208 lines
7.2 KiB
C++
208 lines
7.2 KiB
C++
///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas
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// Digital Ltd. LLC
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//
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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 are
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// met:
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// * 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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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following disclaimer
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// in the documentation and/or other materials provided with the
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// distribution.
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// * Neither the name of Industrial Light & Magic nor the names of
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// its contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// 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
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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///////////////////////////////////////////////////////////////////////////
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#ifndef INCLUDED_IMATHMATH_H
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#define INCLUDED_IMATHMATH_H
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//----------------------------------------------------------------------------
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//
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// ImathMath.h
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//
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// This file contains template functions which call the double-
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// precision math functions defined in math.h (sin(), sqrt(),
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// exp() etc.), with specializations that call the faster
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// single-precision versions (sinf(), sqrtf(), expf() etc.)
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// when appropriate.
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//
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// Example:
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//
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// double x = Math<double>::sqrt (3); // calls ::sqrt(double);
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// float y = Math<float>::sqrt (3); // calls ::sqrtf(float);
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//
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// When would I want to use this?
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//
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// You may be writing a template which needs to call some function
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// defined in math.h, for example to extract a square root, but you
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// don't know whether to call the single- or the double-precision
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// version of this function (sqrt() or sqrtf()):
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//
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// template <class T>
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// T
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// glorp (T x)
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// {
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// return sqrt (x + 1); // should call ::sqrtf(float)
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// } // if x is a float, but we
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// // don't know if it is
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//
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// Using the templates in this file, you can make sure that
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// the appropriate version of the math function is called:
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//
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// template <class T>
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// T
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// glorp (T x, T y)
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// {
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// return Math<T>::sqrt (x + 1); // calls ::sqrtf(float) if x
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// } // is a float, ::sqrt(double)
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// // otherwise
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//
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//----------------------------------------------------------------------------
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#include "ImathPlatform.h"
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#include "ImathLimits.h"
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#include "ImathNamespace.h"
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#include <math.h>
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IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
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template <class T>
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struct Math
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{
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static T acos (T x) {return ::acos (double(x));}
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static T asin (T x) {return ::asin (double(x));}
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static T atan (T x) {return ::atan (double(x));}
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static T atan2 (T x, T y) {return ::atan2 (double(x), double(y));}
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static T cos (T x) {return ::cos (double(x));}
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static T sin (T x) {return ::sin (double(x));}
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static T tan (T x) {return ::tan (double(x));}
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static T cosh (T x) {return ::cosh (double(x));}
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static T sinh (T x) {return ::sinh (double(x));}
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static T tanh (T x) {return ::tanh (double(x));}
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static T exp (T x) {return ::exp (double(x));}
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static T log (T x) {return ::log (double(x));}
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static T log10 (T x) {return ::log10 (double(x));}
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static T modf (T x, T *iptr)
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{
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double ival;
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T rval( ::modf (double(x),&ival));
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*iptr = ival;
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return rval;
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}
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static T pow (T x, T y) {return ::pow (double(x), double(y));}
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static T sqrt (T x) {return ::sqrt (double(x));}
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static T ceil (T x) {return ::ceil (double(x));}
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static T fabs (T x) {return ::fabs (double(x));}
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static T floor (T x) {return ::floor (double(x));}
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static T fmod (T x, T y) {return ::fmod (double(x), double(y));}
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static T hypot (T x, T y) {return ::hypot (double(x), double(y));}
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};
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template <>
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struct Math<float>
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{
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static float acos (float x) {return ::acosf (x);}
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static float asin (float x) {return ::asinf (x);}
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static float atan (float x) {return ::atanf (x);}
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static float atan2 (float x, float y) {return ::atan2f (x, y);}
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static float cos (float x) {return ::cosf (x);}
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static float sin (float x) {return ::sinf (x);}
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static float tan (float x) {return ::tanf (x);}
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static float cosh (float x) {return ::coshf (x);}
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static float sinh (float x) {return ::sinhf (x);}
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static float tanh (float x) {return ::tanhf (x);}
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static float exp (float x) {return ::expf (x);}
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static float log (float x) {return ::logf (x);}
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static float log10 (float x) {return ::log10f (x);}
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static float modf (float x, float *y) {return ::modff (x, y);}
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static float pow (float x, float y) {return ::powf (x, y);}
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static float sqrt (float x) {return ::sqrtf (x);}
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static float ceil (float x) {return ::ceilf (x);}
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static float fabs (float x) {return ::fabsf (x);}
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static float floor (float x) {return ::floorf (x);}
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static float fmod (float x, float y) {return ::fmodf (x, y);}
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#if !defined(_MSC_VER)
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static float hypot (float x, float y) {return ::hypotf (x, y);}
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#else
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static float hypot (float x, float y) {return ::sqrtf(x*x + y*y);}
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#endif
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};
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//--------------------------------------------------------------------------
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// Don Hatch's version of sin(x)/x, which is accurate for very small x.
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// Returns 1 for x == 0.
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//--------------------------------------------------------------------------
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template <class T>
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inline T
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sinx_over_x (T x)
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{
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if (x * x < limits<T>::epsilon())
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return T (1);
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else
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return Math<T>::sin (x) / x;
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}
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//--------------------------------------------------------------------------
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// Compare two numbers and test if they are "approximately equal":
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//
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// equalWithAbsError (x1, x2, e)
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//
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// Returns true if x1 is the same as x2 with an absolute error of
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// no more than e,
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//
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// abs (x1 - x2) <= e
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//
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// equalWithRelError (x1, x2, e)
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//
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// Returns true if x1 is the same as x2 with an relative error of
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// no more than e,
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//
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// abs (x1 - x2) <= e * x1
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//
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//--------------------------------------------------------------------------
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template <class T>
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inline bool
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equalWithAbsError (T x1, T x2, T e)
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{
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return ((x1 > x2)? x1 - x2: x2 - x1) <= e;
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}
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template <class T>
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inline bool
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equalWithRelError (T x1, T x2, T e)
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{
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return ((x1 > x2)? x1 - x2: x2 - x1) <= e * ((x1 > 0)? x1: -x1);
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}
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IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
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#endif // INCLUDED_IMATHMATH_H
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