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4ea49f4c08
without wrapper on aarch64: powf reciprocal-throughput: 4.2x faster powf latency: 2.6x faster old worst-case error: 1.11 ulp new worst-case error: 0.82 ulp aarch64 .text size: -780 bytes aarch64 .rodata size: +144 bytes powf(x,y) is implemented as exp2(y*log2(x)) with the same algorithms that are used in exp2f and log2f, except that the log2f polynomial is larger for extra precision and its output (and exp2f input) may be scaled by a power of 2 (POWF_SCALE) to simplify the argument reduction step of exp2 (possible when efficient round and convert toint operation is available). The special case handling tries to minimize the checks in the hot path. When the input of exp2_inline is checked, int arithmetics is used as that was faster on the tested aarch64 cores. * math/Makefile (type-float-routines): Add e_powf_log2_data. * sysdeps/ieee754/flt-32/e_powf.c: New implementation. * sysdeps/ieee754/flt-32/e_powf_log2_data.c: New file. * sysdeps/ieee754/flt-32/math_config.h (__powf_log2_data): Define. (issignalingf_inline): Likewise. (POWF_LOG2_TABLE_BITS): Likewise. (POWF_LOG2_POLY_ORDER): Likewise. (POWF_SCALE_BITS): Likewise. (POWF_SCALE): Likewise. * sysdeps/i386/fpu/e_powf_log2_data.c: New file. * sysdeps/ia64/fpu/e_powf_log2_data.c: New file. * sysdeps/m68k/m680x0/fpu/e_powf_log2_data.c: New file.
165 lines
3.7 KiB
C
165 lines
3.7 KiB
C
/* Configuration for math routines.
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Copyright (C) 2017 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#ifndef _MATH_CONFIG_H
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#define _MATH_CONFIG_H
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#include <math.h>
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#include <math_private.h>
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#include <nan-high-order-bit.h>
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#include <stdint.h>
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#ifndef WANT_ROUNDING
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/* Correct special case results in non-nearest rounding modes. */
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# define WANT_ROUNDING 1
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#endif
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#ifndef WANT_ERRNO
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/* Set errno according to ISO C with (math_errhandling & MATH_ERRNO) != 0. */
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# define WANT_ERRNO 1
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#endif
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#ifndef WANT_ERRNO_UFLOW
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/* Set errno to ERANGE if result underflows to 0 (in all rounding modes). */
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# define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO)
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#endif
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#ifndef TOINT_INTRINSICS
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# define TOINT_INTRINSICS 0
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#endif
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#ifndef TOINT_RINT
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# define TOINT_RINT 0
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#endif
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#ifndef TOINT_SHIFT
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# define TOINT_SHIFT 1
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#endif
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static inline uint32_t
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asuint (float f)
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{
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union
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{
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float f;
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uint32_t i;
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} u = {f};
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return u.i;
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}
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static inline float
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asfloat (uint32_t i)
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{
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union
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{
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uint32_t i;
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float f;
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} u = {i};
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return u.f;
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}
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static inline uint64_t
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asuint64 (double f)
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{
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union
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{
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double f;
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uint64_t i;
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} u = {f};
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return u.i;
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}
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static inline double
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asdouble (uint64_t i)
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{
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union
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{
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uint64_t i;
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double f;
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} u = {i};
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return u.f;
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}
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static inline int
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issignalingf_inline (float x)
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{
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uint32_t ix = asuint (x);
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if (HIGH_ORDER_BIT_IS_SET_FOR_SNAN)
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return (ix & 0x7fc00000) == 0x7fc00000;
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return 2 * (ix ^ 0x00400000) > 2u * 0x7fc00000;
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}
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#define NOINLINE __attribute__ ((noinline))
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attribute_hidden float __math_oflowf (unsigned long);
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attribute_hidden float __math_uflowf (unsigned long);
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attribute_hidden float __math_may_uflowf (unsigned long);
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attribute_hidden float __math_divzerof (unsigned long);
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attribute_hidden float __math_invalidf (float);
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/* Shared between expf, exp2f and powf. */
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#define EXP2F_TABLE_BITS 5
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#define EXP2F_POLY_ORDER 3
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extern const struct exp2f_data
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{
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uint64_t tab[1 << EXP2F_TABLE_BITS];
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double shift_scaled;
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double poly[EXP2F_POLY_ORDER];
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double shift;
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double invln2_scaled;
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double poly_scaled[EXP2F_POLY_ORDER];
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} __exp2f_data attribute_hidden;
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#define LOGF_TABLE_BITS 4
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#define LOGF_POLY_ORDER 4
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extern const struct logf_data
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{
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struct
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{
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double invc, logc;
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} tab[1 << LOGF_TABLE_BITS];
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double ln2;
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double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */
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} __logf_data attribute_hidden;
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#define LOG2F_TABLE_BITS 4
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#define LOG2F_POLY_ORDER 4
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extern const struct log2f_data
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{
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struct
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{
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double invc, logc;
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} tab[1 << LOG2F_TABLE_BITS];
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double poly[LOG2F_POLY_ORDER];
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} __log2f_data attribute_hidden;
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#define POWF_LOG2_TABLE_BITS 4
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#define POWF_LOG2_POLY_ORDER 5
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#if TOINT_INTRINSICS
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# define POWF_SCALE_BITS EXP2F_TABLE_BITS
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#else
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# define POWF_SCALE_BITS 0
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#endif
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#define POWF_SCALE ((double) (1 << POWF_SCALE_BITS))
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extern const struct powf_log2_data
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{
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struct
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{
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double invc, logc;
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} tab[1 << POWF_LOG2_TABLE_BITS];
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double poly[POWF_LOG2_POLY_ORDER];
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} __powf_log2_data attribute_hidden;
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#endif
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