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- Log ----------------------------------------------------------------- commit f86bc7e7f3c5b617a141ac5d0f32b5fc6b5e77d5 Author: Raymond Toy toy.raymond@gmail.com Date: Mon Mar 7 19:36:35 2011 -0500

Add elliptic K function and tests for it and Jacobi functions.

qd-elliptic.lisp: o Add support for the complete elliptic integral K using Carlson's Rf function.

rt-tests.lisp: o Fix indentation for oct.atan.5 o Add tests for elliptic K o Add tests for Jacobi sn, cn, and dn functions.

diff --git a/qd-elliptic.lisp b/qd-elliptic.lisp index 9240eb0..3336444 100644 --- a/qd-elliptic.lisp +++ b/qd-elliptic.lisp @@ -198,3 +198,59 @@ (* (/ (+ 1 root-mu1) mu) (/ (- (* d d) root-mu1) d))))) + +(defun errtol (&rest args) + ;; Compute error tolerance as sqrt(2^(-fpprec)). Not sure this is + ;; quite right, but it makes the routines more accurate as fpprec + ;; increases. + (sqrt (reduce #'min (mapcar #'(lambda (x) + (if (rationalp x) + double-float-epsilon + (epsilon x))) + args)))) + +(defun carlson-rf (x y z) + (let* ((xn x) + (yn y) + (zn z) + (a (/ (+ xn yn zn) 3)) + (epslon (/ (max (abs (- a xn)) + (abs (- a yn)) + (abs (- a zn))) + (errtol x y z))) + (an a) + (power4 1) + (n 0) + xnroot ynroot znroot lam) + (loop while (> (* power4 epslon) (abs an)) + do + (setf xnroot (sqrt xn)) + (setf ynroot (sqrt yn)) + (setf znroot (sqrt zn)) + (setf lam (+ (* xnroot ynroot) + (* xnroot znroot) + (* ynroot znroot))) + (setf power4 (* power4 1/4)) + (setf xn (* (+ xn lam) 1/4)) + (setf yn (* (+ yn lam) 1/4)) + (setf zn (* (+ zn lam) 1/4)) + (setf an (* (+ an lam) 1/4)) + (incf n)) + ;; c1=-3/14,c2=1/6,c3=9/88,c4=9/22,c5=-3/22,c6=-9/52,c7=3/26 + (let* ((xndev (/ (* (- a x) power4) an)) + (yndev (/ (* (- a y) power4) an)) + (zndev (- (+ xndev yndev))) + (ee2 (- (* xndev yndev) (* 6 zndev zndev))) + (ee3 (* xndev yndev zndev)) + (s (+ 1 + (* -1/10 ee2) + (* 1/14 ee3) + (* 1/24 ee2 ee2) + (* -3/44 ee2 ee3)))) + (/ s (sqrt an))))) + +(defun elliptic-k (m) + (cond ((= m 0) + (/ (float +pi+ m) 2)) + (t + (carlson-rf 0 (- 1 m) 1)))) diff --git a/rt-tests.lisp b/rt-tests.lisp index b9e5867..f4e06c1 100644 --- a/rt-tests.lisp +++ b/rt-tests.lisp @@ -118,8 +118,8 @@

(rt:deftest oct.atan.5 (let* ((arg #q-1q100) - (y (/ (atan arg) +pi+)) - (true #q-.5)) + (y (/ (atan arg) +pi+)) + (true #q-.5)) (check-accuracy 212 y true)) nil)

@@ -761,3 +761,70 @@ (let ((true (cl:atanh #c(2d0 1d-20)))) (check-signs #'atanh #q2 true)) t) + +;; elliptic_k(-1) = gamma(1/4)^2/2^(5/2)/sqrt(%pi) +(rt:deftest oct.elliptic-k.1d + (let* ((val (elliptic-k -1d0)) + (true #q1.311028777146059905232419794945559706841377475715811581408410851900395293535207125115147766480714547q0)) + (check-accuracy 53 val true)) + nil) + +(rt:deftest oct.elliptic-k.1q + (let* ((val (elliptic-k #q-1q0)) + (true #q1.311028777146059905232419794945559706841377475715811581408410851900395293535207125115147766480714547q0)) + (check-accuracy 210 val true)) + nil) + +;; elliptic_k(1/2) = %pi^(3/2)/2/gamma(3/4)^2 +(rt:deftest oct.elliptic-k.2d + (let* ((val (elliptic-k 0.5d0)) + (true #q1.854074677301371918433850347195260046217598823521766905585928045056021776838119978357271861650371897q0)) + (check-accuracy 53 val true)) + nil) + +(rt:deftest oct.elliptic-k.2q + (let* ((val (elliptic-k #q.5)) + (true #q1.854074677301371918433850347195260046217598823521766905585928045056021776838119978357271861650371897q0)) + (check-accuracy 210 val true)) + nil) + +;; jacobi_sn(K,1/2) = 1, where K = elliptic_k(1/2) +(rt:deftest oct.jacobi-sn.1d + (let* ((ek (elliptic-k .5d0)) + (val (jacobi-sn ek .5d0))) + (check-accuracy 54 val 1d0)) + nil) + +(rt:deftest oct.jacobi-sn.1q + (let* ((ek (elliptic-k #q.5)) + (val (jacobi-sn ek #q.5))) + (check-accuracy 212 val #q1)) + nil) + +;; jacobi_cn(K,1/2) = 0 +(rt:deftest oct.jacobi-cn.1d + (let* ((ek (elliptic-k .5d0)) + (val (jacobi-cn ek .5d0))) + (check-accuracy 50 val 0d0)) + nil) + +(rt:deftest oct.jacobi-sn.1q + (let* ((ek (elliptic-k #q.5)) + (val (jacobi-cn ek #q.5))) + (check-accuracy 210 val #q0)) + nil) + +;; jacobi-dn(K, 1/2) = sqrt(1/2) +(rt:deftest oct.jacobi-dn.1d + (let* ((ek (elliptic-k .5d0)) + (true (sqrt .5d0)) + (val (jacobi-dn ek .5d0))) + (check-accuracy 52 val true)) + nil) + +(rt:deftest oct.jacobi-dn.1q + (let* ((ek (elliptic-k #q.5)) + (true (sqrt #q.5)) + (val (jacobi-dn ek #q.5))) + (check-accuracy 212 val true)) + nil)

commit 1a38c9e3dd557620c053919bbccde06741118a36 Author: Raymond Toy toy.raymond@gmail.com Date: Mon Mar 7 19:33:34 2011 -0500

Fix bug in qd-scale-float.

MAKE-QD-D returns a %quad-double, not qd-real. Use +QD-REAL-ONE+ instead.

diff --git a/qd-methods.lisp b/qd-methods.lisp index 037bcc3..4f8065f 100644 --- a/qd-methods.lisp +++ b/qd-methods.lisp @@ -1108,7 +1108,7 @@ underlying floating-point format" ;; a quad-double. For most purposes we want epsilon to be close to ;; the 212 bits of precision (4*53 bits) that we normally have with ;; a quad-double. - (scale-float (make-qd-d 1d0) -212)) + (scale-float +qd-real-one+ -212))

(defmethod epsilon ((m qd-complex)) (epsilon (realpart m)))

-----------------------------------------------------------------------

Summary of changes: qd-elliptic.lisp | 56 ++++++++++++++++++++++++++++++++++++++++++ qd-methods.lisp | 2 +- rt-tests.lisp | 71 ++++++++++++++++++++++++++++++++++++++++++++++++++++- 3 files changed, 126 insertions(+), 3 deletions(-)

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