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Name
Size
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Iex.h
2.34
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IexBaseExc.h
9.06
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IexErrnoExc.h
7.37
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IexExport.h
2.08
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IexForward.h
5.1
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IexMacros.h
5.63
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IexMathExc.h
2.41
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IexMathFloatExc.h
4.58
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IexMathFpu.h
3.3
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IexMathIeeeExc.h
2.3
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IexNamespace.h
4.3
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IexThrowErrnoExc.h
3.4
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IlmBaseConfig.h
1.64
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IlmThread.h
4.78
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IlmThreadExport.h
2.15
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IlmThreadForward.h
2.08
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IlmThreadMutex.h
4.32
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IlmThreadNamespace.h
4.54
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IlmThreadPool.h
5.21
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IlmThreadSemaphore.h
3.38
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ImathBox.h
16.62
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ImathBoxAlgo.h
22.35
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ImathColor.h
14.87
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ImathColorAlgo.h
7.08
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ImathEuler.h
22.88
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ImathExc.h
2.82
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ImathExport.h
2.13
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ImathForward.h
2.68
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ImathFrame.h
6.6
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ImathFrustum.h
22.26
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ImathFrustumTest.h
14.77
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ImathFun.h
5.99
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ImathGL.h
4.52
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ImathGLU.h
2.17
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ImathHalfLimits.h
2.47
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ImathInt64.h
2.4
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ImathInterval.h
5.34
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ImathLimits.h
7.76
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ImathLine.h
4.74
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ImathLineAlgo.h
7.68
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ImathMath.h
7.17
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ImathMatrix.h
82.42
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ImathMatrixAlgo.h
37.97
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ImathNamespace.h
4.38
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ImathPlane.h
6.75
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ImathPlatform.h
3.23
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ImathQuat.h
20.94
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ImathRandom.h
9.84
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ImathRoots.h
5.62
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ImathShear.h
13.85
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ImathSphere.h
4.68
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ImathVec.h
44.17
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ImathVecAlgo.h
4.64
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ImfAcesFile.h
10.27
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ImfArray.h
6.79
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ImfAttribute.h
10.36
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ImfB44Compressor.h
3.67
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ImfBoxAttribute.h
3.1
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ImfCRgbaFile.h
12.5
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ImfChannelList.h
11.2
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ImfChannelListAttribute.h
2.69
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ImfChromaticities.h
4.45
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ImfChromaticitiesAttribute.h
2.74
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ImfCompositeDeepScanLine.h
5.38
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ImfCompression.h
3.25
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ImfCompressionAttribute.h
2.71
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ImfConvert.h
3.39
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ImfDeepCompositing.h
5.97
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ImfDeepFrameBuffer.h
8.79
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ImfDeepImageState.h
3.67
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ImfDeepImageStateAttribute.h
2.64
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ImfDeepScanLineInputFile.h
11.01
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ImfDeepScanLineInputPart.h
6.9
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ImfDeepScanLineOutputFile.h
9.37
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ImfDeepScanLineOutputPart.h
6.41
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ImfDeepTiledInputFile.h
16.08
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ImfDeepTiledInputPart.h
13.27
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ImfDeepTiledOutputFile.h
18.1
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ImfDeepTiledOutputPart.h
14.83
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ImfDoubleAttribute.h
2.29
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ImfEnvmap.h
11.29
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ImfEnvmapAttribute.h
2.67
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ImfExport.h
2.11
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ImfFloatAttribute.h
2.26
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ImfForward.h
3.48
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ImfFrameBuffer.h
11.18
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ImfFramesPerSecond.h
3.79
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ImfGenericInputFile.h
2.26
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ImfGenericOutputFile.h
2.44
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ImfHeader.h
19.27
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ImfHuf.h
2.86
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ImfIO.h
7.45
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ImfInputFile.h
8.28
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ImfInputPart.h
3.52
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ImfInt64.h
2.24
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ImfIntAttribute.h
2.27
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ImfKeyCode.h
4.9
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ImfKeyCodeAttribute.h
2.65
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ImfLineOrder.h
2.42
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ImfLineOrderAttribute.h
2.67
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ImfLut.h
5.12
