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avoid multiple calls to std::log
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Alexander Voigt authored and Alexander Voigt committed Jan 29, 2017
1 parent 8e5d0bc commit 833f1ab
Showing 1 changed file with 52 additions and 38 deletions.
90 changes: 52 additions & 38 deletions src/threshold_loop_functions.cpp
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Expand Up @@ -184,47 +184,51 @@ static double F8_1_1(double x1, double x2)
/// F8(x1,x2) in the limit x1 -> 1
static double F8_1_x2(double x1, double x2)
{
const double lx22 = std::log(sqr(x2));

return -2. + (4.*(-1. + x1)*(-0.5 + 2.*sqr(x2) - 1.5*quad(x2)
+ 1.*quad(x2)*std::log(sqr(x2))))
+ 1.*quad(x2)*lx22))
/cube(-1. + sqr(x2))
+ (2. - 2.*sqr(x2) + 2.*quad(x2)*std::log(sqr(x2)))
+ (2. - 2.*sqr(x2) + 2.*quad(x2)*lx22)
/sqr(-1. + sqr(x2))
- (1.3333333333333333*cube(-1. + x1)*(
-1.*sqr(x2) - 9.*quad(x2) + 9.*pow6(x2)
+ 1.*pow8(x2)
+ (-6.*quad(x2) - 6.*pow6(x2))*std::log(sqr(x2))))
+ (-6.*quad(x2) - 6.*pow6(x2))*lx22))
/pow5(-1. + sqr(x2))
+ (2.*sqr(-1. + x1)*(
-0.16666666666666666 + 1.5*sqr(x2) + 1.5*quad(x2)
- 2.8333333333333335*pow6(x2)
+ (3.*quad(x2) + 1.*pow6(x2))*std::log(sqr(x2))))
+ (3.*quad(x2) + 1.*pow6(x2))*lx22))
/quad(-1. + sqr(x2))
+ (0.26666666666666666*quad(-1. + x1)*(
0.25 + 2.5*sqr(x2) + 80.*quad(x2) - 47.5*pow6(x2)
- 36.25*pow8(x2) + 1.*pow10(x2)
+ (37.5*quad(x2) + 75.*pow6(x2)
+ 7.5*pow8(x2))*std::log(sqr(x2))))
+ 7.5*pow8(x2))*lx22))
/pow6(-1. + sqr(x2));
}

// F8(x1,x2) in the limit x1 -> x2
static double F8_x1_x2(double x1, double x2)
{
const double lx22 = std::log(sqr(x2));

return -2. + (2.*(x1 - x2)*(3.*x2 - 4.*cube(x2) + 1.*pow5(x2) +
2.*x2*std::log(sqr(x2))))/cube(-1. + sqr(x2)) +
(2.*sqr(x2)*(-1. + sqr(x2) - 2.*std::log(sqr(x2)) +
sqr(x2)*std::log(sqr(x2))))/sqr(-1. + sqr(x2)) -
2.*x2*lx22))/cube(-1. + sqr(x2)) +
(2.*sqr(x2)*(-1. + sqr(x2) - 2.*lx22 +
sqr(x2)*lx22))/sqr(-1. + sqr(x2)) -
(0.33333333333333326*sqr(x1 - x2)*
(17.000000000000007 - 9.000000000000007*sqr(x2) -
9.*quad(x2) + 1.*pow6(x2) +
6.000000000000002*std::log(sqr(x2)) +
18.000000000000004*sqr(x2)*std::log(sqr(x2))))/
6.000000000000002*lx22 +
18.000000000000004*sqr(x2)*lx22))/
quad(-1. + sqr(x2)) -
(1.333333333333333*cube(x1 - x2)*
(-1. - 9.000000000000002*sqr(x2) +
9.000000000000002*quad(x2) + 1.*pow6(x2) -
6.*sqr(x2)*std::log(sqr(x2)) -
6.000000000000003*quad(x2)*std::log(sqr(x2))))/
6.*sqr(x2)*lx22 -
6.000000000000003*quad(x2)*lx22))/
(x2*pow5(-1. + sqr(x2)));
}

