Documentation for module mathconstants

Definition of mathematical constants and functions.

source: mathconstants.F
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Parameters:

REAL(dp)
:: degree = 180.0_dp/pi
REAL(dp)
:: dfac(-1:2*MAXFAC+1) = (/0.10000000000000000000e+01_dp,0.10000000000000000000e+01_dp,0.10000000000000000000e+01_dp,0.20000000000000000000e+01_dp,0.30000000000000000000e+01_dp,0.80000000000000000000e+01_dp,0.15000000000000000000e+02_dp,0.48000000000000000000e+02_dp,0.10500000000000000000e+03_dp,0.38400000000000000000e+03_dp,0.94500000000000000000e+03_dp,0.38400000000000000000e+04_dp,0.10395000000000000000e+05_dp,0.46080000000000000000e+05_dp,0.13513500000000000000e+06_dp,0.64512000000000000000e+06_dp,0.20270250000000000000e+07_dp,0.10321920000000000000e+08_dp,0.34459425000000000000e+08_dp,0.18579456000000000000e+09_dp,0.65472907500000000000e+09_dp,0.37158912000000000000e+10_dp,0.13749310575000000000e+11_dp,0.81749606400000000000e+11_dp,0.31623414322500000000e+12_dp,0.19619905536000000000e+13_dp,0.79058535806250000000e+13_dp,0.51011754393600000000e+14_dp,0.21345804667687500000e+15_dp,0.14283291230208000000e+16_dp,0.61902833536293750000e+16_dp,0.42849873690624000000e+17_dp,0.19189878396251062500e+18_dp,0.13711959580999680000e+19_dp,0.63326598707628506250e+19_dp,0.46620662575398912000e+20_dp,0.22164309547669977187e+21_dp,0.16783438527143608320e+22_dp,0.82007945326378915594e+22_dp,0.63777066403145711616e+23_dp,0.31983098677287777082e+24_dp,0.25510826561258284646e+25_dp,0.13113070457687988603e+26_dp,0.10714547155728479551e+27_dp,0.56386202968058350995e+27_dp,0.47144007485205310027e+28_dp,0.25373791335626257948e+29_dp,0.21686243443194442612e+30_dp,0.11925681927744341235e+31_dp,0.10409396852733332454e+32_dp,0.58435841445947272053e+32_dp,0.52046984263666662269e+33_dp,0.29802279137433108747e+34_dp,0.27064431817106664380e+35_dp,0.15795207942839547636e+36_dp,0.14614793181237598765e+37_dp,0.86873643685617511998e+37_dp,0.81842841814930553085e+38_dp,0.49517976900801981839e+39_dp,0.47468848252659720789e+40_dp,0.29215606371473169285e+41_dp,0.28481308951595832474e+42_dp,0.17821519886598633264e+43_dp/)
REAL(dp)
:: euler = 0.57721566490153286060651209_dp
REAL(dp)
:: fac(0:MAXFAC) = (/0.10000000000000000000e+01_dp,0.10000000000000000000e+01_dp,0.20000000000000000000e+01_dp,0.60000000000000000000e+01_dp,0.24000000000000000000e+02_dp,0.12000000000000000000e+03_dp,0.72000000000000000000e+03_dp,0.50400000000000000000e+04_dp,0.40320000000000000000e+05_dp,0.36288000000000000000e+06_dp,0.36288000000000000000e+07_dp,0.39916800000000000000e+08_dp,0.47900160000000000000e+09_dp,0.62270208000000000000e+10_dp,0.87178291200000000000e+11_dp,0.13076743680000000000e+13_dp,0.20922789888000000000e+14_dp,0.35568742809600000000e+15_dp,0.64023737057280000000e+16_dp,0.12164510040883200000e+18_dp,0.24329020081766400000e+19_dp,0.51090942171709440000e+20_dp,0.11240007277776076800e+22_dp,0.25852016738884976640e+23_dp,0.62044840173323943936e+24_dp,0.15511210043330985984e+26_dp,0.40329146112660563558e+27_dp,0.10888869450418352161e+29_dp,0.30488834461171386050e+30_dp,0.88417619937397019545e+31_dp,0.26525285981219105864e+33_dp/)
REAL(dp)
:: fourpi = 12.56637061435917295385057353_dp
REAL(dp)
