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- Log ----------------------------------------------------------------- commit 4d3255aa1a770f59d2851fd2c85707164ca485f5 Author: Raymond Toy toy.raymond@gmail.com Date: Mon Nov 24 15:20:12 2014 -0800

Add log10 implementation for double-doubles.

Since log2 and log10 use basically the same natural log implementation, factor that out the common part into its own routine.

diff --git a/src/code/irrat-dd.lisp b/src/code/irrat-dd.lisp index 45b422e..d0acdd7 100644 --- a/src/code/irrat-dd.lisp +++ b/src/code/irrat-dd.lisp @@ -44,6 +44,20 @@ 4.4269504088896340735992468100189213742664595w-1 _N"log2(e)-1")

+;; l102a+log102b = log10(2) to extra precision +(defconstant l102a + 0.3125w0) + +(defconstant l102b + -1.14700043360188047862611052755069732318101185w-2) + +;; l10ea + l10eb = log10(2) to extra precsion +(defconstant l10ea + 0.5w0) + +(defconstant l10eb + -6.570551809674817234887108108339491770560299w-2) + (defconstant dd-pi 3.141592653589793238462643383279502884197169w0 _N"Pi") @@ -1241,8 +1255,8 @@ pi/4 11001001000011111101101010100010001000010110100011000 010001101001100010 (values (- (dd-%%cos reduced)) (dd-%%sin reduced))))))))

-;;; dd-%log2 -;;; Base 2 logarithm. +;;; dd-%log2 and dd-%log10 +;;; Base 2 and base 10 logarithm. ;;; ;;; The argument is separated into its exponent and fractional ;;; parts. If the exponent is between -1 and +1, the (natural) @@ -1254,6 +1268,9 @@ pi/4 11001001000011111101101010100010001000010110100011000 010001101001100010 ;;; ;;; log(x) = z + z**3 R(z)/S(z). ;;; +;;; This gives the natural log. To get the base 2 and base 10 log, +;;; carefully multiply the natural log by log2(e) or log10(e) as +;;; appropriate. (let ((P (make-array 13 :element-type 'double-double-float :initial-contents '( @@ -1314,52 +1331,82 @@ pi/4 11001001000011111101101010100010001000010110100011000 010001101001100010 -1.332535117259762928288745111081235577029w6 1.701761051846631278975701529965589676574w6 )))) + (flet + ((compute-log (x) + ;; Common routine to extract the exponent and fraction from x + ;; and compute the log(f). Return the exponent, the fraction, + ;; and the parts of the polynomial computation that is needed + ;; to finish off the final logarithm. + (declare (type double-double-float x) + (optimize (speed 3) (space 0) + (inhibit-warnings 3))) + (multiple-value-bind (x e) + (decode-float x) + (declare (type double-double-float x) + (type double-float-exponent e)) + (let ((z 0w0) + (y 0w0)) + (declare (type double-double-float z y)) + (cond ((or (> e 2) + (< e -2)) + (cond ((< x sqrt-1/2) + ;; 2*(2*x-1)/(2*x+1) + (decf e) + (setf z (- x 0.5w0)) + (setf y (+ (* 0.5w0 z) 0.5w0))) + (t + ;; 2*(x-1)/(x+1) + (setf z (- x 0.5w0)) + (decf z 0.5w0) + (setf y (+ (* 0.5w0 x) 0.5w0)))) + (setf x (/ z y)) + (setf z (* x x)) + (setf y (* x (/ (* z (poly-eval z r)) + (poly-eval-1 z s))))) + (t + (cond ((< x sqrt-1/2) + (decf e) + (setf x (- (scale-float x 1) 1))) + (t + (decf x))) + (setf z (* x x)) + (setf y (* x (/ (* z (poly-eval x p)) + (poly-eval-1 x q)))) + (decf y (scale-float z -1)))) + (values e x y z))))) + (defun dd-%log2 (x) (declare (type double-double-float x) (optimize (speed 3) (space 0) (inhibit-warnings 3))) - (multiple-value-bind (x e) - (decode-float x) - (declare (type double-double-float x) - (type double-float-exponent e)) - (let ((z 0w0) - (y 0w0)) - (declare (type double-double-float z y)) - (cond ((or (> e 2) - (< e -2)) - (cond ((< x sqrt-1/2) - ;; 2*(2*x-1)/(2*x+1) - (decf e) - (setf z (- x 0.5w0)) - (setf y (+ (* 0.5w0 z) 0.5w0))) - (t - ;; 2*(x-1)/(x+1) - (setf z (- x 0.5w0)) - (decf z 0.5w0) - (setf y (+ (* 0.5w0 x) 0.5w0)))) - (setf x (/ z y)) - (setf z (* x x)) - (setf y (* x (/ (* z (poly-eval z r)) - (poly-eval-1 z s))))) - (t - (cond ((< x sqrt-1/2) - (decf e) - (setf x (- (scale-float x 1) 1))) - (t - (decf x))) - (setf z (* x x)) - (setf y (* x (/ (* z (poly-eval x p)) - (poly-eval-1 x q)))) - (decf y (scale-float z -1)))) - ;; Multiply log of fraction by log2(e) and base 2 exponent by 1 - ;; - ;; This sequence of operations is critical - (setf z (* y log2ea)) - (setf z (+ z (* x log2ea))) - (setf z (+ z y)) - (setf z (+ z x)) - (setf z (+ z e)) - z)))) + (multiple-value-bind (e x y z) + (compute-log x) + ;; Multiply log of fraction by log2(e) and base 2 exponent by 1 + ;; + ;; This sequence of operations is critical + (setf z (* y log2ea)) + (incf z (* x log2ea)) + (incf z y) + (incf z x) + (incf z e) + z)) + + (defun dd-%log10 (x) + (declare (type double-double-float x) + (optimize (speed 3) (space 0) + (inhibit-warnings 3))) + (multiple-value-bind (e x y z) + (compute-log x) + ;; Multiply log of fraction by log10(e) and base 2 exponent by log10(2). + ;; + ;; This sequence of operations is critical. + (setf z (* y l10eb)) + (incf z (* x l10eb)) + (incf z (* e l102b)) + (incf z (* y l10ea)) + (incf z (* x l10ea)) + (incf z (* e l102a)) + z))))

;;; dd-%exp2 ;;; 2^x

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Summary of changes: src/code/irrat-dd.lisp | 135 +++++++++++++++++++++++++++++++++---------------- 1 file changed, 91 insertions(+), 44 deletions(-)

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