1! { dg-do run } 2! 3! PR fortran/33197 4! 5! Complex inverse trigonometric functions 6! and complex inverse hyperbolic functions 7! 8! Run-time evaluation check 9! 10module test 11 implicit none 12 real(4), parameter :: eps4 = epsilon(0.0_4)*4.0_4 13 real(8), parameter :: eps8 = epsilon(0.0_8)*2.0_8 14 interface check 15 procedure check4, check8 16 end interface check 17contains 18 SUBROUTINE check4(z, zref) 19 complex(4), intent(in) :: z, zref 20 if ( abs (real(z)-real(zref)) > eps4 & 21 .or.abs (aimag(z)-aimag(zref)) > eps4) then 22 print '(a,/,2((2g0," + I ",g0),/))', "check4:"," z=",z,'zref=',zref 23 print '(a,g0," + I*",g0," eps=",g0)', 'Diff: ', & 24 real(z)-real(zref), & 25 aimag(z)-aimag(zref), eps4 26 call abort() 27 end if 28 END SUBROUTINE check4 29 SUBROUTINE check8(z, zref) 30 complex(8), intent(in) :: z, zref 31 if ( abs (real(z)-real(zref)) > eps8 & 32 .or.abs (aimag(z)-aimag(zref)) > eps8) then 33 print '(a,/,2((2g0," + I ",g0),/))', "check8:"," z=",z,'zref=',zref 34 print '(a,g0," + I*",g0," eps=",g0)', 'Diff: ', & 35 real(z)-real(zref), & 36 aimag(z)-aimag(zref), eps8 37 call abort() 38 end if 39 END SUBROUTINE check8 40end module test 41 42PROGRAM ArcTrigHyp 43 use test 44 IMPLICIT NONE 45 complex(4), volatile :: z4 46 complex(8), volatile :: z8 47 48!!!!! ZERO !!!!!! 49 50 ! z = 0 51 z4 = cmplx(0.0_4, 0.0_4, kind=4) 52 z8 = cmplx(0.0_8, 0.0_8, kind=8) 53 54 ! Exact: 0 55 call check(asin(z4), cmplx(0.0_4, 0.0_4, kind=4)) 56 call check(asin(z8), cmplx(0.0_8, 0.0_8, kind=8)) 57 ! Exact: Pi/2 = 1.5707963267948966192313216916397514 58 call check(acos(z4), cmplx(1.57079632679489661920_4, 0.0_4, kind=4)) 59 call check(acos(z8), cmplx(1.57079632679489661920_8, 0.0_8, kind=8)) 60 ! Exact: 0 61 call check(atan(z4), cmplx(0.0_4, 0.0_4, kind=4)) 62 call check(atan(z8), cmplx(0.0_8, 0.0_8, kind=8)) 63 ! Exact: 0 64 call check(asinh(z4), cmplx(0.0_4, 0.0_4, kind=4)) 65 call check(asinh(z8), cmplx(0.0_8, 0.0_8, kind=8)) 66 ! Exact: I*Pi/2 = I*1.5707963267948966192313216916397514 67 call check(acosh(z4), cmplx(0.0_4, 1.57079632679489661920_4, kind=4)) 68 call check(acosh(z8), cmplx(0.0_8, 1.57079632679489661920_8, kind=8)) 69 ! Exact: 0 70 call check(atanh(z4), cmplx(0.0_4, 0.0_4, kind=4)) 71 call check(atanh(z8), cmplx(0.0_8, 0.0_8, kind=8)) 72 73 74!!!!! POSITIVE NUMBERS !!!!!! 75 76 ! z = tanh(1.0) 77 z4 = cmplx(0.76159415595576488811945828260479359_4, 0.0_4, kind=4) 78 z8 = cmplx(0.76159415595576488811945828260479359_8, 0.0_8, kind=8) 79 80 ! Numerically: 0.86576948323965862428960184619184444 81 call check(asin(z4), cmplx(0.86576948323965862428960184619184444_4, 0.0_4, kind=4)) 82 call check(asin(z8), cmplx(0.86576948323965862428960184619184444_8, 0.0_8, kind=8)) 83 ! Numerically: 0.70502684355523799494171984544790700 84 call check(acos(z4), cmplx(0.70502684355523799494171984544790700_4, 0.0_4, kind=4)) 85 call check(acos(z8), cmplx(0.70502684355523799494171984544790700_8, 0.0_8, kind=8)) 86 ! Numerically: 0.65088016802300754993807813168285564 87 call check(atan(z4), cmplx(0.65088016802300754993807813168285564_4, 0.0_4, kind=4)) 88 call check(atan(z8), cmplx(0.65088016802300754993807813168285564_8, 0.0_8, kind=8)) 89 ! Numerically: 0.70239670712987482778422106260749699 90 call check(asinh(z4), cmplx(0.70239670712987482778422106260749699_4, 0.0_4, kind=4)) 91 call check(asinh(z8), cmplx(0.70239670712987482778422106260749699_8, 0.0_8, kind=8)) 92 ! Numerically: 0.70502684355523799494171984544790700*I 93 call check(acosh(z4), cmplx(0.0_4, 0.70502684355523799494171984544790700_4, kind=4)) 94 call check(acosh(z8), cmplx(0.0_8, 