05-Jan-2023 16:12:48 fn_test(): MATLAB/Octave version 4.2.2 Test fn(). I4_MACH_TEST I4_MACH reports the value of constants associated with integer computer arithmetic. Numbers associated with input/output units: I4_MACH(1) = the standard input unit. 5 I4_MACH(2) = the standard output unit. 6 I4_MACH(3) = the standard punch unit. 7 I4_MACH(4) = the standard error message unit. 6 Numbers associated with words: I4_MACH(5) = the number of bits per integer. 32 I4_MACH(6) = the number of characters per integer. 4 Numbers associated with integer values: Assume integers are represented in the S digit base A form: Sign * (X(S-1)*A^(S-1) + ... + X(1)*A + X(0)) where the digits X satisfy 0 <= X(1:S-1) < A. I4_MACH(7) = A, the base. 2 I4_MACH(8) = S, the number of base A digits. 31 I4_MACH(9) = A^S-1, the largest integer. 2147483647 Numbers associated with floating point values: Assume floating point numbers are represented in the T digit base B form: Sign * (B^E) * ((X(1)/B) + ... + (X(T)/B^T) ) where 0 <= X(1:T) < B, 0 < X(1) (unless the value being represented is 0), EMIN <= E <= EMAX. I4_MACH(10) = B, the base. 2 Numbers associated with single precision values: I4_MACH(11) = T, the number of base B digits. 24 I4_MACH(12) = EMIN, the smallest exponent E. -125 I4_MACH(13) = EMAX, the largest exponent E. 128 Numbers associated with double precision values: I4_MACH(14) = T, the number of base B digits. 53 I4_MACH(15) = EMIN, the smallest exponent E. -1021 I4_MACH(16) = EMAX, the largest exponent E. 1024 r8_acos_test(): r8_acos() evaluates the arc-cosine function. X ARCCOS(X) R8_ACOS(X) Diff -0.1 1.67096 1.67096 2.22045e-16 0 1.5708 1.5708 0 0.1 1.47063 1.47063 0 0.2 1.36944 1.36944 2.22045e-16 0.3 1.2661 1.2661 2.22045e-16 0.4 1.15928 1.15928 0 0.5 1.0472 1.0472 0 0.6 0.927295 0.927295 0 0.7 0.795399 0.795399 0 0.8 0.643501 0.643501 1.11022e-16 0.9 0.451027 0.451027 5.55112e-17 1 0 0 0 r8_acosh_test(): r8_acosh() evaluates the hyperbolic arccosine function X ARCCOSH(X) R8_ACOSH(X) Diff 1.0000 0 0 0 1.0100 0.141304 0.141304 8.32667e-17 1.1000 0.443568 0.443568 1.11022e-16 1.2000 0.622363 0.622363 1.11022e-16 1.3000 0.756433 0.756433 0 1.4000 0.867015 0.867015 1.11022e-16 1.5000 0.962424 0.962424 0 2.0000 1.31696 1.31696 2.22045e-16 3.0000 1.76275 1.76275 0 3.1416 1.81153 1.81153 0 4.0000 2.06344 2.06344 4.44089e-16 5.0000 2.29243 2.29243 0 10.0000 2.99322 2.99322 0 100.0000 5.29829 5.29829 0 1000.0000 7.6009 7.6009 0 r8_ai_test(): r8_ai() evaluates the Airy function Ai(X) X AIRY_AI(X) R8_AI(X) Diff 0 0.355028 0.355028 0 0.1 0.329203 0.329203 0 0.2 0.303703 0.303703 0 0.3 0.278806 0.278806 0 0.4 0.254742 0.254742 0 0.5 0.231694 0.231694 0 0.6 0.2098 0.2098 2.77556e-17 0.7 0.189162 0.189162 5.55112e-17 0.8 0.169846 0.169846 5.55112e-17 0.9 0.151887 0.151887 5.55112e-17 1 0.135292 0.135292 2.77556e-17 r8_aid_test(): r8_aid() evaluates the derivative of the Airy function Ai(x) X AIRY_AID(X) R8_AID(X) Diff 0.0000 -0.258819 -0.258819 0 0.1000 -0.25713 -0.25713 5.55112e-17 0.2000 -0.252405 -0.252405 5.55112e-17 0.3000 -0.245146 -0.245146 0 0.4000 -0.235832 -0.235832 2.77556e-17 0.5000 -0.224911 -0.224911 0 0.6000 -0.212793 -0.212793 2.77556e-17 0.7000 -0.199851 -0.199851 2.77556e-17 0.8000 -0.186413 -0.186413 0 0.9000 -0.172764 -0.172764 0 1.0000 -0.159147 -0.159147 0 r8_aint_test(): r8_aint() rounds an R8 towards 0. X AINT(X) R8_AINT(X) Diff -2.0100 -2 -2 0 -1.9900 -1 -1 0 -1.5000 -1 -1 0 -1.1000 -1 -1 0 -1.0100 -1 -1 0 -1.0000 -1 -1 0 -0.9900 0 -0 0 -0.9000 0 -0 0 -0.5100 0 -0 0 -0.5000 0 -0 0 -0.4900 0 -0 0 -0.0100 0 -0 0 0.0000 0 0 0 0.0100 0 0 0 0.4900 0 0 0 0.5000 0 0 0 0.5100 0 0 0 0.9000 0 0 0 0.9900 0 0 0 1.0000 1 1 0 1.0100 1 1 0 1.1000 1 1 0 1.5000 1 1 0 1.9900 1 1 0 2.0100 2 2 0 r8_asin_test(): r8_asin() evaluates the arc sine function X ARCSIN(X) R8_ASIN(X) Diff -0.1000 -0.100167 -0.100167 0 0.0000 0 0 0 0.1000 0.100167 0.100167 0 0.2000 0.201358 0.201358 0 0.3000 0.304693 0.304693 0 0.4000 0.411517 0.411517 5.55112e-17 0.5000 0.523599 0.523599 1.11022e-16 0.6000 0.643501 0.643501 0 0.7000 0.775397 0.775397 1.11022e-16 0.8000 0.927295 0.927295 1.11022e-16 0.9000 1.11977 1.11977 0 1.0000 1.5708 1.5708 0 r8_asinh_test(): r8_asinh() evaluates the arc hyperbolic sine function X ARCSINH(X) R8_ASINH(X) Diff -5.0000 -2.31244 -2.31244 0 -1.0000 -0.881374 -0.881374 0 0.0000 0 0 0 0.1000 0.0998341 0.0998341 1.38778e-17 0.2000 0.19869 0.19869 0 0.3000 0.295673 0.295673 0 0.4000 0.390035 0.390035 5.55112e-17 0.5000 0.481212 0.481212 0 0.6000 0.568825 0.568825 0 0.7000 0.652667 0.652667 0 0.8000 0.732668 0.732668 1.11022e-16 0.9000 0.808867 0.808867 0 1.0000 0.881374 0.881374 0 2.0000 1.44364 1.44364 0 3.0000 1.81845 1.81845 0 4.0000 2.09471 2.09471 0 5.0000 2.31244 2.31244 0 10.0000 2.99822 2.99822 0 100.0000 5.29834 5.29834 0 1000.0000 7.6009 7.6009 0 r8_atan_test(): r8_atan() evaluates the arc tangent function. X ARCTAN(X) R8_ATAN(X) Diff 0.0000 0 0 0 0.2500 0.244979 0.244979 2.77556e-17 0.3333 0.321751 0.321751 0 0.5000 0.463648 0.463648 5.55112e-17 1.0000 0.785398 0.785398 0 2.0000 1.10715 1.10715 2.22045e-16 3.0000 1.24905 1.24905 0 4.0000 1.32582 1.32582 0 5.0000 1.3734 1.3734 0 10.0000 1.47113 1.47113 0 20.0000 1.52084 1.52084 0 r8_atan2_test(): r8_atan2() evaluates the arctangent function X Y ARCTAN2(Y,X) R8_ATAN2(Y,X) Diff 0.0000 -1.0000 -1.5708 -1.5708 0 0.5000 -0.8660 -1.0472 -1.0472 2.22045e-16 0.8660 -0.5000 -0.523599 -0.523599 0 1.0000 0.0000 0 0 0 0.8660 0.5000 0.523599 0.523599 0 0.5000 0.8660 1.0472 1.0472 2.22045e-16 0.0000 1.0000 1.5708 1.5708 0 -0.5000 0.8660 2.0944 2.0944 0 -0.8660 0.5000 2.61799 2.61799 4.44089e-16 -1.0000 0.0000 3.14159 3.14159 0 -0.8660 -0.5000 -2.61799 -2.61799 4.44089e-16 -0.5000 -0.8660 -2.0944 -2.0944 0 0.0000 -1.0000 -1.5708 -1.5708 0 0.5000 -0.8660 -1.0472 -1.0472 