:: gamma0(0:MAXFAC) = (/0.00000000000000000000e+00_dp,0.10000000000000000000e+01_dp,0.10000000000000000000e+01_dp,0.20000000000000000000e+01_dp,0.60000000000000000000e+01_dp,0.24000000000000000000e+02_dp,0.12000000000000000000e+03_dp,0.72000000000000000000e+03_dp,0.50400000000000000000e+04_dp,0.40320000000000000000e+05_dp,0.36288000000000000000e+06_dp,0.36288000000000000000e+07_dp,0.39916800000000000000e+08_dp,0.47900160000000000000e+09_dp,0.62270208000000000000e+10_dp,0.87178291200000000000e+11_dp,0.13076743680000000000e+13_dp,0.20922789888000000000e+14_dp,0.35568742809600000000e+15_dp,0.64023737057280000000e+16_dp,0.12164510040883200000e+18_dp,0.24329020081766400000e+19_dp,0.51090942171709440000e+20_dp,0.11240007277776076800e+22_dp,0.25852016738884976640e+23_dp,0.62044840173323943936e+24_dp,0.15511210043330985984e+26_dp,0.40329146112660563558e+27_dp,0.10888869450418352161e+29_dp,0.30488834461171386050e+30_dp,0.88417619937397019545e+31_dp/)
REAL(dp)
:: gamma1(0:MAXFAC) = (/0.17724538509055160273e+01_dp,0.88622692545275801365e+00_dp,0.13293403881791370205e+01_dp,0.33233509704478425512e+01_dp,0.11631728396567448929e+02_dp,0.52342777784553520181e+02_dp,0.28788527781504436100e+03_dp,0.18712543057977883465e+04_dp,0.14034407293483412599e+05_dp,0.11929246199460900709e+06_dp,0.11332783889487855673e+07_dp,0.11899423083962248457e+08_dp,0.13684336546556585726e+09_dp,0.17105420683195732157e+10_dp,0.23092317922314238412e+11_dp,0.33483860987355645697e+12_dp,0.51899984530401250831e+13_dp,0.85634974475162063871e+14_dp,0.14986120533153361177e+16_dp,0.27724322986333718178e+17_dp,0.54062429823350750447e+18_dp,0.11082798113786903842e+20_dp,0.23828015944641843260e+21_dp,0.53613035875444147334e+22_dp,0.12599063430729374624e+24_dp,0.30867705405286967828e+25_dp,0.78712648783481767961e+26_dp,0.20858851927622668510e+28_dp,0.57361842800962338401e+29_dp,0.16348125198274266444e+31_dp,0.48226969334909086011e+32_dp/)
COMPLEX(dp)
:: gaussi = (0.0_dp,1.0_dp)
REAL(dp)
:: ifac(0:MAXFAC) = (/0.10000000000000000000e+01_dp,0.10000000000000000000e+01_dp,0.50000000000000000000e+00_dp,0.16666666666666666667e+00_dp,0.41666666666666666667e-01_dp,0.83333333333333333333e-02_dp,0.13888888888888888889e-02_dp,0.19841269841269841270e-03_dp,0.24801587301587301587e-04_dp,0.27557319223985890653e-05_dp,0.27557319223985890653e-06_dp,0.25052108385441718775e-07_dp,0.20876756987868098979e-08_dp,0.16059043836821614599e-09_dp,0.11470745597729724714e-10_dp,0.76471637318198164759e-12_dp,0.47794773323873852974e-13_dp,0.28114572543455207632e-14_dp,0.15619206968586226462e-15_dp,0.82206352466243297170e-17_dp,0.41103176233121648585e-18_dp,0.19572941063391261231e-19_dp,0.88967913924505732867e-21_dp,0.38681701706306840377e-22_dp,0.16117375710961183490e-23_dp,0.64469502843844733962e-25_dp,0.24795962632247974601e-26_dp,0.91836898637955461484e-28_dp,0.32798892370698379102e-29_dp,0.11309962886447716932e-30_dp,0.37699876288159056439e-32_dp/)
INTEGER
:: maxfac = 30
REAL(dp)
:: one = 1.0_dp
REAL(dp)
:: oorootpi = 0.56418958354775628694807945_dp
REAL(dp)
:: pi = 3.14159265358979323846264338_dp
REAL(dp)
:: radians = one/degree
REAL(dp)
:: rootpi = 1.77245385090551602729816748_dp
REAL(dp)
:: sqrt105 = 10.24695076595959838322103868_dp
REAL(dp)
:: sqrt15 = 3.87298334620741688517926540_dp
REAL(dp)
:: sqrt2 = 1.41421356237309504880168872_dp
REAL(dp)
:: sqrt21 = 4.58257569495584000658804719_dp
REAL(dp)
:: sqrt3 = 1.73205080756887729352744634_dp
REAL(dp)
:: sqrt35 = 5.91607978309961604256732829_dp
REAL(dp)
:: sqrt5 = 2.23606797749978969640917367_dp
REAL(dp)
:: sqrt7 = 2.64575131106459059050161575_dp
REAL(dp)
:: sqrthalf = 0.70710678118654752440084436_dp
REAL(dp)
:: twopi = 6.28318530717958647692528677_dp
REAL(dp)
:: zero = 0.0_dp