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