13 March 2018 10:44:53.862 AM FN_TEST FORTRAN90 version Test the FN library. I4_MACH_TEST: I4_MACH evaluates integer machine numbers. I4_MACH(1) = the standard input unit. I4_MACH(2) = the standard output unit. I4_MACH(3) = the standard punch unit. I4_MACH(4) = the standard error message unit. I4_MACH(5) = the number of bits per integer storage unit. I4_MACH(6) = the number of characters per integer storage unit. I4_MACH(7) = A, the base. I4_MACH(8) = S, the number of base A digits. I4_MACH(9) = A^S-1, the largest integer. I4_MACH(10) = B, the base. I4_MACH(11) = T, the number of single precision base B digits. I4_MACH(12) = EMIN, the smallest single precision exponent E. I4_MACH(13) = EMAX, the largest single precision exponent E. I4_MACH(14) = T, the number of double precision base B digits. I4_MACH(15) = EMIN, the smallest double precision exponent E. I4_MACH(16) = EMAX, the largest double precision exponent E. I I4_MACH(I) 1 5 2 6 3 7 4 6 5 32 6 4 7 2 8 31 9 2147483647 10 2 11 24 12 -125 13 128 14 53 15 -1021 16 1024 R8_ACOS_TEST: R8_ACOS evaluates the arc cosine. X ARCCOS(X) R8_ACOS(X) Diff -0.100000 1.67096 1.67096 0.222045E-15 0.00000 1.57080 1.57080 0.00000 0.100000 1.47063 1.47063 0.00000 0.200000 1.36944 1.36944 0.222045E-15 0.300000 1.26610 1.26610 0.222045E-15 0.400000 1.15928 1.15928 0.00000 0.500000 1.04720 1.04720 0.00000 0.600000 0.927295 0.927295 0.00000 0.700000 0.795399 0.795399 0.00000 0.800000 0.643501 0.643501 0.111022E-15 0.900000 0.451027 0.451027 0.555112E-16 1.00000 0.00000 0.00000 0.00000 R8_ACOSH_TEST: R8_ACOSH evaluates the inverse hyperbolic cosine. X ARCCOSH(X) R8_ACOSH(X) Diff 1.00000 0.00000 0.00000 0.00000 1.01000 0.141304 0.141304 0.832667E-16 1.10000 0.443568 0.443568 0.111022E-15 1.20000 0.622363 0.622363 0.111022E-15 1.30000 0.756433 0.756433 0.00000 1.40000 0.867015 0.867015 0.111022E-15 1.50000 0.962424 0.962424 0.00000 2.00000 1.31696 1.31696 0.222045E-15 3.00000 1.76275 1.76275 0.00000 3.14159 1.81153 1.81153 0.00000 4.00000 2.06344 2.06344 0.444089E-15 5.00000 2.29243 2.29243 0.00000 10.0000 2.99322 2.99322 0.00000 100.000 5.29829 5.29829 0.00000 1000.00 7.60090 7.60090 0.00000 R8_AI_TEST: R8_AI evaluates the Airy function Ai X AIRY_AI(X) R8_AI(X) Diff 0.00000 0.355028 0.355028 0.00000 0.100000 0.329203 0.329203 0.00000 0.200000 0.303703 0.303703 0.00000 0.300000 0.278806 0.278806 0.00000 0.400000 0.254742 0.254742 0.00000 0.500000 0.231694 0.231694 0.00000 0.600000 0.209800 0.209800 0.277556E-16 0.700000 0.189162 0.189162 0.555112E-16 0.800000 0.169846 0.169846 0.555112E-16 0.900000 0.151887 0.151887 0.555112E-16 1.00000 0.135292 0.135292 0.277556E-16 R8_AID_TEST: R8_AID evaluates the derivative of the Airy function Ai X AIRY_AID(X) R8_AID(X) Diff 0.00000 -0.258819 -0.258819 0.00000 0.100000 -0.257130 -0.257130 0.555112E-16 0.200000 -0.252405 -0.252405 0.555112E-16 0.300000 -0.245146 -0.245146 0.00000 0.400000 -0.235832 -0.235832 0.277556E-16 0.500000 -0.224911 -0.224911 0.00000 0.600000 -0.212793 -0.212793 0.277556E-16 0.700000 -0.199851 -0.199851 0.277556E-16 0.800000 -0.186413 -0.186413 0.00000 0.900000 -0.172764 -0.172764 0.00000 1.00000 -0.159147 -0.159147 0.00000 R8_AINT_TEST: R8_AINT evaluates the aint(X) function (round towards 0) X AINT(X) R8_AINT(X) Diff -2.01000 -2.00000 -2.00000 0.00000 -1.99000 -1.00000 -1.00000 0.00000 -1.50000 -1.00000 -1.00000 0.00000 -1.10000 -1.00000 -1.00000 0.00000 -1.01000 -1.00000 -1.00000 0.00000 -1.00000 -1.00000 -1.00000 0.00000 -0.990000 0.00000 -0.00000 0.00000 -0.900000 0.00000 -0.00000 0.00000 -0.510000 0.00000 -0.00000 0.00000 -0.500000 0.00000 -0.00000 0.00000 -0.490000 0.00000 -0.00000 0.00000 -0.100000E-01 0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.100000E-01 0.00000 0.00000 0.00000 0.490000 0.00000 0.00000 0.00000 0.500000 0.00000 0.00000 0.00000 0.510000 0.00000 0.00000 0.00000 0.900000 0.00000 0.00000 0.00000 0.990000 0.00000 0.00000 0.00000 1.00000 1.00000 1.00000 0.00000 1.01000 1.00000 1.00000 0.00000 1.10000 1.00000 1.00000 0.00000 1.50000 1.00000 1.00000 0.00000 1.99000 1.00000 1.00000 0.00000 2.01000 2.00000 2.00000 0.00000 R8_ASIN_TEST: R8_ASIN evaluates the inverse sine. X ARCSIN(X) R8_ASIN(X) Diff -0.100000 -0.100167 -0.100167 0.00000 0.00000 0.00000 0.00000 0.00000 0.100000 0.100167 0.100167 0.00000 0.200000 0.201358 0.201358 0.00000 0.300000 0.304693 0.304693 0.00000 0.400000 0.411517 0.411517 0.555112E-16 0.500000 0.523599 0.523599 0.111022E-15 0.600000 0.643501 0.643501 0.00000 0.700000 0.775397 0.775397 0.111022E-15 0.800000 0.927295 0.927295 0.111022E-15 0.900000 1.11977 1.11977 0.00000 1.00000 1.57080 1.57080 0.00000 R8_ASINH_TEST: R8_ASINH evaluates the inverse hyperbolic sine function. X ARCSINH(X) R8_ASINH(X) Diff -5.00000 -2.31244 -2.31244 0.00000 -1.00000 -0.881374 -0.881374 0.00000 0.00000 0.00000 0.00000 0.00000 0.100000 0.998341E-01 0.998341E-01 0.138778E-16 0.200000 0.198690 0.198690 0.00000 0.300000 0.295673 0.295673 0.00000 0.400000 0.390035 0.390035 0.555112E-16 0.500000 0.481212 0.481212 0.00000 0.600000 0.568825 0.568825 0.00000 0.700000 0.652667 0.652667 0.00000 0.800000 0.732668 0.732668 0.111022E-15 0.900000 0.808867 0.808867 0.00000 1.00000 0.881374 0.881374 0.00000 2.00000 1.44364 1.44364 0.00000 3.00000 1.81845 1.81845 0.00000 4.00000 2.09471 2.09471 0.00000 5.00000 2.31244 2.31244 0.00000 10.0000 2.99822 2.99822 0.00000 100.000 5.29834 5.29834 0.00000 1000.00 7.60090 7.60090 0.00000 R8_ATAN_TEST: R8_ATAN evaluates the arc tangent function X ARCTAN(X) R8_ATAN(X) Diff 0.00000 0.00000 0.00000 0.00000 0.250000 0.244979 0.244979 0.277556E-16 0.333333 0.321751 0.321751 0.00000 0.500000 0.463648 0.463648 0.555112E-16 1.00000 0.785398 0.785398 0.00000 2.00000 1.10715 1.10715 0.222045E-15 3.00000 1.24905 1.24905 0.00000 4.00000 1.32582 1.32582 0.00000 5.00000 1.37340 1.37340 0.00000 10.0000 1.47113 1.47113 0.00000 20.0000 1.52084 1.52084 0.00000 R8_ATAN2_TEST: R8_ATAN2 evaluates the arc tangent function X Y ARCTAN2(Y,X) R8_ATAN2(Y,X) Diff 0.00000 -1.00000 -1.57080 -1.57080 0.00000 0.500000 -0.866025 -1.04720 -1.04720 0.222045E-15 0.866025 -0.500000 -0.523599 -0.523599 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.866025 0.500000 0.523599 0.523599 0.00000 0.500000 0.866025 1.04720 1.04720 0.222045E-15 0.00000 1.00000 1.57080 1.57080 0.00000 -0.500000 0.866025 2.09440 2.09440 0.00000 -0.866025 0.500000 2.61799 2.61799 0.444089E-15 -1.00000 0.00000 3.14159 3.14159 0.00000 -0.866025 -0.500000 -2.61799 -2.61799 0.444089E-15 -0.500000 -0.866025 -2.09440 -2.09440 0.00000 0.00000 -1.00000 -1.57080 -1.57080 0.00000 0.500000 -0.866025 -1.04720 -1.04720 0.222045E-15 0.866025 -0.500000 -0.523599 -0.523599 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.866025 0.500000 0.523599 0.523599 0.00000 0.500000 0.866025 1.04720 1.04720 0.222045E-15 0.00000 1.00000 1.57080 1.57080 0.00000 R8_ATANH_TEST: R8_ATANH evaluates the arc hyperbolic tangent function. X ARCTANH(X) R8_ATANH(X) Diff -0.500000 -0.549306 -0.549306 0.00000 0.00000 0.00000 0.00000 0.00000 0.100000E-02 0.100000E-02 0.100000E-02 0.00000 0.100000 0.100335 0.100335 0.00000 0.200000 0.202733 0.202733 0.277556E-16 0.300000 0.309520 0.309520 0.00000 0.400000 0.423649 0.423649 0.555112E-16 0.500000 0.549306 