When possible use math constants.

Framework/API/test/PeakFunctionIntegratorTest.h

@@ -30,10 +30,10 @@ public:
   void setCentre(const double c) override { setParameter("Center", c); }
 
   double fwhm() const override {
-    return getParameter("Sigma") * (2.0 * sqrt(2.0 * log(2.0)));
+    return getParameter("Sigma") * (2.0 * sqrt(2.0 * M_LN2));
   }
   void setFwhm(const double w) override {
-    setParameter("Sigma", w / (2.0 * sqrt(2.0 * log(2.0))));
+    setParameter("Sigma", w / (2.0 * sqrt(2.0 * M_LN2)));
   }
 
   double height() const override { return getParameter("Height"); }
@@ -80,8 +80,8 @@ private:
   }
 
   double getGaussianAnalyticalInfiniteIntegral(IPeakFunction_sptr gaussian) {
-    return gaussian->height() * gaussian->fwhm() /
-           (2.0 * sqrt(2.0 * log(2.0))) * sqrt(2.0 * M_PI);
+    return gaussian->height() * gaussian->fwhm() / (2.0 * sqrt(M_LN2)) *
+           sqrt(M_PI);
   }
 
 public:
@@ -169,7 +169,7 @@ public:
      *  -integral from -3 to 3 should give approx. 0.997
      */
     IPeakFunction_sptr gaussian =
-        getGaussian(0.0, 2.0 * sqrt(2.0 * log(2.0)), 1.0 / sqrt(2.0 * M_PI));
+        getGaussian(0.0, 2.0 * sqrt(2.0 * M_LN2), 1.0 / sqrt(2.0 * M_PI));
     PeakFunctionIntegrator integrator(1e-10);
 
     IntegrationResult rOneSigma = integrator.integrate(*gaussian, -1.0, 1.0);

Framework/Algorithms/src/GetAllEi.cpp

@@ -300,7 +300,7 @@ void GetAllEi::exec() {
   // preprocess first monitors peaks;
   g_log.debug() << "*Looking for real energy peaks on first monitor\n";
   findBinRanges(monitorWS->readX(0), monitorWS->readY(0), guess_ei,
-                this->m_min_Eresolution / (2 * std::sqrt(2 * std::log(2.))),
+                this->m_min_Eresolution / (2. * std::sqrt(2. * M_LN2)),
                 irange_min, irange_max, guessValid);
 
   // remove invalid guess values
@@ -311,7 +311,7 @@ void GetAllEi::exec() {
   if (!this->getProperty("IgnoreSecondMonitor")) {
     g_log.debug() << "*Looking for real energy peaks on second monitor\n";
     findBinRanges(monitorWS->readX(1), monitorWS->readY(1), guess_ei,
-                  this->m_min_Eresolution / (2 * std::sqrt(2 * std::log(2.))),
+                  this->m_min_Eresolution / (2. * std::sqrt(2. * M_LN2)),
                   irange1_min, irange1_max, guessValid);
     removeInvalidValues<double>(guessValid, guess_ei);
     removeInvalidValues<size_t>(guessValid, irange_min);
@@ -471,7 +471,7 @@ bool GetAllEi::peakGuess(const API::MatrixWorkspace_sptr &inputWS, size_t index,
                          double &peakTwoSigma) {
 
   // calculate sigma from half-width parameters
-  double maxSigma = Ei * m_min_Eresolution / (2 * std::sqrt(2 * std::log(2.)));
+  double maxSigma = Ei * m_min_Eresolution / (2. * std::sqrt(2. * M_LN2));
 
   double sMin(std::numeric_limits<double>::max());
   double sMax(-sMin);
@@ -621,8 +621,8 @@ bool GetAllEi::findMonitorPeak(const API::MatrixWorkspace_sptr &inputWS,
                                double &position, double &height,
                                double &twoSigma) {
   // calculate sigma from half-width parameters
-  double maxSigma = Ei * m_min_Eresolution / (2 * std::sqrt(2 * std::log(2.)));
-  double minSigma = Ei * m_max_Eresolution / (2 * std::sqrt(2 * std::log(2.)));
+  double maxSigma = Ei * m_min_Eresolution / (2. * std::sqrt(2. * M_LN2));
+  double minSigma = Ei * m_max_Eresolution / (2. * std::sqrt(2. * M_LN2));
   //--------------------------------------------------------------------
   double peak1Pos, peak1TwoSigma, peak1Height;
   if (!peakGuess(inputWS, 0, Ei, monsRangeMin, monsRangeMax, peak1Pos,

