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! { dg-do run }
!
! PR fortran/33197
!
! Complex inverse trigonometric functions
! and complex inverse hyperbolic functions
!
! Run-time evaluation check
!
module test
implicit none
real(4), parameter :: eps4 = epsilon(0.0_4)*4.0_4
real(8), parameter :: eps8 = epsilon(0.0_8)*2.0_8
interface check
procedure check4, check8
end interface check
contains
SUBROUTINE check4(z, zref)
complex(4), intent(in) :: z, zref
if ( abs (real(z)-real(zref)) > eps4 &
.or.abs (aimag(z)-aimag(zref)) > eps4) then
print '(a,/,2((2g0," + I ",g0),/))', "check4:"," z=",z,'zref=',zref
print '(a,g0," + I*",g0," eps=",g0)', 'Diff: ', &
real(z)-real(zref), &
aimag(z)-aimag(zref), eps4
STOP 1
end if
END SUBROUTINE check4
SUBROUTINE check8(z, zref)
complex(8), intent(in) :: z, zref
if ( abs (real(z)-real(zref)) > eps8 &
.or.abs (aimag(z)-aimag(zref)) > eps8) then
print '(a,/,2((2g0," + I ",g0),/))', "check8:"," z=",z,'zref=',zref
print '(a,g0," + I*",g0," eps=",g0)', 'Diff: ', &
real(z)-real(zref), &
aimag(z)-aimag(zref), eps8
STOP 2
end if
END SUBROUTINE check8
end module test
PROGRAM ArcTrigHyp
use test
IMPLICIT NONE
complex(4), volatile :: z4
complex(8), volatile :: z8
!!!!! ZERO !!!!!!
! z = 0
z4 = cmplx(0.0_4, 0.0_4, kind=4)
z8 = cmplx(0.0_8, 0.0_8, kind=8)
! Exact: 0
call check(asin(z4), cmplx(0.0_4, 0.0_4, kind=4))
call check(asin(z8), cmplx(0.0_8, 0.0_8, kind=8))
! Exact: Pi/2 = 1.5707963267948966192313216916397514
call check(acos(z4), cmplx(1.57079632679489661920_4, 0.0_4, kind=4))
call check(acos(z8), cmplx(1.57079632679489661920_8, 0.0_8, kind=8))
! Exact: 0
call check(atan(z4), cmplx(0.0_4, 0.0_4, kind=4))
call check(atan(z8), cmplx(0.0_8, 0.0_8, kind=8))
! Exact: 0
call check(asinh(z4), cmplx(0.0_4, 0.0_4, kind=4))
call check(asinh(z8), cmplx(0.0_8, 0.0_8, kind=8))
! Exact: I*Pi/2 = I*1.5707963267948966192313216916397514
call check(acosh(z4), cmplx(0.0_4, 1.57079632679489661920_4, kind=4))
call check(acosh(z8), cmplx(0.0_8, 1.57079632679489661920_8, kind=8))
! Exact: 0
call check(atanh(z4), cmplx(0.0_4, 0.0_4, kind=4))
call check(atanh(z8), cmplx(0.0_8, 0.0_8, kind=8))
!!!!! POSITIVE NUMBERS !!!!!!
