implement limits of F8 and F9 for xi -> 0

FlexibleSUSY · Feb 2, 2017 · dce90c2 · dce90c2
1 parent 60ea367
commit dce90c2
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diff --git a/src/threshold_loop_functions.cpp b/src/threshold_loop_functions.cpp
@@ -193,6 +193,15 @@ static double F8_1_x2(double x1, double x2)
       /pow6(-1. + sqr(x2));
 }
 
+/// F8(x1,x2) in the limit x1 -> 0
+static double F8_0_x2(double x1, double x2)
+{
+   const double lx22 = std::log(sqr(x2));
+
+   return -2. + (2.*sqr(x1)*lx22)/(-1. + sqr(x2)) +
+      (2.*sqr(x2)*lx22)/(-1. + sqr(x2));
+}
+
 // F8(x1,x2) in the limit x1 -> x2
 static double F8_x1_x2(double x1, double x2)
 {
@@ -245,6 +254,12 @@ double F8(double x1, double x2)
       return F8_1_x2(x2, x1);
    }
 
+   if (is_equal(x1, 0., 0.0001))
+      return F8_0_x2(x1, x2);
+
+   if (is_equal(x2, 0., 0.0001))
+      return F8_0_x2(x2, x1);
+
    if (is_equal(x1, x2, 0.00001))
       return F8_x1_x2(x1, x2);
 
@@ -303,6 +318,12 @@ static double F9_1_x2(double x1, double x2)
       /pow6(-1. + sqr(x2));
 }
 
+/// F9(x1,x2) in the limit x1 -> 0
+static double F9_0_x2(double x1, double x2)
+{
+   return (2.*std::log(sqr(x2)))/(-1. + sqr(x2));
+}
+
 /// F9(x1,x2) in the limit x1 -> x2
 static double F9_x1_x2(double x1, double x2)
 {
@@ -345,6 +366,12 @@ double F9(double x1, double x2)
       return F9_1_x2(x2, x1);
    }
 
+   if (is_equal(x1, 0., 0.0001))
+      return F9_0_x2(x1, x2);
+
+   if (is_equal(x2, 0., 0.0001))
+      return F9_0_x2(x2, x1);
+
    if (is_equal(x1, x2, 0.00001))
       return F9_x1_x2(x1, x2);
 

diff --git a/test/test_threshold_loop_functions.cpp b/test/test_threshold_loop_functions.cpp
@@ -428,6 +428,20 @@ BOOST_AUTO_TEST_CASE(test_F8)
    x = 0.001;   BOOST_CHECK_SMALL(F8(1,x) - F8_bare(1.00001,x), 1e-2);
    x = 0.0001;  BOOST_CHECK_SMALL(F8(1,x) - F8_bare(1.00001,x), 1e-2);
 
+   x = 0.1;     BOOST_CHECK_CLOSE(F8(x,0), F8_bare(x,0.00001), 1e-2);
+   x = 0.02;    BOOST_CHECK_CLOSE(F8(x,0), F8_bare(x,0.00001), 1e-2);
+   x = 0.01;    BOOST_CHECK_CLOSE(F8(x,0), F8_bare(x,0.00001), 1e-2);
+   x = 0.001;   BOOST_CHECK_CLOSE(F8(x,0), F8_bare(x,0.00001), 1e-2);
+   x = 0.0001;  BOOST_CHECK_CLOSE(F8(x,0), F8_bare(x,0.00001), 1e-2);
+
+   x = 0.1;     BOOST_CHECK_CLOSE(F8(0,x), F8_bare(0.00001,x), 1e-2);
+   x = 0.02;    BOOST_CHECK_CLOSE(F8(0,x), F8_bare(0.00001,x), 1e-2);
+   x = 0.01;    BOOST_CHECK_CLOSE(F8(0,x), F8_bare(0.00001,x), 1e-2);
+   x = 0.001;   BOOST_CHECK_CLOSE(F8(0,x), F8_bare(0.00001,x), 1e-2);
+   x = 0.0001;  BOOST_CHECK_CLOSE(F8(0,x), F8_bare(0.00001,x), 1e-2);
+
+   x = 0.0001;  BOOST_CHECK_CLOSE(F8(0,0), F8_bare(x,x+0.00001), 1e-2);
+
    BOOST_CHECK(!std::isnan(F8(0,0)));
    BOOST_CHECK(!std::isnan(F8(0,1)));
    BOOST_CHECK(!std::isnan(F8(1,0)));
@@ -477,6 +491,16 @@ BOOST_AUTO_TEST_CASE(test_F9)
    x = 0.001;   BOOST_CHECK_CLOSE(F9(1,x), F9_bare(1.00001,x), 1e-2);
    x = 0.0001;  BOOST_CHECK_CLOSE(F9(1,x), F9_bare(1.00001,x), 1e-2);
 
+   x = 0.1;     BOOST_CHECK_CLOSE(F9(x,0), F9_bare(x,0.00001), 1e-2);
+   x = 0.02;    BOOST_CHECK_CLOSE(F9(x,0), F9_bare(x,0.00001), 1e-2);
+   x = 0.01;    BOOST_CHECK_CLOSE(F9(x,0), F9_bare(x,0.00001), 1e-2);
+   x = 0.001;   BOOST_CHECK_CLOSE(F9(x,0), F9_bare(x,0.00001), 1e-2);
+
+   x = 0.1;     BOOST_CHECK_CLOSE(F9(0,x), F9_bare(0.00001,x), 1e-2);
+   x = 0.02;    BOOST_CHECK_CLOSE(F9(0,x), F9_bare(0.00001,x), 1e-2);
+   x = 0.01;    BOOST_CHECK_CLOSE(F9(0,x), F9_bare(0.00001,x), 1e-2);
+   x = 0.001;   BOOST_CHECK_CLOSE(F9(0,x), F9_bare(0.00001,x), 1e-2);
+
    BOOST_CHECK(!std::isnan(F9(0,1)));
    BOOST_CHECK(!std::isnan(F9(1,0)));
    BOOST_CHECK(!std::isnan(F9(1,1)));