/* Function exp10f vectorized with SSE4. Copyright (C) 2021-2022 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: * * exp10(x) = 2^x/log10(2) = 2^n * (1 + T[j]) * (1 + P(y)) * where * x = m*log10(2)/K + y, y in [-log10(2)/K..log10(2)/K] * m = n*K + j, m, n,j - signed integer, j in [-K/2..K/2] * * values of 2^j/K are tabulated * * P(y) is a minimax polynomial approximation of exp10(x)-1 * on small interval [-log10(2)/K..log10(2)/K] * * Special cases: * * exp10(NaN) = NaN * exp10(+INF) = +INF * exp10(-INF) = 0 * exp10(x) = 1 for subnormals * For IEEE float * if x > 38.5318412780761720 then exp10f(x) overflow * if x < -45.4555282592773440 then exp10f(x) underflow * */ /* Offsets for data table __svml_sexp10_data_internal */ #define _sT 0 #define _sLg2_10 128 #define _sShifter 144 #define _sInvLg2_10hi 160 #define _sInvLg2_10lo 176 #define _sPC0 192 #define _sPC1 208 #define _sPC2 224 #define _iIndexMask 240 #define _iAbsMask 256 #define _iDomainRange 272 #include .section .text.sse4, "ax", @progbits ENTRY(_ZGVbN4v_exp10f_sse4) subq $72, %rsp cfi_def_cfa_offset(80) movaps %xmm0, %xmm4 /* Load arument */ movups _sLg2_10+__svml_sexp10_data_internal(%rip), %xmm2 lea __svml_sexp10_data_internal(%rip), %r8 mulps %xmm4, %xmm2 movups _sShifter+__svml_sexp10_data_internal(%rip), %xmm5 /* R */ movups _sInvLg2_10hi+__svml_sexp10_data_internal(%rip), %xmm14 addps %xmm5, %xmm2 movaps %xmm2, %xmm1 movups _sInvLg2_10lo+__svml_sexp10_data_internal(%rip), %xmm15 subps %xmm5, %xmm1 mulps %xmm1, %xmm14 movaps %xmm4, %xmm5 mulps %xmm1, %xmm15 subps %xmm14, %xmm5 /* * Polynomial * exp10 = 2^N*(Tj+Tj*poly) * poly(sN) = {1+later} a0+a1*sR */ movups _sPC2+__svml_sexp10_data_internal(%rip), %xmm1 subps %xmm15, %xmm5 mulps %xmm5, %xmm1 movdqu _iIndexMask+__svml_sexp10_data_internal(%rip), %xmm3 /* Index and lookup */ movdqa %xmm3, %xmm10 /* remove index bits */ pandn %xmm2, %xmm3 pand %xmm2, %xmm10 /* 2^N */ pslld $18, %xmm3 /* iIndex *= sizeof(S); */ pslld $2, %xmm10 addps _sPC1+__svml_sexp10_data_internal(%rip), %xmm1 movd %xmm10, %edx pshufd $1, %xmm10, %xmm7 pshufd $2, %xmm10, %xmm9 pshufd $3, %xmm10, %xmm11 movd %xmm7, %ecx movd %xmm9, %esi movd %xmm11, %edi /* Check for overflow\underflow */ movdqu _iAbsMask+__svml_sexp10_data_internal(%rip), %xmm6 pand %xmm4, %xmm6 mulps %xmm1, %xmm5 movslq %edx, %rdx addps _sPC0+__svml_sexp10_data_internal(%rip), %xmm5 movslq %ecx, %rcx movslq %esi, %rsi movslq %edi, %rdi movd (%r8, %rdx), %xmm0 movd (%r8, %rcx), %xmm8 movd (%r8, %rsi), %xmm13 movd (%r8, %rdi), %xmm12 punpckldq %xmm8, %xmm0 punpckldq %xmm12, %xmm13 punpcklqdq %xmm13, %xmm0 /* Tj_l+Tj_h*poly */ mulps %xmm0, %xmm5 pcmpgtd _iDomainRange+__svml_sexp10_data_internal(%rip), %xmm6 addps %xmm5, %xmm0 movmskps %xmm6, %eax /* quick mul 2^N */ paddd %xmm3, %xmm0 /* Finish */ testl %eax, %eax /* Go to special inputs processing branch */ jne L(SPECIAL_VALUES_BRANCH) # LOE rbx rbp r12 r13 r14 r15 eax xmm0 xmm4 /* 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 %xmm4, 32(%rsp) movups %xmm0, 48(%rsp) # LOE rbx rbp r12 r13 r14 r15 eax xorl %edx, %edx movq %r12, 16(%rsp) cfi_offset(12, -64) movl %edx, %r12d movq %r13, 8(%rsp) cfi_offset(13, -72) movl %eax, %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 exp10f@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_exp10f_sse4) .section .rodata, "a" .align 16 #ifdef __svml_sexp10_data_internal_typedef typedef unsigned int VUINT32; typedef struct { __declspec(align(16)) VUINT32 _sT[(1<<5)][1]; __declspec(align(16)) VUINT32 _sLg2_10[4][1]; __declspec(align(16)) VUINT32 _sShifter[4][1]; __declspec(align(16)) VUINT32 _sInvLg2_10hi[4][1]; __declspec(align(16)) VUINT32 _sInvLg2_10lo[4][1]; __declspec(align(16)) VUINT32 _sPC0[4][1]; __declspec(align(16)) VUINT32 _sPC1[4][1]; __declspec(align(16)) VUINT32 _sPC2[4][1]; __declspec(align(16)) VUINT32 _iIndexMask[4][1]; __declspec(align(16)) VUINT32 _iAbsMask[4][1]; __declspec(align(16)) VUINT32 _iDomainRange[4][1]; } __svml_sexp10_data_internal; #endif __svml_sexp10_data_internal: /* _sT */ .long 0x3f800000 // 2^( 0 /32 ) .long 0x3f82cd87 // 2^( 1 /32 ) .long 0x3f85aac3 // 2^( 2 /32 ) .long 0x3f88980f // 2^( 3 /32 ) .long 0x3f8b95c2 // 2^( 4 /32 ) .long 0x3f8ea43a // 2^( 5 /32 ) .long 0x3f91c3d3 // 2^( 6 /32 ) .long 0x3f94f4f0 // 2^( 7 /32 ) .long 0x3f9837f0 // 2^( 8 /32 ) .long 0x3f9b8d3a // 2^( 9 /32 ) .long 0x3f9ef532 // 2^( 10/32 ) .long 0x3fa27043 // 2^( 11/32 ) .long 0x3fa5fed7 // 2^( 12/32 ) .long 0x3fa9a15b // 2^( 13/32 ) .long 0x3fad583f // 2^( 14/32 ) .long 0x3fb123f6 // 2^( 15/32 ) .long 0x3fb504f3 // 2^( 16/32 ) .long 0x3fb8fbaf // 2^( 17/32 ) .long 0x3fbd08a4 // 2^( 18/32 ) .long 0x3fc12c4d // 2^( 19/32 ) .long 0x3fc5672a // 2^( 20/32 ) .long 0x3fc9b9be // 2^( 21/32 ) .long 0x3fce248c // 2^( 22/32 ) .long 0x3fd2a81e // 2^( 23/32 ) .long 0x3fd744fd // 2^( 24/32 ) .long 0x3fdbfbb8 // 2^( 25/32 ) .long 0x3fe0ccdf // 2^( 26/32 ) .long 0x3fe5b907 // 2^( 27/32 ) .long 0x3feac0c7 // 2^( 28/32 ) .long 0x3fefe4ba // 2^( 29/32 ) .long 0x3ff5257d // 2^( 30/32 ) .long 0x3ffa83b3 // 2^( 31/32 ) .align 16 .long 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78 /* _sLg2_10*2^K */ .align 16 .long 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000 /* _sShifter) */ .align 16 .long 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000 /* _sInvLg2_10hi/2^K hi (24-K-7) bits */ .align 16 .long 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc /* _sInvLg2_10lo/2^K lo bits */ // otherwise exp10(0) won't produce exact 1.0 .align 16 .long 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868 /* _sPC0 */ .align 16 .long 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b /* _sPC1 */ .align 16 .long 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2 /* _sPC2 */ .align 16 .long 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f /* _iIndexMask =(2^K-1) */ //common .align 16 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */ .align 16 .long 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818 /* _iDomainRange=-log10(max_denormal=0x007fffff) RZ */ .align 16 .type __svml_sexp10_data_internal, @object .size __svml_sexp10_data_internal, .-__svml_sexp10_data_internal