! z = tanh(1.0)
z4 = cmplx(0.76159415595576488811945828260479359_4, 0.0_4, kind=4)
z8 = cmplx(0.76159415595576488811945828260479359_8, 0.0_8, kind=8)
! Numerically: 0.86576948323965862428960184619184444
call check(asin(z4), cmplx(0.86576948323965862428960184619184444_4, 0.0_4, kind=4))
call check(asin(z8), cmplx(0.86576948323965862428960184619184444_8, 0.0_8, kind=8))
! Numerically: 0.70502684355523799494171984544790700
call check(acos(z4), cmplx(0.70502684355523799494171984544790700_4, 0.0_4, kind=4))
call check(acos(z8), cmplx(0.70502684355523799494171984544790700_8, 0.0_8, kind=8))
! Numerically: 0.65088016802300754993807813168285564
call check(atan(z4), cmplx(0.65088016802300754993807813168285564_4, 0.0_4, kind=4))
call check(atan(z8), cmplx(0.65088016802300754993807813168285564_8, 0.0_8, kind=8))
! Numerically: 0.70239670712987482778422106260749699
call check(asinh(z4), cmplx(0.70239670712987482778422106260749699_4, 0.0_4, kind=4))
call check(asinh(z8), cmplx(0.70239670712987482778422106260749699_8, 0.0_8, kind=8))
! Numerically: 0.70502684355523799494171984544790700*I
call check(acosh(z4), cmplx(0.0_4, 0.70502684355523799494171984544790700_4, kind=4))
call check(acosh(z8), cmplx(0.0_8, 0.70502684355523799494171984544790700_8, kind=8))
! Exact: 1
call check(atanh(z4), cmplx(1.0_4, 0.0_4, kind=4))
call check(atanh(z8), cmplx(1.0_8, 0.0_8, kind=8))
! z = I*tanh(1.0)
z4 = cmplx(0.0_4, 0.76159415595576488811945828260479359_4, kind=4)
z8 = cmplx(0.0_8, 0.76159415595576488811945828260479359_8, kind=8)
! Numerically: I*0.70239670712987482778422106260749699
call check(asin(z4), cmplx(0.0_4, 0.70239670712987482778422106260749699_4, kind=4))
call check(asin(z8), cmplx(0.0_8, 0.70239670712987482778422106260749699_8, kind=8))
! Numerically: 1.5707963267948966192313216916397514 - I*0.7023967071298748277842210626074970
call check(acos(z4), cmplx(1.5707963267948966192313216916397514_4, -0.7023967071298748277842210626074970_4, kind=4))
call check(acos(z8), cmplx(1.5707963267948966192313216916397514_8, -0.7023967071298748277842210626074970_8, kind=8))
! Exact: I*1
call check(atan(z4), cmplx(0.0_4, 1.0_4, kind=4))
call check(atan(z8), cmplx(0.0_8, 1.0_8, kind=8))
! Numerically: I*0.86576948323965862428960184619184444
call check(asinh(z4), cmplx(0.0_4, 0.86576948323965862428960184619184444_4, kind=4))
call check(asinh(z8), cmplx(0.0_8, 0.86576948323965862428960184619184444_8, kind=8))
! Numerically: 0.7023967071298748277842210626074970 + I*1.5707963267948966192313216916397514
call check(acosh(z4), cmplx(0.7023967071298748277842210626074970_4, 1.5707963267948966192313216916397514_4, kind=4))
call check(acosh(z8), cmplx(0.7023967071298748277842210626074970_8, 1.5707963267948966192313216916397514_8, kind=8))
! Numerically: I*0.65088016802300754993807813168285564
call check(atanh(z4), cmplx(0.0_4, 0.65088016802300754993807813168285564_4, kind=4))
call check(atanh(z8), cmplx(0.0_8, 0.65088016802300754993807813168285564_8, kind=8))
! z = (1+I)*tanh(1.0)
z4 = cmplx(0.76159415595576488811945828260479359_4, 0.76159415595576488811945828260479359_4, kind=4)
z8 = cmplx(0.76159415595576488811945828260479359_8, 0.76159415595576488811945828260479359_8, kind=8)
! Numerically: 0.59507386031622633330574869409179139 + I*0.82342412550090412964986631390412834
call check(asin(z4), cmplx(0.59507386031622633330574869409179139_4, 0.82342412550090412964986631390412834_4, kind=4))
call check(asin(z8), cmplx(0.59507386031622633330574869409179139_8, 0.82342412550090412964986631390412834_8, kind=8))
! Numerically: 0.97572246647867028592557299754796005 - I*0.82342412550090412964986631390412834
call check(acos(z4), cmplx(0.97572246647867028592557299754796005_4, -0.82342412550090412964986631390412834_4, kind=4))
call check(acos(z8), cmplx(0.97572246647867028592557299754796005_8, -0.82342412550090412964986631390412834_8, kind=8))