Framework/Algorithms/src/GetDetOffsetsMultiPeaks.cpp

@@ -26,7 +26,7 @@ namespace Mantid {
 namespace Algorithms {
 namespace {
 /// Factor to convert full width half max to sigma for calculations of I/sigma.
-const double FWHM_TO_SIGMA = 2.0 * sqrt(2.0 * std::log(2.0));
+const double FWHM_TO_SIGMA = 2.0 * sqrt(2.0 * M_LN2);
 const double BAD_OFFSET(1000.); // mark things that didn't work with this
 
 //--------------------------------------------------------------------------------------------
@@ -1087,7 +1087,7 @@ void GetDetOffsetsMultiPeaks::generatePeaksList(
     vec_widthDivPos.push_back(widthdevpos);
 
     // g_log.debug() << " h:" << height << " c:" << centre << " w:" <<
-    // (width/(2.*std::sqrt(2.*std::log(2.))))
+    // (width/(2.*std::sqrt(2.*M_LN2)))
     //               << " b:" << background << " chisq:" << chi2 << "\n";
 
     // Add peak to vectors

Framework/Algorithms/src/GetDetectorOffsets.cpp

@@ -249,7 +249,7 @@ IFunction_sptr GetDetectorOffsets::createFunction(const double peakHeight,
   peak->setHeight(peakHeight);
   peak->setCentre(peakLoc);
   const double sigma(10.0);
-  peak->setFwhm(2.0 * std::sqrt(2.0 * std::log(2.0)) * sigma);
+  peak->setFwhm(2.0 * std::sqrt(2.0 * M_LN2) * sigma);
 
   auto fitFunc = new CompositeFunction(); // Takes ownership of the functions
   fitFunc->addFunction(background);

Framework/Algorithms/test/ConvertFromDistributionTest.h

@@ -53,7 +53,7 @@ public:
     for (size_t i = 0; i < Y.size(); ++i) {
       TS_ASSERT_EQUALS(X[i], static_cast<double>(i) / 2.0)
       TS_ASSERT_EQUALS(Y[i], 1)
-      TS_ASSERT_EQUALS(E[i], sqrt(2.0) / 2.0)
+      TS_ASSERT_EQUALS(E[i], M_SQRT2 / 2.0)
     }
     TS_ASSERT(!output->isDistribution())
 

Framework/Algorithms/test/ConvertToDistributionTest.h

@@ -55,7 +55,7 @@ public:
     for (size_t i = 0; i < Y.size(); ++i) {
       TS_ASSERT_EQUALS(X[i], static_cast<double>(i) / 2.0)
       TS_ASSERT_EQUALS(Y[i], 4)
-      TS_ASSERT_EQUALS(E[i], sqrt(2.0) / 0.5)
+      TS_ASSERT_EQUALS(E[i], M_SQRT2 / 0.5)
     }
     TS_ASSERT(output->isDistribution())
   }

Framework/Algorithms/test/ConvertToEventWorkspaceTest.h

@@ -47,7 +47,7 @@ public:
     inWS->dataY(0)[2] = 0.0;
     inWS->dataE(0)[2] = 0.0;
     inWS->dataY(0)[3] = 2.0;
-    inWS->dataE(0)[3] = sqrt(2.0);
+    inWS->dataE(0)[3] = M_SQRT2;
     inWS->dataY(0)[4] = 10000.0;
     inWS->dataE(0)[4] = 100.0;
 

Framework/Algorithms/test/ConvertToHistogramTest.h

@@ -88,7 +88,7 @@ public:
     //   {
     // 	// Now the data. Y and E unchanged
     // 	TS_ASSERT_EQUALS(yValues[j], 2.0);
-    // 	TS_ASSERT_EQUALS(eValues[j], sqrt(2.0));
+    // 	TS_ASSERT_EQUALS(eValues[j], M_SQRT2);
 