2.22045e-16 0.8660 -0.5000 -0.523599 -0.523599 0 1.0000 0.0000 0 0 0 0.8660 0.5000 0.523599 0.523599 0 0.5000 0.8660 1.0472 1.0472 2.22045e-16 0.0000 1.0000 1.5708 1.5708 0 r8_atanh_test(): r8_atanh() evaluates the hyperbolic arctangent function. X ARCTANH(X) R8_ATANH(X) Diff -0.500000 -0.549306 -0.549306 0 0.000000 0 0 0 0.001000 0.001 0.001 0 0.100000 0.100335 0.100335 0 0.200000 0.202733 0.202733 2.77556e-17 0.300000 0.30952 0.30952 0 0.400000 0.423649 0.423649 5.55112e-17 0.500000 0.549306 0.549306 0 0.600000 0.693147 0.693147 0 0.700000 0.867301 0.867301 0 0.800000 1.09861 1.09861 0 0.900000 1.47222 1.47222 2.22045e-16 0.990000 2.64665 2.64665 4.44089e-16 0.999000 3.8002 3.8002 0 0.999999 7.25433 7.25433 1.43778e-11 R8_BESI0_TEST: R8_BESI0 evaluates the Bessel I0(x) function. X BESI0(X) R8_BESI0(X) Diff 0.0000 1 1 0 0.2000 1.01003 1.01003 0 0.4000 1.0404 1.0404 0 0.6000 1.09205 1.09205 4.44089e-16 0.8000 1.16651 1.16651 4.44089e-16 1.0000 1.26607 1.26607 6.66134e-16 1.2000 1.39373 1.39373 2.22045e-16 1.4000 1.5534 1.5534 4.44089e-16 1.6000 1.74998 1.74998 4.44089e-16 1.8000 1.98956 1.98956 0 2.0000 2.27959 2.27959 4.44089e-16 2.5000 3.28984 3.28984 4.44089e-16 3.0000 4.88079 4.88079 0 3.5000 7.3782 7.3782 8.88178e-16 4.0000 11.3019 11.3019 1.77636e-15 4.5000 17.4812 17.4812 3.55271e-15 5.0000 27.2399 27.2399 0 6.0000 67.2344 67.2344 1.42109e-14 8.0000 427.564 427.564 5.68434e-14 10.0000 2815.72 2815.72 4.54747e-13 R8_BESI1_TEST: R8_BESI1 evaluates the Bessel I1(x) function X BESI1(X) R8_BESI1(X) Diff 0.0000 0 0 0 0.2000 0.100501 0.100501 4.16334e-17 0.4000 0.204027 0.204027 2.77556e-17 0.6000 0.313704 0.313704 0 0.8000 0.432865 0.432865 5.55112e-17 1.0000 0.565159 0.565159 0 1.2000 0.714678 0.714678 0 1.4000 0.886092 0.886092 2.22045e-16 1.6000 1.08481 1.08481 4.44089e-16 1.8000 1.31717 1.31717 0 2.0000 1.59064 1.59064 0 2.5000 2.51672 2.51672 4.44089e-16 3.0000 3.95337 3.95337 4.44089e-16 3.5000 6.20583 6.20583 0 4.0000 9.75947 9.75947 0 4.5000 15.3892 15.3892 3.55271e-15 5.0000 24.3356 24.3356 3.55271e-15 6.0000 61.3419 61.3419 7.10543e-15 8.0000 399.873 399.873 0 10.0000 2670.99 2670.99 4.54747e-13 R8_BESJ0_TEST: R8_BESJ0 evaluates the Bessel J0(x) function X BESJ0(X) R8_BESJ0(X) Diff -5.0000 -0.177597 -0.177597 1.38778e-16 -4.0000 -0.39715 -0.39715 5.55112e-17 -3.0000 -0.260052 -0.260052 5.55112e-17 -2.0000 0.223891 0.223891 8.32667e-17 -1.0000 0.765198 0.765198 0 0.0000 1 1 0 1.0000 0.765198 0.765198 0 2.0000 0.223891 0.223891 8.32667e-17 3.0000 -0.260052 -0.260052 5.55112e-17 4.0000 -0.39715 -0.39715 5.55112e-17 5.0000 -0.177597 -0.177597 1.38778e-16 6.0000 0.150645 0.150645 5.55112e-17 7.0000 0.300079 0.300079 0 8.0000 0.171651 0.171651 2.77556e-17 9.0000 -0.0903336 -0.0903336 2.91434e-16 10.0000 -0.245936 -0.245936 0 11.0000 -0.17119 -0.17119 5.55112e-17 12.0000 0.0476893 0.0476893 2.70617e-16 13.0000 0.206926 0.206926 8.32667e-17 14.0000 0.171073 0.171073 0 15.0000 -0.0142245 -0.0142245 1.30104e-16 R8_BESJ1_TEST: R8_BESJ1 evaluates the Bessel J1(x) function X BESJ1(X) R8_BESJ1(X) Diff -5.0000 0.327579 0.327579 1.11022e-16 -4.0000 0.0660433 0.0660433 1.52656e-16 -3.0000 -0.339059 -0.339059 0 -2.0000 -0.576725 -0.576725 0 -1.0000 -0.440051 -0.440051 0 0.0000 0 0 0 1.0000 0.440051 0.440051 0 2.0000 0.576725 0.576725 0 3.0000 0.339059 0.339059 0 4.0000 -0.0660433 -0.0660433 1.52656e-16 5.0000 -0.327579 -0.327579 1.11022e-16 6.0000 -0.276684 -0.276684 0 7.0000 -0.00468282 -0.00468282 9.28077e-17 8.0000 0.234636 0.234636 0 9.0000 0.245312 0.245312 2.77556e-17 10.0000 0.0434727 0.0434727 5.55112e-17 11.0000 -0.176785 -0.176785 2.77556e-16 12.0000 -0.223447 -0.223447 1.11022e-16 13.0000 -0.0703181 -0.0703181 2.08167e-16 14.0000 0.133375 0.133375 0 15.0000 0.205104 0.205104 5.55112e-17 R8_BESK_TEST: R8_BESK evaluates Bessel K functtions K(NU,X). NU X BESK(X) R8_BESK(X) Diff 0.5 0.2000 2.29449 2.29449 4.44089e-16 0.5 1.0000 0.461069 0.461069 1.66533e-16 0.5 2.0000 0.119938 0.119938 2.77556e-16 0.5 2.5000 0.0650659 0.0650659 1.38778e-17 0.5 3.0000 0.036026 0.036026 6.93889e-18 0.5 5.0000 0.00377661 0.00377661 4.33681e-19 0.5 10.0000 1.79935e-05 1.79935e-05 0 0.5 20.0000 5.77637e-10 5.77637e-10 0 1.5 1.0000 0.922137 0.922137 1.11022e-16 1.5 2.0000 0.179907 0.179907 1.38778e-16 1.5 5.0000 0.00453194 0.00453194 0 1.5 10.0000 1.97928e-05 1.97928e-05 0 1.5 50.0000 3.48699e-23 3.48699e-23 5.87747e-39 2.5 1.0000 3.22748 3.22748 4.44089e-16 2.5 2.0000 0.389798 0.389798 5.55112e-17 2.5 5.0000 0.00649578 0.00649578 0 2.5 10.0000 2.39313e-05 2.39313e-05 0 2.5 50.0000 3.62784e-23 3.62784e-23 0 1.25 1.0000 0.731145 0.731145 1.11022e-16 1.25 2.0000 0.156748 0.156748 1.94289e-16 1.25 5.0000 0.00425739 0.00425739 3.46945e-18 1.25 10.0000 1.91554e-05 1.91554e-05 0 1.25 50.0000 3.46334e-23 3.46334e-23 1.76324e-38 2.75 1.0000 4.73118 4.73118 0 2.75 2.0000 0.497688 0.497688 1.11022e-16 2.75 5.0000 0.00730086 0.00730086 1.73472e-18 2.75 10.0000 2.54642e-05 2.54642e-05 6.77626e-21 2.75 50.0000 3.67528e-23 3.67528e-23 1.17549e-38 R8_BESK0_TEST: R8_BESK0 evaluates Bessel functions K0(X) X BESK0(X) R8_BESK0(X) Diff 0.1000 2.42707 2.42707 4.44089e-16 0.2000 1.7527 1.7527 0 0.4000 1.11453 1.11453 0 0.6000 0.777522 0.777522 1.11022e-16 0.8000 0.565347 0.565347 1.11022e-16 1.0000 0.421024 0.421024 1.66533e-16 1.2000 0.318508 0.318508 5.55112e-17 1.4000 0.243655 0.243655 0 1.6000 0.187955 0.187955 5.55112e-17 1.8000 0.145931 0.145931 0 2.0000 0.113894 0.113894 1.38778e-17 2.5000 0.0623476 0.0623476 0 3.0000 0.0347395 0.0347395 6.93889e-18 3.5000 0.0195989 0.0195989 0 4.0000 0.0111597 0.0111597 3.46945e-18 4.5000 0.00639986 0.00639986 0 5.0000 0.0036911 0.0036911 4.33681e-19 6.0000 0.00124399 0.00124399 2.1684e-19 8.0000 0.000146471 0.000146471 0 10.0000 1.77801e-05 1.77801e-05 3.38813e-21 R8_BESK1_TEST: R8_BESK1 evaluates