d7/dc7/erf_8f_source.html

 *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

inits
function inits(OS, NOS, ETA)
Definition: inits.f:2

csevl
function csevl(X, CS, N)
Definition: csevl.f:2

erfc
function erfc(X)
Definition: erfc.f:2

erf
function erf(X)
Definition: erf.f:2

log
OCTAVE_EXPORT octave_value_list or N dimensional array whose elements are all equal to the base of natural logarithms The constant ex $e satisfies the equation log(e)

false
is false
Definition: cellfun.cc:398

to
may be zero for pure relative error test tem the relative tolerance must be greater than or equal to
Definition: Quad-opts.cc:233

dimension
OCTAVE_EXPORT octave_value_list etc The functions then dimension(columns)

abs
OCTAVE_EXPORT octave_value_list return the value of the option it must match the dimension of the state and the relative tolerance must also be a vector of the same length tem it must match the dimension of the state and the absolute tolerance must also be a vector of the same length The local error test applied at each integration step is xample roup abs(local error in x(i))<

octave_value::sqrt
octave_value sqrt(void) const
Definition: ov.h:1388