196 lines
5.9 KiB
C
196 lines
5.9 KiB
C
/*
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(C) Copyright IBM Corp. 2009
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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 are met:
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* Redistributions of source code must retain the above copyright notice,
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this list of conditions and the following disclaimer.
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* 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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* Neither the name of IBM nor the names of its contributors may be
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used to endorse or promote products derived from this software without
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specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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AND 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 COPYRIGHT OWNER OR CONTRIBUTORS BE
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LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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POSSIBILITY OF SUCH DAMAGE.
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*/
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#include <math.h>
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#include "local.h"
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#ifdef _LDBL_EQ_DBL
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/* On platforms where long double is as wide as double. */
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long double
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sqrtl (long double x)
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{
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return sqrt(x);
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}
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#else
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/* This code is based upon the version in the BSD math's library.
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That code is...
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*
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* Copyright (c) 2007 Steven G. Kargl
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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 unmodified, this list of conditions, and the following
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* 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 ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#include <float.h>
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#include "ieeefp.h"
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#ifndef LDBL_NBIT
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#define LDBL_NBIT 0
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#endif
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#ifndef LDBL_MAX_EXP
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#define LDBL_MAX_EXP DBL_MAX_EXP
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#endif
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/* Return (x + ulp) for normal positive x. Assumes no overflow. */
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static inline long double
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inc (long double x)
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{
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union ieee_ext_u ux = { .extu_ld = x, };
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if (++ux.extu_ext.ext_fracl == 0)
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{
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if (++ux.extu_ext.ext_frach == 0)
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{
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ux.extu_ext.ext_exp++;
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ux.extu_ext.ext_frach |= LDBL_NBIT;
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}
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}
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return ux.extu_ld;
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}
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/* Return (x - ulp) for normal positive x. Assumes no underflow. */
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static inline long double
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dec (long double x)
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{
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union ieee_ext_u ux = { .extu_ld = x, };
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if (ux.extu_ext.ext_fracl-- == 0)
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{
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if (ux.extu_ext.ext_frach-- == LDBL_NBIT)
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{
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ux.extu_ext.ext_exp--;
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ux.extu_ext.ext_frach |= LDBL_NBIT;
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}
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}
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return ux.extu_ld;
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}
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/* This is slow, but simple and portable. */
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long double
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sqrtl (long double x)
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{
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union ieee_ext_u ux = { .extu_ld = x, };
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int k;
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long double lo, xn;
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/* If x = NaN, then sqrt(x) = NaN. */
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/* If x = Inf, then sqrt(x) = Inf. */
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/* If x = -Inf, then sqrt(x) = NaN. */
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if (ux.extu_ext.ext_exp == LDBL_MAX_EXP * 2 - 1)
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return (x * x + x);
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/* If x = +-0, then sqrt(x) = +-0. */
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if (x == 0.0L || x == -0.0L)
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return x;
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/* If x < 0, then raise invalid and return NaN. */
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if (ux.extu_ext.ext_sign)
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return ((x - x) / (x - x));
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if (ux.extu_ext.ext_exp == 0)
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{
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/* Adjust subnormal numbers. */
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ux.extu_ld *= 0x1.0p514;
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k = -514;
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}
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else
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k = 0;
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/* ux.extu_ld is a normal number, so break it into ux.extu_ld = e*2^n where
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ux.extu_ld = (2*e)*2^2k for odd n and ux.extu_ld = (4*e)*2^2k for even n. */
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if ((ux.extu_ext.ext_exp - EXT_EXP_BIAS) & 1)
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{
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/* n is even. */
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k += ux.extu_ext.ext_exp - EXT_EXP_BIAS - 1; /* 2k = n - 2. */
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ux.extu_ext.ext_exp = EXT_EXP_BIAS + 1; /* ux.extu_ld in [2,4). */
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}
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else
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{
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k += ux.extu_ext.ext_exp - EXT_EXP_BIAS; /* 2k = n - 1. */
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ux.extu_ext.ext_exp = EXT_EXP_BIAS; /* ux.extu_ld in [1,2). */
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}
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/* Newton's iteration.
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Split ux.extu_ld into a high and low part to achieve additional precision. */
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xn = sqrt ((double) ux.extu_ld); /* 53-bit estimate of sqrtl(x). */
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#if LDBL_MANT_DIG > 100
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xn = (xn + (ux.extu_ld / xn)) * 0.5; /* 106-bit estimate. */
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#endif
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lo = ux.extu_ld;
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ux.extu_ext.ext_fracl = 0; /* Zero out lower bits. */
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lo = (lo - ux.extu_ld) / xn; /* Low bits divided by xn. */
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xn = xn + (ux.extu_ld / xn); /* High portion of estimate. */
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ux.extu_ld = xn + lo; /* Combine everything. */
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ux.extu_ext.ext_exp += (k >> 1) - 1;
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xn = x / ux.extu_ld; /* Chopped quotient (inexact?). */
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/* For simplicity we round to nearest. */
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xn = inc (xn); /* xn = xn + ulp. */
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ux.extu_ld = ux.extu_ld + xn; /* Chopped sum. */
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ux.extu_ext.ext_exp--;
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return ux.extu_ld;
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}
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#endif /* ! _LDBL_EQ_DBL */
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