     // 	// X data originally was 0->10 in steps of 1. Now it should be the
     // centre of each bin which is

Framework/Algorithms/test/ConvertToPointDataTest.h

@@ -78,7 +78,7 @@ public:
       for (int j = 0; j < numBins; ++j) {
         // Now the data. Y and E unchanged
         TS_ASSERT_EQUALS(yValues[j], 2.0);
-        TS_ASSERT_EQUALS(eValues[j], sqrt(2.0));
+        TS_ASSERT_EQUALS(eValues[j], M_SQRT2);
         // X data originally was 0->10 in steps of 1. Now it should be the
         // centre of each bin which is
         // 1.0 away from the last centre
@@ -128,7 +128,7 @@ public:
       for (size_t j = 0; j < numBins; ++j) {
         // Now the data. Y and E unchanged
         TS_ASSERT_EQUALS(yValues[j], 2.0);
-        TS_ASSERT_EQUALS(eValues[j], sqrt(2.0));
+        TS_ASSERT_EQUALS(eValues[j], M_SQRT2);
         // X data originally was 0->10 in steps of 1. Now it should be the
         // centre of each bin which is
         // 1.0 away from the last centre

Framework/Algorithms/test/ExtractSpectraTest.h

@@ -633,7 +633,7 @@ private:
         TS_ASSERT(ws.hasDx(0));
         TS_ASSERT_EQUALS(ws.readDx(0)[0], 0.0);
         TS_ASSERT_EQUALS(ws.readDx(0)[1], 1.0);
-        TS_ASSERT_EQUALS(ws.readDx(0)[2], sqrt(2.0));
+        TS_ASSERT_EQUALS(ws.readDx(0)[2], M_SQRT2);
         TS_ASSERT_EQUALS(ws.readDx(0)[3], sqrt(3.0));
         // Check that the length of x and dx is the same
         auto x = ws.readX(0);
@@ -644,7 +644,7 @@ private:
         TS_ASSERT(ws.hasDx(0));
         TS_ASSERT_EQUALS(ws.readDx(0)[0], 0.0 + 1.0);
         TS_ASSERT_EQUALS(ws.readDx(0)[1], 1.0 + 1.0);
-        TS_ASSERT_EQUALS(ws.readDx(0)[2], sqrt(2.0) + 1.0);
+        TS_ASSERT_EQUALS(ws.readDx(0)[2], M_SQRT2 + 1.0);
         TS_ASSERT_EQUALS(ws.readDx(0)[3], sqrt(3.0) + 1.0);
       } else {
         TSM_ASSERT("Should never reach here", false);

Framework/Algorithms/test/MaskBinsTest.h

@@ -72,7 +72,7 @@ public:
           TS_ASSERT_EQUALS(outputWS->readE(i)[j], 0.0);
         } else {
           TS_ASSERT_EQUALS(outputWS->readY(i)[j], 2.0);
-          TS_ASSERT_DELTA(outputWS->readE(i)[j], sqrt(2.0), 0.0001);
+          TS_ASSERT_DELTA(outputWS->readE(i)[j], M_SQRT2, 0.0001);
         }
         TS_ASSERT_EQUALS(outputWS->readX(i)[j], j);
       }

Framework/Algorithms/test/NormaliseByCurrentTest.h

@@ -130,7 +130,7 @@ public:
   void testExec() {
     AnalysisDataService::Instance().add(
         "normIn", WorkspaceCreationHelper::Create2DWorkspaceBinned(10, 3, 1));
-    doTest("normIn", "normOut", 1.0, sqrt(2.0) / 2.0);
+    doTest("normIn", "normOut", 1.0, 0.5 * M_SQRT2);
     AnalysisDataService::Instance().remove("normIn");
     AnalysisDataService::Instance().remove("normOut");
   }
@@ -268,7 +268,7 @@ public:
   void testExec_InPlace() {
     AnalysisDataService::Instance().add(
         "normIn", WorkspaceCreationHelper::Create2DWorkspaceBinned(10, 3, 1));
-    doTest("normIn", "normIn", 1.0, sqrt(2.0) / 2.0);
+    doTest("normIn", "normIn", 1.0, 0.5 * M_SQRT2);
     AnalysisDataService::Instance().remove("normIn");
   }
 
