diff --git a/src/math.f90 b/src/math.f90 index d8f0da778..440ee5303 100644 --- a/src/math.f90 +++ b/src/math.f90 @@ -12,7 +12,7 @@ module math implicit none private - real(pReal), parameter, public :: PI = 3.141592653589793_pReal !< ratio of a circle's circumference to its diameter + real(pReal), parameter, public :: PI = acos(-1.0_pReal) !< ratio of a circle's circumference to its diameter real(pReal), parameter, public :: INDEG = 180.0_pReal/PI !< conversion from radian into degree real(pReal), parameter, public :: INRAD = PI/180.0_pReal !< conversion from degree into radian complex(pReal), parameter, public :: TWOPIIMG = (0.0_pReal,2.0_pReal)*(PI,0.0_pReal) !< Re(0.0), Im(2xPi) @@ -36,13 +36,13 @@ module math real(pReal), dimension(6), parameter, private :: & nrmMandel = [& - 1.0_pReal, 1.0_pReal, 1.0_pReal,& - 1.414213562373095_pReal, 1.414213562373095_pReal, 1.414213562373095_pReal ] !< weighting for Mandel notation (forward) + 1.0_pReal, 1.0_pReal, 1.0_pReal, & + sqrt(2.0_pReal), sqrt(2.0_pReal), sqrt(2.0_pReal) ] !< weighting for Mandel notation (forward) real(pReal), dimension(6), parameter , public :: & invnrmMandel = [& - 1.0_pReal, 1.0_pReal, 1.0_pReal,& - 0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal ] !< weighting for Mandel notation (backward) + 1.0_pReal, 1.0_pReal, 1.0_pReal, & + 1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal) ] !< weighting for Mandel notation (backward) integer(pInt), dimension (2,6), parameter, private :: & mapVoigt = reshape([& @@ -160,7 +160,7 @@ module math math_rotate_forward33, & math_rotate_backward33, & math_rotate_forward3333, & - math_limit + math_clip private :: & math_check, & halton @@ -1366,16 +1366,16 @@ pure function math_RtoEuler(R) sqhk =sqrt(R(1,3)*R(1,3)+R(2,3)*R(2,3)) ! calculate PHI - math_RtoEuler(2) = acos(math_limit(R(3,3)/sqhkl,-1.0_pReal, 1.0_pReal)) + math_RtoEuler(2) = acos(math_clip(R(3,3)/sqhkl,-1.0_pReal, 1.0_pReal)) if((math_RtoEuler(2) < 1.0e-8_pReal) .or. (pi-math_RtoEuler(2) < 1.0e-8_pReal)) then math_RtoEuler(3) = 0.0_pReal - math_RtoEuler(1) = acos(math_limit(R(1,1)/squvw, -1.0_pReal, 1.0_pReal)) + math_RtoEuler(1) = acos(math_clip(R(1,1)/squvw, -1.0_pReal, 1.0_pReal)) if(R(2,1) > 0.0_pReal) math_RtoEuler(1) = 2.0_pReal*pi-math_RtoEuler(1) else - math_RtoEuler(3) = acos(math_limit(R(2,3)/sqhk, -1.0_pReal, 1.0_pReal)) + math_RtoEuler(3) = acos(math_clip(R(2,3)/sqhk, -1.0_pReal, 1.0_pReal)) if(R(1,3) < 0.0) math_RtoEuler(3) = 2.0_pReal*pi-math_RtoEuler(3) - math_RtoEuler(1) = acos(math_limit(-R(3,2)/sin(math_RtoEuler(2)), -1.0_pReal, 1.0_pReal)) + math_RtoEuler(1) = acos(math_clip(-R(3,2)/sin(math_RtoEuler(2)), -1.0_pReal, 1.0_pReal)) if(R(3,1) < 0.0) math_RtoEuler(1) = 2.0_pReal*pi-math_RtoEuler(1) end if @@ -1657,7 +1657,7 @@ pure function math_qToEuler(qPassive) math_qToEuler(2) = acos(1.0_pReal-2.0_pReal*(q(2)**2+q(3)**2)) if (abs(math_qToEuler(2)) < 1.0e-6_pReal) then - math_qToEuler(1) = sign(2.0_pReal*acos(math_limit(q(1),-1.0_pReal, 1.0_pReal)),q(4)) + math_qToEuler(1) = sign(2.0_pReal*acos(math_clip(q(1),-1.0_pReal, 1.0_pReal)),q(4)) math_qToEuler(3) = 