0.549306 0.00000 0.600000 0.693147 0.693147 0.00000 0.700000 0.867301 0.867301 0.00000 0.800000 1.09861 1.09861 0.00000 0.900000 1.47222 1.47222 0.222045E-15 0.990000 2.64665 2.64665 0.444089E-15 0.999000 3.80020 3.80020 0.00000 0.999999 7.25433 7.25433 0.143778E-10 R8_BESI0_TEST: R8_BESI0 evaluates the Bessel I0(x) function. X BESI0(X) R8_BESI0(X) Diff 0.00000 1.00000 1.00000 0.00000 0.200000 1.01003 1.01003 0.00000 0.400000 1.04040 1.04040 0.00000 0.600000 1.09205 1.09205 0.444089E-15 0.800000 1.16651 1.16651 0.444089E-15 1.00000 1.26607 1.26607 0.666134E-15 1.20000 1.39373 1.39373 0.222045E-15 1.40000 1.55340 1.55340 0.444089E-15 1.60000 1.74998 1.74998 0.444089E-15 1.80000 1.98956 1.98956 0.00000 2.00000 2.27959 2.27959 0.444089E-15 2.50000 3.28984 3.28984 0.444089E-15 3.00000 4.88079 4.88079 0.00000 3.50000 7.37820 7.37820 0.888178E-15 4.00000 11.3019 11.3019 0.177636E-14 4.50000 17.4812 17.4812 0.355271E-14 5.00000 27.2399 27.2399 0.00000 6.00000 67.2344 67.2344 0.142109E-13 8.00000 427.564 427.564 0.568434E-13 10.0000 2815.72 2815.72 0.454747E-12 R8_BESI1_TEST: R8_BESI1 evaluates the Bessel I1(x) function. X BESI1(X) R8_BESI1(X) Diff 0.00000 0.00000 0.00000 0.00000 0.200000 0.100501 0.100501 0.416334E-16 0.400000 0.204027 0.204027 0.277556E-16 0.600000 0.313704 0.313704 0.00000 0.800000 0.432865 0.432865 0.555112E-16 1.00000 0.565159 0.565159 0.00000 1.20000 0.714678 0.714678 0.00000 1.40000 0.886092 0.886092 0.222045E-15 1.60000 1.08481 1.08481 0.444089E-15 1.80000 1.31717 1.31717 0.00000 2.00000 1.59064 1.59064 0.00000 2.50000 2.51672 2.51672 0.444089E-15 3.00000 3.95337 3.95337 0.444089E-15 3.50000 6.20583 6.20583 0.00000 4.00000 9.75947 9.75947 0.00000 4.50000 15.3892 15.3892 0.355271E-14 5.00000 24.3356 24.3356 0.355271E-14 6.00000 61.3419 61.3419 0.710543E-14 8.00000 399.873 399.873 0.00000 10.0000 2670.99 2670.99 0.454747E-12 R8_BESJ0_TEST: R8_BESJ0 evaluates the Bessel function J0(X). X BESJ0(X) R8_BESJ0(X) Diff -5.00000 -0.177597 -0.177597 0.138778E-15 -4.00000 -0.397150 -0.397150 0.555112E-16 -3.00000 -0.260052 -0.260052 0.555112E-16 -2.00000 0.223891 0.223891 0.832667E-16 -1.00000 0.765198 0.765198 0.00000 0.00000 1.00000 1.00000 0.00000 1.00000 0.765198 0.765198 0.00000 2.00000 0.223891 0.223891 0.832667E-16 3.00000 -0.260052 -0.260052 0.555112E-16 4.00000 -0.397150 -0.397150 0.555112E-16 5.00000 -0.177597 -0.177597 0.138778E-15 6.00000 0.150645 0.150645 0.555112E-16 7.00000 0.300079 0.300079 0.00000 8.00000 0.171651 0.171651 0.277556E-16 9.00000 -0.903336E-01 -0.903336E-01 0.291434E-15 10.0000 -0.245936 -0.245936 0.00000 11.0000 -0.171190 -0.171190 0.555112E-16 12.0000 0.476893E-01 0.476893E-01 0.270617E-15 13.0000 0.206926 0.206926 0.832667E-16 14.0000 0.171073 0.171073 0.00000 15.0000 -0.142245E-01 -0.142245E-01 0.130104E-15 R8_BESJ1_TEST: R8_BESJ1 evaluates the Bessel function J1(x) X BESJ1(X) R8_BESJ1(X) Diff -5.00000 0.327579 0.327579 0.111022E-15 -4.00000 0.660433E-01 0.660433E-01 0.152656E-15 -3.00000 -0.339059 -0.339059 0.00000 -2.00000 -0.576725 -0.576725 0.00000 -1.00000 -0.440051 -0.440051 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 0.440051 0.440051 0.00000 2.00000 0.576725 0.576725 0.00000 3.00000 0.339059 0.339059 0.00000 4.00000 -0.660433E-01 -0.660433E-01 0.152656E-15 5.00000 -0.327579 -0.327579 0.111022E-15 6.00000 -0.276684 -0.276684 0.00000 7.00000 -0.468282E-02 -0.468282E-02 0.928077E-16 8.00000 0.234636 0.234636 0.00000 9.00000 0.245312 0.245312 0.277556E-16 10.0000 0.434727E-01 0.434727E-01 0.555112E-16 11.0000 -0.176785 -0.176785 0.277556E-15 12.0000 -0.223447 -0.223447 0.111022E-15 13.0000 -0.703181E-01 -0.703181E-01 0.208167E-15 14.0000 0.133375 0.133375 0.00000 15.0000 0.205104 0.205104 0.555112E-16 R8_BESK_TEST: R8_BESK evaluates Bessel functions K(Nu,X) NU X BESK(X) R8_BESK(X) Diff 0.500000 0.200000 2.29449 2.29449 0.444089E-15 0.500000 1.00000 0.461069 0.461069 0.166533E-15 0.500000 2.00000 0.119938 0.119938 0.277556E-15 0.500000 2.50000 0.650659E-01 0.650659E-01 0.138778E-16 0.500000 3.00000 0.360260E-01 0.360260E-01 0.693889E-17 0.500000 5.00000 0.377661E-02 0.377661E-02 0.433681E-18 0.500000 10.0000 0.179935E-04 0.179935E-04 0.00000 0.500000 20.0000 0.577637E-09 0.577637E-09 0.00000 1.50000 1.00000 0.922137 0.922137 0.111022E-15 1.50000 2.00000 0.179907 0.179907 0.138778E-15 1.50000 5.00000 0.453194E-02 0.453194E-02 0.00000 1.50000 10.0000 0.197928E-04 0.197928E-04 0.00000 1.50000 50.0000 0.348699E-22 0.348699E-22 0.587747E-38 2.50000 1.00000 3.22748 3.22748 0.444089E-15 2.50000 2.00000 0.389798 0.389798 0.555112E-16 2.50000 5.00000 0.649578E-02 0.649578E-02 0.00000 2.50000 10.0000 0.239313E-04 0.239313E-04 0.00000 2.50000 50.0000 0.362784E-22 0.362784E-22 0.00000 1.25000 1.00000 0.731145 0.731145 0.111022E-15 1.25000 2.00000 0.156748 0.156748 0.194289E-15 1.25000 5.00000 0.425739E-02 0.425739E-02 0.346945E-17 1.25000 10.0000 0.191554E-04 0.191554E-04 0.00000 1.25000 50.0000 0.346334E-22 0.346334E-22 0.176324E-37 2.75000 1.00000 4.73118 4.73118 0.00000 2.75000 2.00000 0.497688 0.497688 0.111022E-15 2.75000 5.00000 0.730086E-02 0.730086E-02 0.173472E-17 2.75000 10.0000 0.254642E-04 0.254642E-04 0.677626E-20 2.75000 50.0000 0.367528E-22 0.367528E-22 0.117549E-37 R8_BESK0_TEST: R8_BESK0 evaluates Bessel functions K0(X) X BESK0(X) R8_BESK0(X) Diff 0.100000 2.42707 2.42707 0.444089E-15 0.200000 1.75270 1.75270 0.00000 0.400000 1.11453 1.11453 0.00000 0.600000 0.777522 0.777522 0.111022E-15 0.800000 0.565347 0.565347 0.111022E-15 1.00000 0.421024 0.421024 0.166533E-15 1.20000 0.318508 0.318508 0.555112E-16 1.40000 0.243655 0.243655 0.00000 1.60000 0.187955 0.187955 0.555112E-16 1.80000 0.145931 0.145931 0.00000 2.00000 0.113894 0.113894 0.138778E-16 2.50000 0.623476E-01 0.623476E-01 0.00000 3.00000 0.347395E-01 0.347395E-01 0.693889E-17 3.50000 0.195989E-01 0.195989E-01 0.00000 4.00000 0.111597E-01 0.111597E-01 0.346945E-17 4.50000 0.639986E-02 0.639986E-02 0.00000 5.00000 0.369110E-02 0.369110E-02 0.433681E-18 6.00000 0.124399E-02 0.124399E-02 0.216840E-18 8.00000 0.146471E-03 0.146471E-03 0.00000 10.0000 0.177801E-04 0.177801E-04 0.338813E-20 R8_BESK1_TEST: R8_BESK1 evaluates Bessel functions K1(X) X BESK1(X) R8_BESK1(X) Diff 0.100000 9.85384 9.85384 0.00000 0.200000 4.77597 4.77597 0.888178E-15 0.400000 2.18435 2.18435 0.00000 0.600000 1.30283 1.30283 0.222045E-15 0.800000 0.861782 0.861782 0.00000 1.00000 0.601907 0.601907 0.00000 1.20000 0.434592 0.434592 0.00000 1.40000 0.320836 0.320836 0.00000 1.60000 0.240634 0.240634 0.277556E-16 1.80000 0.182623 0.182623 0.111022E-15 2.00000 0.139866 0.139866 0.277556E-16 2.50000 0.738908E-01 0.738908E-01 0.00000 3.00000 0.401564E-01 0.401564E-01 0.693889E-17 3.50000 0.222394E-01 0.222394E-01 0.346945E-17 4.00000 0.124835E-01 0.124835E-01 0.00000 4.50000 0.707809E-02 0.707809E-02 0.00000 5.00000 0.404461E-02 0.404461E-02 0.867362E-18 6.00000 0.134392E-02 0.134392E-02 0.216840E-18 8.00000 0.155369E-03 0.155369E-03 0.271051E-19 10.0000 0.186488E-04 0.186488E-04 0.338813E-20 R8_BESY0_TEST: R8_BESY0 evaluates Bessel functions Y0(X) X BESY0(X) R8_BESY0(X) Diff 0.100000 -1.53424 -1.53424 0.222045E-15 1.00000 0.882570E-01 0.882570E-01 0.416334E-16 2.00000 0.510376 0.510376 0.00000 3.00000 0.376850 