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- Log ----------------------------------------------------------------- commit 2e182540e895f16b26224ba11b2f38de93ab2672 Author: Raymond Toy toy.raymond@gmail.com Date: Sat Sep 20 11:55:27 2014 -0700

Make (log (scale-float 1d0 k) 2) = k

* src/code/irrat.lisp * Improve accuracy of log2 for the case when x=2^k. There might be some loss in accuracy for other values of x, however. * tests/float.lisp * Add test for log2(2^k) = k.

diff --git a/src/code/irrat.lisp b/src/code/irrat.lisp index 5f24bf9..2591907 100644 --- a/src/code/irrat.lisp +++ b/src/code/irrat.lisp @@ -598,7 +598,17 @@ (float 2 float-type))))))))) (etypecase x (float - (/ (log (float x float-type)) (log-of-2 float-type))) + (multiple-value-bind (f e s) + (decode-float x) + ;; If x = 2^e*f then log2(x) = e + log2(f) = e + + ;; log(f)/log(2). Accuracy could be improved some since this + ;; has 2 rounding operations instead of just 1 for + ;; log(x)/log(2). + (let ((log2 (+ e (/ (log (float f float-type)) + (log-of-2 float-type))))) + (if (minusp s) + (complex log2 (log-2-pi float-type)) + log2)))) (ratio (let ((top (numerator x)) (bot (denominator x))) diff --git a/tests/float.lisp b/tests/float.lisp index 6fe1f50..ff07270 100644 --- a/tests/float.lisp +++ b/tests/float.lisp @@ -10,3 +10,8 @@ (declare (type (double-float (0d0)) x)) (decode-float x))) 1d0))) + +(define-test log2 + (loop for k from -1074 to 1023 do + (let ((x (scale-float 1d0 k))) + (assert-equal k (log x 2)))))

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Summary of changes: src/code/irrat.lisp | 12 +++++++++++- tests/float.lisp | 5 +++++ 2 files changed, 16 insertions(+), 1 deletion(-)

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