0.0_pReal else math_qToEuler(1) = atan2(+q(1)*q(3)+q(2)*q(4), q(1)*q(2)-q(3)*q(4)) @@ -1684,7 +1684,7 @@ pure function math_qToAxisAngle(Q) real(pReal) :: halfAngle, sinHalfAngle real(pReal), dimension(4) :: math_qToAxisAngle - halfAngle = acos(math_limit(Q(1),-1.0_pReal,1.0_pReal)) + halfAngle = acos(math_clip(Q(1),-1.0_pReal,1.0_pReal)) sinHalfAngle = sin(halfAngle) smallRotation: if (sinHalfAngle <= 1.0e-4_pReal) then @@ -1744,7 +1744,7 @@ real(pReal) pure function math_EulerMisorientation(EulerA,EulerB) cosTheta = (math_trace33(math_mul33x33(math_EulerToR(EulerB), & transpose(math_EulerToR(EulerA)))) - 1.0_pReal) * 0.5_pReal - math_EulerMisorientation = acos(math_limit(cosTheta,-1.0_pReal,1.0_pReal)) + math_EulerMisorientation = acos(math_clip(cosTheta,-1.0_pReal,1.0_pReal)) end function math_EulerMisorientation @@ -2055,7 +2055,7 @@ function math_eigenvectorBasisSym33(m) EB(3,3,3)=1.0_pReal else threeSimilarEigenvalues rho=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal - phi=acos(math_limit(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal)) + phi=acos(math_clip(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal)) values = 2.0_pReal*rho**(1.0_pReal/3.0_pReal)* & [cos(phi/3.0_pReal), & cos((phi+2.0_pReal*PI)/3.0_pReal), & @@ -2120,7 +2120,7 @@ function math_eigenvectorBasisSym33_log(m) EB(3,3,3)=1.0_pReal else threeSimilarEigenvalues rho=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal - phi=acos(math_limit(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal)) + phi=acos(math_clip(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal)) values = 2.0_pReal*rho**(1.0_pReal/3.0_pReal)* & [cos(phi/3.0_pReal), & cos((phi+2.0_pReal*PI)/3.0_pReal), & @@ -2232,7 +2232,7 @@ function math_eigenvaluesSym33(m) math_eigenvaluesSym33 = math_eigenvaluesSym(m) else rho=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal - phi=acos(math_limit(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal)) + phi=acos(math_clip(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal)) math_eigenvaluesSym33 = 2.0_pReal*rho**(1.0_pReal/3.0_pReal)* & [cos(phi/3.0_pReal), & cos((phi+2.0_pReal*PI)/3.0_pReal), & @@ -2617,7 +2617,7 @@ end function math_rotate_forward3333 !> @brief limits a scalar value to a certain range (either one or two sided) ! Will return NaN if left > right !-------------------------------------------------------------------------------------------------- -real(pReal) pure function math_limit(a, left, right) +real(pReal) pure function math_clip(a, left, right) use, intrinsic :: & IEEE_arithmetic @@ -2626,14 +2626,14 @@ real(pReal) pure function math_limit(a, left, right) real(pReal), intent(in), optional :: left, right - math_limit = min ( & + math_clip = min ( & max (merge(left, -huge(a), present(left)), a), & merge(right, huge(a), present(right)) & ) if (present(left) .and. present(right)) & - math_limit = merge (IEEE_value(1.0_pReal,IEEE_quiet_NaN),math_limit, left>right) + math_clip = merge (IEEE_value(1.0_pReal,IEEE_quiet_NaN),math_clip, left>right) -end function math_limit +end function math_clip end module math