0.376850 0.00000 4.00000 -0.169407E-01 -0.169407E-01 0.312250E-16 5.00000 -0.308518 -0.308518 0.555112E-16 6.00000 -0.288195 -0.288195 0.00000 7.00000 -0.259497E-01 -0.259497E-01 0.111022E-15 8.00000 0.223521 0.223521 0.555112E-16 9.00000 0.249937 0.249937 0.555112E-16 10.0000 0.556712E-01 0.556712E-01 0.832667E-16 11.0000 -0.168847 -0.168847 0.00000 12.0000 -0.225237 -0.225237 0.832667E-16 13.0000 -0.782079E-01 -0.782079E-01 0.291434E-15 14.0000 0.127193 0.127193 0.277556E-16 15.0000 0.205464 0.205464 0.277556E-16 R8_BESY1_TEST: R8_BESY1 evaluates Bessel functions Y1(X) X BESY1(X) R8_BESY1(X) Diff 0.100000 -6.45895 -6.45895 0.888178E-15 1.00000 -0.781213 -0.781213 0.111022E-15 2.00000 -0.107032 -0.107032 0.00000 3.00000 0.324674 0.324674 0.00000 4.00000 0.397926 0.397926 0.555112E-16 5.00000 0.147863 0.147863 0.277556E-16 6.00000 -0.175010 -0.175010 0.277556E-16 7.00000 -0.302667 -0.302667 0.111022E-15 8.00000 -0.158060 -0.158060 0.555112E-16 9.00000 0.104315 0.104315 0.138778E-16 10.0000 0.249015 0.249015 0.555112E-16 11.0000 0.163706 0.163706 0.305311E-15 12.0000 -0.570992E-01 -0.570992E-01 0.409395E-15 13.0000 -0.210081 -0.210081 0.832667E-16 14.0000 -0.166645 -0.166645 0.555112E-16 15.0000 0.210736E-01 0.210736E-01 0.485723E-16 R8_BETA_TEST: R8_BETA evaluates the Beta function. A B BETA(A,B) R8_BETA(A,B) Diff 0.200000 1.00000 5.00000 5.00000 0.888178E-15 0.400000 1.00000 2.50000 2.50000 0.00000 0.600000 1.00000 1.66667 1.66667 0.444089E-15 0.800000 1.00000 1.25000 1.25000 0.222045E-15 1.00000 0.200000 5.00000 5.00000 0.888178E-15 1.00000 0.400000 2.50000 2.50000 0.00000 1.00000 1.00000 1.00000 1.00000 0.00000 2.00000 2.00000 0.166667 0.166667 0.555112E-16 3.00000 3.00000 0.333333E-01 0.333333E-01 0.00000 4.00000 4.00000 0.714286E-02 0.714286E-02 0.00000 5.00000 5.00000 0.158730E-02 0.158730E-02 0.216840E-18 6.00000 2.00000 0.238095E-01 0.238095E-01 0.346945E-17 6.00000 3.00000 0.595238E-02 0.595238E-02 0.00000 6.00000 4.00000 0.198413E-02 0.198413E-02 0.00000 6.00000 5.00000 0.793651E-03 0.793651E-03 0.184314E-17 6.00000 6.00000 0.360750E-03 0.360750E-03 0.162630E-17 7.00000 7.00000 0.832501E-04 0.832501E-04 0.149078E-18 R8_BETAI_TEST: R8_BETAI evaluates the incomplete Beta function. X A B BETAI(A,B) R8_BETAI(A,B) Diff 0.100000E-01 0.500000 0.500000 0.637686E-01 0.637686E-01 0.00000 0.100000 0.500000 0.500000 0.204833 0.204833 0.555112E-16 1.00000 0.500000 0.500000 1.00000 1.00000 0.00000 0.00000 1.00000 0.500000 0.00000 0.00000 0.00000 0.100000E-01 1.00000 0.500000 0.501256E-02 0.501256E-02 0.346945E-17 0.100000 1.00000 0.500000 0.513167E-01 0.513167E-01 0.138778E-16 0.500000 1.00000 0.500000 0.292893 0.292893 0.111022E-15 0.500000 1.00000 1.00000 0.500000 0.500000 0.00000 0.100000 2.00000 2.00000 0.280000E-01 0.280000E-01 0.104083E-16 0.200000 2.00000 2.00000 0.104000 0.104000 0.138778E-16 0.300000 2.00000 2.00000 0.216000 0.216000 0.832667E-16 0.400000 2.00000 2.00000 0.352000 0.352000 0.555112E-16 0.500000 2.00000 2.00000 0.500000 0.500000 0.00000 0.600000 2.00000 2.00000 0.648000 0.648000 0.111022E-15 0.700000 2.00000 2.00000 0.784000 0.784000 0.111022E-15 0.800000 2.00000 2.00000 0.896000 0.896000 0.00000 0.900000 2.00000 2.00000 0.972000 0.972000 0.00000 0.500000 5.50000 5.00000 0.436191 0.436191 0.777156E-15 0.900000 10.0000 0.500000 0.151641 0.151641 0.144329E-14 0.500000 10.0000 5.00000 0.897827E-01 0.897827E-01 0.263678E-15 1.00000 10.0000 5.00000 1.00000 1.00000 0.00000 0.500000 10.0000 10.0000 0.500000 0.500000 0.111022E-15 0.800000 20.0000 5.00000 0.459877 0.459877 0.111022E-15 0.600000 20.0000 10.0000 0.214682 0.214682 0.108247E-14 0.800000 20.0000 10.0000 0.950736 0.950736 0.222045E-15 0.500000 20.0000 20.0000 0.500000 0.500000 0.00000 0.600000 20.0000 20.0000 0.897941 0.897941 0.255351E-14 0.700000 30.0000 10.0000 0.224130 0.224130 0.416334E-15 0.800000 30.0000 10.0000 0.758641 0.758641 0.333067E-15 0.700000 40.0000 20.0000 0.700178 0.700178 0.555112E-15 0.100000 1.00000 0.500000 0.513167E-01 0.513167E-01 0.138778E-16 0.200000 1.00000 0.500000 0.105573 0.105573 0.138778E-16 0.300000 1.00000 0.500000 0.163340 0.163340 0.00000 0.400000 1.00000 0.500000 0.225403 0.225403 0.832667E-16 0.200000 1.00000 2.00000 0.360000 0.360000 0.00000 0.200000 1.00000 3.00000 0.488000 0.488000 0.111022E-15 0.200000 1.00000 4.00000 0.590400 0.590400 0.111022E-15 0.200000 1.00000 5.00000 0.672320 0.672320 0.111022E-15 0.300000 2.00000 2.00000 0.216000 0.216000 0.832667E-16 0.300000 3.00000 2.00000 0.837000E-01 0.837000E-01 0.555112E-16 0.300000 4.00000 2.00000 0.307800E-01 0.307800E-01 0.173472E-16 0.300000 5.00000 2.00000 0.109350E-01 0.109350E-01 0.346945E-17 0.225609 1.30625 11.7562 0.918885 0.918885 0.222045E-15 0.335568E-01 1.30625 11.7562 0.210530 0.210530 0.388578E-15 0.295222E-01 1.30625 11.7562 0.182413 0.182413 0.249800E-15 R8_BI_TEST: R8_BI evaluates the Airy function Bi(X) X AIRY_BI(X) R8_BI(X) Diff 0.00000 0.614927 0.614927 0.00000 0.100000 0.659862 0.659862 0.111022E-15 0.200000 0.705464 0.705464 0.00000 0.300000 0.752486 0.752486 0.111022E-15 0.400000 0.801773 0.801773 0.111022E-15 0.500000 0.854277 0.854277 0.00000 0.600000 0.911063 0.911063 0.111022E-15 0.700000 0.973329 0.973329 0.111022E-15 0.800000 1.04242 1.04242 0.222045E-15 0.900000 1.11987 1.11987 0.222045E-15 1.00000 1.20742 1.20742 0.222045E-15 R8_BID_TEST: R8_BID evaluates the derivative of the Airy function Bi(X) X AIRY_BID(X) R8_BID(X) Diff 0.00000 0.448288 0.448288 0.555112E-16 0.100000 0.451513 0.451513 0.00000 0.200000 0.461789 0.461789 0.555112E-16 0.300000 0.480049 0.480049 0.555112E-16 0.400000 0.507282 0.507282 0.111022E-15 0.500000 0.544573 0.544573 0.00000 0.600000 0.593144 0.593144 0.00000 0.700000 0.654406 0.654406 0.00000 0.800000 0.730007 0.730007 0.111022E-15 0.900000 0.821904 0.821904 0.111022E-15 1.00000 0.932436 0.932436 0.00000 R8_BINOM_TEST: R8_BINOM evaluates the binomial coefficient. A B BINOM(A,B) R8_BINOM(A,B) Diff 1 0 1 1.00000 0.00000 6 1 6 6.00000 0.00000 6 3 20 20.0000 0.00000 6 5 6 6.00000 0.00000 15 1 15 15.0000 0.00000 15 3 455 455.000 0.00000 15 5 3003 3003.00 0.00000 15 7 6435 6435.00 0.00000 15 9 5005 5005.00 0.00000 15 11 1365 1365.00 0.00000 15 13 105 105.000 0.00000 25 1 25 25.0000 0.00000 25 3 2300 2300.00 0.00000 25 5 53130 53130.0 0.00000 25 7 480700 480700. 