/* Function exp2f 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: * * exp2(x) = 2^n * T[j] * (1 + P(y)) * where * x = m*(1/K) + y, y in [-1/K..1/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 exp2(x)-1 * on small interval [-1/K..1/K] * * Special cases: * * exp2(NaN) = NaN * exp2(+INF) = +INF * exp2(-INF) = 0 * exp2(x) = 1 for subnormals * For IEEE float * if x >= 128.0 then exp2f(x) overflow * if x < -151.0 then exp2f(x) underflow * */ /* Offsets for data table __svml_sexp2_data_internal */ #define _sShifter 0 #define _sPC0 16 #define _sPC1 32 #define _sPC2 48 #define _sPC3 64 #define _sPC4 80 #define _sPC5 96 #define _sPC6 112 #define _iAbsMask 128 #define _iDomainRange 144 #include .text .section .text.sse4,"ax",@progbits ENTRY(_ZGVbN4v_exp2f_sse4) subq $72, %rsp cfi_def_cfa_offset(80) /* Check for overflow\underflow */ movups __svml_sexp2_data_internal(%rip), %xmm1 /* Implementation */ movaps %xmm1, %xmm5 /* Polynomial */ movups _sPC6+__svml_sexp2_data_internal(%rip), %xmm4 addps %xmm0, %xmm5 movaps %xmm5, %xmm3 /* 2^N */ pslld $23, %xmm5 /* Check for overflow\underflow */ movdqu _iAbsMask+__svml_sexp2_data_internal(%rip), %xmm2 subps %xmm1, %xmm3 /* R */ movaps %xmm0, %xmm1 pand %xmm0, %xmm2 pcmpgtd _iDomainRange+__svml_sexp2_data_internal(%rip), %xmm2 subps %xmm3, %xmm1 movmskps %xmm2, %edx mulps %xmm1, %xmm4 addps _sPC5+__svml_sexp2_data_internal(%rip), %xmm4 mulps %xmm1, %xmm4 addps _sPC4+__svml_sexp2_data_internal(%rip), %xmm4 mulps %xmm1, %xmm4 addps _sPC3+__svml_sexp2_data_internal(%rip), %xmm4 mulps %xmm1, %xmm4 addps _sPC2+__svml_sexp2_data_internal(%rip), %xmm4 mulps %xmm1, %xmm4 addps _sPC1+__svml_sexp2_data_internal(%rip), %xmm4 mulps %xmm4, %xmm1 addps _sPC0+__svml_sexp2_data_internal(%rip), %xmm1 /* Reconstruction */ paddd %xmm5, %xmm1 testl %edx, %edx /* Go to special inputs processing branch */ jne L(SPECIAL_VALUES_BRANCH) # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1 /* Restore registers * and exit the function */ L(EXIT): movaps %xmm1, %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 %xmm1, 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), %xmm1 /* 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 xmm1 /* Scalar math fucntion call * to process special input */ L(SCALAR_MATH_CALL): movl %r12d, %r14d movss 32(%rsp,%r14,4), %xmm0 call exp2f@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_exp2f_sse4) .section .rodata, "a" .align 16 #ifdef __svml_sexp2_data_internal_typedef typedef unsigned int VUINT32; typedef struct { __declspec(align(16)) VUINT32 _sShifter[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 _sPC3[4][1]; __declspec(align(16)) VUINT32 _sPC4[4][1]; __declspec(align(16)) VUINT32 _sPC5[4][1]; __declspec(align(16)) VUINT32 _sPC6[4][1]; __declspec(align(16)) VUINT32 _iAbsMask[4][1]; __declspec(align(16)) VUINT32 _iDomainRange[4][1]; } __svml_sexp2_data_internal; #endif __svml_sexp2_data_internal: .long 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000 /* _sShifter */ .align 16 .long 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000 /* _sPC0 */ .align 16 .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 /* _sPC1 */ .align 16 .long 0x3e75fdef, 0x3e75fdef, 0x3e75fdef, 0x3e75fdef /* _sPC2 */ .align 16 .long 0x3d6357cf, 0x3d6357cf, 0x3d6357cf, 0x3d6357cf /* _sPC3 */ .align 16 .long 0x3c1d962c, 0x3c1d962c, 0x3c1d962c, 0x3c1d962c /* _sPC4 */ .align 16 .long 0x3aaf7a51, 0x3aaf7a51, 0x3aaf7a51, 0x3aaf7a51 /* _sPC5 */ .align 16 .long 0x39213c8c, 0x39213c8c, 0x39213c8c, 0x39213c8c /* _sPC6 */ //common .align 16 .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */ .align 16 .long 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000 /* _iDomainRange=126.0 */ .align 16 .type __svml_sexp2_data_internal,@object .size __svml_sexp2_data_internal,.-__svml_sexp2_data_internal