102 lines
3.3 KiB
C
102 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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SPDX-License-Identifier: BSD-3-Clause
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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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