0.00000 25 9 2042975 0.204298E+07 0.00000 25 11 4457400 0.445740E+07 0.00000 25 13 5200300 0.520030E+07 0.00000 25 15 3268760 0.326876E+07 0.00000 25 17 1081575 0.108158E+07 0.00000 R8_CBRT_TEST: R8_CBRT computes the cube root X CBRT(X) R8_CBRT(X) Diff 0.00000 0.00000 0.00000 0.00000 -0.810000E-08 -0.200830E-02 -0.200830E-02 0.433681E-18 0.900000E-01 0.448140 0.448140 0.00000 -0.100000 -0.464159 -0.464159 0.555112E-16 0.400000 0.736806 0.736806 0.111022E-15 -1.00000 -1.00000 -1.00000 0.00000 2.00000 1.25992 1.25992 0.00000 -3.00000 -1.44225 -1.44225 0.222045E-15 3.14159 1.46459 1.46459 0.00000 -19.0000 -2.66840 -2.66840 0.444089E-15 29.0000 3.07232 3.07232 0.444089E-15 -71.0000 -4.14082 -4.14082 0.00000 97.0000 4.59470 4.59470 0.888178E-15 -0.123457E+09 -497.934 -497.934 0.00000 R8_CHI_TEST: R8_CHI evaluates the hyperbolic cosine integral. X CHI(X) R8_CHI(X) Diff 0.500000 -0.527768E-01 -0.527768E-01 0.693889E-17 0.600000 0.157751 0.157751 0.832667E-16 0.700000 0.345569 0.345569 0.111022E-15 0.800000 0.518400 0.518400 0.111022E-15 0.900000 0.681314 0.681314 0.111022E-15 1.00000 0.837867 0.837867 0.111022E-15 1.20000 1.14184 1.14184 0.666134E-15 1.40000 1.44549 1.44549 0.222045E-15 1.60000 1.75951 1.75951 0.00000 1.80000 2.09258 2.09258 0.888178E-15 2.00000 2.45267 2.45267 0.444089E-15 2.50000 3.52443 3.52443 0.444089E-15 3.00000 4.96039 4.96039 0.888178E-15 3.50000 6.95919 6.95919 0.00000 4.00000 9.81355 9.81355 0.355271E-14 4.50000 13.9658 13.9658 0.355271E-14 R8_CHU_TEST: R8_CHU evaluates the hypergeometric U function. A B X CHU(A,B,X) Diff -2.50000 3.30000 0.250000 -68.6936 -68.6936 0.568434E-13 -0.500000 1.10000 0.250000 -0.297106E-02 -0.297106E-02 0.475748E-15 0.500000 1.10000 0.250000 1.50086 1.50086 0.111022E-14 2.50000 3.30000 0.250000 20.6147 20.6147 0.106581E-13 -2.50000 3.30000 1.55000 7.45638 7.45638 0.177636E-14 -0.500000 1.10000 1.55000 1.01558 1.01558 0.222045E-15 0.500000 1.10000 1.55000 0.734465 0.734465 0.999201E-15 2.50000 3.30000 1.55000 0.280464 0.280464 0.166533E-15 -2.50000 3.30000 2.85000 3.45082 3.45082 0.577316E-14 -0.500000 1.10000 2.85000 1.51566 1.51566 0.444089E-15 0.500000 1.10000 2.85000 0.560421 0.560421 0.111022E-15 2.50000 3.30000 2.85000 0.648971E-01 0.648971E-01 0.00000 0.825000 6.70000 0.250000 223432. 223432. 0.582077E-10 1.10000 6.70000 0.250000 263079. 263079. 0.174623E-09 1.65000 6.70000 0.250000 269803. 269803. 0.116415E-09 3.30000 6.70000 0.250000 82809.3 82809.3 0.436557E-10 0.825000 6.70000 1.55000 26.4657 26.4657 0.710543E-14 1.10000 6.70000 1.55000 28.0935 28.0935 0.177636E-13 1.65000 6.70000 1.55000 23.8892 23.8892 0.00000 3.30000 6.70000 1.55000 4.53388 4.53388 0.00000 0.825000 6.70000 2.85000 3.02245 3.02245 0.888178E-15 1.10000 6.70000 2.85000 2.80407 2.80407 0.133227E-14 1.65000 6.70000 2.85000 1.92626 1.92626 0.222045E-15 3.30000 6.70000 2.85000 0.230205 0.230205 0.00000 R8_CI_TEST: R8_CI evaluates the cosine integral. X CI(X) R8_CI(X) Diff 0.500000 -0.177784 -0.177784 0.555112E-16 0.600000 -0.222707E-01 -0.222707E-01 0.763278E-16 0.700000 0.100515 0.100515 0.693889E-16 0.800000 0.198279 0.198279 0.222045E-15 0.900000 0.276068 0.276068 0.555112E-16 1.00000 0.337404 0.337404 0.111022E-15 1.20000 0.420459 0.420459 0.555112E-16 1.40000 0.462007 0.462007 0.555112E-16 1.60000 0.471733 0.471733 0.166533E-15 1.80000 0.456811 0.456811 0.111022E-15 2.00000 0.422981 0.422981 0.111022E-15 2.50000 0.285871 0.285871 0.111022E-15 3.00000 0.119630 0.119630 0.152656E-15 3.50000 -0.321285E-01 -0.321285E-01 0.277556E-16 4.00000 -0.140982 -0.140982 0.832667E-16 4.50000 -0.193491 -0.193491 0.555112E-16 R8_CIN_TEST: R8_CIN evaluates the alternate cosine integral. X CIN(X) R4_CIN(X) Diff R8_CIN(X) Diff 0.500000 0.618526E-01 0.618526E-01 0.693889E-17 0.600000 0.886607E-01 0.886607E-01 0.138778E-16 0.700000 0.120026 0.120026 0.416334E-16 0.800000 0.155793 0.155793 0.555112E-16 0.900000 0.195787 0.195787 0.00000 1.00000 0.239812 0.239812 0.00000 1.20000 0.339078 0.339078 0.555112E-16 1.40000 0.451681 0.451681 0.555112E-16 1.60000 0.575487 0.575487 0.00000 1.80000 0.708191 0.708191 0.00000 2.00000 0.847382 0.847382 0.00000 2.50000 1.20764 1.20764 0.444089E-15 3.00000 1.55620 1.55620 0.444089E-15 3.50000 1.86211 1.86211 0.222045E-15 4.00000 2.10449 2.10449 0.00000 4.50000 2.27478 2.27478 0.444089E-15 R8_CINH_TEST: R8_CINH evaluates the alternate hyperbolic cosine integral X CINH(X) R8_CINH(X) Diff 0.00000 0.00000 0.00000 0.00000 0.500000 0.631547E-01 0.631547E-01 0.138778E-16 0.600000 0.913609E-01 0.913609E-01 0.138778E-16 0.700000 0.125028 0.125028 0.00000 0.800000 0.164328 0.164328 0.111022E-15 0.900000 0.209459 0.209459 0.277556E-16 1.00000 0.260651 0.260651 0.00000 1.20000 0.382305 0.382305 0.111022E-15 1.40000 0.531806 0.531806 0.111022E-15 1.60000 0.712287 0.712287 0.222045E-15 1.80000 0.927575 0.927575 0.00000 2.00000 1.18230 1.18230 0.222045E-15 2.50000 2.03092 2.03092 0.444089E-15 3.00000 3.28456 3.28456 0.444089E-15 3.50000 5.12921 5.12921 0.888178E-15 4.00000 7.85004 7.85004 0.355271E-14 4.50000 11.8845 11.8845 0.532907E-14 R8_COS_TEST: R8_COS evaluates the cosine function. X COS(X) R8_COS(X) Diff 0.00000 1.00000 1.00000 0.00000 0.261799 0.965926 0.965926 0.111022E-15 0.500000 0.877583 0.877583 0.111022E-15 0.523599 0.866025 0.866025 0.00000 0.785398 0.707107 0.707107 0.00000 1.00000 0.540302 0.540302 0.00000 1.04720 0.500000 0.500000 0.555112E-16 1.57080 0.00000 0.612574E-16 0.612574E-16 2.00000 -0.416147 -0.416147 0.00000 3.00000 -0.989992 -0.989992 0.00000 3.14159 -1.00000 -1.00000 0.111022E-15 4.00000 -0.653644 -0.653644 0.00000 5.00000 0.283662 0.283662 0.555112E-16 R8_COS_DEG_TEST: R8_COS_DEG evaluates the cosine for degree arguments. X COS_DEG(X) R4_COS_DEG(X) Diff R8_COS_DEG(X) Diff -5.00000 0.996195 0.996195 0.00000 0.00000 1.00000 1.00000 0.00000 1.00000 0.999848 0.999848 0.00000 2.00000 0.999391 0.999391 0.00000 3.00000 0.998630 0.998630 0.00000 4.00000 0.997564 0.997564 0.00000 5.00000 0.996195 0.996195 0.00000 10.0000 0.984808 0.984808 0.00000 15.0000 0.965926 0.965926 0.00000 30.0000 0.866025 0.866025 0.111022E-15 45.0000 0.707107 0.707107 0.00000 60.0000 0.500000 0.500000 0.111022E-15 75.0000 0.258819 0.258819 0.00000 85.0000 0.871557E-01 0.871557E-01 0.416334E-16 86.0000 0.697565E-01 0.697565E-01 0.693889E-16 87.0000 0.523360E-01 0.523360E-01 0.131839E-15 88.0000 0.348995E-01 0.348995E-01 0.111022E-15 89.0000 0.174524E-01 0.174524E-01 0.867362E-16 90.0000 0.00000 0.00000 0.00000 91.0000 -0.174524E-01 -0.174524E-01 0.346945E-16 105.000 -0.258819 -0.258819 0.111022E-15 180.000 -1.00000 -1.00000 0.00000 R8_COSH_TEST: R8_COSH evaluates the hyperbolic cosine function. X COSH(X) R8_COSH(X) Diff -5.00000 74.2099 74.2099 0.00000 -1.00000 1.54308 1.54308 0.00000 0.00000 1.00000 1.00000 0.00000 0.100000 1.00500 1.00500 0.00000 0.200000 1.02007 1.02007 0.00000 0.300000 1.04534 1.04534 0.00000 0.400000 1.08107 1.08107 0.222045E-15 0.500000 1.12763 1.12763 0.00000 0.600000 1.18547 1.18547 0.222045E-15 0.700000 1.25517 1.25517 0.00000 0.800000 1.33743 1.33743 0.222045E-15 0.900000 1.43309 1.43309 0.222045E-15 1.00000 1.54308 1.54308 0.00000 2.00000 3.76220 3.76220 0.00000 3.00000 10.0677 10.0677 0.00000 4.00000 27.3082 27.3082 0.00000 5.00000 74.2099 74.2099 0.00000 10.0000 11013.2 11013.2 0.181899E-11 R8_COT_TEST: R8_COT evaluates the cotangent function. X COT(X) R8_COT(X) Diff 0.833333E-01 11.9722 11.9722 0.00000 0.261799 3.73205 3.73205 0.00000 0.500000 1.83049 1.83049 0.222045E-15 0.523599 1.73205 1.73205 0.00000 0.785398 1.00000 1.00000 0.00000 1.00000 0.642093 0.642093 0.111022E-15 1.04720 0.577350 0.577350 0.111022E-15 1.30900 0.267949 0.267949 0.555112E-16 1.57080 0.00000 -0.00000 0.00000 1.43990 0.131652 0.131652 0.832667E-16 1.50535 0.655435E-01 0.655435E-01 0.138778E-15 2.00000 -0.457658 -0.457658 0.111022E-15 3.00000 -7.01525 -7.01525 0.888178E-15 4.00000 0.863691 0.863691 0.00000 5.00000 -0.295813 -0.295813 0.555112E-16 R8_CSEVL_TEST: R8_CSEVL evaluates a Chebyshev approximant of N terms at a point X. Here we use an approximant to the exponential function. and average the absolute error at 21 points. N error 1 0.605859 2 0.172657 3 0.290247E-01 4 0.362759E-02 5 