0.70502684355523799494171984544790700_8, kind=8)) 95 ! Exact: 1 96 call check(atanh(z4), cmplx(1.0_4, 0.0_4, kind=4)) 97 call check(atanh(z8), cmplx(1.0_8, 0.0_8, kind=8)) 98 99 100 ! z = I*tanh(1.0) 101 z4 = cmplx(0.0_4, 0.76159415595576488811945828260479359_4, kind=4) 102 z8 = cmplx(0.0_8, 0.76159415595576488811945828260479359_8, kind=8) 103 104 ! Numerically: I*0.70239670712987482778422106260749699 105 call check(asin(z4), cmplx(0.0_4, 0.70239670712987482778422106260749699_4, kind=4)) 106 call check(asin(z8), cmplx(0.0_8, 0.70239670712987482778422106260749699_8, kind=8)) 107 ! Numerically: 1.5707963267948966192313216916397514 - I*0.7023967071298748277842210626074970 108 call check(acos(z4), cmplx(1.5707963267948966192313216916397514_4, -0.7023967071298748277842210626074970_4, kind=4)) 109 call check(acos(z8), cmplx(1.5707963267948966192313216916397514_8, -0.7023967071298748277842210626074970_8, kind=8)) 110 ! Exact: I*1 111 call check(atan(z4), cmplx(0.0_4, 1.0_4, kind=4)) 112 call check(atan(z8), cmplx(0.0_8, 1.0_8, kind=8)) 113 ! Numerically: I*0.86576948323965862428960184619184444 114 call check(asinh(z4), cmplx(0.0_4, 0.86576948323965862428960184619184444_4, kind=4)) 115 call check(asinh(z8), cmplx(0.0_8, 0.86576948323965862428960184619184444_8, kind=8)) 116 ! Numerically: 0.7023967071298748277842210626074970 + I*1.5707963267948966192313216916397514 117 call check(acosh(z4), cmplx(0.7023967071298748277842210626074970_4, 1.5707963267948966192313216916397514_4, kind=4)) 118 call check(acosh(z8), cmplx(0.7023967071298748277842210626074970_8, 1.5707963267948966192313216916397514_8, kind=8)) 119 ! Numerically: I*0.65088016802300754993807813168285564 120 call check(atanh(z4), cmplx(0.0_4, 0.65088016802300754993807813168285564_4, kind=4)) 121 call check(atanh(z8), cmplx(0.0_8, 0.65088016802300754993807813168285564_8, kind=8)) 122 123 124 ! z = (1+I)*tanh(1.0) 125 z4 = cmplx(0.76159415595576488811945828260479359_4, 0.76159415595576488811945828260479359_4, kind=4) 126 z8 = cmplx(0.76159415595576488811945828260479359_8, 0.76159415595576488811945828260479359_8, kind=8) 127 128 ! Numerically: 0.59507386031622633330574869409179139 + I*0.82342412550090412964986631390412834 129 call check(asin(z4), cmplx(0.59507386031622633330574869409179139_4, 0.82342412550090412964986631390412834_4, kind=4)) 130 call check(asin(z8), cmplx(0.59507386031622633330574869409179139_8, 0.82342412550090412964986631390412834_8, kind=8)) 131 ! Numerically: 0.97572246647867028592557299754796005 - I*0.82342412550090412964986631390412834 132 call check(acos(z4), cmplx(0.97572246647867028592557299754796005_4, -0.82342412550090412964986631390412834_4, kind=4)) 133 call check(acos(z8), cmplx(0.97572246647867028592557299754796005_8, -0.82342412550090412964986631390412834_8, kind=8)) 134 ! Numerically: 0.83774433133636226305479129936568267 + I*0.43874835208710654149508159123595167 135 call check(atan(z4), cmplx(0.83774433133636226305479129936568267_4, 0.43874835208710654149508159123595167_4, kind=4)) 136 call check(atan(z8), cmplx(0.83774433133636226305479129936568267_8, 0.43874835208710654149508159123595167_8, kind=8)) 137 ! Numerically: 0.82342412550090412964986631390412834 + I*0.59507386031622633330574869409179139 138 call check(asinh(z4), cmplx(0.82342412550090412964986631390412834_4, 0.59507386031622633330574869409179139_4, kind=4)) 139 call check(asinh(z8), cmplx(0.82342412550090412964986631390412834_8, 0.59507386031622633330574869409179139_8, kind=8)) 140 ! Numerically: 0.82342412550090412964986631390412834 + I*0.97572246647867028592557299754796005 