1 DOUBLE PRECISION FUNCTION DERF(X) 2C***BEGIN PROLOGUE DERF 3C***DATE WRITTEN 770701 (YYMMDD) 4C***REVISION DATE 840425 (YYMMDD) 5C***REVISION HISTORY (YYMMDD) 6C 000601 Added EXTERNAL statement for DERFC 7C***CATEGORY NO. C8A,L5A1E 8C***KEYWORDS DOUBLE PRECISION,ERROR FUNCTION,SPECIAL FUNCTION 9C***AUTHOR FULLERTON, W., (LANL) 10C***PURPOSE Computes the d.p. error function, ERF, of X. 11C***DESCRIPTION 12C 13C DERF(X) calculates the double precision error function for double 14C precision argument X. 15C 16C Series for ERF on the interval 0. to 1.00000E+00 17C with weighted error 1.28E-32 18C log weighted error 31.89 19C significant figures required 31.05 20C decimal places required 32.55 21C***REFERENCES (NONE) 22C***ROUTINES CALLED D1MACH,DCSEVL,DERFC,INITDS 23C***END PROLOGUE DERF 24 DOUBLE PRECISION X, ERFCS(21), SQEPS, SQRTPI, XBIG, Y, D1MACH, 25 1 DCSEVL, DERFC 26 EXTERNAL DERFC 27 DATA ERF CS( 1) / -.4904612123 4691808039 9845440333 76 D-1 / 28 DATA ERF CS( 2) / -.1422612051 0371364237 8247418996 31 D+0 / 29 DATA ERF CS( 3) / +.1003558218 7599795575 7546767129 33 D-1 / 30 DATA ERF CS( 4) / -.5768764699 7674847650 8270255091 67 D-3 / 31 DATA ERF CS( 5) / +.2741993125 2196061034 4221607914 71 D-4 / 32 DATA ERF CS( 6) / -.1104317550 7344507604 1353812959 05 D-5 / 33 DATA ERF CS( 7) / +.3848875542 0345036949 9613114981 74 D-7 / 34 DATA ERF CS( 8) / -.1180858253 3875466969 6317518015 81 D-8 / 35 DATA ERF CS( 9) / +.3233421582 6050909646 4029309533 54 D-10 / 36 DATA ERF CS( 10) / -.7991015947 0045487581 6073747085 95 D-12 / 37 DATA ERF CS( 11) / +.1799072511 3961455611 9672454866 34 D-13 / 38 DATA ERF CS( 12) / -.3718635487 8186926382 3168282094 93 D-15 / 39 DATA ERF CS( 13) / +.7103599003 7142529711 6899083946 66 D-17 / 40 DATA ERF CS( 14) / -.1261245511 9155225832 4954248533 33 D-18 / 41 DATA ERF CS( 15) / +.2091640694 1769294369 1705002666 66 D-20 / 42 DATA ERF CS( 16) / -.3253973102 9314072982 3641600000 00 D-22 / 43 DATA ERF CS( 17) / +.4766867209 7976748332 3733333333 33 D-24 / 44 DATA ERF CS( 18) / -.6598012078 2851343155 1999999999 99 D-26 / 45 DATA ERF CS( 19) / +.8655011469 9637626197 3333333333 33 D-28 / 46 DATA ERF CS( 20) / -.1078892517 7498064213 3333333333 33 D-29 / 47 DATA ERF CS( 21) / +.1281188399 3017002666 6666666666 66 D-31 / 48 DATA SQRTPI / 1.772453850 9055160272 9816748334 115D0 / 49 DATA NTERF, XBIG, SQEPS / 0, 2*0.D0 / 50C***FIRST EXECUTABLE STATEMENT DERF 51 IF (NTERF.NE.0) GO TO 10 52 NTERF = INITDS (ERFCS, 21, 0.1*SNGL(D1MACH(3))) 53 XBIG = DSQRT (-DLOG(SQRTPI*D1MACH(3))) 54 SQEPS = DSQRT (2.0D0*D1MACH(3)) 55C 56 10 Y = DABS(X) 57 IF (Y.GT.1.D0) GO TO 20 58C 59C ERF(X) = 1.0 - ERFC(X) FOR -1.0 .LE. X .LE. 1.0 60C 61 IF (Y.LE.SQEPS) DERF = 2.0D0*X/SQRTPI 62 IF (Y.GT.SQEPS) DERF = X*(1.0D0 + DCSEVL (2.D0*X*X-1.D0, 63 1 ERFCS, NTERF)) 64 RETURN 65C 66C ERF(X) = 1.0 - ERFC(X) FOR ABS(X) .GT. 1.0 67C 68 20 IF (Y.LE.XBIG) DERF = DSIGN (1.0D0-DERFC(Y), X) 69 IF (Y.GT.XBIG) DERF = DSIGN (1.0D0, X) 70C 71 RETURN 72 END 73