! Numerically: 0.83774433133636226305479129936568267 + I*0.43874835208710654149508159123595167
call check(atan(z4), cmplx(0.83774433133636226305479129936568267_4, 0.43874835208710654149508159123595167_4, kind=4))
call check(atan(z8), cmplx(0.83774433133636226305479129936568267_8, 0.43874835208710654149508159123595167_8, kind=8))
! Numerically: 0.82342412550090412964986631390412834 + I*0.59507386031622633330574869409179139
call check(asinh(z4), cmplx(0.82342412550090412964986631390412834_4, 0.59507386031622633330574869409179139_4, kind=4))
call check(asinh(z8), cmplx(0.82342412550090412964986631390412834_8, 0.59507386031622633330574869409179139_8, kind=8))
! Numerically: 0.82342412550090412964986631390412834 + I*0.97572246647867028592557299754796005
call check(acosh(z4), cmplx(0.82342412550090412964986631390412834_4, 0.97572246647867028592557299754796005_4, kind=4))
call check(acosh(z8), cmplx(0.82342412550090412964986631390412834_8, 0.97572246647867028592557299754796005_8, kind=8))
! Numerically: 0.43874835208710654149508159123595167 + I*0.83774433133636226305479129936568267
call check(atanh(z4), cmplx(0.43874835208710654149508159123595167_4, 0.83774433133636226305479129936568267_4, kind=4))
call check(atanh(z8), cmplx(0.43874835208710654149508159123595167_8, 0.83774433133636226305479129936568267_8, kind=8))
! z = 1+I
z4 = cmplx(1.0_4, 1.0_4, kind=4)
z8 = cmplx(1.0_8, 1.0_8, kind=8)
! Numerically: 0.66623943249251525510400489597779272 + I*1.06127506190503565203301891621357349
call check(asin(z4), cmplx(0.66623943249251525510400489597779272_4, 1.06127506190503565203301891621357349_4, kind=4))
call check(asin(z8), cmplx(0.66623943249251525510400489597779272_8, 1.06127506190503565203301891621357349_8, kind=8))
! Numerically: 0.90455689430238136412731679566195872 - I*1.06127506190503565203301891621357349
call check(acos(z4), cmplx(0.90455689430238136412731679566195872_4, -1.06127506190503565203301891621357349_4, kind=4))
call check(acos(z8), cmplx(0.90455689430238136412731679566195872_8, -1.06127506190503565203301891621357349_8, kind=8))
! Numerically: 1.01722196789785136772278896155048292 + I*0.40235947810852509365018983330654691
call check(atan(z4), cmplx(1.01722196789785136772278896155048292_4, 0.40235947810852509365018983330654691_4, kind=4))
call check(atan(z8), cmplx(1.01722196789785136772278896155048292_8, 0.40235947810852509365018983330654691_8, kind=8))
! Numerically: 1.06127506190503565203301891621357349 + I*0.66623943249251525510400489597779272
call check(asinh(z4), cmplx(1.06127506190503565203301891621357349_4, 0.66623943249251525510400489597779272_4, kind=4))
call check(asinh(z8), cmplx(1.06127506190503565203301891621357349_8, 0.66623943249251525510400489597779272_8, kind=8))
! Numerically: 1.06127506190503565203301891621357349 + I*0.90455689430238136412731679566195872
call check(acosh(z4), cmplx(1.06127506190503565203301891621357349_4, 0.90455689430238136412731679566195872_4, kind=4))
call check(acosh(z8), cmplx(1.06127506190503565203301891621357349_8, 0.90455689430238136412731679566195872_8, kind=8))
! Numerically: 0.40235947810852509365018983330654691 + I*1.01722196789785136772278896155048292
call check(atanh(z4), cmplx(0.40235947810852509365018983330654691_4, 1.01722196789785136772278896155048292_4, kind=4))
call check(atanh(z8), cmplx(0.40235947810852509365018983330654691_8, 1.01722196789785136772278896155048292_8, kind=8))
! z = (1+I)*1.1
z4 = cmplx(1.1_4, 1.1_4, kind=4)
z8 = cmplx(1.1_8, 1.1_8, kind=8)
! Numerically: 0.68549840630267734494444454677951503 + I*1.15012680127435581678415521738176733
call check(asin(z4), cmplx(0.68549840630267734494444454677951503_4, 1.15012680127435581678415521738176733_4, kind=4))
call check(asin(z8), cmplx(0.68549840630267734494444454677951503_8, 1.15012680127435581678415521738176733_8, kind=8))
