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understanding floating point precision 

double can use 16 or 17 significant figures
- if the leading number is high (above 5 or so), only 16 figures are
significant.
- a trailing 1 is never significant
This commit is contained in:
Martin Diehl 2021-07-21 17:51:58 +02:00
parent f25dee4c3a
commit b1ba64e6af
1 changed files with 31 additions and 39 deletions
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70
src/mesh/FEM_quadrature.f90
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@ -51,65 +51,64 @@ subroutine FEM_quadrature_init
FEM_nQuadrature(2,1) = 1 FEM_nQuadrature(2,1) = 1
allocate(FEM_quadrature_weights(2,1)%p(1)) allocate(FEM_quadrature_weights(2,1)%p(1))
FEM_quadrature_weights(2,1)%p(1) = 1.0_pReal FEM_quadrature_weights(2,1)%p(1) = 1._pReal
allocate(FEM_quadrature_points (2,1)%p(2)) allocate(FEM_quadrature_points (2,1)%p(2))
FEM_quadrature_points (2,1)%p(1:2) = permutationStar3([1.0_pReal/3.0_pReal]) FEM_quadrature_points (2,1)%p(1:2) = permutationStar3([1._pReal/3._pReal])
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! 2D quadratic ! 2D quadratic
FEM_nQuadrature(2,2) = 3 FEM_nQuadrature(2,2) = 3
allocate(FEM_quadrature_weights(2,2)%p(3)) allocate(FEM_quadrature_weights(2,2)%p(3))
FEM_quadrature_weights(2,2)%p(1:3) = 1.0_pReal/3.0_pReal FEM_quadrature_weights(2,2)%p(1:3) = 1._pReal/3._pReal
allocate(FEM_quadrature_points (2,2)%p(6)) allocate(FEM_quadrature_points (2,2)%p(6))
FEM_quadrature_points (2,2)%p(1:6) = permutationStar21([1.0_pReal/6.0_pReal]) FEM_quadrature_points (2,2)%p(1:6) = permutationStar21([1._pReal/6._pReal])
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! 2D cubic ! 2D cubic
FEM_nQuadrature(2,3) = 6 FEM_nQuadrature(2,3) = 6
allocate(FEM_quadrature_weights(2,3)%p(6)) allocate(FEM_quadrature_weights(2,3)%p(6))
FEM_quadrature_weights(2,3)%p(1:3) = 0.2233815896780115_pReal FEM_quadrature_weights(2,3)%p(1:3) = 2.2338158967801147e-1_pReal
FEM_quadrature_weights(2,3)%p(4:6) = 0.1099517436553219_pReal FEM_quadrature_weights(2,3)%p(4:6) = 1.0995174365532187e-1_pReal
allocate(FEM_quadrature_points (2,3)%p(12)) allocate(FEM_quadrature_points (2,3)%p(12))
FEM_quadrature_points (2,3)%p(1:6) = permutationStar21([0.4459484909159649_pReal]) FEM_quadrature_points (2,3)%p(1:6) = permutationStar21([4.4594849091596489e-1_pReal])
FEM_quadrature_points (2,3)%p(7:12)= permutationStar21([0.09157621350977074_pReal]) FEM_quadrature_points (2,3)%p(7:12)= permutationStar21([9.157621350977074e-2_pReal])
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! 2D quartic ! 2D quartic
FEM_nQuadrature(2,4) = 12 FEM_nQuadrature(2,4) = 12
allocate(FEM_quadrature_weights(2,4)%p(12)) allocate(FEM_quadrature_weights(2,4)%p(12))
FEM_quadrature_weights(2,4)%p(1:3) = 0.1167862757263794_pReal FEM_quadrature_weights(2,4)%p(1:3) = 1.1678627572637937e-1_pReal
FEM_quadrature_weights(2,4)%p(4:6) = 0.0508449063702068_pReal FEM_quadrature_weights(2,4)%p(4:6) = 5.0844906370206817e-2_pReal
FEM_quadrature_weights(2,4)%p(7:12) = 0.08285107561837358_pReal FEM_quadrature_weights(2,4)%p(7:12) = 8.285107561837358e-2_pReal
allocate(FEM_quadrature_points (2,4)%p(24)) allocate(FEM_quadrature_points (2,4)%p(24))
FEM_quadrature_points (2,4)%p(1:6) = permutationStar21([0.2492867451709104_pReal]) FEM_quadrature_points (2,4)%p(1:6) = permutationStar21([2.4928674517091042e-1_pReal])
