*DECK ERF FUNCTION ERF (X) C***BEGIN PROLOGUE ERF C***PURPOSE Compute the error function. C***LIBRARY SLATEC (FNLIB) C***CATEGORY C8A, L5A1E C***TYPE SINGLE PRECISION (ERF-S, DERF-D) C***KEYWORDS ERF, ERROR FUNCTION, FNLIB, SPECIAL FUNCTIONS C***AUTHOR Fullerton, W., (LANL) C***DESCRIPTION C C ERF(X) calculates the single precision error function for C single precision argument X. C C Series for ERF on the interval 0. to 1.00000D+00 C with weighted error 7.10E-18 C log weighted error 17.15 C significant figures required 16.31 C decimal places required 17.71 C C***REFERENCES (NONE) C***ROUTINES CALLED CSEVL, ERFC, INITS, R1MACH C***REVISION HISTORY (YYMMDD) C 770401 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 ERF DIMENSION ERFCS(13) LOGICAL FIRST EXTERNAL ERFC SAVE ERFCS, SQRTPI, NTERF, XBIG, SQEPS, FIRST DATA ERFCS( 1) / -.0490461212 34691808E0 / DATA ERFCS( 2) / -.1422612051 0371364E0 / DATA ERFCS( 3) / .0100355821 87599796E0 / DATA ERFCS( 4) / -.0005768764 69976748E0 / DATA ERFCS( 5) / .0000274199 31252196E0 / DATA ERFCS( 6) / -.0000011043 17550734E0 / DATA ERFCS( 7) / .0000000384 88755420E0 / DATA ERFCS( 8) / -.0000000011 80858253E0 / DATA ERFCS( 9) / .0000000000 32334215E0 / DATA ERFCS(10) / -.0000000000 00799101E0 / DATA ERFCS(11) / .0000000000 00017990E0 / DATA ERFCS(12) / -.0000000000 00000371E0 / DATA ERFCS(13) / .0000000000 00000007E0 / DATA SQRTPI /1.772453850 9055160E0/ DATA FIRST /.TRUE./ C***FIRST EXECUTABLE STATEMENT ERF IF (FIRST) THEN NTERF = INITS (ERFCS, 13, 0.1*R1MACH(3)) XBIG = SQRT(-LOG(SQRTPI*R1MACH(3))) SQEPS = SQRT(2.0*R1MACH(3)) ENDIF FIRST = .FALSE. C Y = ABS(X) IF (Y.GT.1.) GO TO 20 C C ERF(X) = 1. - ERFC(X) FOR -1. .LE. X .LE. 1. C IF (Y.LE.SQEPS) ERF = 2.0*X/SQRTPI IF (Y.GT.SQEPS) ERF = X*(1.0 + CSEVL(2.*X**2-1., ERFCS, NTERF)) RETURN C C ERF(X) = 1. - ERFC(X) FOR ABS(X) .GT. 1. C 20 IF (Y.LE.XBIG) ERF = SIGN (1.0-ERFC(Y), X) IF (Y.GT.XBIG) ERF = SIGN (1.0, X) C RETURN END