An algorithm is given for computing the incomplete gamma function ratios
P
(
a
,
x
) and
Q>
(
a
,
x
) for
a
⪈ 0,
x
⪈ 0,
a
+
x
≠ 0. Temme's uniform asymptotic expansions are used. The algorithm is robust; results accurate to 14 significant digits can be obtained. An' extensive set of coefficients for the Temme expansions is included.
An algorithm, employing third-order Schröder iteration supported by Newton-Raphson iteration, is provided for computing
x
when
a
,
P
(
a
,
x
), and
Q
(
a
,
x
) are given. Three iterations at most are required to obtain 10 significant digit accuracy for
x
.
An algorithm is given for evaluating the incomplete beta function ratio
I
x
(a,b)
and its complement
1 - I
x
(a,b)
. A new continued fraction and a new asymptotic series are used with classical results. A transportable Fortran subroutine based on this algorithm is currently in use. It is accurate to 14 significant digits when precision is not restricted by inherent error.
In July 1980, the proposed final form of the Ada programming language was released by the U.S. Department of Defense [1]. Even though Ada was not designed specifically for general numeric scientific computation, nevertheless the question arises to whether it is appropriate for this purpose. This question can best be answered by consideration of the following question: Is Ada a suitable replacement for the programming language FORTRAN? This paper discusses those constructs of Ada which are pertinent to the matter and are considered defective. It is noted that the array defects are exceptionally critical, not providing needed capabilities that exist in FORTRAN and have been extensively used for a quarter century.
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