Bessel functions K1(x) X BESK1(X) R8_BESK1(X) Diff 0.1000 9.85384 9.85384 0 0.2000 4.77597 4.77597 8.88178e-16 0.4000 2.18435 2.18435 0 0.6000 1.30283 1.30283 2.22045e-16 0.8000 0.861782 0.861782 0 1.0000 0.601907 0.601907 0 1.2000 0.434592 0.434592 0 1.4000 0.320836 0.320836 0 1.6000 0.240634 0.240634 2.77556e-17 1.8000 0.182623 0.182623 1.11022e-16 2.0000 0.139866 0.139866 2.77556e-17 2.5000 0.0738908 0.0738908 0 3.0000 0.0401564 0.0401564 6.93889e-18 3.5000 0.0222394 0.0222394 3.46945e-18 4.0000 0.0124835 0.0124835 0 4.5000 0.00707809 0.00707809 0 5.0000 0.00404461 0.00404461 8.67362e-19 6.0000 0.00134392 0.00134392 2.1684e-19 8.0000 0.000155369 0.000155369 2.71051e-20 10.0000 1.86488e-05 1.86488e-05 3.38813e-21 R8_BESY0_TEST: R8_BESY0 evaluates the Bessel Y0(X) function. X BESY0(X) R8_BESY0(X) Diff 0.1 -1.53424 -1.53424 2.22045e-16 1 0.088257 0.088257 4.16334e-17 2 0.510376 0.510376 0 3 0.37685 0.37685 0 4 -0.0169407 -0.0169407 3.1225e-17 5 -0.308518 -0.308518 5.55112e-17 6 -0.288195 -0.288195 0 7 -0.0259497 -0.0259497 1.11022e-16 8 0.223521 0.223521 5.55112e-17 9 0.249937 0.249937 5.55112e-17 10 0.0556712 0.0556712 8.32667e-17 11 -0.168847 -0.168847 0 12 -0.225237 -0.225237 8.32667e-17 13 -0.0782079 -0.0782079 2.91434e-16 14 0.127193 0.127193 2.77556e-17 15 0.205464 0.205464 2.77556e-17 R8_BESY1_TEST: R8_BESY1 evaluates the Bessel Y1(x) function X BESY1(X) R8_BESY1(X) Diff 0.1 -6.45895 -6.45895 8.88178e-16 1 -0.781213 -0.781213 1.11022e-16 2 -0.107032 -0.107032 0 3 0.324674 0.324674 0 4 0.397926 0.397926 5.55112e-17 5 0.147863 0.147863 2.77556e-17 6 -0.17501 -0.17501 2.77556e-17 7 -0.302667 -0.302667 1.11022e-16 8 -0.15806 -0.15806 5.55112e-17 9 0.104315 0.104315 1.38778e-17 10 0.249015 0.249015 5.55112e-17 11 0.163706 0.163706 3.05311e-16 12 -0.0570992 -0.0570992 4.09395e-16 13 -0.210081 -0.210081 8.32667e-17 14 -0.166645 -0.166645 5.55112e-17 15 0.0210736 0.0210736 4.85723e-17 R8_BETA_TEST: R8_BETA evaluates the Beta function. A B BETA(A,B) R8_BETA(A,B) Diff 0.2 1 5 5 8.88178e-16 0.4 1 2.5 2.5 4.44089e-16 0.6 1 1.66667 1.66667 6.66134e-16 0.8 1 1.25 1.25 2.22045e-16 1 0.2 5 5 8.88178e-16 1 0.4 2.5 2.5 4.44089e-16 1 1 1 1 0 2 2 0.166667 0.166667 5.55112e-17 3 3 0.0333333 0.0333333 0 4 4 0.00714286 0.00714286 0 5 5 0.0015873 0.0015873 2.1684e-19 6 2 0.0238095 0.0238095 3.46945e-18 6 3 0.00595238 0.00595238 0 6 4 0.00198413 0.00198413 0 6 5 0.000793651 0.000793651 1.84314e-18 6 6 0.00036075 0.00036075 1.6263e-18 7 7 8.32501e-05 8.32501e-05 1.49078e-19 R8_BETAI_TEST: R8_BETAI evaluates the incomplete Beta function. X A B BETAI(A,B) R8_BETAI(A,B) Diff 0.0100 0.5000 0.5 0.0637686 0.0637686 0 0.1000 0.5000 0.5 0.204833 0.204833 5.55112e-17 1.0000 0.5000 0.5 1 1 0 0.0000 1.0000 0.5 0 0 0 0.0100 1.0000 0.5 0.00501256 0.00501256 3.46945e-18 0.1000 1.0000 0.5 0.0513167 0.0513167 1.38778e-17 0.5000 1.0000 0.5 0.292893 0.292893 1.11022e-16 0.5000 1.0000 1 0.5 0.5 0 0.1000 2.0000 2 0.028 0.028 1.04083e-17 0.2000 2.0000 2 0.104 0.104 1.38778e-17 0.3000 2.0000 2 0.216 0.216 8.32667e-17 0.4000 2.0000 2 0.352 0.352 5.55112e-17 0.5000 2.0000 2 0.5 0.5 0 0.6000 2.0000 2 0.648 0.648 1.11022e-16 0.7000 2.0000 2 0.784 0.784 1.11022e-16 0.8000 2.0000 2 0.896 0.896 0 0.9000 2.0000 2 0.972 0.972 0 0.5000 5.5000 5 0.436191 0.436191 7.77156e-16 0.9000 10.0000 0.5 0.151641 0.151641 1.44329e-15 0.5000 10.0000 5 0.0897827 0.0897827 2.63678e-16 1.0000 10.0000 5 1 1 0 0.5000 10.0000 10 0.5 0.5 1.11022e-16 0.8000 20.0000 5 0.459877 0.459877 1.11022e-16 0.6000 20.0000 10 0.214682 0.214682 1.08247e-15 0.8000 20.0000 10 0.950736 0.950736 2.22045e-16 0.5000 20.0000 20 0.5 0.5 0 0.6000 20.0000 20 0.897941 0.897941 2.55351e-15 0.7000 30.0000 10 0.22413 0.22413 4.16334e-16 0.8000 30.0000 10 0.758641 0.758641 3.33067e-16 0.7000 40.0000 20 0.700178 0.700178 5.55112e-16 0.1000 1.0000 0.5 0.0513167 0.0513167 1.38778e-17 0.2000 1.0000 0.5 0.105573 0.105573 1.38778e-17 0.3000 1.0000 0.5 0.16334 0.16334 0 0.4000 1.0000 0.5 0.225403 0.225403 8.32667e-17 0.2000 1.0000 2 0.36 0.36 0 0.2000 1.0000 3 0.488 0.488 1.11022e-16 0.2000 1.0000 4 0.5904 0.5904 1.11022e-16 0.2000 1.0000 5 0.67232 0.67232 1.11022e-16 0.3000 2.0000 2 0.216 0.216 8.32667e-17 0.3000 3.0000 2 0.0837 0.0837 5.55112e-17 0.3000 4.0000 2 0.03078 0.03078 1.73472e-17 0.3000 5.0000 2 0.010935 0.010935 3.46945e-18 0.2256 1.3062 11.76 0.918885 0.918885 2.22045e-16 0.0336 1.3062 11.76 0.21053 0.21053 3.88578e-16 0.0295 1.3062 11.76 0.182413 0.182413 2.498e-16 R8_BI_TEST: R8_BI evaluates the Airy Bi(X) function X AIRY_BI(X) R8_BI(X) Diff 0 0.614927 0.614927 0 0.1 0.659862 0.659862 1.11022e-16 0.2 0.705464 0.705464 0 0.3 0.752486 0.752486 1.11022e-16 0.4 0.801773 0.801773 1.11022e-16 0.5 0.854277 0.854277 0 0.6 0.911063 0.911063 1.11022e-16 0.7 0.973329 0.973329 1.11022e-16 0.8 1.04242 1.04242 2.22045e-16 0.9 1.11987 1.11987 2.22045e-16 1 1.20742 1.20742 2.22045e-16 R8_BID_TEST: R8_BID evaluates the derivative of the Airy function Bi(X) X AIRY_BID(X) R8_BID(X) Diff 0.0000 0.448288 0.448288 5.55112e-17 0.1000 0.451513 0.451513 0 0.2000 0.461789 0.461789 5.55112e-17 0.3000 0.480049 0.480049 5.55112e-17 0.4000 0.507282 0.507282 1.11022e-16 0.5000 0.544573 0.544573 0 0.6000 0.593144 0.593144 0 0.7000 0.654406 0.654406 0 0.8000 0.730007 0.730007 1.11022e-16 0.9000 0.821904 0.821904 1.11022e-16 1.0000 0.932436 0.932436 0 R8_BINOM_TEST: R8_BINOM evaluates the binomial coefficient. A B BINOM(A,B) R8_BINOM(A,B) Diff 1 0 1 1 0 6 1 6 6 0 6 3 20 20 0 6 5 6 6 0 15 1 15 15 0 15 3 455 455 0 15 5 3003 3003 0 15 7 6435 6435 0 15 9 5005 5005 0 15 11 1365 1365 0 15 13 105 105 0 25 1 25 25 0 25 3 2300 2300 0 25 5 53130 53130 0 25 7 480700 480700 0 25 9 2042975 2042975 0 25 11 4457400 4457400 0 25 13 5200300 5200300 0 25 15 3268760 3268760 0 25 17 1081575 1081575 0 R8_CBRT_TEST: R8_CBRT evaluates