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ImfMatrixAttribute.h
3.65
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ImfMisc.h
16.33
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ImfMultiPartInputFile.h
3.94
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ImfMultiPartOutputFile.h
4.29
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ImfMultiView.h
6.29
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ImfName.h
3.52
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ImfNamespace.h
4.46
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ImfOpaqueAttribute.h
3.55
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ImfOutputFile.h
9.66
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ImfOutputPart.h
3.04
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ImfPartHelper.h
7.66
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ImfPartType.h
2.38
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ImfPixelType.h
2.34
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ImfPreviewImage.h
4.65
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ImfPreviewImageAttribute.h
2.68
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ImfRational.h
3.17
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ImfRationalAttribute.h
2.63
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ImfRgba.h
3.08
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ImfRgbaFile.h
13.09
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ImfRgbaYca.h
8.21
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ImfStandardAttributes.h
13.26
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ImfStringAttribute.h
2.58
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ImfStringVectorAttribute.h
2.7
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ImfTestFile.h
3.55
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ImfThreading.h
4.24
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ImfTileDescription.h
3.13
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ImfTileDescriptionAttribute.h
2.7
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ImfTiledInputFile.h
13.82
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ImfTiledInputPart.h
4.55
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ImfTiledOutputFile.h
17.83
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ImfTiledOutputPart.h
4.75
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ImfTiledRgbaFile.h
15.89
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ImfTimeCode.h
7
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ImfTimeCodeAttribute.h
2.64
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ImfVecAttribute.h
4.45
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ImfVersion.h
4.64
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ImfWav.h
2.73
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ImfXdr.h
18.74
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OpenEXRConfig.h
1.8
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half.h
17.22
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halfExport.h
757
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halfFunction.h
4.83
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halfLimits.h
3.73
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Code Editor : ImathRoots.h
/////////////////////////////////////////////////////////////////////////// // // Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas // Digital Ltd. LLC // // All rights reserved. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above // copyright notice, this list of conditions and the following disclaimer // in the documentation and/or other materials provided with the // distribution. // * Neither the name of Industrial Light & Magic nor the names of // its contributors may be used to endorse or promote products derived // from this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. // /////////////////////////////////////////////////////////////////////////// #ifndef INCLUDED_IMATHROOTS_H #define INCLUDED_IMATHROOTS_H //--------------------------------------------------------------------- // // Functions to solve linear, quadratic or cubic equations // //--------------------------------------------------------------------- #include "ImathMath.h" #include "ImathNamespace.h" #include <complex> IMATH_INTERNAL_NAMESPACE_HEADER_ENTER //-------------------------------------------------------------------------- // Find the real solutions of a linear, quadratic or cubic equation: // // function equation solved // // solveLinear (a, b, x) a * x + b == 0 // solveQuadratic (a, b, c, x) a * x*x + b * x + c == 0 // solveNormalizedCubic (r, s, t, x) x*x*x + r * x*x + s * x + t == 0 // solveCubic (a, b, c, d, x) a * x*x*x + b * x*x + c * x + d == 0 // // Return value: // // 3 three real solutions, stored in x[0], x[1] and x[2] // 2 two real solutions, stored in x[0] and x[1] // 1 one real solution, stored in x[1] // 0 no real solutions // -1 all real numbers are solutions // // Notes: // // * It is possible that an equation has real solutions, but that the // solutions (or some intermediate result) are not representable. // In this case, either some of the solutions returned are invalid // (nan or infinity), or, if floating-point exceptions have been // enabled with Iex::mathExcOn(), an Iex::MathExc exception is // thrown. // // * Cubic equations are solved using Cardano's Formula; even though // only real solutions are produced, some intermediate results are // complex (std::complex<T>). // //-------------------------------------------------------------------------- template <class T> int solveLinear (T a, T b, T &x); template <class T> int solveQuadratic (T a, T b, T c, T x[2]); template <class T> int solveNormalizedCubic (T r, T s, T t, T x[3]); template <class T> int solveCubic (T a, T b, T c, T d, T x[3]); //--------------- // Implementation //--------------- template <class T> int solveLinear (T a, T b, T &x) { if (a != 0) { x = -b / a; return 1; } else if (b != 0) { return 0; } else { return -1; } } template <class T> int solveQuadratic (T a, T b, T c, T x[2]) { if (a == 0) { return solveLinear (b, c, x[0]); } else { T D = b * b - 4 * a * c; if (D > 0) { T s = Math<T>::sqrt (D); T q = -(b + (b > 0 ? 1 : -1) * s) / T(2); x[0] = q / a; x[1] = c / q; return 2; } if (D == 0) { x[0] = -b / (2 * a); return 1; } else { return 0; } } } template <class T> int solveNormalizedCubic (T r, T s, T t, T x[3]) { T p = (3 * s - r * r) / 3; T q = 2 * r * r * r / 27 - r * s / 3 + t; T p3 = p / 3; T q2 = q / 2; T D = p3 * p3 * p3 + q2 * q2; if (D == 0 && p3 == 0) { x[0] = -r / 3; x[1] = -r / 3; x[2] = -r / 3; return 1; } std::complex<T> u = std::pow (-q / 2 + std::sqrt (std::complex<T> (D)), T (1) / T (3)); std::complex<T> v = -p / (T (3) * u); const T sqrt3 = T (1.73205080756887729352744634150587); // enough digits // for long double std::complex<T> y0 (u + v); std::complex<T> y1 (-(u + v) / T (2) + (u - v) / T (2) * std::complex<T> (0, sqrt3)); std::complex<T> y2 (-(u + v) / T (2) - (u - v) / T (2) * std::complex<T> (0, sqrt3)); if (D > 0) { x[0] = y0.real() - r / 3; return 1; } else if (D == 0) { x[0] = y0.real() - r / 3; x[1] = y1.real() - r / 3; return 2; } else { x[0] = y0.real() - r / 3; x[1] = y1.real() - r / 3; x[2] = y2.real() - r / 3; return 3; } } template <class T> int solveCubic (T a, T b, T c, T d, T x[3]) { if (a == 0) { return solveQuadratic (b, c, d, x); } else { return solveNormalizedCubic (b / a, c / a, d / a, x); } } IMATH_INTERNAL_NAMESPACE_HEADER_EXIT #endif // INCLUDED_IMATHROOTS_H
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