# de1.f

          DOUBLE PRECISION FUNCTION DE1 (X)
    C***BEGIN PROLOGUE  DE1
    C***PURPOSE  Compute the exponential integral E1(X).
    C***LIBRARY   SLATEC (FNLIB)
    C***CATEGORY  C5
    C***TYPE      DOUBLE PRECISION (E1-S, DE1-D)
    C***KEYWORDS  E1 FUNCTION, EXPONENTIAL INTEGRAL, FNLIB,
    C             SPECIAL FUNCTIONS
    C***AUTHOR  Fullerton, W., (LANL)
    C***DESCRIPTION
    C
    C DE1 calculates the double precision exponential integral, E1(X), for
    C positive double precision argument X and the Cauchy principal value
    C for negative X.  If principal values are used everywhere, then, for
    C all X,
    C
    C    E1(X) = -Ei(-X)
    C or
    C    Ei(X) = -E1(-X).
    C
    C
    C Series for AE10       on the interval -3.12500E-02 to  0.
    C                                        with weighted error   4.62E-32
    C                                         log weighted error  31.34
    C                               significant figures required  29.70
    C                                    decimal places required  32.18
    C
    C
    C Series for AE11       on the interval -1.25000E-01 to -3.12500E-02
    C                                        with weighted error   2.22E-32
    C                                         log weighted error  31.65
    C                               significant figures required  30.75
    C                                    decimal places required  32.54
    C
    C
    C Series for AE12       on the interval -2.50000E-01 to -1.25000E-01
    C                                        with weighted error   5.19E-32
    C                                         log weighted error  31.28
    C                               significant figures required  30.82
    C                                    decimal places required  32.09
    C
    C
    C Series for E11        on the interval -4.00000E+00 to -1.00000E+00
    C                                        with weighted error   8.49E-34
    C                                         log weighted error  33.07
    C                               significant figures required  34.13
    C                                    decimal places required  33.80
    C
    C
    C Series for E12        on the interval -1.00000E+00 to  1.00000E+00
    C                                        with weighted error   8.08E-33
    C                                         log weighted error  32.09
    C                        approx significant figures required  30.4
    C                                    decimal places required  32.79
    C
    C
    C Series for AE13       on the interval  2.50000E-01 to  1.00000E+00
    C                                        with weighted error   6.65E-32
    C                                         log weighted error  31.18
    C                               significant figures required  30.69
    C                                    decimal places required  32.03
    C
    C
    C Series for AE14       on the interval  0.          to  2.50000E-01
    C                                        with weighted error   5.07E-32
    C                                         log weighted error  31.30
    C                               significant figures required  30.40
    C                                    decimal places required  32.20
    C
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  D1MACH, DCSEVL, INITDS, XERMSG
    C***REVISION HISTORY  (YYMMDD)
    C   770701  DATE WRITTEN
    C   890531  Changed all specific intrinsics to generic.  (WRB)
    C   891115  Modified prologue description.  (WRB)
    C   891115  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
    C   920618  Removed space from variable names.  (RWC, WRB)
    C***END PROLOGUE  DE1