the cube root function. X CBRT(X) R8_CBRT(X) Diff 0.0000 0 0 0 -0.0000 -0.0020083 -0.0020083 4.33681e-19 0.0900 0.44814 0.44814 0 -0.1000 -0.464159 -0.464159 5.55112e-17 0.4000 0.736806 0.736806 1.11022e-16 -1.0000 -1 -1 0 2.0000 1.25992 1.25992 0 -3.0000 -1.44225 -1.44225 2.22045e-16 3.1416 1.46459 1.46459 0 -19.0000 -2.6684 -2.6684 4.44089e-16 29.0000 3.07232 3.07232 4.44089e-16 -71.0000 -4.14082 -4.14082 0 97.0000 4.5947 4.5947 8.88178e-16 -123456789.0000 -497.934 -497.934 0 R8_CHI_TEST: R8_CHI evaluates the hyperbolic cosine integral. X CHI(X) R8_CHI(X) Diff 0.5000 -0.0527768 -0.0527768 6.93889e-18 0.6000 0.157751 0.157751 8.32667e-17 0.7000 0.345569 0.345569 1.11022e-16 0.8000 0.5184 0.5184 1.11022e-16 0.9000 0.681314 0.681314 1.11022e-16 1.0000 0.837867 0.837867 1.11022e-16 1.2000 1.14184 1.14184 6.66134e-16 1.4000 1.44549 1.44549 2.22045e-16 1.6000 1.75951 1.75951 0 1.8000 2.09258 2.09258 8.88178e-16 2.0000 2.45267 2.45267 4.44089e-16 2.5000 3.52443 3.52443 4.44089e-16 3.0000 4.96039 4.96039 8.88178e-16 3.5000 6.95919 6.95919 0 4.0000 9.81355 9.81355 3.55271e-15 4.5000 13.9658 13.9658 3.55271e-15 R8_CHU_TEST: R8_CHU evaluates the hypergeometric U function. A B X CHU(A,B,X) R8_CHU(A,B,X) Diff -2.5000 3.3000 0.25 -68.6936 -68.6936 5.68434e-14 -0.5000 1.1000 0.25 -0.00297106 -0.00297106 4.75748e-16 0.5000 1.1000 0.25 1.50086 1.50086 1.11022e-15 2.5000 3.3000 0.25 20.6147 20.6147 1.06581e-14 -2.5000 3.3000 1.55 7.45638 7.45638 1.77636e-15 -0.5000 1.1000 1.55 1.01558 1.01558 2.22045e-16 0.5000 1.1000 1.55 0.734465 0.734465 9.99201e-16 2.5000 3.3000 1.55 0.280464 0.280464 1.66533e-16 -2.5000 3.3000 2.85 3.45082 3.45082 5.77316e-15 -0.5000 1.1000 2.85 1.51566 1.51566 4.44089e-16 0.5000 1.1000 2.85 0.560421 0.560421 1.11022e-16 2.5000 3.3000 2.85 0.0648971 0.0648971 0 0.8250 6.7000 0.25 223432 223432 5.82077e-11 1.1000 6.7000 0.25 263079 263079 1.74623e-10 1.6500 6.7000 0.25 269803 269803 1.16415e-10 3.3000 6.7000 0.25 82809.3 82809.3 4.36557e-11 0.8250 6.7000 1.55 26.4657 26.4657 3.55271e-15 1.1000 6.7000 1.55 28.0935 28.0935 7.10543e-15 1.6500 6.7000 1.55 23.8892 23.8892 0 3.3000 6.7000 1.55 4.53388 4.53388 8.88178e-16 0.8250 6.7000 2.85 3.02245 3.02245 8.88178e-16 1.1000 6.7000 2.85 2.80407 2.80407 1.33227e-15 1.6500 6.7000 2.85 1.92626 1.92626 2.22045e-16 3.3000 6.7000 2.85 0.230205 0.230205 0 R8_CI_TEST: R8_CI evaluates the cosine integral. X CI(X) R8_CI(X) Diff 0.5000 -0.177784 -0.177784 5.55112e-17 0.6000 -0.0222707 -0.0222707 7.63278e-17 0.7000 0.100515 0.100515 6.93889e-17 0.8000 0.198279 0.198279 2.22045e-16 0.9000 0.276068 0.276068 5.55112e-17 1.0000 0.337404 0.337404 1.11022e-16 1.2000 0.420459 0.420459 5.55112e-17 1.4000 0.462007 0.462007 5.55112e-17 1.6000 0.471733 0.471733 1.66533e-16 1.8000 0.456811 0.456811 1.11022e-16 2.0000 0.422981 0.422981 1.11022e-16 2.5000 0.285871 0.285871 1.11022e-16 3.0000 0.11963 0.11963 1.52656e-16 3.5000 -0.0321285 -0.0321285 2.77556e-17 4.0000 -0.140982 -0.140982 8.32667e-17 4.5000 -0.193491 -0.193491 5.55112e-17 R8_CIN_TEST: R8_CIN evaluates the alternate hyperbolic cosine integral. X CIN(X) R8_CIN(X) Diff 0.5000 0.0618526 0.0618526 6.93889e-18 0.6000 0.0886607 0.0886607 1.38778e-17 0.7000 0.120026 0.120026 4.16334e-17 0.8000 0.155793 0.155793 5.55112e-17 0.9000 0.195787 0.195787 0 1.0000 0.239812 0.239812 0 1.2000 0.339078 0.339078 5.55112e-17 1.4000 0.451681 0.451681 5.55112e-17 1.6000 0.575487 0.575487 0 1.8000 0.708191 0.708191 0 2.0000 0.847382 0.847382 0 2.5000 1.20764 1.20764 4.44089e-16 3.0000 1.5562 1.5562 4.44089e-16 3.5000 1.86211 1.86211 2.22045e-16 4.0000 2.10449 2.10449 0 4.5000 2.27478 2.27478 4.44089e-16 R8_CINH_TEST: R8_CINH evaluates the alternate hyperbolic cosine integral. X CINH(X) R8_CINH(X) Diff 0.0000 0 0 0 0.5000 0.0631547 0.0631547 1.38778e-17 0.6000 0.0913609 0.0913609 1.38778e-17 0.7000 0.125028 0.125028 0 0.8000 0.164328 0.164328 1.11022e-16 0.9000 0.209459 0.209459 2.77556e-17 1.0000 0.260651 0.260651 0 1.2000 0.382305 0.382305 1.11022e-16 1.4000 0.531806 0.531806 1.11022e-16 1.6000 0.712287 0.712287 2.22045e-16 1.8000 0.927575 0.927575 0 2.0000 1.1823 1.1823 2.22045e-16 2.5000 2.03092 2.03092 4.44089e-16 3.0000 3.28456 3.28456 4.44089e-16 3.5000 5.12921 5.12921 8.88178e-16 4.0000 7.85004 7.85004 3.55271e-15 4.5000 11.8845 11.8845 5.32907e-15 R8_COS_TEST: R8_COS evaluates the cosine function. X COS(X) R8_COS(X) Diff 0.0000 1 1 0 0.2618 0.965926 0.965926 1.11022e-16 0.5000 0.877583 0.877583 1.11022e-16 0.5236 0.866025 0.866025 0 0.7854 0.707107 0.707107 0 1.0000 0.540302 0.540302 0 1.0472 0.5 0.5 5.55112e-17 1.5708 0 6.12574e-17 6.12574e-17 2.0000 -0.416147 -0.416147 0 3.0000 -0.989992 -0.989992 0 3.1416 -1 -1 1.11022e-16 4.0000 -0.653644 -0.653644 0 5.0000 0.283662 0.283662 5.55112e-17 R8_COS_DEG_TEST: R8_COS_DEG evaluates the cosine of an argument in degrees. X COS_DEG(X) R8_COS_DEG(X) Diff -5.0000 0.996195 0.996195 0 0.0000 1 1 0 1.0000 0.999848 0.999848 0 2.0000 0.999391 0.999391 0 3.0000 0.99863 0.99863 0 4.0000 0.997564 0.997564 0 5.0000 0.996195 0.996195 0 10.0000 0.984808 0.984808 0 15.0000 0.965926 0.965926 0 30.0000 0.866025 0.866025 1.11022e-16 45.0000 0.707107 0.707107 0 60.0000 0.5 0.5 1.11022e-16 75.0000 0.258819 0.258819 0 85.0000 0.0871557 0.0871557 4.16334e-17 86.0000 0.0697565 0.0697565 6.93889e-17 87.0000 0.052336 0.052336 1.31839e-16 88.0000 0.0348995 0.0348995 1.11022e-16 89.0000 0.0174524 0.0174524 8.67362e-17 90.0000 0 0 0 91.0000 -0.0174524 -0.0174524 3.46945e-17 105.0000 -0.258819 -0.258819 1.11022e-16 180.0000 -1 -1 0 R8_COSH_TEST: R8_COSH evaluates the hyperbolic cosine function. X COSH(X) R8_COSH(X) Diff -5.0000 74.2099 74.2099 0 -1.0000 1.54308 1.54308 0 0.0000 1 1 0 0.1000 1.005 1.005 0 0.2000 1.02007 1.02007 0 0.3000 1.04534 1.04534 0 0.4000 1.08107 1.08107 2.22045e-16 0.5000 1.12763 