derf.f

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*DECK DERF
      DOUBLE PRECISION FUNCTION derf (X)
C***BEGIN PROLOGUE  DERF
C***PURPOSE  Compute the error function.
C***LIBRARY   SLATEC (FNLIB)
C***CATEGORY  C8A, L5A1E
C***TYPE      DOUBLE PRECISION (ERF-S, DERF-D)
C***KEYWORDS  ERF, ERROR FUNCTION, FNLIB, SPECIAL FUNCTIONS
C***AUTHOR  Fullerton, W., (LANL)
C***DESCRIPTION
C
C DERF(X) calculates the double precision error function for double
C precision argument X.
C
C Series for ERF        on the interval  0.          to  1.00000E+00
C                                        with weighted error   1.28E-32
C                                         log weighted error  31.89
C                               significant figures required  31.05
C                                    decimal places required  32.55
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  D1MACH, DCSEVL, DERFC, INITDS
C***REVISION HISTORY  (YYMMDD)
C   770701  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890531  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900727  Added EXTERNAL statement.  (WRB)
C   920618  Removed space from variable name.  (RWC, WRB)
C***END PROLOGUE  DERF
      DOUBLE PRECISION X, ERFCS(21), SQEPS, SQRTPI, XBIG, Y, D1MACH,
     1  dcsevl, derfc
      LOGICAL FIRST
      EXTERNAL derfc
      SAVE erfcs, sqrtpi, nterf, xbig, sqeps, first
      DATA erfcs(  1) / -.4904612123 4691808039 9845440333 76 d-1     /
      DATA erfcs(  2) / -.1422612051 0371364237 8247418996 31 d+0     /
      DATA erfcs(  3) / +.1003558218 7599795575 7546767129 33 d-1     /
      DATA erfcs(  4) / -.5768764699 7674847650 8270255091 67 d-3     /
      DATA erfcs(  5) / +.2741993125 2196061034 4221607914 71 d-4     /
      DATA erfcs(  6) / -.1104317550 7344507604 1353812959 05 d-5     /
      DATA erfcs(  7) / +.3848875542 0345036949 9613114981 74 d-7     /
      DATA erfcs(  8) / -.1180858253 3875466969 6317518015 81 d-8     /
      DATA erfcs(  9) / +.3233421582 6050909646 4029309533 54 d-10    /
      DATA erfcs( 10) / -.7991015947 0045487581 6073747085 95 d-12    /
      DATA erfcs( 11) / +.1799072511 3961455611 9672454866 34 d-13    /
      DATA erfcs( 12) / -.3718635487 8186926382 3168282094 93 d-15    /
      DATA erfcs( 13) / +.7103599003 7142529711 6899083946 66 d-17    /
      DATA erfcs( 14) / -.1261245511 9155225832 4954248533 33 d-18    /
      DATA erfcs( 15) / +.2091640694 1769294369 1705002666 66 d-20    /
      DATA erfcs( 16) / -.3253973102 9314072982 3641600000 00 d-22    /
      DATA erfcs( 17) / +.4766867209 7976748332 3733333333 33 d-24    /
      DATA erfcs( 18) / -.6598012078 2851343155 1999999999 99 d-26    /
      DATA erfcs( 19) / +.8655011469 9637626197 3333333333 33 d-28    /
      DATA erfcs( 20) / -.1078892517 7498064213 3333333333 33 d-29    /
      DATA erfcs( 21) / +.1281188399 3017002666 6666666666 66 d-31    /
      DATA sqrtpi / 1.772453850 9055160272 9816748334 115d0 /
      DATA first /.true./
C***FIRST EXECUTABLE STATEMENT  DERF
      IF (first) THEN
         nterf = initds(erfcs, 21, 0.1*REAL(d1mach(3)))
         xbig = sqrt(-log(sqrtpi*d1mach(3)))
         sqeps = sqrt(2.0d0*d1mach(3))
      ENDIF
      first = .false.
C
      y = abs(x)
      IF (y.GT.1.d0) go to 20
C
C ERF(X) = 1.0 - ERFC(X)  FOR  -1.0 .LE. X .LE. 1.0
C
      IF (y.LE.sqeps) derf = 2.0d0*x/sqrtpi
      IF (y.GT.sqeps) derf = x*(1.0d0 + dcsevl(2.d0*x*x-1.d0,
     1  erfcs, nterf))
      RETURN
C
C ERF(X) = 1.0 - ERFC(X) FOR ABS(X) .GT. 1.0
C
 20   IF (y.LE.xbig) derf = sign(1.0d0-derfc(y), x)
      IF (y.GT.xbig) derf = sign(1.0d0, x)
C
      RETURN
      END