141 call check(acosh(z4), cmplx(0.82342412550090412964986631390412834_4, 0.97572246647867028592557299754796005_4, kind=4)) 142 call check(acosh(z8), cmplx(0.82342412550090412964986631390412834_8, 0.97572246647867028592557299754796005_8, kind=8)) 143 ! Numerically: 0.43874835208710654149508159123595167 + I*0.83774433133636226305479129936568267 144 call check(atanh(z4), cmplx(0.43874835208710654149508159123595167_4, 0.83774433133636226305479129936568267_4, kind=4)) 145 call check(atanh(z8), cmplx(0.43874835208710654149508159123595167_8, 0.83774433133636226305479129936568267_8, kind=8)) 146 147 148 ! z = 1+I 149 z4 = cmplx(1.0_4, 1.0_4, kind=4) 150 z8 = cmplx(1.0_8, 1.0_8, kind=8) 151 152 ! Numerically: 0.66623943249251525510400489597779272 + I*1.06127506190503565203301891621357349 153 call check(asin(z4), cmplx(0.66623943249251525510400489597779272_4, 1.06127506190503565203301891621357349_4, kind=4)) 154 call check(asin(z8), cmplx(0.66623943249251525510400489597779272_8, 1.06127506190503565203301891621357349_8, kind=8)) 155 ! Numerically: 0.90455689430238136412731679566195872 - I*1.06127506190503565203301891621357349 156 call check(acos(z4), cmplx(0.90455689430238136412731679566195872_4, -1.06127506190503565203301891621357349_4, kind=4)) 157 call check(acos(z8), cmplx(0.90455689430238136412731679566195872_8, -1.06127506190503565203301891621357349_8, kind=8)) 158 ! Numerically: 1.01722196789785136772278896155048292 + I*0.40235947810852509365018983330654691 159 call check(atan(z4), cmplx(1.01722196789785136772278896155048292_4, 0.40235947810852509365018983330654691_4, kind=4)) 160 call check(atan(z8), cmplx(1.01722196789785136772278896155048292_8, 0.40235947810852509365018983330654691_8, kind=8)) 161 ! Numerically: 1.06127506190503565203301891621357349 + I*0.66623943249251525510400489597779272 162 call check(asinh(z4), cmplx(1.06127506190503565203301891621357349_4, 0.66623943249251525510400489597779272_4, kind=4)) 163 call check(asinh(z8), cmplx(1.06127506190503565203301891621357349_8, 0.66623943249251525510400489597779272_8, kind=8)) 164 ! Numerically: 1.06127506190503565203301891621357349 + I*0.90455689430238136412731679566195872 165 call check(acosh(z4), cmplx(1.06127506190503565203301891621357349_4, 0.90455689430238136412731679566195872_4, kind=4)) 166 call check(acosh(z8), cmplx(1.06127506190503565203301891621357349_8, 0.90455689430238136412731679566195872_8, kind=8)) 167 ! Numerically: 0.40235947810852509365018983330654691 + I*1.01722196789785136772278896155048292 168 call check(atanh(z4), cmplx(0.40235947810852509365018983330654691_4, 1.01722196789785136772278896155048292_4, kind=4)) 169 call check(atanh(z8), cmplx(0.40235947810852509365018983330654691_8, 1.01722196789785136772278896155048292_8, kind=8)) 170 171 172 ! z = (1+I)*1.1 173 z4 = cmplx(1.1_4, 1.1_4, kind=4) 174 z8 = cmplx(1.1_8, 1.1_8, kind=8) 175 176 ! Numerically: 0.68549840630267734494444454677951503 + I*1.15012680127435581678415521738176733 177 call check(asin(z4), cmplx(0.68549840630267734494444454677951503_4, 1.15012680127435581678415521738176733_4, kind=4)) 178 call check(asin(z8), cmplx(0.68549840630267734494444454677951503_8, 1.15012680127435581678415521738176733_8, kind=8)) 179 ! Numerically: 0.8852979204922192742868771448602364 - I*1.1501268012743558167841552173817673 180 call check(acos(z4), cmplx(0.8852979204922192742868771448602364_4, -1.1501268012743558167841552173817673_4, kind=4)) 181 call check(acos(z8), cmplx(0.8852979204922192742868771448602364_8, -1.1501268012743558167841552173817673_8, kind=8)) 182 ! Numerically: 