +1,509 @@ +/* Function asinhf 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 asinh(x) as log(x + sqrt(x*x + 1)) + * + * Special cases: + * + * asinh(NaN) = quiet NaN, and raise invalid exception + * asinh(INF) = that INF + * asinh(0) = that 0 + * + */ + +/* Offsets for data table __svml_sasinh_data_internal + */ +#define SgnMask 0 +#define sOne 16 +#define sPoly 32 +#define iBrkValue 160 +#define iOffExpoMask 176 +#define sBigThreshold 192 +#define sC2 208 +#define sC3 224 +#define sHalf 240 +#define sLargestFinite 256 +#define sLittleThreshold 272 +#define sSign 288 +#define sThirtyOne 304 +#define sTopMask11 320 +#define sTopMask8 336 +#define XScale 352 +#define sLn2 368 + +#include <sysdep.h> + + .text + .section .text.sse4,"ax",@progbits +ENTRY(_ZGVbN4v_asinhf_sse4) + subq $72, %rsp + cfi_def_cfa_offset(80) + movaps %xmm0, %xmm8 + +/* + * Split X into high and low parts, XHi (<= 11 bits) and XLo (<= 13 bits) + * We could use either X or |X| here, but it doesn't seem to matter + */ + movups sTopMask11+__svml_sasinh_data_internal(%rip), %xmm10 + movaps %xmm8, %xmm2 + andps %xmm8, %xmm10 + +/* + * Compute X^2 = (XHi + XLo)^2 = XHi^2 + XLo * (X + XHi) + * The two parts are shifted off by around 11 bits. So even though + * the low bit will not in general be exact, it's near enough + */ + movaps %xmm10, %xmm3 + subps %xmm10, %xmm2 + mulps %xmm10, %xmm3 + addps %xmm8, %xmm10 + +/* Load the constant 1 and a sign mask */ + movups sOne+__svml_sasinh_data_internal(%rip), %xmm7 + +/* + * Finally, express Y + W = X^2 + 1 accurately where Y has <= 8 bits. + * If |X| <= 1 then |XHi| <= 1 and so |X2Hi| <= 1, so we can treat 1 + * as the dominant component in the compensated summation. Otherwise, + * if |X| >= 1, then since X2Hi only has 22 significant bits, the basic + * addition will be exact anyway until we get to |X| >= 2^24. But by + * that time the log function is well-conditioned enough that the + * rounding error doesn't matter. Hence we can treat 1 as dominant even + * if it literally isn't. + */ + movaps %xmm7, %xmm11 + movaps %xmm7, %xmm4 + movups sTopMask8+__svml_sasinh_data_internal(%rip), %xmm12 + addps %xmm3, %xmm11 + mulps %xmm10, %xmm2 + subps %xmm11, %xmm4 + movaps %xmm12, %xmm0 + addps %xmm3, %xmm4 + +/* + * Unfortunately, we can still be in trouble if |X| <= 2^-5, since + * the absolute error 2^-(7+24)-ish in sqrt(1 + X^2) gets scaled up + * by 1/X and comes close to our threshold. Hence if |X| <= 2^-4, + * perform an alternative computation + * sqrt(1 + X^2) - 1 = X^2/2 - X^4/8 + X^6/16 + * X2 = X^2 + */ + addps %xmm2, %xmm3 + addps %xmm2, %xmm4 + andps %xmm11, %xmm0 + +/* + * 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 %xmm0, %xmm14 + subps %xmm0, %xmm11 + andps %xmm12, %xmm14 + addps %xmm11, %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 %xmm14, %xmm0 + mulps %xmm14, %xmm4 + +/* + * Get the absolute value of the input, since we will exploit antisymmetry + * and mostly assume X >= 0 in the core computation + */ + movups SgnMask+__svml_sasinh_data_internal(%rip), %xmm6 + +/* + * 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 %xmm14, %xmm13 + andps %xmm8, %xmm6 + +/* + * Obtain sqrt(1 + X^2) - 1 in two pieces + * sqrt(1 + X^2) - 1 + * = sqrt(Y + W) - 1 + * = (S + T) * (1 + Corr) - 1 + * = [S - 1] + [T + (S + T) * Corr] + * We need a compensated summation