 
      DOUBLE PRECISION FUNCTION DE1(X)
C***BEGIN PROLOGUE  DE1
C***DATE WRITTEN   770701   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  C5
C***KEYWORDS  DOUBLE PRECISION,EXPONENTIAL INTEGRAL,SPECIAL FUNCTION
C***AUTHOR  FULLERTON, W., (LANL)
C***PURPOSE  Computes the d.p. exponential integral E1(X).
C***DESCRIPTION
C
C DE1(X) calculates the double precision exponential integral
C E1(X) for positive double precision argument X and the
C Cauchy principal value for negative X.  If principal values are
C used everywhere, then for all X
C
C        Ei(X) = -E1(-X)   or
C        E1(X) = -Ei(-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***REFERENCES  (NONE)
C***ROUTINES CALLED  D1MACH,DCSEVL,INITDS,XERROR
C***END PROLOGUE  DE1
 
 