@@ -279,7 +279,7 @@ public:
 
     EventWorkspace_const_sptr outputEvent;
     outputEvent = boost::dynamic_pointer_cast<const EventWorkspace>(
-        doTest("normInEvent", "normOutEvent", 1.0, sqrt(2.0) / 2.0));
+        doTest("normInEvent", "normOutEvent", 1.0, 0.5 * M_SQRT2));
     // Output is an event workspace
     TS_ASSERT(outputEvent);
 
@@ -294,7 +294,7 @@ public:
 
     EventWorkspace_const_sptr outputEvent;
     outputEvent = boost::dynamic_pointer_cast<const EventWorkspace>(
-        doTest("normInEvent", "normInEvent", 1.0, sqrt(2.0) / 2.0));
+        doTest("normInEvent", "normInEvent", 1.0, 0.5 * M_SQRT2));
     // Output is an event workspace
     TS_ASSERT(outputEvent);
 

Framework/Algorithms/test/SignalOverErrorTest.h

@@ -47,7 +47,7 @@ public:
       return;
 
     // Check the results
-    TS_ASSERT_DELTA(ws->readY(0)[0], sqrt(2.0), 1e-5);
+    TS_ASSERT_DELTA(ws->readY(0)[0], M_SQRT2, 1e-5);
     TS_ASSERT_DELTA(ws->readE(0)[0], 0.0, 1e-5);
 
     // Remove workspace from the data service.

Framework/Algorithms/test/WeightedMeanTest.h

@@ -62,7 +62,7 @@ public:
     TS_ASSERT_DELTA(result->readE(0)[1176], 104.841321, 0.000001)
     // Now one where first is zero
     TS_ASSERT_EQUALS(result->readY(0)[2], 2.0)
-    TS_ASSERT_EQUALS(result->readE(0)[2], std::sqrt(2.0))
+    TS_ASSERT_EQUALS(result->readE(0)[2], M_SQRT2)
     // And one where second is zero
     TS_ASSERT_EQUALS(result->readY(0)[113], 97.0)
     TS_ASSERT_EQUALS(result->readE(0)[113], std::sqrt(97.0))

Framework/Crystal/src/TOFExtinction.cpp

@@ -123,8 +123,8 @@ void TOFExtinction::exec() {
       sigfsq_ys = getSigFsqr(EgLaueI, cell, wl, twoth, tbar, fsq, sigfsq);
     } else if (cType.compare("Type I Gaussian") == 0) {
       // Apply correction to fsq with Type-I BCG for testing
-      double EgLaueI = std::sqrt(2.0) *
-                       getEgLaue(Eg, twoth, wl, divBeam, betaBeam) * 2.0 / 3.0;
+      double EgLaueI =
+          M_SQRT2 * getEgLaue(Eg, twoth, wl, divBeam, betaBeam) * 2.0 / 3.0;
       double Xqt = getXqt(EgLaueI, cell, wl, twoth, tbar, fsq);
       y_corr = getGaussian(Xqt, twoth);
       sigfsq_ys = getSigFsqr(EgLaueI, cell, wl, twoth, tbar, fsq, sigfsq);

Framework/CurveFitting/src/Functions/Bk2BkExpConvPV.cpp

@@ -226,7 +226,7 @@ void Bk2BkExpConvPV::geneatePeak(double *out, const double *xValues,
 void Bk2BkExpConvPV::calHandEta(double sigma2, double gamma, double &H,
                                 double &eta) const {
   // 1. Calculate H
-  double H_G = sqrt(8.0 * sigma2 * log(2.0));
+  double H_G = sqrt(8.0 * sigma2 * M_LN2);
   double H_L = gamma;
 
   double temp1 = std::pow(H_L, 5) + 0.07842 * H_G * std::pow(H_L, 4) +

Framework/CurveFitting/src/Functions/CrystalElectricField.cpp

@@ -662,8 +662,8 @@ void calculateEigesystem(DoubleFortranVector &eigenvalues,
   // -------------------------------------------------------------------
 