1.12763 0 0.6000 1.18547 1.18547 2.22045e-16 0.7000 1.25517 1.25517 0 0.8000 1.33743 1.33743 2.22045e-16 0.9000 1.43309 1.43309 2.22045e-16 1.0000 1.54308 1.54308 0 2.0000 3.7622 3.7622 0 3.0000 10.0677 10.0677 0 4.0000 27.3082 27.3082 0 5.0000 74.2099 74.2099 0 10.0000 11013.2 11013.2 1.81899e-12 R8_COT_TEST: R8_COT evaluates the cotangent function. X COT(X) R8_COT(X) Diff 0.0833 11.9722 11.9722 0 0.2618 3.73205 3.73205 0 0.5000 1.83049 1.83049 2.22045e-16 0.5236 1.73205 1.73205 0 0.7854 1 1 0 1.0000 0.642093 0.642093 1.11022e-16 1.0472 0.57735 0.57735 1.11022e-16 1.3090 0.267949 0.267949 5.55112e-17 1.5708 0 -0 0 1.4399 0.131652 0.131652 8.32667e-17 1.5053 0.0655435 0.0655435 1.38778e-16 2.0000 -0.457658 -0.457658 1.11022e-16 3.0000 -7.01525 -7.01525 8.88178e-16 4.0000 0.863691 0.863691 0 5.0000 -0.295813 -0.295813 5.55112e-17 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 0.0290247 4 0.00362759 5 0.000367891 6 3.07777e-05 7 2.19352e-06 8 1.37199e-07 9 7.67356e-09 10 3.5653e-10 11 1.62784e-11 12 6.53432e-13 R8_DAWSON_TEST: R8_DAWSON evaluates Dawson's integral. X DAWSON(X) R8_DAWSON(X) Diff 0.0000 0 0 0 0.1000 0.099336 0.099336 1.38778e-17 0.2000 0.194751 0.194751 5.55112e-17 0.3000 0.282632 0.282632 5.55112e-17 0.4000 0.359943 0.359943 0 0.5000 0.424436 0.424436 0 0.6000 0.474763 0.474763 5.55112e-17 0.7000 0.510504 0.510504 0 0.8000 0.532102 0.532102 0 0.9000 0.540724 0.540724 1.11022e-16 1.0000 0.53808 0.53808 0 1.1000 0.526207 0.526207 1.11022e-16 1.2000 0.507273 0.507273 2.22045e-16 1.3000 0.483398 0.483398 1.11022e-16 1.4000 0.456507 0.456507 0 1.5000 0.428249 0.428249 5.55112e-17 1.6000 0.39994 0.39994 0 1.7000 0.372559 0.372559 5.55112e-17 1.8000 0.346773 0.346773 0 1.9000 0.322974 0.322974 1.11022e-16 2.0000 0.30134 0.30134 5.55112e-17 R8_E1_TEST: R8_E1 evaluates the E1(x) exponential function. X E1(X) R8_E1(X) Diff 0.5000 0.559774 0.559774 0 0.6000 0.45438 0.45438 0 0.7000 0.373769 0.373769 5.55112e-17 0.8000 0.310597 0.310597 0 0.9000 0.260184 0.260184 5.55112e-17 1.0000 0.219384 0.219384 5.55112e-17 1.1000 0.185991 0.185991 5.55112e-17 1.2000 0.158408 0.158408 2.77556e-17 1.3000 0.135451 0.135451 2.77556e-17 1.4000 0.116219 0.116219 1.38778e-17 1.5000 0.10002 0.10002 4.16334e-17 1.6000 0.0863083 0.0863083 2.77556e-17 1.7000 0.0746546 0.0746546 0 1.8000 0.0647131 0.0647131 1.38778e-17 1.9000 0.0562044 0.0562044 0 2.0000 0.0489005 0.0489005 6.93889e-18 R8_EI_TEST: R8_EI evaluates the exponential integral Ei(X). X EI(X) R8_EI(X) Diff 0.5000 0.45422 0.45422 0 0.6000 0.769881 0.769881 0 0.7000 1.06491 1.06491 6.66134e-16 0.8000 1.3474 1.3474 0 0.9000 1.62281 1.62281 4.44089e-16 1.0000 1.89512 1.89512 2.22045e-16 1.1000 2.16738 2.16738 1.33227e-15 1.2000 2.44209 2.44209 4.44089e-16 1.3000 2.7214 2.7214 1.77636e-15 1.4000 3.00721 3.00721 0 1.5000 3.30129 3.30129 1.33227e-15 1.6000 3.60532 3.60532 8.88178e-16 1.7000 3.92096 3.92096 8.88178e-16 1.8000 4.24987 4.24987 8.88178e-16 1.9000 4.59371 4.59371 8.88178e-16 2.0000 4.95423 4.95423 8.88178e-16 R8_ERF_TEST: R8_ERF evaluates the error function. X ERF(X) R8_ERF(X) Diff 0.0000 0 0 0 0.1000 0.112463 0.112463 0 0.2000 0.222703 0.222703 2.77556e-17 0.3000 0.328627 0.328627 0 0.4000 0.428392 0.428392 5.55112e-17 0.5000 0.5205 0.5205 0 0.6000 0.603856 0.603856 0 0.7000 0.677801 0.677801 1.11022e-16 0.8000 0.742101 0.742101 0 0.9000 0.796908 0.796908 1.11022e-16 1.0000 0.842701 0.842701 1.11022e-16 1.1000 0.880205 0.880205 0 1.2000 0.910314 0.910314 1.11022e-16 1.3000 0.934008 0.934008 0 1.4000 0.952285 0.952285 0 1.5000 0.966105 0.966105 1.11022e-16 1.6000 0.976348 0.976348 0 1.7000 0.98379 0.98379 1.11022e-16 1.8000 0.989091 0.989091 1.11022e-16 1.9000 0.99279 0.99279 0 2.0000 0.995322 0.995322 0 R8_ERFC_TEST: R8_ERFC evaluates the complementary error function. X ERFC(X) R8_ERFC(X) Diff 0.0000 1 1 0 0.2000 0.777297 0.777297 0 0.4000 0.571608 0.571608 1.11022e-16 0.6000 0.396144 0.396144 0 0.8000 0.257899 0.257899 0 1.0000 0.157299 0.157299 1.11022e-16 1.2000 0.089686 0.089686 0 1.4000 0.0477149 0.0477149 1.38778e-17 1.6000 0.0236516 0.0236516 6.93889e-18 1.8000 0.0109095 0.0109095 6.93889e-18 2.0000 0.00467773 0.00467773 8.67362e-19 2.2000 0.00186285 0.00186285 1.0842e-18 2.4000 0.000688514 0.000688514 2.1684e-19 2.6000 0.000236034 0.000236034 1.6263e-19 2.8000 7.50132e-05 7.50132e-05 6.77626e-20 3.0000 2.20905e-05 2.20905e-05 6.77626e-21 3.2000 6.02576e-06 6.02576e-06 1.35525e-20 3.4000 1.52199e-06 1.52199e-06 2.11758e-21 3.6000 3.55863e-07 3.55863e-07 3.70577e-22 3.8000 7.70039e-08 7.70039e-08 5.29396e-23 4.0000 1.54173e-08 1.54173e-08 3.30872e-24 R8_EXP_TEST: R8_EXP evaluates the exponential function. X EXP(X) R8_EXP(X) Diff -10.0000 4.53999e-05 4.53999e-05 0 -5.0000 0.00673795 0.00673795 0 -1.0000 0.367879 0.367879 0 0.0000 1 1 0 0.0000 1 1 0 0.0001 1.0001 1.0001 0 0.0010 1.001 1.001 0 0.0100 1.01005 1.01005 0 0.1000 1.10517 1.10517 0 0.2000 1.2214 1.2214 0 0.3000 1.34986 1.34986 0 0.4000 1.49182 1.49182 0 0.5000 1.64872 1.64872 0 0.6000 1.82212 1.82212 0 0.7000 2.01375 2.01375 4.44089e-16 0.8000 2.22554 2.22554 4.44089e-16 0.9000 2.4596 2.4596 4.44089e-16 1.0000 2.71828 2.71828 0 2.0000 7.38906 7.38906 0 3.1416 23.1407 23.1407 3.55271e-15 5.0000 148.413 148.413 0 10.0000 22026.5 22026.5 0 20.0000 4.85165e+08 4.85165e+08 0 40.0000 2.35385e+17 2.35385e+17 32 R8_FAC_TEST: R8_FAC evaluates the factorial function. N FAC(N) R8_FAC(N) Diff 0 1 1 0 1 1 1 0 2 2 2 0 3 6 6 0 4 24 24 0 5 120 120 0 6 720 720 0 7 5040 5040 0 8 40320 40320 0 9 362880 362880 0 10 3.6288e+06 3.6288e+06 0 11 3.99168e+07 3.99168e+07 0 12 4.79002e+08 4.79002e+08 0 13 6.22702e+09 6.22702e+09 0 14 8.71783e+10 8.71783e+10 0 15 1.30767e+12 1.30767e+12 0 16 2.09228e+13 2.09228e+13 0 17 3.55687e+14 3.55687e+14 0 18 6.40237e+15 6.40237e+15 0 19 1.21645e+17 1.21645e+17 0 