1.07198475450905931839240655913126728 + I*0.38187020129010862908881230531688930 183 call check(atan(z4), cmplx(1.07198475450905931839240655913126728_4, 0.38187020129010862908881230531688930_4, kind=4)) 184 call check(atan(z8), cmplx(1.07198475450905931839240655913126728_8, 0.38187020129010862908881230531688930_8, kind=8)) 185 ! Numerically: 1.15012680127435581678415521738176733 + I*0.68549840630267734494444454677951503 186 call check(asinh(z4), cmplx(1.15012680127435581678415521738176733_4, 0.68549840630267734494444454677951503_4, kind=4)) 187 call check(asinh(z8), cmplx(1.15012680127435581678415521738176733_8, 0.68549840630267734494444454677951503_8, kind=8)) 188 ! Numerically: 1.1501268012743558167841552173817673 + I*0.8852979204922192742868771448602364 189 call check(acosh(z4), cmplx(1.1501268012743558167841552173817673_4, 0.8852979204922192742868771448602364_4, kind=4)) 190 call check(acosh(z8), cmplx(1.1501268012743558167841552173817673_8, 0.8852979204922192742868771448602364_8, kind=8)) 191 ! Numerically: 0.38187020129010862908881230531688930 + I*1.07198475450905931839240655913126728 192 call check(atanh(z4), cmplx(0.38187020129010862908881230531688930_4, 1.07198475450905931839240655913126728_4, kind=4)) 193 call check(atanh(z8), cmplx(0.38187020129010862908881230531688930_8, 1.07198475450905931839240655913126728_8, kind=8)) 194 195 196!!!!! Negative NUMBERS !!!!!! 197 ! z = -(1+I)*1.1 198 z4 = cmplx(-1.1_4, -1.1_4, kind=4) 199 z8 = cmplx(-1.1_8, -1.1_8, kind=8) 200 201 ! Numerically: -0.68549840630267734494444454677951503 - I*1.15012680127435581678415521738176733 202 call check(asin(z4), cmplx(-0.68549840630267734494444454677951503_4, -1.15012680127435581678415521738176733_4, kind=4)) 203 call check(asin(z8), cmplx(-0.68549840630267734494444454677951503_8, -1.15012680127435581678415521738176733_8, kind=8)) 204 ! Numerically: 2.2562947330975739641757662384192665 + I*1.1501268012743558167841552173817673 205 call check(acos(z4), cmplx(2.2562947330975739641757662384192665_4, 1.1501268012743558167841552173817673_4, kind=4)) 206 call check(acos(z8), cmplx(2.2562947330975739641757662384192665_8, 1.1501268012743558167841552173817673_8, kind=8)) 207 ! Numerically: -1.07198475450905931839240655913126728 - I*0.38187020129010862908881230531688930 208 call check(atan(z4), cmplx(-1.07198475450905931839240655913126728_4, -0.38187020129010862908881230531688930_4, kind=4)) 209 call check(atan(z8), cmplx(-1.07198475450905931839240655913126728_8, -0.38187020129010862908881230531688930_8, kind=8)) 210 ! Numerically: -1.15012680127435581678415521738176733 - I*0.68549840630267734494444454677951503 211 call check(asinh(z4), cmplx(-1.15012680127435581678415521738176733_4, -0.68549840630267734494444454677951503_4, kind=4)) 212 call check(asinh(z8), cmplx(-1.15012680127435581678415521738176733_8, -0.68549840630267734494444454677951503_8, kind=8)) 213 ! Numerically: 1.1501268012743558167841552173817673 - I*2.2562947330975739641757662384192665 214 call check(acosh(z4), cmplx(1.1501268012743558167841552173817673_4, -2.2562947330975739641757662384192665_4, kind=4)) 215 call check(acosh(z8), cmplx(1.1501268012743558167841552173817673_8, -2.2562947330975739641757662384192665_8, kind=8)) 216 ! Numerically: 0.38187020129010862908881230531688930 + I*1.07198475450905931839240655913126728 217 call check(atanh(z4), cmplx(-0.38187020129010862908881230531688930_4, -1.07198475450905931839240655913126728_4, kind=4)) 218 call check(atanh(z8), cmplx(-0.38187020129010862908881230531688930_8, -1.07198475450905931839240655913126728_8, kind=8)) 219END PROGRAM ArcTrigHyp 220