0.367891E-03 6 0.307777E-04 7 0.219352E-05 8 0.137199E-06 9 0.767356E-08 10 0.356530E-09 11 0.162784E-10 12 0.653432E-12 R8_DAWSON_TEST: R8_DAWSON evaluates Dawson's integral. X DAWSON(X) R8_DAWSON(X) Diff 0.00000 0.00000 0.00000 0.00000 0.100000 0.993360E-01 0.993360E-01 0.138778E-16 0.200000 0.194751 0.194751 0.555112E-16 0.300000 0.282632 0.282632 0.555112E-16 0.400000 0.359943 0.359943 0.00000 0.500000 0.424436 0.424436 0.00000 0.600000 0.474763 0.474763 0.555112E-16 0.700000 0.510504 0.510504 0.00000 0.800000 0.532102 0.532102 0.00000 0.900000 0.540724 0.540724 0.111022E-15 1.00000 0.538080 0.538080 0.00000 1.10000 0.526207 0.526207 0.111022E-15 1.20000 0.507273 0.507273 0.222045E-15 1.30000 0.483398 0.483398 0.111022E-15 1.40000 0.456507 0.456507 0.00000 1.50000 0.428249 0.428249 0.555112E-16 1.60000 0.399940 0.399940 0.00000 1.70000 0.372559 0.372559 0.555112E-16 1.80000 0.346773 0.346773 0.00000 1.90000 0.322974 0.322974 0.111022E-15 2.00000 0.301340 0.301340 0.555112E-16 R8_E1_TEST: R8_E1 evaluates the exponential integral E1(x). X E1(X) R8_E1(X) Diff 0.500000 0.559774 0.559774 0.00000 0.600000 0.454380 0.454380 0.00000 0.700000 0.373769 0.373769 0.555112E-16 0.800000 0.310597 0.310597 0.00000 0.900000 0.260184 0.260184 0.555112E-16 1.00000 0.219384 0.219384 0.555112E-16 1.10000 0.185991 0.185991 0.555112E-16 1.20000 0.158408 0.158408 0.277556E-16 1.30000 0.135451 0.135451 0.277556E-16 1.40000 0.116219 0.116219 0.138778E-16 1.50000 0.100020 0.100020 0.416334E-16 1.60000 0.863083E-01 0.863083E-01 0.277556E-16 1.70000 0.746546E-01 0.746546E-01 0.00000 1.80000 0.647131E-01 0.647131E-01 0.138778E-16 1.90000 0.562044E-01 0.562044E-01 0.00000 2.00000 0.489005E-01 0.489005E-01 0.693889E-17 R8_EI_TEST: R8_EI evaluates the exponential integral Ei(X). X EI(X) R8_EI(X) Diff 0.500000 0.454220 0.454220 0.00000 0.600000 0.769881 0.769881 0.00000 0.700000 1.06491 1.06491 0.666134E-15 0.800000 1.34740 1.34740 0.00000 0.900000 1.62281 1.62281 0.444089E-15 1.00000 1.89512 1.89512 0.222045E-15 1.10000 2.16738 2.16738 0.133227E-14 1.20000 2.44209 2.44209 0.444089E-15 1.30000 2.72140 2.72140 0.177636E-14 1.40000 3.00721 3.00721 0.00000 1.50000 3.30129 3.30129 0.133227E-14 1.60000 3.60532 3.60532 0.888178E-15 1.70000 3.92096 3.92096 0.888178E-15 1.80000 4.24987 4.24987 0.888178E-15 1.90000 4.59371 4.59371 0.888178E-15 2.00000 4.95423 4.95423 0.888178E-15 R8_ERF_TEST: R8_ERF evaluates the error function. X ERF(X) R8_ERF(X) Diff 0.00000 0.00000 0.00000 0.00000 0.100000 0.112463 0.112463 0.00000 0.200000 0.222703 0.222703 0.277556E-16 0.300000 0.328627 0.328627 0.00000 0.400000 0.428392 0.428392 0.555112E-16 0.500000 0.520500 0.520500 0.00000 0.600000 0.603856 0.603856 0.00000 0.700000 0.677801 0.677801 0.111022E-15 0.800000 0.742101 0.742101 0.00000 0.900000 0.796908 0.796908 0.111022E-15 1.00000 0.842701 0.842701 0.111022E-15 1.10000 0.880205 0.880205 0.00000 1.20000 0.910314 0.910314 0.111022E-15 1.30000 0.934008 0.934008 0.00000 1.40000 0.952285 0.952285 0.00000 1.50000 0.966105 0.966105 0.111022E-15 1.60000 0.976348 0.976348 0.00000 1.70000 0.983790 0.983790 0.111022E-15 1.80000 0.989091 0.989091 0.111022E-15 1.90000 0.992790 0.992790 0.00000 2.00000 0.995322 0.995322 0.00000 R8_ERFC_TEST: R8_ERFC evaluates the complementary error function. X ERFC(X) R8_ERFC(X) Diff 0.00000 1.00000 1.00000 0.00000 0.200000 0.777297 0.777297 0.00000 0.400000 0.571608 0.571608 0.111022E-15 0.600000 0.396144 0.396144 0.00000 0.800000 0.257899 0.257899 0.00000 1.00000 0.157299 0.157299 0.111022E-15 1.20000 0.896860E-01 0.896860E-01 0.00000 1.40000 0.477149E-01 0.477149E-01 0.138778E-16 1.60000 0.236516E-01 0.236516E-01 0.693889E-17 1.80000 0.109095E-01 0.109095E-01 0.693889E-17 2.00000 0.467773E-02 0.467773E-02 0.867362E-18 2.20000 0.186285E-02 0.186285E-02 0.108420E-17 2.40000 0.688514E-03 0.688514E-03 0.216840E-18 2.60000 0.236034E-03 0.236034E-03 0.162630E-18 2.80000 0.750132E-04 0.750132E-04 0.677626E-19 3.00000 0.220905E-04 0.220905E-04 0.677626E-20 3.20000 0.602576E-05 0.602576E-05 0.135525E-19 3.40000 0.152199E-05 0.152199E-05 0.211758E-20 3.60000 0.355863E-06 0.355863E-06 0.370577E-21 3.80000 0.770039E-07 0.770039E-07 0.529396E-22 4.00000 0.154173E-07 0.154173E-07 0.330872E-23 R8_EXP_TEST: R8_EXP evaluates the exponential function. X EXP(X) R8_EXP(X) Diff -10.0000 0.453999E-04 0.453999E-04 0.00000 -5.00000 0.673795E-02 0.673795E-02 0.00000 -1.00000 0.367879 0.367879 0.00000 0.00000 1.00000 1.00000 0.00000 0.100000E-07 1.00000 1.00000 0.00000 0.100000E-03 1.00010 1.00010 0.00000 0.100000E-02 1.00100 1.00100 0.00000 0.100000E-01 1.01005 1.01005 0.00000 0.100000 1.10517 1.10517 0.00000 0.200000 1.22140 1.22140 0.00000 0.300000 1.34986 1.34986 0.00000 0.400000 1.49182 1.49182 0.00000 0.500000 1.64872 1.64872 0.00000 0.600000 1.82212 1.82212 0.00000 0.700000 2.01375 2.01375 0.444089E-15 0.800000 2.22554 2.22554 0.444089E-15 0.900000 2.45960 2.45960 0.444089E-15 1.00000 2.71828 2.71828 0.00000 2.00000 7.38906 7.38906 0.00000 3.14159 23.1407 23.1407 0.355271E-14 5.00000 148.413 148.413 0.00000 10.0000 22026.5 22026.5 0.00000 20.0000 0.485165E+09 0.485165E+09 0.00000 40.0000 0.235385E+18 0.235385E+18 32.0000 R8_FAC_TEST: R8_FAC evaluates the factorial. N FAC(N) R8_FAC(N) Diff 0 1.00000 1.00000 0.00000 1 1.00000 1.00000 0.00000 2 2.00000 2.00000 0.00000 3 6.00000 6.00000 0.00000 4 24.0000 24.0000 0.00000 5 120.000 120.000 0.00000 6 720.000 720.000 0.00000 7 5040.00 5040.00 0.00000 8 40320.0 40320.0 0.00000 9 362880. 362880. 0.00000 10 0.362880E+07 0.362880E+07 0.00000 11 0.399168E+08 0.399168E+08 0.00000 12 0.479002E+09 0.479002E+09 0.00000 13 0.622702E+10 0.622702E+10 0.00000 14 0.871783E+11 0.871783E+11 0.00000 15 0.130767E+13 0.130767E+13 0.00000 16 0.209228E+14 0.209228E+14 0.00000 17 0.355687E+15 0.355687E+15 0.00000 18 0.640237E+16 0.640237E+16 0.00000 19 0.121645E+18 0.121645E+18 0.00000 20 0.243290E+19 0.243290E+19 0.00000 25 0.155112E+26 0.155112E+26 0.429497E+10 50 0.304141E+65 0.304141E+65 0.362452E+51 100 0.933262+158 0.933262+158 0.190232+145 150 0.571338+263 0.571338+263 0.499922+250 R8_GAMIC_TEST: R8_GAMIC evaluates the incomplete Gamma function. A X GAMIC(A,X) R8_GAMIC(A,X) Diff 0.100000 0.300000E-01 2.49030 2.49030 0.133227E-14 0.100000 0.300000 0.871837 0.871837 0.00000 0.100000 1.50000 0.107921 0.107921 0.277556E-16 0.500000 0.750000E-01 1.23812 1.23812 0.444089E-15 0.500000 0.750000 0.391130 0.391130 0.222045E-15 0.500000 3.50000 0.144472E-01 0.144472E-01 0.00000 1.00000 0.100000 0.904837 0.904837 0.111022E-15 1.00000 1.00000 0.367879 0.367879 0.555112E-16 1.00000 5.00000 0.673795E-02 0.673795E-02 0.00000 1.10000 0.100000 0.882797 0.882797 0.00000 1.10000 1.00000 0.390833 0.390833 0.222045E-15 1.10000 5.00000 0.805146E-02 0.805146E-02 0.346945E-17 2.00000 0.150000 0.989814 0.989814 0.00000 2.00000 1.50000 0.557825 0.557825 0.111022E-15 2.00000 7.00000 0.729506E-02 0.729506E-02 0.173472E-17 6.00000 2.50000 114.957 114.957 0.994760E-13 6.00000 12.0000 2.44092 2.44092 0.266454E-14 11.0000 16.0000 280855. 280855. 