for the last part. We treat S - 1 + * as the larger part; it certainly is until about X < 2^-4, and in that + * case, the error is affordable since X dominates over sqrt(1 + X^2) - 1 + * Final sum is dTmp5 (hi) + dTmp7 (lo) + */ + movaps %xmm0, %xmm1 + +/* + * Check whether the input is finite, by checking |X| <= MaxFloat + * Otherwise set the rangemask so that the callout will get used. + * Note that this will also use the callout for NaNs since not(NaN <= MaxFloat) + */ + movaps %xmm6, %xmm9 + +/* + * The following computation can go wrong for very large X, basically + * because X^2 overflows. But for large X we have + * asinh(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 do do this. + */ + movaps %xmm6, %xmm5 + cmpnleps sLargestFinite+__svml_sasinh_data_internal(%rip), %xmm9 + cmpltps sBigThreshold+__svml_sasinh_data_internal(%rip), %xmm5 + mulps %xmm0, %xmm13 + addps %xmm4, %xmm1 + subps %xmm7, %xmm0 + mulps %xmm4, %xmm14 + movmskps %xmm9, %edx + movaps %xmm7, %xmm9 + +/* + * 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_sasinh_data_internal(%rip), %xmm15 + subps %xmm13, %xmm9 + movups sHalf+__svml_sasinh_data_internal(%rip), %xmm10 + subps %xmm14, %xmm9 + +/* sX2over2 = X^2/2 */ + mulps %xmm10, %xmm3 + mulps %xmm9, %xmm15 + +/* sX46 = -X^4/4 + X^6/8 */ + movaps %xmm3, %xmm2 + movaps %xmm3, %xmm12 + +/* + * Now do another compensated sum to add |X| + [sqrt(1 + X^2) - 1]. + * It's always safe to assume |X| is larger. + * This is the final 2-part argument to the log1p function + */ + movaps %xmm6, %xmm14 + addps sC2+__svml_sasinh_data_internal(%rip), %xmm15 + mulps %xmm9, %xmm15 + addps %xmm10, %xmm15 + mulps %xmm15, %xmm9 + mulps %xmm1, %xmm9 + +/* Now multiplex to the case X = 2^-30 * input, Xl = sL = 0 in the "big" case. */ + movups XScale+__svml_sasinh_data_internal(%rip), %xmm15 + addps %xmm9, %xmm4 + movaps %xmm4, %xmm11 + addps %xmm0, %xmm11 + subps %xmm11, %xmm0 + addps %xmm0, %xmm4 + +/* sX4over4 = X^4/4 */ + movaps %xmm3, %xmm0 + mulps %xmm3, %xmm0 + mulps %xmm0, %xmm2 + subps %xmm0, %xmm2 + +/* + * 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 %xmm7, %xmm0 + +/* sX46over2 = -X^4/8 + x^6/16 */ + mulps %xmm2, %xmm10 + movaps %xmm7, %xmm2 + addps %xmm10, %xmm12 + subps %xmm12, %xmm3 + addps %xmm3, %xmm10 + +/* Now multiplex the two possible computations */ + movaps %xmm6, %xmm3 + cmpleps sLittleThreshold+__svml_sasinh_data_internal(%rip), %xmm3 + movaps %xmm3, %xmm13 + andps %xmm3, %xmm12 + andnps %xmm11, %xmm13 + movaps %xmm3, %xmm1 + orps %xmm12, %xmm13 + andnps %xmm4, %xmm1 + andps %xmm3, %xmm10 + movaps %xmm6, %xmm4 + orps %xmm10, %xmm1 + addps %xmm13, %xmm14 + mulps %xmm15, %xmm6 + maxps %xmm14, %xmm0 + minps %xmm14, %xmm2 + subps %xmm14, %xmm4 + movaps %xmm0, %xmm3 + addps %xmm4, %xmm13 + addps %xmm2, %xmm3 + addps %xmm13, %xmm1 + subps %xmm3, %xmm0 + movaps %xmm5, %xmm4 + andps %xmm5, %xmm3 + andnps %xmm6, %xmm4 + addps %xmm0, %xmm2 + +/* + * Now resume the main code. + * reduction: compute r,n + */ + movdqu iBrkValue+__svml_sasinh_data_internal(%rip), %xmm6 + orps %xmm3, %xmm4 + psubd %xmm6, %xmm4 + movaps %xmm7, %xmm0 + addps %xmm2, %xmm1 + movdqu iOffExpoMask+__svml_sasinh_data_internal(%rip), %xmm2 + pand %xmm4, %xmm2 + psrad $23, %xmm4 + cvtdq2ps %xmm4, %xmm3 + pslld $23, %xmm4 + andps %xmm5, %xmm1 + paddd %xmm6, %xmm2 + psubd %xmm4, %xmm0 + mulps %xmm0, %xmm1 + +/* polynomial evaluation */ + subps %xmm7, %xmm2 + movups sPoly+112+__svml_sasinh_data_internal(%rip), %xmm7 + addps %xmm2, %xmm1 + mulps %xmm1, %xmm7 + movaps %xmm5, %xmm2 + +/* Add 31 to the exponent in the "large" case to get log(2 * input) */ + movups sThirtyOne+__svml_sasinh_data_internal(%rip), %xmm0 + addps sPoly+96+__svml_sasinh_data_internal(%rip), %xmm7 + addps %xmm3, %xmm0 + mulps %xmm1, %xmm7 + andnps %xmm0, %xmm2 + andps %xmm5, %xmm3 + orps %xmm3, %xmm2 + addps sPoly+80+__svml_sasinh_data_internal(%rip), %xmm7 + +/* final reconstruction */ + mulps sLn2+__svml_sasinh_data_internal(%rip), %xmm2 + mulps %xmm1, %xmm7 + +/* Finally, reincorporate the original sign. */ + movups sSign+__svml_sasinh_data_internal(%rip), %xmm0 + andps %xmm8, %xmm0 + addps sPoly+64+__svml_sasinh_data_internal(%rip), %xmm7 + mulps %xmm1, %xmm7 + addps sPoly+48+__svml_sasinh_data_internal(%rip), %xmm7 + mulps %xmm1, %xmm7 + addps sPoly+32+__svml_sasinh_data_internal(%rip), %xmm7 + mulps %xmm1, %xmm7 + addps sPoly+16+__svml_sasinh_data_internal(%rip), %xmm7 + mulps %xmm1, %xmm7 + addps sPoly+__svml_sasinh_data_internal(%rip), %xmm7 + mulps %xmm1, %xmm7 + mulps %xmm1, %xmm7 + addps %xmm7, %xmm1 + addps %xmm2, %xmm1 + pxor %xmm1, %xmm0 + testl %edx, %edx + +/* Go to special inputs processing branch */ + jne L(SPECIAL_VALUES_BRANCH) + # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm8 + +/* Restore registers + * and exit the function + */ + +L(EXIT): + addq $72, %rsp + cfi_def_cfa_offset(8) + ret + cfi_def_cfa_offset(80) + +/* Branch to process + * special inputs + */ + +L(SPECIAL_VALUES_BRANCH): + movups %xmm8, 32(%rsp) + movups %xmm0, 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), %xmm0 + +/* 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 xmm0 + +/* Scalar math fucntion call + * to process special input + */ + +L(SCALAR_MATH_CALL): + movl %r12d, %r14d + movss 32(%rsp,%r14,4), %xmm0 + call asinhf@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_asinhf_sse4) + + .section .rodata, "a" + .align 16 + +#ifdef __svml_sasinh_data_internal_typedef +typedef unsigned int VUINT32; +typedef struct { + __declspec(align(16)) VUINT32 SgnMask[4][1]; + __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 sLittleThreshold[4][1]; + __declspec(align(16)) VUINT32 sSign[4][1]; + __declspec(align(16)) VUINT32 sThirtyOne[4][1]; + __declspec(align(16)) VUINT32 sTopMask11[4][1]; + __declspec(align(16)) VUINT32 sTopMask8[4][1]; + __declspec(align(16)) VUINT32 XScale[4][1]; + __declspec(align(16)) VUINT32 sLn2[4][1]; +} __svml_sasinh_data_internal; +#endif +__svml_sasinh_data_internal: + /*== SgnMask ==*/ + .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff + /*== sOne = SP 1.0 ==*/ + .align 16 + .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 + /*== sLittleThreshold ==*/ + .align 16 + .long 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000 + /*== sSign ==*/ + .align 16 + .long 0x80000000, 0x80000000, 0x80000000, 0x80000000 + /*== sThirtyOne ==*/ + .align 16 + .long 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000 + /*== sTopMask11 ==*/ + .align 16 + .long 0xFFFFE000, 0xFFFFE000, 0xFFFFE000, 0xFFFFE000 + /*== 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_sasinh_data_internal,@object + .size __svml_sasinh_data_internal,.-__svml_sasinh_data_internal |