GCC Code Coverage Report
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File: lib/libm/src/s_exp2f.c Lines: 0 25 0.0 %
Date: 2017-11-13 Branches: 0 14 0.0 %

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/*	$OpenBSD: s_exp2f.c,v 1.2 2012/12/05 23:20:04 deraadt Exp $	*/
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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 <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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}