5980be9b3c
This work is based in part on code from NetBSD libm, libc and kernel. The library is partly public domain and partly BSD-style licensed.
140 lines
4.2 KiB
C
140 lines
4.2 KiB
C
/*-
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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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__RCSID("$NetBSD: s_exp2f.c,v 1.1 2010/01/11 16:28:39 christos Exp $");
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#ifdef __FBSDID
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__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2f.c,v 1.9 2008/02/22 02:27:34 das Exp $");
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#endif
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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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huge = 0x1p100f,
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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 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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