0.582077E-10 26.0000 25.0000 0.857648E+25 0.857648E+25 0.322123E+10 41.0000 45.0000 0.208503E+48 0.208503E+48 0.283954E+33 R8_GAMIT_TEST: R8_GAMIT evaluates Tricomi's Incomplete Gamma. A X GAMIT(A,X) R8_GAMIT(A,X) Diff 0.100000 0.300000E-01 1.04829 1.04829 0.444089E-15 0.100000 0.300000 1.02458 1.02458 0.222045E-15 0.100000 1.50000 0.949371 0.949371 0.00000 0.500000 0.750000E-01 1.10079 1.10079 0.222045E-15 0.500000 0.750000 0.899891 0.899891 0.111022E-15 0.500000 3.50000 0.530166 0.530166 0.00000 1.00000 0.100000 0.951626 0.951626 0.00000 1.00000 1.00000 0.632121 0.632121 0.111022E-15 1.00000 5.00000 0.198652 0.198652 0.277556E-16 1.10000 0.100000 0.907178 0.907178 0.00000 1.10000 1.00000 0.589181 0.589181 0.00000 1.10000 5.00000 0.168827 0.168827 0.555112E-16 2.00000 0.150000 0.452703 0.452703 0.00000 2.00000 1.50000 0.196522 0.196522 0.00000 2.00000 7.00000 0.202593E-01 0.202593E-01 0.693889E-17 6.00000 2.50000 0.172118E-03 0.172118E-03 0.813152E-19 6.00000 12.0000 0.328086E-06 0.328086E-06 0.317637E-21 11.0000 16.0000 0.524440E-13 0.524440E-13 0.946633E-28 26.0000 25.0000 0.201346E-36 0.201346E-36 0.417619E-52 41.0000 45.0000 0.123062E-67 0.123062E-67 0.177076E-81 R8_GAML_TEST: R8_GAML returns bounds for the argument of the gamma function. Lower limit XMIN = -170.433 Upper limit XMAX = 171.480 R8_GAMMA_TEST: R8_GAMMA evaluates the gamma function. X GAMMA(X) R8_GAMMA(X) Diff -0.500000 -3.54491 -3.54491 0.00000 -0.100000E-01 -100.587 -100.587 0.284217E-13 0.100000E-01 99.4326 99.4326 0.142109E-13 0.100000 9.51351 9.51351 0.177636E-14 0.200000 4.59084 4.59084 0.00000 0.400000 2.21816 2.21816 0.00000 0.500000 1.77245 1.77245 0.00000 0.600000 1.48919 1.48919 0.00000 0.800000 1.16423 1.16423 0.222045E-15 1.00000 1.00000 1.00000 0.00000 1.10000 0.951351 0.951351 0.00000 1.20000 0.918169 0.918169 0.00000 1.30000 0.897471 0.897471 0.00000 1.40000 0.887264 0.887264 0.00000 1.50000 0.886227 0.886227 0.00000 1.60000 0.893515 0.893515 0.00000 1.70000 0.908639 0.908639 0.00000 1.80000 0.931384 0.931384 0.00000 1.90000 0.961766 0.961766 0.00000 2.00000 1.00000 1.00000 0.00000 3.00000 2.00000 2.00000 0.00000 4.00000 6.00000 6.00000 0.00000 10.0000 362880. 362880. 0.00000 20.0000 0.121645E+18 0.121645E+18 80.0000 30.0000 0.884176E+31 0.884176E+31 0.754353E+17 R8_GAMR_TEST: R8_GAMR computes 1/Gamma(x). X 1/GAMMA(X) R8_GAMR(X) Diff -0.500000 -0.282095 -0.282095 0.00000 -0.100000E-01 -0.994162E-02 -0.994162E-02 0.346945E-17 0.100000E-01 0.100571E-01 0.100571E-01 0.173472E-17 0.100000 0.105114 0.105114 0.138778E-16 0.200000 0.217825 0.217825 0.00000 0.400000 0.450824 0.450824 0.00000 0.500000 0.564190 0.564190 0.00000 0.600000 0.671505 0.671505 0.00000 0.800000 0.858937 0.858937 0.111022E-15 1.00000 1.00000 1.00000 0.00000 1.10000 1.05114 1.05114 0.00000 1.20000 1.08912 1.08912 0.00000 1.30000 1.11424 1.11424 0.00000 1.40000 1.12706 1.12706 0.00000 1.50000 1.12838 1.12838 0.00000 1.60000 1.11917 1.11917 0.00000 1.70000 1.10055 1.10055 0.00000 1.80000 1.07367 1.07367 0.00000 1.90000 1.03975 1.03975 0.00000 2.00000 1.00000 1.00000 0.00000 3.00000 0.500000 0.500000 0.00000 4.00000 0.166667 0.166667 0.00000 10.0000 0.275573E-05 0.275573E-05 0.00000 20.0000 0.822064E-17 0.822064E-17 0.462223E-32 30.0000 0.113100E-30 0.113100E-30 0.963393E-45 R8_INITS_TEST: R8_INITS determines the Chebyshev interpolant degree necessary to guarantee a desired accuracy level. Here, we use a 15 term Chebyshev expansion for the sine function. Accuracy Terms Needed 1.00000 1 0.100000 2 0.100000E-01 2 0.100000E-02 3 0.100000E-03 3 0.100000E-04 4 0.100000E-05 4 0.100000E-06 5 0.100000E-07 5 0.100000E-08 6 0.100000E-09 6 0.100000E-10 7 0.100000E-11 7 0.100000E-12 7 0.100000E-13 8 0.100000E-14 8 0.100000E-15 9 0.100000E-16 9 R8_INT_TEST: R8_INT evaluates the Int(X) function X INT(X) R8_INT(X) Diff -2.01000 -2.00000 -2.00000 0.00000 -1.99000 -1.00000 -1.00000 0.00000 -1.50000 -1.00000 -1.00000 0.00000 -1.10000 -1.00000 -1.00000 0.00000 -1.01000 -1.00000 -1.00000 0.00000 -1.00000 -1.00000 -1.00000 0.00000 -0.990000 0.00000 0.00000 0.00000 -0.900000 0.00000 0.00000 0.00000 -0.510000 0.00000 0.00000 0.00000 -0.500000 0.00000 0.00000 0.00000 -0.490000 0.00000 0.00000 0.00000 -0.100000E-01 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.100000E-01 0.00000 0.00000 0.00000 0.490000 0.00000 0.00000 0.00000 0.500000 0.00000 0.00000 0.00000 0.510000 0.00000 0.00000 0.00000 0.900000 0.00000 0.00000 0.00000 0.990000 0.00000 0.00000 0.00000 1.00000 1.00000 1.00000 0.00000 1.01000 1.00000 1.00000 0.00000 1.10000 1.00000 1.00000 0.00000 1.50000 1.00000 1.00000 0.00000 1.99000 1.00000 1.00000 0.00000 2.01000 2.00000 2.00000 0.00000 R8_LBETA_TEST: R8_LBETA evaluates the logarithm of the Beta function. A B LBETA(A,B) R8_LBETA(A,B) Diff 0.200000 1.00000 1.60944 1.60944 0.222045E-15 0.400000 1.00000 0.916291 0.916291 0.00000 0.600000 1.00000 0.510826 0.510826 0.00000 0.800000 1.00000 0.223144 0.223144 0.222045E-15 1.00000 0.200000 1.60944 1.60944 0.222045E-15 1.00000 0.400000 0.916291 0.916291 0.00000 1.00000 1.00000 0.00000 0.00000 0.00000 2.00000 2.00000 -1.79176 -1.79176 0.00000 3.00000 3.00000 -3.40120 -3.40120 0.444089E-15 4.00000 4.00000 -4.94164 -4.94164 0.00000 5.00000 5.00000 -6.44572 -6.44572 0.888178E-15 6.00000 2.00000 -3.73767 -3.73767 0.444089E-15 6.00000 3.00000 -5.12396 -5.12396 0.00000 6.00000 4.00000 -6.22258 -6.22258 0.00000 6.00000 5.00000 -7.13887 -7.13887 0.266454E-14 6.00000 6.00000 -7.92732 -7.92732 0.444089E-14 7.00000 7.00000 -9.39366 -9.39366 0.177636E-14 R8_LGAMS_TEST: R8_LGAMS evaluates the sign of Gamma(x) and the logarithm of the absolute value of Gamma(x). X LNGAM(X) Sign(Gamma(X)) ALNGAM Diff 0.200000 1.52406 1.00000 1.52406 0.444089E-15 0.400000 0.796678 1.00000 0.796678 0.111022E-15 0.600000 0.398234 1.00000 0.398234 0.111022E-15 0.800000 0.152060 1.00000 0.152060 0.00000 1.00000 0.00000 1.00000 0.00000 0.00000 1.10000 -0.498724E-01 1.00000 -0.498724E-01 0.138778E-16 1.20000 -0.853741E-01 1.00000 -0.853741E-01 0.277556E-16 1.30000 -0.108175 1.00000 -0.108175 0.693889E-16 1.40000 -0.119613 1.00000 -0.119613 0.138778E-15 1.50000 -0.120782 1.00000 -0.120782 0.277556E-16 1.60000 -0.112592 1.00000 -0.112592 0.693889E-16 1.70000 -0.958077E-01 1.00000 -0.958077E-01 0.138778E-16 1.80000 -0.710839E-01 1.00000 -0.710839E-01 0.138778E-16 1.90000 -0.389843E-01 1.00000 -0.389843E-01 0.138778E-16 2.00000 0.00000 1.00000 0.00000 0.00000 3.00000 0.693147 1.00000 0.693147 0.00000 4.00000 1.79176 1.00000 1.79176 0.00000 10.0000 12.8018 1.00000 12.8018 0.00000 20.0000 39.3399 1.00000 39.3399 0.00000 30.0000 71.2570 1.00000 71.2570 0.142109E-13 R8_LGMC_TEST: R8_LGMC evaluates the correction log gamma factor. r8_lgmc(x) = log ( gamma ( x ) ) - log ( sqrt ( 2 * pi ) - ( x - 0.5 ) * log ( x ) + x X LGMC(X) R8_LGMC(X) Diff 10.0000 0.833056E-02 0.833056E-02 0.162197E-14 20.0000 0.416632E-02 0.416632E-02 0.667869E-16 30.0000 0.277767E-02 0.277767E-02 0.741638E-14 R8_LI_TEST: R8_LI evaluates the logarithmic integral. X LI(X) R8_LI(X) Diff 0.00000 0.00000 0.00000 0.00000 0.100000 -0.323898E-01 -0.323898E-01 0.693889E-17 0.200000 -0.851265E-01 -0.851265E-01 0.138778E-16 0.300000 -0.157415 -0.157415 0.555112E-16 0.400000 -0.252949 -0.252949 0.00000 0.500000 -0.378671 -0.378671 0.555112E-16 0.600000 -0.546851 -0.546851 0.111022E-15 0.700000 -0.780947 -0.780947 0.222045E-15 0.800000 -1.13401 -1.13401 0.222045E-15 0.900000 -1.77580 -1.77580 0.222045E-15 