FEM_quadrature_points (2,4)%p(7:12) = permutationStar21([0.06308901449150223_pReal]) FEM_quadrature_points (2,4)%p(7:12) = permutationStar21([6.308901449150223e-2_pReal])
FEM_quadrature_points (2,4)%p(13:24)= permutationStar111([0.3103524510337844_pReal, 0.05314504984481695_pReal]) FEM_quadrature_points (2,4)%p(13:24)= permutationStar111([3.1035245103378440e-1_pReal, 5.3145049844816947e-2_pReal])
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! 2D quintic ! 2D quintic
FEM_nQuadrature(2,5) = 16 FEM_nQuadrature(2,5) = 16
allocate(FEM_quadrature_weights(2,5)%p(16)) allocate(FEM_quadrature_weights(2,5)%p(16))
FEM_quadrature_weights(2,5)%p(1 ) = 0.1443156076777871_pReal FEM_quadrature_weights(2,5)%p(1 ) = 1.4431560767778717e-1_pReal
FEM_quadrature_weights(2,5)%p(2:4) = 0.09509163426728462_pReal FEM_quadrature_weights(2,5)%p(2:4) = 9.509163426728463e-2_pReal
FEM_quadrature_weights(2,5)%p(5:7) = 0.1032173705347183_pReal FEM_quadrature_weights(2,5)%p(5:7) = 1.0321737053471825e-1_pReal
FEM_quadrature_weights(2,5)%p(8:10) = 0.03245849762319808_pReal FEM_quadrature_weights(2,5)%p(8:10) = 3.2458497623198080e-2_pReal
FEM_quadrature_weights(2,5)%p(11:16)= 0.02723031417443499_pReal FEM_quadrature_weights(2,5)%p(11:16)= 2.7230314174434994e-2_pReal
allocate(FEM_quadrature_points (2,5)%p(32)) allocate(FEM_quadrature_points (2,5)%p(32))
FEM_quadrature_points (2,5)%p(1:2) = permutationStar3([1._pReal/3._pReal])
FEM_quadrature_points (2,5)%p(1:2) = permutationStar3([0.3333333333333333_pReal]) FEM_quadrature_points (2,5)%p(3:8) = permutationStar21([4.5929258829272316e-1_pReal])
FEM_quadrature_points (2,5)%p(3:8) = permutationStar21([0.4592925882927231_pReal]) FEM_quadrature_points (2,5)%p(9:14) = permutationStar21([1.705693077517602e-1_pReal])
FEM_quadrature_points (2,5)%p(9:14) = permutationStar21([0.1705693077517602_pReal]) FEM_quadrature_points (2,5)%p(15:20)= permutationStar21([5.0547228317030975e-2_pReal])
FEM_quadrature_points (2,5)%p(15:20)= permutationStar21([0.0505472283170310_pReal]) FEM_quadrature_points (2,5)%p(21:32)= permutationStar111([2.631128296346381e-1_pReal, 8.3947774099576053e-2_pReal])
FEM_quadrature_points (2,5)%p(21:32)= permutationStar111([0.2631128296346381_pReal, 0.008394777409957605_pReal])
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! 3D linear ! 3D linear
@ -129,7 +128,6 @@ subroutine FEM_quadrature_init
FEM_quadrature_weights(3,2)%p(1:4) = 0.25_pReal FEM_quadrature_weights(3,2)%p(1:4) = 0.25_pReal
allocate(FEM_quadrature_points (3,2)%p(12)) allocate(FEM_quadrature_points (3,2)%p(12))
FEM_quadrature_points (3,2)%p(1:12)= permutationStar31([0.1381966011250105_pReal]) FEM_quadrature_points (3,2)%p(1:12)= permutationStar31([0.1381966011250105_pReal])
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
@ -137,23 +135,20 @@ subroutine FEM_quadrature_init
FEM_nQuadrature(3,3) = 14 FEM_nQuadrature(3,3) = 14
allocate(FEM_quadrature_weights(3,3)%p(14)) allocate(FEM_quadrature_weights(3,3)%p(14))
FEM_quadrature_weights(3,3)%p(5:8) = 1.1268792571801585e-1_pReal
FEM_quadrature_weights(3,3)%p(5:8) = 0.1126879257180159_pReal FEM_quadrature_weights(3,3)%p(1:4) = 7.3493043116361949e-2_pReal
FEM_quadrature_weights(3,3)%p(1:4) = 0.0734930431163620_pReal FEM_quadrature_weights(3,3)%p(9:14) = 4.2546020777081467e-2_pReal
FEM_quadrature_weights(3,3)%p(9:14) = 0.0425460207770815_pReal
allocate(FEM_quadrature_points (3,3)%p(42)) allocate(FEM_quadrature_points (3,3)%p(42))
FEM_quadrature_points (3,3)%p(1:12) = permutationStar31([9.273525031089123e-2_pReal])
