5e53a4f90f
Mainly focus on files that use BSD 2-Clause license, however the tool I was using mis-identified many licenses so this was mostly a manual - error prone - task. The Software Package Data Exchange (SPDX) group provides a specification to make it easier for automated tools to detect and summarize well known opensource licenses. We are gradually adopting the specification, noting that the tags are considered only advisory and do not, in any way, superceed or replace the license texts.
140 lines
4.1 KiB
C
140 lines
4.1 KiB
C
/*-
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* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
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*
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* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
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* All rights reserved.
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*
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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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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <float.h>
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#include "math.h"
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#include "math_private.h"
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#define TBLBITS 4
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#define TBLSIZE (1 << TBLBITS)
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static const float
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redux = 0x1.8p23f / TBLSIZE,
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P1 = 0x1.62e430p-1f,
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P2 = 0x1.ebfbe0p-3f,
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P3 = 0x1.c6b348p-5f,
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P4 = 0x1.3b2c9cp-7f;
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static volatile float
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huge = 0x1p100f,
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twom100 = 0x1p-100f;
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static const double exp2ft[TBLSIZE] = {
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0x1.6a09e667f3bcdp-1,
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0x1.7a11473eb0187p-1,
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0x1.8ace5422aa0dbp-1,
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0x1.9c49182a3f090p-1,
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0x1.ae89f995ad3adp-1,
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0x1.c199bdd85529cp-1,
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0x1.d5818dcfba487p-1,
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0x1.ea4afa2a490dap-1,
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0x1.0000000000000p+0,
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0x1.0b5586cf9890fp+0,
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0x1.172b83c7d517bp+0,
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0x1.2387a6e756238p+0,
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0x1.306fe0a31b715p+0,
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0x1.3dea64c123422p+0,
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0x1.4bfdad5362a27p+0,
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0x1.5ab07dd485429p+0,
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};
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/*
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* exp2f(x): compute the base 2 exponential of x
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*
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* Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
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*
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* Method: (equally-spaced tables)
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*
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* Reduce x:
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* x = 2**k + y, for integer k and |y| <= 1/2.
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* Thus we have exp2f(x) = 2**k * exp2(y).
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*
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* Reduce y:
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* y = i/TBLSIZE + z for integer i near y * TBLSIZE.
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* Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
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* with |z| <= 2**-(TBLSIZE+1).
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*
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* We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
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* degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
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* Using double precision for everything except the reduction makes
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* roundoff error insignificant and simplifies the scaling step.
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*
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* This method is due to Tang, but I do not use his suggested parameters:
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*
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* Tang, P. Table-driven Implementation of the Exponential Function
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* in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
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*/
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float
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exp2f(float x)
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{
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double tv, twopk, u, z;
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float t;
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uint32_t hx, ix, i0;
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int32_t k;
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/* Filter out exceptional cases. */
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GET_FLOAT_WORD(hx, x);
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ix = hx & 0x7fffffff; /* high word of |x| */
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if(ix >= 0x43000000) { /* |x| >= 128 */
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if(ix >= 0x7f800000) {
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if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0)
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return (x + x); /* x is NaN or +Inf */
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else
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return (0.0); /* x is -Inf */
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}
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if(x >= 0x1.0p7f)
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return (huge * huge); /* overflow */
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if(x <= -0x1.2cp7f)
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return (twom100 * twom100); /* underflow */
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} else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
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return (1.0f + x);
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}
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/* Reduce x, computing z, i0, and k. */
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STRICT_ASSIGN(float, t, x + redux);
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GET_FLOAT_WORD(i0, t);
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i0 += TBLSIZE / 2;
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k = (i0 >> TBLBITS) << 20;
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i0 &= TBLSIZE - 1;
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t -= redux;
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z = x - t;
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INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
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/* Compute r = exp2(y) = exp2ft[i0] * p(z). */
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tv = exp2ft[i0];
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u = tv * z;
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tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4);
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/* Scale by 2**(k>>20). */
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return (tv * twopk);
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}
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