5 ! Complex inverse trigonometric functions
6 ! and complex inverse hyperbolic functions
8 ! Run-time evaluation check
12 real(4), parameter :: eps4
= epsilon(0.0_4
)*4.0_4
13 real(8), parameter :: eps8
= epsilon(0.0_8
)*2.0_8
15 procedure check4
, check8
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: ', &
25 aimag(z
)-aimag(zref
), eps4
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: ', &
36 aimag(z
)-aimag(zref
), eps8
45 complex(4), volatile :: z4
46 complex(8), volatile :: z8
51 z4
= cmplx(0.0_4
, 0.0_4
, kind
=4)
52 z8
= cmplx(0.0_8
, 0.0_8
, kind
=8)
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))
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))
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))
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))
74 !!!!! POSITIVE NUMBERS !!!!!!
77 z4
= cmplx(0.76159415595576488811945828260479359_4
, 0.0_4
, kind
=4)
78 z8
= cmplx(0.76159415595576488811945828260479359_8
, 0.0_8
, kind
=8)
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))
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))
101 z4
= cmplx(0.0_4
, 0.76159415595576488811945828260479359_4
, kind
=4)
102 z8
= cmplx(0.0_8
, 0.76159415595576488811945828260479359_8
, kind
=8)
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))
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))
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)
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))
149 z4
= cmplx(1.0_4
, 1.0_4
, kind
=4)
150 z8
= cmplx(1.0_8
, 1.0_8
, kind
=8)
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))
173 z4
= cmplx(1.1_4
, 1.1_4
, kind
=4)
174 z8
= cmplx(1.1_8
, 1.1_8
, kind
=8)
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))
196 !!!!! Negative NUMBERS !!!!!!
198 z4
= cmplx(-1.1_4
, -1.1_4
, kind
=4)
199 z8
= cmplx(-1.1_8
, -1.1_8
, kind
=8)
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))
219 END PROGRAM ArcTrigHyp