20 2.4329e+18 2.4329e+18 0 25 1.55112e+25 1.55112e+25 4.29497e+09 50 3.04141e+64 3.04141e+64 3.62452e+50 100 9.33262e+157 9.33262e+157 1.90232e+144 150 5.71338e+262 5.71338e+262 4.99922e+249 R8_GAMIC_TEST: R8_GAMIC evaluates the incomplete Gamma function. A X GAMIC(A,X) R8_GAMIC(A,X) Diff 0.1000 0.0300 2.4903 2.4903 1.33227e-15 0.1000 0.3000 0.871837 0.871837 0 0.1000 1.5000 0.107921 0.107921 2.77556e-17 0.5000 0.0750 1.23812 1.23812 4.44089e-16 0.5000 0.7500 0.39113 0.39113 2.22045e-16 0.5000 3.5000 0.0144472 0.0144472 0 1.0000 0.1000 0.904837 0.904837 1.11022e-16 1.0000 1.0000 0.367879 0.367879 5.55112e-17 1.0000 5.0000 0.00673795 0.00673795 0 1.1000 0.1000 0.882797 0.882797 0 1.1000 1.0000 0.390833 0.390833 2.22045e-16 1.1000 5.0000 0.00805146 0.00805146 3.46945e-18 2.0000 0.1500 0.989814 0.989814 0 2.0000 1.5000 0.557825 0.557825 1.11022e-16 2.0000 7.0000 0.00729506 0.00729506 1.73472e-18 6.0000 2.5000 114.957 114.957 9.9476e-14 6.0000 12.0000 2.44092 2.44092 2.66454e-15 11.0000 16.0000 280855 280855 5.82077e-11 26.0000 25.0000 8.57648e+24 8.57648e+24 3.22123e+09 41.0000 45.0000 2.08503e+47 2.08503e+47 2.83954e+32 R8_GAMIT_TEST: R8_GAMIT evaluates Tricomi's incomplete Gamma function A X GAMIT(A,X) R8_GAMIT(A,X) Diff 0.1000 0.03 1.04829 1.04829 4.44089e-16 0.1000 0.3 1.02458 1.02458 2.22045e-16 0.1000 1.5 0.949371 0.949371 0 0.5000 0.075 1.10079 1.10079 2.22045e-16 0.5000 0.75 0.899891 0.899891 1.11022e-16 0.5000 3.5 0.530166 0.530166 0 1.0000 0.1 0.951626 0.951626 0 1.0000 1 0.632121 0.632121 1.11022e-16 1.0000 5 0.198652 0.198652 2.77556e-17 1.1000 0.1 0.907178 0.907178 0 1.1000 1 0.589181 0.589181 0 1.1000 5 0.168827 0.168827 5.55112e-17 2.0000 0.15 0.452703 0.452703 0 2.0000 1.5 0.196522 0.196522 0 2.0000 7 0.0202593 0.0202593 6.93889e-18 6.0000 2.5 0.000172118 0.000172118 8.13152e-20 6.0000 12 3.28086e-07 3.28086e-07 3.17637e-22 11.0000 16 5.2444e-14 5.2444e-14 9.46633e-29 26.0000 25 2.01346e-37 2.01346e-37 4.17619e-53 41.0000 45 1.23062e-68 1.23062e-68 1.77076e-82 R8_GAML_TEST: R8_GAML returns bounds for the argument of the gamma function. Lower limit XMIN = -170.345 Upper limit XMAX = 171.345 R8_GAMMA_TEST: R8_GAMMA computes the Gamma function. X GAMMA(X) R8_GAMMA(X) Diff -0.5000 -3.54491 -3.54491 0 -0.0100 -100.587 -100.587 1.13687e-13 0.0100 99.4326 99.4326 9.9476e-14 0.1000 9.51351 9.51351 8.88178e-15 0.2000 4.59084 4.59084 1.77636e-15 0.4000 2.21816 2.21816 4.44089e-16 0.5000 1.77245 1.77245 0 0.6000 1.48919 1.48919 2.22045e-16 0.8000 1.16423 1.16423 2.22045e-16 1.0000 1 1 0 1.1000 0.951351 0.951351 0 1.2000 0.918169 0.918169 0 1.3000 0.897471 0.897471 0 1.4000 0.887264 0.887264 0 1.5000 0.886227 0.886227 0 1.6000 0.893515 0.893515 0 1.7000 0.908639 0.908639 0 1.8000 0.931384 0.931384 0 1.9000 0.961766 0.961766 0 2.0000 1 1 0 3.0000 2 2 0 4.0000 6 6 0 10.0000 362880 362880 0 20.0000 1.21645e+17 1.21645e+17 80 30.0000 8.84176e+30 8.84176e+30 7.54353e+16 R8_GAMR_TEST: R8_GAMR computes 1/Gamma(x). X 1/GAMMA(X) R8_GAMR(X) Diff -0.5 -0.282095 -0.282095 0 -0.01 -0.00994162 -0.00994162 1.21431e-17 0.01 0.0100571 0.0100571 1.04083e-17 0.1 0.105114 0.105114 9.71445e-17 0.2 0.217825 0.217825 8.32667e-17 0.4 0.450824 0.450824 1.11022e-16 0.5 0.56419 0.56419 0 0.6 0.671505 0.671505 0 0.8 0.858937 0.858937 1.11022e-16 1 1 1 0 1.1 1.05114 1.05114 0 1.2 1.08912 1.08912 0 1.3 1.11424 1.11424 0 1.4 1.12706 1.12706 0 1.5 1.12838 1.12838 0 1.6 1.11917 1.11917 0 1.7 1.10055 1.10055 0 1.8 1.07367 1.07367 0 1.9 1.03975 1.03975 0 2 1 1 0 3 0.5 0.5 0 4 0.166667 0.166667 0 10 2.75573e-06 2.75573e-06 0 20 8.22064e-18 8.22064e-18 4.62223e-33 30 1.131e-31 1.131e-31 9.63393e-46 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 1 0.1 2 0.01 2 0.001 3 0.0001 3 1e-05 4 1e-06 4 1e-07 5 1e-08 5 1e-09 6 1e-10 6 1e-11 7 1e-12 7 1e-13 7 1e-14 8 1e-15 8 1e-16 9 1e-17 9 R8_INT_TEST: R8_INT computes the integer part of an R8. X INT(X) R8_INT(X) Diff -2.0100 -2 -2 0 -1.9900 -1 -1 0 -1.5000 -1 -1 0 -1.1000 -1 -1 0 -1.0100 -1 -1 0 -1.0000 -1 -1 0 -0.9900 0 -0 0 -0.9000 0 -0 0 -0.5100 0 -0 0 -0.5000 0 -0 0 -0.4900 0 -0 0 -0.0100 0 -0 0 0.0000 0 0 0 0.0100 0 0 0 0.4900 0 0 0 0.5000 0 0 0 0.5100 0 0 0 0.9000 0 0 0 0.9900 0 0 0 1.0000 1 1 0 1.0100 1 1 0 1.1000 1 1 0 1.5000 1 1 0 1.9900 1 1 0 2.0100 2 2 0 R8_LBETA_TEST: R8_LBETA evaluates the logarithm of the Beta function. A B LBETA(A,B) R8_LBETA(A,B) Diff 0.2000 1 1.60944 1.60944 4.44089e-16 0.4000 1 0.916291 0.916291 1.11022e-16 0.6000 1 0.510826 0.510826 1.11022e-16 0.8000 1 0.223144 0.223144 2.22045e-16 1.0000 0.2 1.60944 1.60944 4.44089e-16 1.0000 0.4 0.916291 0.916291 1.11022e-16 1.0000 1 0 0 0 2.0000 2 -1.79176 -1.79176 0 3.0000 3 -3.4012 -3.4012 4.44089e-16 4.0000 4 -4.94164 -4.94164 0 5.0000 5 -6.44572 -6.44572 8.88178e-16 6.0000 2 -3.73767 -3.73767 4.44089e-16 6.0000 3 -5.12396 -5.12396 0 6.0000 4 -6.22258 -6.22258 0 6.0000 5 -7.13887 -7.13887 2.66454e-15 6.0000 6 -7.92732 -7.92732 4.44089e-15 7.0000 7 -9.39366 -9.39366 1.77636e-15 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)) Log(|Gamma(x)|) Diff 0.2 1.52406 1 1.52406 6.66134e-16 0.4 0.796678 1 0.796678 2.22045e-16 0.6 0.398234 1 0.398234 5.55112e-17 0.8 0.15206 1 0.15206 0 1 0 1 0 0 1.1 -0.0498724 1 -0.0498724 1.38778e-17 1.2 -0.0853741 1 -0.0853741 2.77556e-17 1.3 -0.108175 1 -0.108175 6.93889e-17 1.4 -0.119613 1 -0.119613 1.38778e-16 1.5 -0.120782 1 -0.120782 2.77556e-17 1.6 -0.112592 1 -0.112592 6.93889e-17 1.7 -0.0958077 1 -0.0958077 1.38778e-17 1.8 -0.0710839 1 -0.0710839 1.38778e-17 1.9 -0.0389843 1 -0.0389843 1.38778e-17 2 0 1 0 0 3 0.693147 1 0.693147 0 4 1.79176 1 1.79176 0 10 12.8018 1 12.8018 0 20 39.3399 1 39.3399 0 30 71.257 1 71.257 1.42109e-14 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 0.00833056 0.00833056 1.62197e-15 20.0000 0.00416632 0.00416632 6.67869e-17 30.0000 0.00277767 