# gaussian-cdf.txt,  3 May 10

!title Gaussian-cdf

!fuzz 0.0001

!msgpostfix Table of Normal/Gaussian cumulative distribution function\n

!need all
# 0.0
0.50000 00000 00000
# 0.5
0.69146 24612 74013
# 1.0
0.84134 47460 68543
# 1.5
0.93319 27987 31142
# 2.0
0.97724 98680 51821
# 2.5
0.99379 03346 74224
# 3.0
0.99865 01019 68370
# 3.5
0.99976 73709

!fuzz 0.000005

!msgpostfix  Cumulative distribution function for Normal/Gaussian distribution (error < 2.5e-4) from Abramowitz and Stegun 26.2.18\n

!need all
0.196854
0.115194
0.000344
0.019527


!fuzz 0.000001

!msgpostfix  Cumulative distribution function for Normal/Gaussian distribution (error < 7.5e-8) from Abramowitz and Stegun 26.2.17\n

!need all
 0.2316419

 0.319381530
-0.356563782
 1.781477937
-1.821255978
 1.330274429

#  Algorithm 5666, J.F.Hart et al. (1968) 'COMPUTER APPROXIMATIONS'
#  Accurate to 15 decimal places

!msgpostfix  Cumulative distribution function for Normal/Gaussian distribution (error < 1e-14) from J.F. Hart\n

!need all
0.22020 68679 12376 1e3
0.22121 35961 69931 1e3
0.11207 92914 97870 9e3
0.33912 86607 83830 0e2
0.63739 62203 53165 0e1
0.70038 30644 43688 1e0
0.35262 49659 98910 9e-1

0.44041 37358 24752 2e3
0.79382 65125 19948 4e3
0.63733 36333 78831 1e3
0.29656 42487 79673 7e3
0.86780 73220 29460 8e2
0.16064 17757 92069 5e2
0.17556 67163 18264 2e1
0.88388 34764 83184 4e-1


!fuzz 0.0000001

!msgpostfix Cumulative distribution function for Normal/Gaussian distribution using a rational function approximation\n

!msgprefix fabs(x) < 0.66291  
!need all

   2.2352520354606839287
 161.02823106855587881
 1067.6894854603709582
18154.981253343561249
    0.065682337918207449113

47.20258190468824187
976.09855173777669322
10260.932208618978205
45507.789335026729956


!msgprefix 0.66291 < fabs(x) < sqrt(32) 
!need all

    0.39894151208813466764
    8.8831497943883759412
   93.506656132177855979
  597.27027639480026226
 2494.5375852903726711
 6848.1904505362823326
11602.651437647350124
 9842.7148383839780218
    1.0765576773720192317e-8

   22.266688044328115691
  235.38790178262499861
 1519.377599407554805
 6485.558298266760755
18615.571640885098091
34900.952721145977266
38912.003286093271411
19685.429676859990727


!msgprefix sqrt(32) < fabs(x) 
!need all

0.21589853405795699
0.1274011611602473639
0.022235277870649807
0.001421619193227893466
2.9112874951168792e-5
0.02307344176494017303

1.28426009614491121
0.468238212480865118
0.0659881378689285515
0.00378239633202758244
7.29751555083966205e-5