0.950000 -2.44362 -2.44362 0.444089E-15 0.975000 -3.12419 -3.12419 0.888178E-15 1.03125 -2.87294 -2.87294 0.444089E-15 1.06250 -2.16428 -2.16428 0.444089E-15 1.12500 -1.44035 -1.44035 0.222045E-15 1.25000 -0.686488 -0.686488 0.00000 1.50000 0.125065 0.125065 0.00000 2.00000 1.04516 1.04516 0.00000 4.00000 2.96759 2.96759 0.00000 8.00000 5.25372 5.25372 0.888178E-15 16.0000 8.51972 8.51972 0.00000 32.0000 13.6051 13.6051 0.355271E-14 64.0000 21.9347 21.9347 0.106581E-13 128.000 36.0425 36.0425 0.710543E-14 256.000 60.5131 60.5131 0.710543E-14 512.000 103.721 103.721 0.284217E-13 1024.00 181.078 181.078 0.284217E-13 2048.00 321.114 321.114 0.00000 R8_LNGAM_TEST: R8_LNGAM evaluates the logarithm of the gamma function. X LNGAM(X) R8_LNGAM(X) Diff 0.200000 1.52406 1.52406 0.444089E-15 0.400000 0.796678 0.796678 0.111022E-15 0.600000 0.398234 0.398234 0.111022E-15 0.800000 0.152060 0.152060 0.00000 1.00000 0.00000 0.00000 0.00000 1.10000 -0.498724E-01 -0.498724E-01 0.138778E-16 1.20000 -0.853741E-01 -0.853741E-01 0.277556E-16 1.30000 -0.108175 -0.108175 0.693889E-16 1.40000 -0.119613 -0.119613 0.138778E-15 1.50000 -0.120782 -0.120782 0.277556E-16 1.60000 -0.112592 -0.112592 0.693889E-16 1.70000 -0.958077E-01 -0.958077E-01 0.138778E-16 1.80000 -0.710839E-01 -0.710839E-01 0.138778E-16 1.90000 -0.389843E-01 -0.389843E-01 0.138778E-16 2.00000 0.00000 0.00000 0.00000 3.00000 0.693147 0.693147 0.00000 4.00000 1.79176 1.79176 0.00000 10.0000 12.8018 12.8018 0.00000 20.0000 39.3399 39.3399 0.00000 30.0000 71.2570 71.2570 0.142109E-13 R8_LNREL_TEST: R8_LNREL evaluates LOG(X+1). X LOG(X+1) R8_LNREL(X) Diff -0.999990 -11.5129 -11.5129 0.455103E-11 -0.990000 -4.60517 -4.60517 0.888178E-15 -0.900000 -2.30259 -2.30259 0.00000 -0.800000 -1.60944 -1.60944 0.222045E-15 -0.700000 -1.20397 -1.20397 0.00000 -0.600000 -0.916291 -0.916291 0.111022E-15 -0.500000 -0.693147 -0.693147 0.00000 -0.400000 -0.510826 -0.510826 0.00000 -0.300000 -0.356675 -0.356675 0.111022E-15 -0.200000 -0.223144 -0.223144 0.555112E-16 -0.100000 -0.105361 -0.105361 0.277556E-16 0.00000 0.00000 0.00000 0.00000 1.00000 0.693147 0.693147 0.00000 2.00000 1.09861 1.09861 0.00000 2.14159 1.14473 1.14473 0.00000 4.00000 1.60944 1.60944 0.00000 9.00000 2.30259 2.30259 0.00000 19.0000 2.99573 2.99573 0.00000 99.0000 4.60517 4.60517 0.00000 0.123457E+09 18.6314 18.6314 0.00000 R8_LOG_TEST: R8_LOG evaluates the logarithm function. X LOG(X) R8_LOG(X) Diff 0.100000E-04 -11.5129 -11.5129 0.00000 0.100000E-01 -4.60517 -4.60517 0.00000 0.100000 -2.30259 -2.30259 0.444089E-15 0.200000 -1.60944 -1.60944 0.00000 0.300000 -1.20397 -1.20397 0.222045E-15 0.400000 -0.916291 -0.916291 0.111022E-15 0.500000 -0.693147 -0.693147 0.00000 0.600000 -0.510826 -0.510826 0.00000 0.700000 -0.356675 -0.356675 0.555112E-16 0.800000 -0.223144 -0.223144 0.111022E-15 0.900000 -0.105361 -0.105361 0.693889E-16 1.00000 0.00000 0.00000 0.00000 2.00000 0.693147 0.693147 0.00000 3.00000 1.09861 1.09861 0.222045E-15 3.14159 1.14473 1.14473 0.00000 5.00000 1.60944 1.60944 0.222045E-15 10.0000 2.30259 2.30259 0.00000 20.0000 2.99573 2.99573 0.00000 100.000 4.60517 4.60517 0.00000 0.123457E+09 18.6314 18.6314 0.00000 R8_LOG10_TEST: R8_LOG10 evaluates the logarithm base 10 function. X LOG10(X) R8_LOG10(X) Diff 0.100000E-04 -5.00000 -5.00000 0.00000 0.100000E-01 -2.00000 -2.00000 0.222045E-15 0.100000 -1.00000 -1.00000 0.111022E-15 0.200000 -0.698970 -0.698970 0.111022E-15 0.300000 -0.522879 -0.522879 0.111022E-15 0.400000 -0.397940 -0.397940 0.555112E-16 0.500000 -0.301030 -0.301030 0.00000 0.600000 -0.221849 -0.221849 0.00000 0.700000 -0.154902 -0.154902 0.277556E-16 0.800000 -0.969100E-01 -0.969100E-01 0.277556E-16 0.900000 -0.457575E-01 -0.457575E-01 0.693889E-17 1.00000 0.00000 0.00000 0.00000 2.00000 0.301030 0.301030 0.00000 3.00000 0.477121 0.477121 0.555112E-16 3.14159 0.497150 0.497150 0.00000 5.00000 0.698970 0.698970 0.111022E-15 10.0000 1.00000 1.00000 0.00000 20.0000 1.30103 1.30103 0.222045E-15 100.000 2.00000 2.00000 0.00000 0.123457E+09 8.09151 8.09151 0.00000 R8_MACH_TEST: R8_MACH evaluates double precision machine numbers. R8_MACH (1) = B^(EMIN-1), the smallest positive magnitude. R8_MACH (2) = B^EMAX*(1 - B^(-T)), the largest magnitude. R8_MACH (3) = B^(-T), the smallest relative spacing. R8_MACH (4) = B^(1-T), the largest relative spacing. R8_MACH (5) = LOG10(B) I R8_MACH(I) 1 0.445015-307 2 0.898847+308 3 0.111022E-15 4 0.222045E-15 5 0.301030 R8_PAK_TEST: R8_PAK converts a mantissa and base 2 exponent to an R8. Mantissa Exponent R8 0.5000000000000000 7 64.00000000000000 0.5000000000000000 8 128.0000000000000 -0.5000000000000000 7 -64.00000000000000 0.7500000000000000 7 96.00000000000000 0.9375000000000000 4 15.00000000000000 0.5000000000000000 0 0.5000000000000000 0.5000000000000000 -1 0.2500000000000000 0.6250000000000000 0 0.6250000000000000 0.5048828125000000 7 64.62500000000000 0.7853981633974483 2 3.141592653589793 0.000000000000000 0 0.000000000000000 R8_POCH_TEST: R8_POCH evaluates the Pochhammer symbol. A X POCH(A,X) R8_POCH(A,X) Diff 5.00000 4.00000 1680.00 1680.00 0.00000 5.25000 4.00000 1962.60 1962.60 0.00000 5.50000 4.00000 2279.06 2279.06 0.00000 5.75000 4.00000 2631.97 2631.97 0.00000 6.00000 4.00000 3024.00 3024.00 0.00000 7.50000 0.00000 1.00000 1.00000 0.00000 7.50000 1.00000 7.50000 7.50000 0.00000 7.50000 2.00000 63.7500 63.7500 0.00000 7.50000 3.00000 605.625 605.625 0.00000 7.50000 4.00000 6359.06 6359.06 0.00000 7.50000 5.00000 73129.2 73129.2 0.00000 7.50000 6.00000 914115. 914115. 0.00000 7.50000 7.00000 0.123406E+08 0.123406E+08 0.00000 7.50000 8.00000 0.178938E+09 0.178938E+09 0.596046E-07 7.50000 9.00000 0.277354E+10 0.277354E+10 0.00000 R8_PSI_TEST: R8_PSI evaluates the Psi function. X PSI(X) R8_PSI(X) Diff 0.100000 -10.4238 -10.4238 0.177636E-14 0.200000 -5.28904 -5.28904 0.888178E-15 0.300000 -3.50252 -3.50252 0.00000 0.400000 -2.56138 -2.56138 0.00000 0.500000 -1.96351 -1.96351 0.444089E-15 0.600000 -1.54062 -1.54062 0.444089E-15 0.700000 -1.22002 -1.22002 0.222045E-15 0.800000 -0.965009 -0.965009 0.00000 0.900000 -0.754927 -0.754927 0.00000 1.00000 -0.577216 -0.577216 0.00000 1.10000 -0.423755 -0.423755 0.111022E-15 1.20000 -0.289040 -0.289040 0.111022E-15 1.30000 -0.169191 -0.169191 0.138778E-15 1.40000 -0.613845E-01 -0.613845E-01 0.693889E-16 1.50000 0.364900E-01 0.364900E-01 0.00000 1.60000 0.126047 0.126047 0.277556E-16 1.70000 0.208548 0.208548 0.555112E-16 1.80000 0.284991 0.284991 0.00000 1.90000 0.356184 0.356184 0.111022E-15 2.00000 0.422784 0.422784 0.555112E-16 R8_RAND_TEST: R8_RAND is a random number generator. I R8_RAND Expected 1 0.412703E-03 0.412703E-03 2 0.675084 0.675084 3 0.161475 0.161475 4 0.908620 0.908620 10 0.552779 0.552779 100 0.360089 0.360089 1000 0.217699 0.217699 Average = 0.499900 0.500000 Variance = 0.832492E-01 0.833333E-01 R8_RANDGS_TEST: R8_RANDGS is a normal random number generator. Mean = 3.00000 Standard Deviation = 2.00000 I R8_RANDGS 1 4.40826 2 2.94895 3 2.13857 4 1.57902 5 8.76356 6 1.08396 7 3.87796 8 4.96727 9 0.673294 10 2.13816 Sequence mean = 2.98999 Sequence standard deviation = 2.03537 R8_RANDOM_TEST: R8_RANDOM is a random number generator. I R8_RANDOM 1 0.913844E-01 2 0.161475 3 0.658159 4 