0.00277767 7.41638e-15 R8_LI_TEST: R8_LI evaluates the logarithmic integral. X LI(X) R8_LI(X) Diff 0.0000 0 0 0 0.1000 -0.0323898 -0.0323898 6.93889e-18 0.2000 -0.0851265 -0.0851265 1.38778e-17 0.3000 -0.157415 -0.157415 5.55112e-17 0.4000 -0.252949 -0.252949 0 0.5000 -0.378671 -0.378671 5.55112e-17 0.6000 -0.546851 -0.546851 1.11022e-16 0.7000 -0.780947 -0.780947 2.22045e-16 0.8000 -1.13401 -1.13401 2.22045e-16 0.9000 -1.7758 -1.7758 2.22045e-16 0.9500 -2.44362 -2.44362 4.44089e-16 0.9750 -3.12419 -3.12419 8.88178e-16 1.0312 -2.87294 -2.87294 4.44089e-16 1.0625 -2.16428 -2.16428 4.44089e-16 1.1250 -1.44035 -1.44035 2.22045e-16 1.2500 -0.686488 -0.686488 0 1.5000 0.125065 0.125065 0 2.0000 1.04516 1.04516 0 4.0000 2.96759 2.96759 0 8.0000 5.25372 5.25372 8.88178e-16 16.0000 8.51972 8.51972 0 32.0000 13.6051 13.6051 3.55271e-15 64.0000 21.9347 21.9347 1.06581e-14 128.0000 36.0425 36.0425 7.10543e-15 256.0000 60.5131 60.5131 7.10543e-15 512.0000 103.721 103.721 2.84217e-14 1024.0000 181.078 181.078 2.84217e-14 2048.0000 321.114 321.114 0 R8_LNGAM_TEST: R8_LNGAM evaluates the logarithm of the Gamma function. X LNGAM(X) R8_LNGAM(X) Diff 0.2000 1.52406 1.52406 6.66134e-16 0.4000 0.796678 0.796678 2.22045e-16 0.6000 0.398234 0.398234 5.55112e-17 0.8000 0.15206 0.15206 0 1.0000 0 0 0 1.1000 -0.0498724 -0.0498724 1.38778e-17 1.2000 -0.0853741 -0.0853741 2.77556e-17 1.3000 -0.108175 -0.108175 6.93889e-17 1.4000 -0.119613 -0.119613 1.38778e-16 1.5000 -0.120782 -0.120782 2.77556e-17 1.6000 -0.112592 -0.112592 6.93889e-17 1.7000 -0.0958077 -0.0958077 1.38778e-17 1.8000 -0.0710839 -0.0710839 1.38778e-17 1.9000 -0.0389843 -0.0389843 1.38778e-17 2.0000 0 0 0 3.0000 0.693147 0.693147 0 4.0000 1.79176 1.79176 0 10.0000 12.8018 12.8018 0 20.0000 39.3399 39.3399 0 30.0000 71.257 71.257 1.42109e-14 R8_LNREL_TEST: R8_LNREL evaluates ln(1+X). X LN(1+X) R8_LNREL(X) Diff -0.99999 -11.5129 -11.5129 4.55103e-12 -0.99 -4.60517 -4.60517 8.88178e-16 -0.9 -2.30259 -2.30259 0 -0.8 -1.60944 -1.60944 2.22045e-16 -0.7 -1.20397 -1.20397 0 -0.6 -0.916291 -0.916291 1.11022e-16 -0.5 -0.693147 -0.693147 0 -0.4 -0.510826 -0.510826 0 -0.3 -0.356675 -0.356675 1.11022e-16 -0.2 -0.223144 -0.223144 5.55112e-17 -0.1 -0.105361 -0.105361 2.77556e-17 0 0 0 0 1 0.693147 0.693147 0 2 1.09861 1.09861 0 2.14159 1.14473 1.14473 0 4 1.60944 1.60944 0 9 2.30259 2.30259 0 19 2.99573 2.99573 0 99 4.60517 4.60517 0 1.23457e+08 18.6314 18.6314 0 R8_LOG_TEST: R8_LOG evaluates the logarithm. X LOG(X) R8_LOG(X) Diff 1e-05 -11.5129 -11.5129 0 0.01 -4.60517 -4.60517 0 0.1 -2.30259 -2.30259 4.44089e-16 0.2 -1.60944 -1.60944 0 0.3 -1.20397 -1.20397 2.22045e-16 0.4 -0.916291 -0.916291 1.11022e-16 0.5 -0.693147 -0.693147 0 0.6 -0.510826 -0.510826 0 0.7 -0.356675 -0.356675 5.55112e-17 0.8 -0.223144 -0.223144 1.11022e-16 0.9 -0.105361 -0.105361 6.93889e-17 1 0 0 0 2 0.693147 0.693147 0 3 1.09861 1.09861 2.22045e-16 3.142 1.14473 1.14473 0 5 1.60944 1.60944 2.22045e-16 10 2.30259 2.30259 0 20 2.99573 2.99573 0 100 4.60517 4.60517 0 1.235e+08 18.6314 18.6314 0 R8_LOG10_TEST: R8_LOG10 evaluates the logarithm base 10. X LOG10(X) R8_LOG10(X) Diff 0.0000 -5 -5 0 0.0100 -2 -2 2.22045e-16 0.1000 -1 -1 1.11022e-16 0.2000 -0.69897 -0.69897 1.11022e-16 0.3000 -0.522879 -0.522879 1.11022e-16 0.4000 -0.39794 -0.39794 5.55112e-17 0.5000 -0.30103 -0.30103 0 0.6000 -0.221849 -0.221849 0 0.7000 -0.154902 -0.154902 2.77556e-17 0.8000 -0.09691 -0.09691 2.77556e-17 0.9000 -0.0457575 -0.0457575 6.93889e-18 1.0000 0 0 0 2.0000 0.30103 0.30103 0 3.0000 0.477121 0.477121 5.55112e-17 3.1416 0.49715 0.49715 0 5.0000 0.69897 0.69897 1.11022e-16 10.0000 1 1 0 20.0000 1.30103 1.30103 2.22045e-16 100.0000 2 2 0 123456789.0000 8.09151 8.09151 0 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 1.11254e-308 2 4.49423e+307 3 1.11022e-16 4 2.22045e-16 5 0.30103 R8_MOP_TEST R8_MOP evaluates (-1.0)^I4 as an R8. I4 R8_MOP(I4) -64 1.0 21 -1.0 14 1.0 -71 -1.0 -92 1.0 -58 1.0 -10 1.0 72 1.0 4 1.0 -82 1.0 R8_PAK_TEST: R8_PAK converts a mantissa and base 2 exponent to an R8. Mantissa Exponent R8 0.5 7 64 0.5 8 128 -0.5 7 -64 0.75 7 96 0.9375 4 15 0.5 0 0.5 0.5 -1 0.25 0.625 0 0.625 0.5048828125 7 64.625 0.7853981633974483 2 3.141592653589793 0 0 0 R8_POCH_TEST: R8_POCH evaluates the Pochhammer symbol. A X POCH(A,X) R8_POCH(A,X) Diff 5 4 1680 1680 0 5.25 4 1962.6 1962.6 0 5.5 4 2279.06 2279.06 0 5.75 4 2631.97 2631.97 0 6 4 3024 3024 0 7.5 0 1 1 0 7.5 1 7.5 7.5 0 7.5 2 63.75 63.75 0 7.5 3 605.625 605.625 0 7.5 4 6359.06 6359.06 0 7.5 5 73129.2 73129.2 0 7.5 6 914115 914115 0 7.5 7 1.23406e+07 1.23406e+07 0 7.5 8 1.78938e+08 1.78938e+08 5.96046e-08 7.5 9 2.77354e+09 2.77354e+09 0 R8_PSI_TEST: R8_PSI evaluates the Psi function X PSI(X) R8_PSI(X) Diff 0.1 -10.4238 -10.4238 1.06581e-14 0.2 -5.28904 -5.28904 1.77636e-15 0.3 -3.50252 -3.50252 4.44089e-16 0.4 -2.56138 -2.56138 4.44089e-16 0.5 -1.96351 -1.96351 4.44089e-16 0.6 -1.54062 -1.54062 2.22045e-16 0.7 -1.22002 -1.22002 2.22045e-16 0.8 -0.965009 -0.965009 0 0.9 -0.754927 -0.754927 0 1 -0.577216 -0.577216 0 1.1 -0.423755 -0.423755 1.11022e-16 1.2 -0.28904 -0.28904 1.11022e-16 1.3 -0.169191 -0.169191 1.38778e-16 1.4 -0.0613845 -0.0613845 6.93889e-17 1.5 0.03649 0.03649 0 1.6 0.126047 0.126047 2.77556e-17 1.7 0.208548 0.208548 5.55112e-17 1.8 0.284991 0.284991 0 1.9 0.356184 0.356184 1.11022e-16 2 0.422784 0.422784 5.55112e-17 R8_RAND_TEST: R8_RAND is a random number generator. I R8_RAND Expected 1 0.000412703 0.000412703 2 0.675084 0.675084 3 0.161475 0.161475 4 0.90862 0.90862 10 0.552779 0.552779 100 0.360089 0.360089 1000 0.217699 0.217699 Average = 0.4999 0.5 Variance = 0.0832492 0.0833333 R8_RANDGS_TEST: R8_RANDGS is a normal random number generator. Mean = 3 Standard Deviation = 2 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 0.0913844 