# Remark on Algorithm 745.

["Computation of the Complete and Incomplete Fermi-Dirac Integral," by Michele Goano, ACM Trans. Math. Softw. 21, 3 (Sept. 1995), 221-232.] www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/

The subroutine FERMID, which computes the complete Fermi-Dirac integral, fails when the absolute value of the argument X is large. (The actual maximum value of X depends on the order ORD of the integral, on the relative error RELERR imposed to the algorithm, and on the floating-point arithmetic system of the computer).

The fix is to insert an IF statement in the subroutine FDNEG, preventing the computation of the series expansion if the exponential of the argument X is smaller than XMIN, the smallest nonzero number which can be represented in the floating-point arithmetic system.

Thus, in the routine FDNEG, insert the statement

IF (X.GT.XTINY) THEN

before the statement

XN = X

and insert

END IF

before the RETURN statement.

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Title Annotation: | 'Computation of the complete and incomplete Fermi-Dirac integral,' ACM Transactions on Mathematical Software, vol. 21, no. 3, p. 221, September 1995 |
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Author: | Goano, Michele |

Publication: | ACM Transactions on Mathematical Software |

Article Type: | Correction Notice |

Date: | Jun 1, 1997 |

Words: | 150 |

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