0.272802 10 0.174952 100 0.820123 1000 0.640682 Average = 0.499899 0.500000 Variance = 0.832494E-01 0.833333E-01 R8_REN_TEST: R8_REN is a random number generator. I R8_REN Expected 1 0.470393 0.470393 2 0.799066 0.799066 3 0.883261 0.883261 4 0.407667 0.407667 10 0.955566 0.955566 100 0.173576 0.173576 1000 0.121733E-01 0.121733E-01 Average = 0.499841 0.500000 Variance = 0.833074E-01 0.833333E-01 R8_SHI_TEST: R8_SHI evaluates the hyperbolic sine integral. X SHI(X) R8_SHI(X) Diff 0.500000 0.506997 0.506997 0.00000 0.600000 0.612130 0.612130 0.00000 0.700000 0.719338 0.719338 0.111022E-15 0.800000 0.828997 0.828997 0.00000 0.900000 0.941498 0.941498 0.00000 1.00000 1.05725 1.05725 0.444089E-15 1.20000 1.30025 1.30025 0.00000 1.40000 1.56171 1.56171 0.00000 1.60000 1.84581 1.84581 0.666134E-15 1.80000 2.15729 2.15729 0.888178E-15 2.00000 2.50157 2.50157 0.00000 2.50000 3.54934 3.54934 0.00000 3.00000 4.97344 4.97344 0.00000 3.50000 6.96616 6.96616 0.00000 4.00000 9.81733 9.81733 0.00000 4.50000 13.9679 13.9679 0.177636E-14 R8_SI_TEST: R8_SI evaluates the Sine integral. X SI(X) R8_SI(X) Diff 0.500000 0.493107 0.493107 0.555112E-16 0.600000 0.588129 0.588129 0.111022E-15 0.700000 0.681222 0.681222 0.00000 0.800000 0.772096 0.772096 0.00000 0.900000 0.860471 0.860471 0.00000 1.00000 0.946083 0.946083 0.00000 1.20000 1.10805 1.10805 0.444089E-15 1.40000 1.25623 1.25623 0.00000 1.60000 1.38918 1.38918 0.666134E-15 1.80000 1.50582 1.50582 0.444089E-15 2.00000 1.60541 1.60541 0.222045E-15 2.50000 1.77852 1.77852 0.222045E-15 3.00000 1.84865 1.84865 0.222045E-15 3.50000 1.83313 1.83313 0.00000 4.00000 1.75820 1.75820 0.00000 4.50000 1.65414 1.65414 0.00000 R8_SIN_TEST: R8_SIN evaluates the sine function. X SIN(X) R8_SIN(X) Diff 0.00000 0.00000 0.00000 0.00000 0.261799 0.258819 0.258819 0.555112E-16 0.500000 0.479426 0.479426 0.00000 0.523599 0.500000 0.500000 0.00000 0.785398 0.707107 0.707107 0.111022E-15 1.00000 0.841471 0.841471 0.00000 1.04720 0.866025 0.866025 0.111022E-15 1.57080 1.00000 1.00000 0.111022E-15 2.00000 0.909297 0.909297 0.00000 3.00000 0.141120 0.141120 0.00000 3.14159 0.00000 0.122515E-15 0.122515E-15 4.00000 -0.756802 -0.756802 0.00000 5.00000 -0.958924 -0.958924 0.111022E-15 R8_SIN_DEG_TEST: R8_SIN_DEG evaluates the sine of a degree argument. X SIN_DEG(X) R8_SIN_DEG(X) Diff -5.00000 -0.871557E-01 -0.871557E-01 0.138778E-16 0.00000 0.00000 0.00000 0.00000 1.00000 0.174524E-01 0.174524E-01 0.00000 2.00000 0.348995E-01 0.348995E-01 0.00000 3.00000 0.523360E-01 0.523360E-01 0.00000 4.00000 0.697565E-01 0.697565E-01 0.00000 5.00000 0.871557E-01 0.871557E-01 0.138778E-16 10.0000 0.173648 0.173648 0.277556E-16 15.0000 0.258819 0.258819 0.00000 30.0000 0.500000 0.500000 0.555112E-16 45.0000 0.707107 0.707107 0.111022E-15 60.0000 0.866025 0.866025 0.00000 75.0000 0.965926 0.965926 0.00000 85.0000 0.996195 0.996195 0.00000 86.0000 0.997564 0.997564 0.00000 87.0000 0.998630 0.998630 0.00000 88.0000 0.999391 0.999391 0.00000 89.0000 0.999848 0.999848 0.00000 90.0000 1.00000 1.00000 0.00000 91.0000 0.999848 0.999848 0.00000 105.000 0.965926 0.965926 0.00000 180.000 0.00000 0.00000 0.00000 R8_SINH_TEST: R8_SINH evaluates the hyperbolic sine function. X SINH(X) R8_SINH(X) Diff -5.00000 -74.2032 -74.2032 0.00000 -1.00000 -1.17520 -1.17520 0.00000 0.00000 0.00000 0.00000 0.00000 0.100000 0.100167 0.100167 0.138778E-16 0.200000 0.201336 0.201336 0.277556E-16 0.300000 0.304520 0.304520 0.00000 0.400000 0.410752 0.410752 0.00000 0.500000 0.521095 0.521095 0.00000 0.600000 0.636654 0.636654 0.111022E-15 0.700000 0.758584 0.758584 0.111022E-15 0.800000 0.888106 0.888106 0.00000 0.900000 1.02652 1.02652 0.00000 1.00000 1.17520 1.17520 0.00000 2.00000 3.62686 3.62686 0.444089E-15 3.00000 10.0179 10.0179 0.00000 4.00000 27.2899 27.2899 0.355271E-14 5.00000 74.2032 74.2032 0.00000 10.0000 11013.2 11013.2 0.00000 R8_SPENCE_TEST: R8_SPENCE evaluates the dilogarithm function. X SPENCE(X) R8_SPENCE(X) Diff 0.00000 0.00000 0.00000 0.00000 0.500000E-01 0.506393E-01 0.506393E-01 0.00000 0.100000 0.102618 0.102618 0.277556E-16 0.150000 0.156035 0.156035 0.00000 0.200000 0.211004 0.211004 0.277556E-16 0.250000 0.267653 0.267653 0.00000 0.300000 0.326130 0.326130 0.00000 0.350000 0.386606 0.386606 0.00000 0.400000 0.449283 0.449283 0.555112E-16 0.450000 0.514399 0.514399 0.111022E-15 0.500000 0.582241 0.582241 0.00000 0.550000 0.653158 0.653158 0.00000 0.600000 0.727586 0.727586 0.00000 0.650000 0.806083 0.806083 0.00000 0.700000 0.889378 0.889378 0.222045E-15 0.750000 0.978469 0.978469 0.111022E-15 0.800000 1.07479 1.07479 0.444089E-15 0.850000 1.18058 1.18058 0.00000 0.900000 1.29971 1.29971 0.222045E-15 0.950000 1.44063 1.44063 0.444089E-15 1.00000 1.64493 1.64493 0.444089E-15 R8_SQRT_TEST: R8_SQRT evaluates the square root function. X SQRT(X) R8_SQRT(X) Diff 0.00000 0.00000 0.00000 0.00000 0.810000E-08 0.900000E-04 0.900000E-04 0.135525E-19 0.900000E-01 0.300000 0.300000 0.555112E-16 0.100000 0.316228 0.316228 0.111022E-15 0.400000 0.632456 0.632456 0.111022E-15 1.00000 1.00000 1.00000 0.222045E-15 2.00000 1.41421 1.41421 0.222045E-15 3.00000 1.73205 1.73205 0.222045E-15 3.14159 1.77245 1.77245 0.222045E-15 19.0000 4.35890 4.35890 0.00000 29.0000 5.38516 5.38516 0.00000 71.0000 8.42615 8.42615 0.00000 97.0000 9.84886 9.84886 0.00000 0.123457E+09 11111.1 11111.1 0.545697E-11 R8_TAN_TEST: R8_TAN evaluates the tangent function X TAN(X) R8_TAN(X) Diff 0.00000 0.00000 0.00000 0.00000 0.261799 0.267949 0.267949 0.555112E-16 0.500000 0.546302 0.546302 0.00000 0.523599 0.577350 0.577350 0.222045E-15 0.785398 1.00000 1.00000 0.00000 1.00000 1.55741 1.55741 0.222045E-15 1.04720 1.73205 1.73205 0.111022E-14 1.30900 3.73205 3.73205 0.888178E-15 1.43990 7.59575 7.59575 0.799361E-14 1.50535 15.2571 15.2571 0.195399E-13 2.00000 -2.18504 -2.18504 0.444089E-15 3.00000 -0.142547 -0.142547 0.277556E-16 3.14159 0.00000 -0.111022E-15 0.111022E-15 4.00000 1.15782 1.15782 0.444089E-15 5.00000 -3.38052 -3.38052 0.00000 R8_TANH_TEST: R8_TANH evaluates the hyperbolic tangent function. X TANH(X) R8_TANH(X) Diff -5.00000 -0.999909 -0.999909 0.111022E-15 -1.00000 -0.761594 -0.761594 0.00000 0.00000 0.00000 0.00000 0.00000 0.100000 0.996680E-01 0.996680E-01 0.00000 0.200000 0.197375 0.197375 0.00000 0.300000 0.291313 0.291313 0.00000 0.400000 0.379949 0.379949 0.00000 0.500000 0.462117 0.462117 0.555112E-16 0.600000 0.537050 0.537050 0.111022E-15 0.700000 0.604368 0.604368 0.00000 0.800000 0.664037 0.664037 0.111022E-15 0.900000 0.716298 0.716298 0.00000 1.00000 0.761594 0.761594 0.00000 2.00000 0.964028 0.964028 0.111022E-15 3.00000 0.995055 0.995055 0.111022E-15 4.00000 0.999329 0.999329 0.111022E-15 5.00000 0.999909 0.999909 0.111022E-15 10.0000 1.00000 1.00000 0.111022E-15 R8_UPAK_TEST: R8_UPAK converts an R8 to a mantissa and base 2 exponent. X Mantissa Exponent 64.0000 0.5000000000000000 7 128.000 0.5000000000000000 8 -64.0000 -0.5000000000000000 7 96.0000 0.7500000000000000 7 15.0000 0.9375000000000000 4 0.500000 0.5000000000000000 0 0.250000 0.5000000000000000 -1 0.625000 0.6250000000000000 0 64.6250 0.5048828125000000 7 3.14159 0.7853981633974483 2 0.00000 0.000000000000000 0 FN_TEST Normal end of execution. 13 March 2018 10:44:53.984 AM