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- Log ----------------------------------------------------------------- commit af9fc6fcdb824757c5aeeadc6ccae2098d243313 Author: Raymond Toy toy.raymond@gmail.com Date: Tue Mar 29 09:58:45 2011 -0400

Make gamma accurate for integers; add precision test for incomplete-gamma-tail.

qd-gamma.lisp: o For integer values, just compute the gamma value directly by multiplication. This works around the problem that the current algorithm is not as accurate as we would like.

rt-test.lisp: o Reduce required accuracy in gamma-incomplete-tail.3.d. o Add precision test for gamm incomplete tail near the negative real axis.

diff --git a/qd-gamma.lisp b/qd-gamma.lisp index 7048b80..8cab1bb 100644 --- a/qd-gamma.lisp +++ b/qd-gamma.lisp @@ -142,6 +142,18 @@ (/ (float-pi z) (sin (* (float-pi z) z)) (gamma-aux (- 1 z) limit nterms))) + ((and (zerop (imagpart z)) + (= z (truncate z))) + ;; We have gamma(n) where an integer value n and is small + ;; enough. In this case, just compute the product + ;; directly. We do this because our current implementation + ;; has some round-off for these values, and that's annoying + ;; and unexpected. + (let ((n (truncate z))) + (loop + for prod = (apply-contagion 1 precision) then (* prod k) + for k from 2 below n + finally (return (apply-contagion prod precision))))) (t (let ((absz (abs z))) (cond ((>= absz limit) @@ -168,7 +180,6 @@ (defmethod gamma ((z qd-complex)) (gamma-aux z 39 32))

- ;; Lentz's algorithm for evaluating continued fractions. ;; ;; Let the continued fraction be: diff --git a/rt-tests.lisp b/rt-tests.lisp index 66aab0c..acc8b74 100644 --- a/rt-tests.lisp +++ b/rt-tests.lisp @@ -1230,7 +1230,7 @@ (let* ((z -5d0) (gi (incomplete-gamma-tail 2 z)) (true (* (+ z 1) (exp (- z))))) - (check-accuracy 52 gi true)) + (check-accuracy 50 gi true)) nil)

(rt:deftest gamma-incomplete-tail.3.q @@ -1240,6 +1240,16 @@ (check-accuracy 206 gi true)) nil)

+;; See http://www.wolframalpha.com/input/?i=Gamma%5B1%2F2%2C-100%2Bi%2F%2810%5E10%2...] + +(rt:deftest gamma-incomplete-tail.4.q + (let* ((z #q(#q-100 #q1q-10)) + (gi (incomplete-gamma-tail 1/2 z)) + (true #q(#q-2.68811714181613544840818982228135651231579313476267430888499241497530341422025007816745898370049200133136q32 + #q-2.70176456134384383878883307528351227886457379834795655467745609829086928772079968479767583764284583465328q42))) + (check-accuracy 205 gi true)) + nil) +  ;; Fresnel integrals. ;;

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Summary of changes: qd-gamma.lisp | 13 ++++++++++++- rt-tests.lisp | 12 +++++++++++- 2 files changed, 23 insertions(+), 2 deletions(-)

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