2 0.161475 3 0.658159 4 0.272802 10 0.174952 100 0.820123 1000 0.640682 Average = 0.499899 0.5 Variance = 0.0832494 0.0833333 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 0.0121733 0.0121733 Average = 0.499841 0.5 Variance = 0.0833074 0.0833333 R8_SHI_TEST: R8_SHI evaluates the hyperbolic sine integral. X SHI(X) R8_SHI(X) Diff 0.5000 0.506997 0.506997 0 0.6000 0.61213 0.61213 0 0.7000 0.719338 0.719338 1.11022e-16 0.8000 0.828997 0.828997 0 0.9000 0.941498 0.941498 0 1.0000 1.05725 1.05725 4.44089e-16 1.2000 1.30025 1.30025 0 1.4000 1.56171 1.56171 0 1.6000 1.84581 1.84581 6.66134e-16 1.8000 2.15729 2.15729 8.88178e-16 2.0000 2.50157 2.50157 0 2.5000 3.54934 3.54934 0 3.0000 4.97344 4.97344 0 3.5000 6.96616 6.96616 0 4.0000 9.81733 9.81733 0 4.5000 13.9679 13.9679 1.77636e-15 R8_SI_TEST: R8_SI evaluates the sine integral. X SI(X) R8_SI(X) Diff 0.5 0.493107 0.493107 5.55112e-17 0.6 0.588129 0.588129 1.11022e-16 0.7 0.681222 0.681222 0 0.8 0.772096 0.772096 0 0.9 0.860471 0.860471 0 1 0.946083 0.946083 0 1.2 1.10805 1.10805 4.44089e-16 1.4 1.25623 1.25623 0 1.6 1.38918 1.38918 6.66134e-16 1.8 1.50582 1.50582 4.44089e-16 2 1.60541 1.60541 2.22045e-16 2.5 1.77852 1.77852 2.22045e-16 3 1.84865 1.84865 2.22045e-16 3.5 1.83313 1.83313 0 4 1.7582 1.7582 0 4.5 1.65414 1.65414 0 R8_SIN_TEST: R8_SIN evaluates the sine function. X SIN(X) R8_SIN(X) Diff 0.0000 0 0 0 0.2618 0.258819 0.258819 5.55112e-17 0.5000 0.479426 0.479426 0 0.5236 0.5 0.5 0 0.7854 0.707107 0.707107 1.11022e-16 1.0000 0.841471 0.841471 0 1.0472 0.866025 0.866025 1.11022e-16 1.5708 1 1 1.11022e-16 2.0000 0.909297 0.909297 0 3.0000 0.14112 0.14112 0 3.1416 0 1.22515e-16 1.22515e-16 4.0000 -0.756802 -0.756802 0 5.0000 -0.958924 -0.958924 1.11022e-16 R8_SIN_DEG_TEST: R8_SIN_DEG evaluates the sine of an argument in degrees. X SIN_DEG(X) R8_SIN_DEG(X) Diff -5.0000 -0.0871557 -0.0871557 1.38778e-17 0.0000 0 0 0 1.0000 0.0174524 0.0174524 0 2.0000 0.0348995 0.0348995 0 3.0000 0.052336 0.052336 0 4.0000 0.0697565 0.0697565 0 5.0000 0.0871557 0.0871557 1.38778e-17 10.0000 0.173648 0.173648 2.77556e-17 15.0000 0.258819 0.258819 0 30.0000 0.5 0.5 5.55112e-17 45.0000 0.707107 0.707107 1.11022e-16 60.0000 0.866025 0.866025 0 75.0000 0.965926 0.965926 0 85.0000 0.996195 0.996195 0 86.0000 0.997564 0.997564 0 87.0000 0.99863 0.99863 0 88.0000 0.999391 0.999391 0 89.0000 0.999848 0.999848 0 90.0000 1 1 0 91.0000 0.999848 0.999848 0 105.0000 0.965926 0.965926 0 180.0000 0 0 0 R8_SINH_TEST: R8_SINH evaluates the hyperbolic sine function. X SINH(X) R8_SINH(X) Diff -5.0000 -74.2032 -74.2032 0 -1.0000 -1.1752 -1.1752 0 0.0000 0 0 0 0.1000 0.100167 0.100167 1.38778e-17 0.2000 0.201336 0.201336 2.77556e-17 0.3000 0.30452 0.30452 0 0.4000 0.410752 0.410752 0 0.5000 0.521095 0.521095 0 0.6000 0.636654 0.636654 1.11022e-16 0.7000 0.758584 0.758584 1.11022e-16 0.8000 0.888106 0.888106 0 0.9000 1.02652 1.02652 0 1.0000 1.1752 1.1752 0 2.0000 3.62686 3.62686 4.44089e-16 3.0000 10.0179 10.0179 0 4.0000 27.2899 27.2899 3.55271e-15 5.0000 74.2032 74.2032 0 10.0000 11013.2 11013.2 0 R8_SPENCE_TEST: R8_SPENCE evaluates Spence's integral. X SPENCE(X) R8_SPENCE(X) Diff 0.0000 0 0 0 0.0500 0.0506393 0.0506393 0 0.1000 0.102618 0.102618 2.77556e-17 0.1500 0.156035 0.156035 0 0.2000 0.211004 0.211004 2.77556e-17 0.2500 0.267653 0.267653 0 0.3000 0.32613 0.32613 0 0.3500 0.386606 0.386606 0 0.4000 0.449283 0.449283 5.55112e-17 0.4500 0.514399 0.514399 1.11022e-16 0.5000 0.582241 0.582241 0 0.5500 0.653158 0.653158 0 0.6000 0.727586 0.727586 0 0.6500 0.806083 0.806083 0 0.7000 0.889378 0.889378 2.22045e-16 0.7500 0.978469 0.978469 1.11022e-16 0.8000 1.07479 1.07479 4.44089e-16 0.8500 1.18058 1.18058 0 0.9000 1.29971 1.29971 2.22045e-16 0.9500 1.44063 1.44063 4.44089e-16 1.0000 1.64493 1.64493 4.44089e-16 R8_SQRT_TEST: R8_SQRT evaluates the square root function. X SQRT(X) R8_SQRT(X) Diff 0.0000 0 0 0 0.0000 9e-05 9e-05 1.35525e-20 0.0900 0.3 0.3 5.55112e-17 0.1000 0.316228 0.316228 1.11022e-16 0.4000 0.632456 0.632456 1.11022e-16 1.0000 1 1 2.22045e-16 2.0000 1.41421 1.41421 2.22045e-16 3.0000 1.73205 1.73205 2.22045e-16 3.1416 1.77245 1.77245 2.22045e-16 19.0000 4.3589 4.3589 0 29.0000 5.38516 5.38516 0 71.0000 8.42615 8.42615 0 97.0000 9.84886 9.84886 0 123456789.0000 11111.1 11111.1 5.45697e-12 R8_TAN_TEST: R8_TAN evaluates the tangent function. X TAN(X) R8_TAN(X) Diff 0 0 0 0 0.2618 0.267949 0.267949 5.55112e-17 0.5 0.546302 0.546302 0 0.5236 0.57735 0.57735 2.22045e-16 0.7854 1 1 0 1 1.55741 1.55741 2.22045e-16 1.047 1.73205 1.73205 1.11022e-15 1.309 3.73205 3.73205 8.88178e-16 1.44 7.59575 7.59575 7.99361e-15 1.505 15.2571 15.2571 1.95399e-14 2 -2.18504 -2.18504 4.44089e-16 3 -0.142547 -0.142547 2.77556e-17 3.142 0 -1.11022e-16 1.11022e-16 4 1.15782 1.15782 4.44089e-16 5 -3.38052 -3.38052 0 R8_TANH_TEST: R8_TANH evaluates the hyperbolic tangent function. TANH_VALUES returns some exact values. X TANH(X) R8_TANH(X) Diff -5.0000 -0.999909 -0.999909 1.11022e-16 -1.0000 -0.761594 -0.761594 0 0.0000 0 0 0 0.1000 0.099668 0.099668 0 0.2000 0.197375 0.197375 0 0.3000 0.291313 0.291313 0 0.4000 0.379949 0.379949 0 0.5000 0.462117 0.462117 5.55112e-17 0.6000 0.53705 0.53705 1.11022e-16 0.7000 0.604368 0.604368 0 0.8000 0.664037 0.664037 1.11022e-16 0.9000 0.716298 0.716298 0 1.0000 0.761594 0.761594 0 2.0000 0.964028 0.964028 1.11022e-16 3.0000 0.995055 0.995055 1.11022e-16 4.0000 0.999329 0.999329 1.11022e-16 5.0000 0.999909 0.999909 1.11022e-16 10.0000 1 1 1.11022e-16 R8_UPAK_TEST: R8_UPAK converts an R8 to a mantissa and base 2 exponent. X Mantissa Exponent 64 0.5 7 128 0.5 8 -64 -0.5 7 96 0.75 7 15 0.9375 4 0.5 0.5 0 0.25 0.5 -1 0.625 0.625 0 64.625 0.5048828125 7 3.141592653589793 0.7853981633974483 2 0 0 0 fn_test(): Normal end of execution. 05-Jan-2023 16:16:28