   ComplexFortranMatrix bex(1, 1, -1, 1);
-  bex(1, 1) = -(bext(1) - i * bext(2)) / sqrt(2.0);
-  bex(1, -1) = (bext(1) + i * bext(2)) / sqrt(2.0);
+  bex(1, 1) = -(bext(1) - i * bext(2)) * M_SQRT1_2;
+  bex(1, -1) = (bext(1) + i * bext(2)) * M_SQRT1_2;
   bex(1, 0) = bext(3);
 
   //  calculates Bex(1,q) for a canted moment
@@ -683,8 +683,8 @@ void calculateEigesystem(DoubleFortranVector &eigenvalues,
   }
 
   ComplexType rbextp, rbextm, rbextz;
-  rbextp = rbex(1, -1) * sqrt(2.0);
-  rbextm = rbex(1, 1) * (-sqrt(2.0));
+  rbextp = rbex(1, -1) * M_SQRT2;
+  rbextm = rbex(1, 1) * (-M_SQRT2);
   rbextz = rbex(1, 0);
 
   auto facmol = 2 * (gj - 1) * myb;

Framework/CurveFitting/src/Functions/Gaussian.cpp

@@ -77,7 +77,7 @@ double Gaussian::activeParameter(size_t i) const {
 double Gaussian::centre() const { return getParameter("PeakCentre"); }
 double Gaussian::height() const { return getParameter("Height"); }
 double Gaussian::fwhm() const {
-  return 2.0 * sqrt(2.0 * std::log(2.0)) * getParameter("Sigma");
+  return 2.0 * sqrt(2.0 * M_LN2) * getParameter("Sigma");
 }
 double Gaussian::intensity() const {
   auto sigma = getParameter("Sigma");
@@ -96,7 +96,7 @@ double Gaussian::intensity() const {
 void Gaussian::setCentre(const double c) { setParameter("PeakCentre", c); }
 void Gaussian::setHeight(const double h) { setParameter("Height", h); }
 void Gaussian::setFwhm(const double w) {
-  setParameter("Sigma", w / (2.0 * sqrt(2.0 * std::log(2.0))));
+  setParameter("Sigma", w / (2.0 * sqrt(2.0 * M_LN2)));
 }
 void Gaussian::setIntensity(const double i) {
   m_intensityCache = i;

Framework/CurveFitting/src/Functions/GramCharlierComptonProfile.cpp

@@ -293,7 +293,7 @@ void GramCharlierComptonProfile::addMassProfile(
   const double denom = ((std::pow(2.0, static_cast<int>(npoly))) * factorial);
 
   for (int j = 0; j < NFINE_Y; ++j) {
-    const double y = m_yfine[j] / std::sqrt(2.) / wg;
+    const double y = m_yfine[j] * M_SQRT1_2 / wg;
     const double hermiteI = Math::hermitePoly(npoly, y);
     result[j] += ampNorm * std::exp(-y * y) * hermiteI * hermiteCoeff / denom;
   }
@@ -316,7 +316,7 @@ void GramCharlierComptonProfile::addFSETerm(std::vector<double> &lhs) const {
     kfse *= getParameter("C_0");
 
   for (int j = 0; j < NFINE_Y; ++j) {
-    const double y = m_yfine[j] / std::sqrt(2.) / wg;
+    const double y = m_yfine[j] * M_SQRT1_2 / wg;
     const double he3 = Math::hermitePoly(3, y);
     lhs[j] += ampNorm * std::exp(-y * y) * he3 * (kfse / m_qfine[j]);
   }

Framework/CurveFitting/src/Functions/NeutronBk2BkExpConvPVoigt.cpp

@@ -398,7 +398,7 @@ void NeutronBk2BkExpConvPVoigt::function1D(double *out, const double *xValues,
 void NeutronBk2BkExpConvPVoigt::calHandEta(double sigma2, double gamma,
                                            double &H, double &eta) const {
   // 1. Calculate H
-  double H_G = sqrt(8.0 * sigma2 * log(2.0));
+  double H_G = sqrt(8.0 * sigma2 * M_LN2);
   double H_L = gamma;
 
   double temp1 = std::pow(H_L, 5) + 0.07842 * H_G * std::pow(H_L, 4) +