c156098271
Based on code from https://github.com/ARM-software/optimized-routines/ This patch adds a highly optimized generic implementation of expf, exp2f, logf, log2f and powf. The new functions are not only faster (6x for powf!), but are also smaller and more accurate. In order to achieve this, the algorithm uses double precision arithmetic for accuracy, avoids divisions and uses small table lookups to minimize the polynomials. Special cases are handled inline to avoid the unnecessary overhead of wrapper functions and set errno to POSIX requirements. The new functions are added under newlib/libm/common, but the old implementations are kept (in newlib/libm/math) for non-IEEE or pre-C99 systems. Targets can enable the new math code by defining __OBSOLETE_MATH_DEFAULT to 0 in newlib/libc/include/machine/ieeefp.h, users can override the default by defining __OBSOLETE_MATH. Currently the new code is enabled for AArch64 and AArch32 with VFP. Targets with a single precision FPU may still prefer the old implementation. libm.a size changes: arm: -1692 arm/thumb/v7-a/nofp: -878 arm/thumb/v7-a+fp/hard: -864 arm/thumb/v7-a+fp/softfp: -908 aarch64: -1476
100 lines
3.3 KiB
C
100 lines
3.3 KiB
C
/* Single-precision log2 function.
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Copyright (c) 2017 ARM Ltd. All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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1. Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. The name of the company may not be used to endorse or promote
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products derived from this software without specific prior written
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permission.
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THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
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WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
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MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
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TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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#include "fdlibm.h"
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#if !__OBSOLETE_MATH
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#include <math.h>
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#include <stdint.h>
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#include "math_config.h"
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/*
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LOG2F_TABLE_BITS = 4
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LOG2F_POLY_ORDER = 4
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ULP error: 0.752 (nearest rounding.)
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Relative error: 1.9 * 2^-26 (before rounding.)
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*/
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#define N (1 << LOG2F_TABLE_BITS)
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#define T __log2f_data.tab
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#define A __log2f_data.poly
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#define OFF 0x3f330000
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float
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log2f (float x)
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{
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/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
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double_t z, r, r2, p, y, y0, invc, logc;
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uint32_t ix, iz, top, tmp;
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int k, i;
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ix = asuint (x);
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#if WANT_ROUNDING
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/* Fix sign of zero with downward rounding when x==1. */
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if (__builtin_expect (ix == 0x3f800000, 0))
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return 0;
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#endif
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if (__builtin_expect (ix - 0x00800000 >= 0x7f800000 - 0x00800000, 0))
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{
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/* x < 0x1p-126 or inf or nan. */
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if (ix * 2 == 0)
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return __math_divzerof (1);
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if (ix == 0x7f800000) /* log2(inf) == inf. */
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return x;
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if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
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return __math_invalidf (x);
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/* x is subnormal, normalize it. */
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ix = asuint (x * 0x1p23f);
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ix -= 23 << 23;
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}
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/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
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The range is split into N subintervals.
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The ith subinterval contains z and c is near its center. */
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tmp = ix - OFF;
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i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
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top = tmp & 0xff800000;
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iz = ix - top;
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k = (int32_t) tmp >> 23; /* arithmetic shift */
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invc = T[i].invc;
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logc = T[i].logc;
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z = (double_t) asfloat (iz);
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/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
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r = z * invc - 1;
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y0 = logc + (double_t) k;
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/* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
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r2 = r * r;
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y = A[1] * r + A[2];
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y = A[0] * r2 + y;
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p = A[3] * r + y0;
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y = y * r2 + p;
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return (float) y;
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}
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#endif /* !__OBSOLETE_MATH */
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