# e1.f

          FUNCTION E1 (X)
    C***BEGIN PROLOGUE  E1
    C***PURPOSE  Compute the exponential integral E1(X).
    C***LIBRARY   SLATEC (FNLIB)
    C***CATEGORY  C5
    C***TYPE      SINGLE PRECISION (E1-S, DE1-D)
    C***KEYWORDS  E1 FUNCTION, EXPONENTIAL INTEGRAL, FNLIB,
    C             SPECIAL FUNCTIONS
    C***AUTHOR  Fullerton, W., (LANL)
    C***DESCRIPTION
    C
    C E1 calculates the single precision exponential integral, E1(X), for
    C positive single 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 AE11       on the interval -1.00000D-01 to  0.
    C                                        with weighted error   1.76E-17
    C                                         log weighted error  16.75
    C                               significant figures required  15.70
    C                                    decimal places required  17.55
    C
    C
    C Series for AE12       on the interval -2.50000D-01 to -1.00000D-01
    C                                        with weighted error   5.83E-17
    C                                         log weighted error  16.23
    C                               significant figures required  15.76
    C                                    decimal places required  16.93
    C
    C
    C Series for E11        on the interval -4.00000D+00 to -1.00000D+00
    C                                        with weighted error   1.08E-18
    C                                         log weighted error  17.97
    C                               significant figures required  19.02
    C                                    decimal places required  18.61
    C
    C
    C Series for E12        on the interval -1.00000D+00 to  1.00000D+00
    C                                        with weighted error   3.15E-18
    C                                         log weighted error  17.50
    C                        approx significant figures required  15.8
    C                                    decimal places required  18.10
    C
    C
    C Series for AE13       on the interval  2.50000D-01 to  1.00000D+00
    C                                        with weighted error   2.34E-17
    C                                         log weighted error  16.63
    C                               significant figures required  16.14
    C                                    decimal places required  17.33
    C
    C
    C Series for AE14       on the interval  0.          to  2.50000D-01
    C                                        with weighted error   5.41E-17
    C                                         log weighted error  16.27
    C                               significant figures required  15.38
    C                                    decimal places required  16.97
    C
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  CSEVL, INITS, R1MACH, 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  E1