FEM_quadrature_points (3,3)%p(1:12) = permutationStar31([0.09273525031089123_pReal]) FEM_quadrature_points (3,3)%p(13:24)= permutationStar31([3.108859192633006e-1_pReal])
FEM_quadrature_points (3,3)%p(13:24)= permutationStar31([0.3108859192633006_pReal]) FEM_quadrature_points (3,3)%p(25:42)= permutationStar22([4.5503704125649649e-2_pReal])
FEM_quadrature_points (3,3)%p(25:42)= permutationStar22([0.04550370412564965_pReal])
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! 3D quartic ! 3D quartic
FEM_nQuadrature(3,4) = 35 FEM_nQuadrature(3,4) = 35
allocate(FEM_quadrature_weights(3,4)%p(35)) allocate(FEM_quadrature_weights(3,4)%p(35))
FEM_quadrature_weights(3,4)%p(1:4) = 0.0021900463965388_pReal FEM_quadrature_weights(3,4)%p(1:4) = 0.0021900463965388_pReal
FEM_quadrature_weights(3,4)%p(5:16) = 0.0143395670177665_pReal FEM_quadrature_weights(3,4)%p(5:16) = 0.0143395670177665_pReal
FEM_quadrature_weights(3,4)%p(17:22) = 0.0250305395686746_pReal FEM_quadrature_weights(3,4)%p(17:22) = 0.0250305395686746_pReal
@ -161,7 +156,6 @@ subroutine FEM_quadrature_init
FEM_quadrature_weights(3,4)%p(35) = 0.0931745731195340_pReal FEM_quadrature_weights(3,4)%p(35) = 0.0931745731195340_pReal
allocate(FEM_quadrature_points (3,4)%p(105)) allocate(FEM_quadrature_points (3,4)%p(105))
FEM_quadrature_points (3,4)%p(1:12) = permutationStar31([0.0267367755543735_pReal]) FEM_quadrature_points (3,4)%p(1:12) = permutationStar31([0.0267367755543735_pReal])
FEM_quadrature_points (3,4)%p(13:48) = permutationStar211([0.0391022406356488_pReal, 0.7477598884818090_pReal]) FEM_quadrature_points (3,4)%p(13:48) = permutationStar211([0.0391022406356488_pReal, 0.7477598884818090_pReal])
FEM_quadrature_points (3,4)%p(49:66) = permutationStar22([0.4547545999844830_pReal]) FEM_quadrature_points (3,4)%p(49:66) = permutationStar22([0.4547545999844830_pReal])
@ -173,7 +167,6 @@ subroutine FEM_quadrature_init
FEM_nQuadrature(3,5) = 56 FEM_nQuadrature(3,5) = 56
allocate(FEM_quadrature_weights(3,5)%p(56)) allocate(FEM_quadrature_weights(3,5)%p(56))
FEM_quadrature_weights(3,5)%p(1:4) = 0.0010373112336140_pReal FEM_quadrature_weights(3,5)%p(1:4) = 0.0010373112336140_pReal
FEM_quadrature_weights(3,5)%p(5:16) = 0.0096016645399480_pReal FEM_quadrature_weights(3,5)%p(5:16) = 0.0096016645399480_pReal
FEM_quadrature_weights(3,5)%p(17:28) = 0.0164493976798232_pReal FEM_quadrature_weights(3,5)%p(17:28) = 0.0164493976798232_pReal
@ -182,7 +175,6 @@ subroutine FEM_quadrature_init
FEM_quadrature_weights(3,5)%p(53:56) = 0.0366291366405108_pReal FEM_quadrature_weights(3,5)%p(53:56) = 0.0366291366405108_pReal
allocate(FEM_quadrature_points (3,5)%p(168)) allocate(FEM_quadrature_points (3,5)%p(168))
FEM_quadrature_points (3,5)%p(1:12) = permutationStar31([0.0149520651530592_pReal]) FEM_quadrature_points (3,5)%p(1:12) = permutationStar31([0.0149520651530592_pReal])
FEM_quadrature_points (3,5)%p(13:48) = permutationStar211([0.0340960211962615_pReal, 0.1518319491659370_pReal]) FEM_quadrature_points (3,5)%p(13:48) = permutationStar211([0.0340960211962615_pReal, 0.1518319491659370_pReal])
FEM_quadrature_points (3,5)%p(49:84) = permutationStar211([0.0462051504150017_pReal, 0.3549340560639790_pReal]) FEM_quadrature_points (3,5)%p(49:84) = permutationStar211([0.0462051504150017_pReal, 0.3549340560639790_pReal])
@ -377,4 +369,4 @@ pure function permutationStar1111(point) result(qPt)
end function permutationStar1111 end function permutationStar1111
end module FEM_quadrature end module FEM_quadrature