Expand Down Expand Up @@ -276,43 +280,47 @@ static double F9_1_1(double x1, double x2)
/// F9(x1,x2) in the limit x1 -> 1
static double F9_1_x2(double x1, double x2)
{
const double lx22 = std::log(sqr(x2));

return (-2.*(-1. + x1)*cube(-1. + sqr(x2))*(
-1. + 1.*quad(x2) - 2.*sqr(x2)*std::log(sqr(x2)))
-1. + 1.*quad(x2) - 2.*sqr(x2)*lx22)
+ 2.*quad(-1. + sqr(x2))*(
1. - 1.*sqr(x2) + 1.*sqr(x2)*std::log(sqr(x2)))
1. - 1.*sqr(x2) + 1.*sqr(x2)*lx22)
- 1.3333333333333333*cube(-1. + x1)*(
-1. + sqr(x2))*(
-1. - 9.*sqr(x2) + 9.*quad(x2) + 1.*pow6(x2)
+ (-6.*sqr(x2) - 6.*quad(x2))*std::log(sqr(x2)))
+ (-6.*sqr(x2) - 6.*quad(x2))*lx22)
+ 0.3333333333333333*sqr(-1. + x1)*sqr(-1. + sqr(x2))
*(5. + 15.*sqr(x2) - 21.*quad(x2) + 1.*pow6(x2)
+ (18.*sqr(x2) + 6.*quad(x2))*std::log(sqr(x2)))
+ (18.*sqr(x2) + 6.*quad(x2))*lx22)
- 0.06666666666666667*quad(-1. + x1)*(
-16. - 305.*sqr(x2) + 170.*quad(x2) + 160.*pow6(x2)
- 10.*pow8(x2) + 1.*pow10(x2)
+ (-150.*sqr(x2) - 300.*quad(x2)
- 30.*pow6(x2))*std::log(sqr(x2))))
- 30.*pow6(x2))*lx22))
/pow6(-1. + sqr(x2));
}

/// F9(x1,x2) in the limit x1 -> x2
static double F9_x1_x2(double x1, double x2)
{
return (2.*(-1. + 1.*sqr(x2) - 1.*std::log(sqr(x2))))/
const double lx22 = std::log(sqr(x2));

return (2.*(-1. + 1.*sqr(x2) - 1.*lx22))/
sqr(-1. + sqr(x2)) -
(2.*(x1 - x2)*(-1. + 1.*quad(x2) -
2.*sqr(x2)*std::log(sqr(x2))))/
2.*sqr(x2)*lx22))/
(x2*cube(-1. + sqr(x2))) -
(1.3333333333333333*cube(x1 - x2)*
(-1.0000000000000002 - 9.*sqr(x2) + 9.*quad(x2) +
1.*pow6(x2) - 6.*sqr(x2)*std::log(sqr(x2)) -
6.*quad(x2)*std::log(sqr(x2))))/
1.*pow6(x2) - 6.*sqr(x2)*lx22 -
6.*quad(x2)*lx22))/
(x2*pow5(-1. + sqr(x2))) +
(1.6666666666666665*sqr(x1 - x2)*
(0.2000000000000001 - 4.200000000000001*sqr(x2) +
3.000000000000001*quad(x2) + 1.*pow6(x2) -
1.2000000000000002*sqr(x2)*std::log(sqr(x2)) -
3.6000000000000005*quad(x2)*std::log(sqr(x2))))/
1.2000000000000002*sqr(x2)*lx22 -
3.6000000000000005*quad(x2)*lx22))/
(sqr(x2)*quad(-1. + sqr(x2)));
}

Expand Down Expand Up @@ -427,6 +435,8 @@ static double f5_1_1(double r1, double r2)
/// f5(r1,r2) in the limit r1 -> 1
static double f5_1_r2(double r1, double r2)
{
const double lr22 = std::log(sqr(r2));

return (-0.025*cube(-1. + r1)*(
4. - 17.*r2 + 4.*sqr(r2)
- 25.*cube(r2)
Expand All @@ -435,31 +445,31 @@ static double f5_1_r2(double r1, double r2)
+ 12.*pow6(r2)
+ pow7(r2)
+ (-30.*cube(r2) - 30.*pow5(r2))
*std::log(sqr(r2))))/(pow6(-1. + r2)*sqr(1. + r2))
*lr22))/(pow6(-1. + r2)*sqr(1. + r2))
- (0.125*sqr(-1. + r1)*(
1. - 4.*r2 + sqr(r2)
- 4.*cube(r2)
- 5.*quad(r2)
+ 8.*pow5(r2)
+ 3.*pow6(r2)
+ (-6.*cube(r2) - 6.*pow5(r2))
*std::log(sqr(r2))))/(pow5(-1. + r2)*sqr(1. + r2))
*lr22))/(pow5(-1. + r2)*sqr(1. + r2))
+ (0.75*(-1 + r2 + 2*sqr(r2)
- quad(r2)
- pow5(r2)
+ (cube(r2) + pow5(r2))
*std::log(sqr(r2))))/(cube(-1 + r2)*sqr(1 + r2))
*lr22))/(cube(-1 + r2)*sqr(1 + r2))
+ (0.25*(-1. + r1)*(
1. - 1.*r2 - 2.*sqr(r2) + 8.*cube(r2)
+ quad(r2) - 7.*pow5(r2)
+ (3.*cube(r2) + 3.*pow5(r2))
*std::log(sqr(r2))))/(quad(-1. + r2)*sqr(1. + r2))
*lr22))/(quad(-1. + r2)*sqr(1. + r2))
+ (0.05*quad(-1. + r1)*(
-1. + 4.5*r2 + 2.*sqr(r2)
+ 16.5*cube(r2) - 16.5*pow5(r2) - 2.*pow6(r2)
- 4.5*pow7(r2) + 1.*pow8(r2)
+ (15.*cube(r2) + 15.*pow5(r2))
*std::log(sqr(r2))))/(pow7(-1. + r2)*sqr(1. + r2));
*lr22))/(pow7(-1. + r2)*sqr(1. + r2));
}