! Numerically: 0.8852979204922192742868771448602364 - I*1.1501268012743558167841552173817673
call check(acos(z4), cmplx(0.8852979204922192742868771448602364_4, -1.1501268012743558167841552173817673_4, kind=4))
call check(acos(z8), cmplx(0.8852979204922192742868771448602364_8, -1.1501268012743558167841552173817673_8, kind=8))
! Numerically: 1.07198475450905931839240655913126728 + I*0.38187020129010862908881230531688930
call check(atan(z4), cmplx(1.07198475450905931839240655913126728_4, 0.38187020129010862908881230531688930_4, kind=4))
call check(atan(z8), cmplx(1.07198475450905931839240655913126728_8, 0.38187020129010862908881230531688930_8, kind=8))
! Numerically: 1.15012680127435581678415521738176733 + I*0.68549840630267734494444454677951503
call check(asinh(z4), cmplx(1.15012680127435581678415521738176733_4, 0.68549840630267734494444454677951503_4, kind=4))
call check(asinh(z8), cmplx(1.15012680127435581678415521738176733_8, 0.68549840630267734494444454677951503_8, kind=8))
! Numerically: 1.1501268012743558167841552173817673 + I*0.8852979204922192742868771448602364
call check(acosh(z4), cmplx(1.1501268012743558167841552173817673_4, 0.8852979204922192742868771448602364_4, kind=4))
call check(acosh(z8), cmplx(1.1501268012743558167841552173817673_8, 0.8852979204922192742868771448602364_8, kind=8))
! Numerically: 0.38187020129010862908881230531688930 + I*1.07198475450905931839240655913126728
call check(atanh(z4), cmplx(0.38187020129010862908881230531688930_4, 1.07198475450905931839240655913126728_4, kind=4))
call check(atanh(z8), cmplx(0.38187020129010862908881230531688930_8, 1.07198475450905931839240655913126728_8, kind=8))
!!!!! Negative NUMBERS !!!!!!
! z = -(1+I)*1.1
z4 = cmplx(-1.1_4, -1.1_4, kind=4)
z8 = cmplx(-1.1_8, -1.1_8, kind=8)
! Numerically: -0.68549840630267734494444454677951503 - I*1.15012680127435581678415521738176733
call check(asin(z4), cmplx(-0.68549840630267734494444454677951503_4, -1.15012680127435581678415521738176733_4, kind=4))
call check(asin(z8), cmplx(-0.68549840630267734494444454677951503_8, -1.15012680127435581678415521738176733_8, kind=8))
! Numerically: 2.2562947330975739641757662384192665 + I*1.1501268012743558167841552173817673
call check(acos(z4), cmplx(2.2562947330975739641757662384192665_4, 1.1501268012743558167841552173817673_4, kind=4))
call check(acos(z8), cmplx(2.2562947330975739641757662384192665_8, 1.1501268012743558167841552173817673_8, kind=8))
! Numerically: -1.07198475450905931839240655913126728 - I*0.38187020129010862908881230531688930
call check(atan(z4), cmplx(-1.07198475450905931839240655913126728_4, -0.38187020129010862908881230531688930_4, kind=4))
call check(atan(z8), cmplx(-1.07198475450905931839240655913126728_8, -0.38187020129010862908881230531688930_8, kind=8))
! Numerically: -1.15012680127435581678415521738176733 - I*0.68549840630267734494444454677951503
call check(asinh(z4), cmplx(-1.15012680127435581678415521738176733_4, -0.68549840630267734494444454677951503_4, kind=4))
call check(asinh(z8), cmplx(-1.15012680127435581678415521738176733_8, -0.68549840630267734494444454677951503_8, kind=8))
! Numerically: 1.1501268012743558167841552173817673 - I*2.2562947330975739641757662384192665
call check(acosh(z4), cmplx(1.1501268012743558167841552173817673_4, -2.2562947330975739641757662384192665_4, kind=4))
call check(acosh(z8), cmplx(1.1501268012743558167841552173817673_8, -2.2562947330975739641757662384192665_8, kind=8))
! Numerically: 0.38187020129010862908881230531688930 + I*1.07198475450905931839240655913126728
call check(atanh(z4), cmplx(-0.38187020129010862908881230531688930_4, -1.07198475450905931839240655913126728_4, kind=4))
call check(atanh(z8), cmplx(-0.38187020129010862908881230531688930_8, -1.07198475450905931839240655913126728_8, kind=8))
END PROGRAM ArcTrigHyp
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