double f5(double r1, double r2)
Expand Down Expand Up @@ -570,23 +580,25 @@ static double f7_1_1(double r1, double r2)
/// f7(r1,r2) in the limit r1 -> 1
static double f7_1_r2(double r1, double r2)
{
const double lr22 = std::log(sqr(r2));

return (-10*(-1 + r1)*cube(-1 + r2)*(
2 - 5*r2 - 4*sqr(r2) + 4*cube(r2) + 2*quad(r2)
+ pow5(r2) - 6*cube(r2)*std::log(sqr(r2)))
+ pow5(r2) - 6*cube(r2)*lr22)
- 30*quad(-1 + r2)*(
1 - 2*r2 - 2*sqr(r2) + 2*cube(r2) + quad(r2)
- 2*cube(r2)*std::log(sqr(r2)))
- 2*cube(r2)*lr22)
+ 10*sqr(-1 + r1)*sqr(-1 + r2)*(
-1 + 3*r2 + 3*sqr(r2) - 3*quad(r2) - 3*pow5(r2)
+ pow6(r2) + 6*cube(r2)*std::log(sqr(r2)))
+ pow6(r2) + 6*cube(r2)*lr22)
+ 2*cube(-1 + r1)*(-1 + r2)*(
-2 + 6*r2 + 18*sqr(r2) + 15*cube(r2) - 30*quad(r2)
- 18*pow5(r2) + 14*pow6(r2) - 3*pow7(r2)
+ 30*cube(r2)*std::log(sqr(r2)))
+ 30*cube(r2)*lr22)
+ quad(-1 + r1)*(
-1 + 48*sqr(r2) + 42*cube(r2) - 90*quad(r2)
- 24*pow5(r2) + 40*pow6(r2) - 18*pow7(r2)
+ 3*pow8(r2) + 60*cube(r2)*std::log(sqr(r2))))
+ 3*pow8(r2) + 60*cube(r2)*lr22))
/(10.*pow7(-1 + r2)*sqr(1 + r2));
}

Expand Down Expand Up @@ -634,25 +646,27 @@ static double f8_1_1(double r1, double r2)
/// f8(r1,r2) in the limit r1 -> 1
static double f8_1_r2(double r1, double r2)
{
const double lr22 = std::log(sqr(r2));

return (30*quad(-1 + r2)*(
-1 + 4*sqr(r2) - 3*quad(r2)
+ 2*quad(r2)*std::log(sqr(r2)))
+ 2*quad(r2)*lr22)
+ 10*sqr(-1 + r1)*sqr(-1 + r2)*(
1 - 4*r2 + 4*sqr(r2) + 8*cube(r2)
- 5*quad(r2) - 4*pow5(r2)
+ 6*quad(r2)*std::log(sqr(r2)))
+ 6*quad(r2)*lr22)
+ 10*(-1 + r1)*cube(-1 + r2)*(
1 - 4*r2 + 4*sqr(r2) + 8*cube(r2)
- 5*quad(r2) - 4*pow5(r2)
+ 6*quad(r2)*std::log(sqr(r2)))
+ 6*quad(r2)*lr22)
+ 2*cube(-1 + r1)*(-1 + r2)*(
3 - 14*r2 + 18*sqr(r2) + 30*cube(r2)
- 15*quad(r2) - 18*pow5(r2) - 6*pow6(r2)
+ 2*pow7(r2) + 30*quad(r2)*std::log(sqr(r2)))
+ 2*pow7(r2) + 30*quad(r2)*lr22)
+ quad(-1 + r1)*(
3 - 16*r2 + 24*sqr(r2) + 48*cube(r2)
- 48*pow5(r2) - 24*pow6(r2) + 16*pow7(r2)
- 3*pow8(r2) + 60*quad(r2)*std::log(sqr(r2))))
- 3*pow8(r2) + 60*quad(r2)*lr22))
/(40.*pow7(-1 + r2)*sqr(1 + r2));
}

Expand Down

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