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- Log ----------------------------------------------------------------- commit cc23f1098858d652c66728ea85c1c331bfb0fbb8 Author: Raymond Toy toy.raymond@gmail.com Date: Mon Mar 21 19:39:24 2011 -0400

Move the uses of foo-t before the use of foo-t.

diff --git a/qd.lisp b/qd.lisp index fb3e4e1..9f1ec3d 100644 --- a/qd.lisp +++ b/qd.lisp @@ -409,11 +409,6 @@ If TARGET is given, TARGET is destructively modified to contain the result." ;; which don't do a very good job with dataflow. CMUCL is one of ;; those compilers.

-(defun add-qd (a b &optional (target #+oct-array (%make-qd-d 0d0 0d0 0d0 0d0))) - "Return the sum of the %QUAD-DOUBLE numbers A and B. -If TARGET is given, TARGET is destructively modified to contain the result." - (add-qd-t a b target)) -

(defun add-qd-t (a b target) (declare (type %quad-double a b #+oct-array target) @@ -476,6 +471,12 @@ If TARGET is given, TARGET is destructively modified to contain the result." (%store-qd-d target (+ a0 b0) 0d0 0d0 0d0) (%store-qd-d target s0 s1 s2 s3)))))))))))

+(defun add-qd (a b &optional (target #+oct-array (%make-qd-d 0d0 0d0 0d0 0d0))) + "Return the sum of the %QUAD-DOUBLE numbers A and B. +If TARGET is given, TARGET is destructively modified to contain the result." + (add-qd-t a b target)) + + (defun neg-qd-t (a target) (declare (type %quad-double a #+oct-array target) #+(and cmu (not oct-array)) (ignore target)) @@ -666,11 +667,6 @@ If TARGET is given, TARGET is destructively modified to contain the result." ;; Clisp says ;; 14.142135623730950488016887242096980785696718753769480731766797379908L0

-(defun mul-qd (a b &optional (target #+oct-array (%make-qd-d 0d0 0d0 0d0 0d0))) - "Returns the product of the %QUAD-DOUBLE numbers A and B. -If TARGET is given, TARGET is destructively modified to contain the result." - (mul-qd-t a b target)) - (defun mul-qd-t (a b target) (declare (type %quad-double a b #+oct-array target) (optimize (speed 3) @@ -736,6 +732,10 @@ If TARGET is given, TARGET is destructively modified to contain the result." (%store-qd-d target p0 0d0 0d0 0d0) (%store-qd-d target r0 r1 s0 s1))))))))))))))

+(defun mul-qd (a b &optional (target #+oct-array (%make-qd-d 0d0 0d0 0d0 0d0))) + "Returns the product of the %QUAD-DOUBLE numbers A and B. +If TARGET is given, TARGET is destructively modified to contain the result." + (mul-qd-t a b target))

;; This is the non-sloppy version. I think this works just fine, but ;; since qd defaults to the sloppy multiplication version, we do the @@ -838,11 +838,6 @@ If TARGET is given, TARGET is destructively modified to contain the result." (multiple-value-call #'%make-qd-d (renorm-5 p0 p1 s0 t0 t1))))))))))))))))))))

-(defun sqr-qd (a &optional (target #+oct-array (%make-qd-d 0d0 0d0 0d0 0d0))) - "Return the square of the %QUAD-DOUBLE number A. If TARGET is also given, -it is destructively modified with the result." - (sqr-qd-t a target)) - (defun sqr-qd-t (a target) "Square A" (declare (type %quad-double a #+oct-array target) @@ -890,12 +885,11 @@ it is destructively modified with the result." (multiple-value-bind (a0 a1 a2 a3) (renorm-5 p0 p1 p2 p3 p4) (%store-qd-d target a0 a1 a2 a3))))))))) -

-(defun div-qd (a b &optional (target #+oct-array (%make-qd-d 0d0 0d0 0d0 0d0))) - "Return the quotient of the two %QUAD-DOUBLE numbers A and B. -If TARGET is given, it destrutively modified with the result." - (div-qd-t a b target)) +(defun sqr-qd (a &optional (target #+oct-array (%make-qd-d 0d0 0d0 0d0 0d0))) + "Return the square of the %QUAD-DOUBLE number A. If TARGET is also given, +it is destructively modified with the result." + (sqr-qd-t a target))

#+nil (defun div-qd-t (a b target) @@ -948,6 +942,11 @@ If TARGET is given, it destrutively modified with the result." (renorm-4 q0 q1 q2 q3) (%store-qd-d target q0 q1 q2 q3))))))))

+(defun div-qd (a b &optional (target #+oct-array (%make-qd-d 0d0 0d0 0d0 0d0))) + "Return the quotient of the two %QUAD-DOUBLE numbers A and B. +If TARGET is given, it destrutively modified with the result." + (div-qd-t a b target)) + (declaim (inline invert-qd))

(defun invert-qd (v)

commit 6b8dc51d96004406780ec1faa2cd4ce3b127c287 Author: Raymond Toy toy.raymond@gmail.com Date: Sat Mar 19 11:38:43 2011 -0400

Add rem and mod functions that were left out.

diff --git a/qd-methods.lisp b/qd-methods.lisp index cbf0daa..29b296d 100644 --- a/qd-methods.lisp +++ b/qd-methods.lisp @@ -671,6 +671,12 @@ underlying floating-point format" (ceiling x y) (floor x y)))

+(defun rem (x y) + (nth-value 1 (truncate x y))) + +(defun mod (x y) + (nth-value 1 (floor x y))) + (defun ftruncate (x &optional (y 1)) (if (minusp x) (fceiling x y) diff --git a/qd-package.lisp b/qd-package.lisp index b102435..7db5cd3 100644 --- a/qd-package.lisp +++ b/qd-package.lisp @@ -188,6 +188,8 @@ #:ftruncate #:round #:fround + #:rem + #:mod #:realpart #:imagpart #:conjugate @@ -258,6 +260,8 @@ #:ftruncate #:round #:fround + #:rem + #:mod #:realpart #:imagpart #:conjugate

commit 97bc71a13186735474eba77043d685b0bd0a00d6 Author: Raymond Toy toy.raymond@gmail.com Date: Fri Mar 18 09:06:10 2011 -0400

Add series for incomplete-gamma for when the fraction is slow.

o Add series for incomplete gamma function for small a and z. Needed because the continued fraction is slow in this range. o In INCOMPLETE-GAMMA-TAIL, call INCOMPLETE-GAMMA instead of CF-INCOMPLETE-GAMMA just in case a and z are small. o In INCOMPLETE-GAMMA, use the series for small a and z. o Simplify evaluation of Si(z) when z is real.

diff --git a/qd-gamma.lisp b/qd-gamma.lisp index a6fc7cf..c0cacaa 100644 --- a/qd-gamma.lisp +++ b/qd-gamma.lisp @@ -265,6 +265,21 @@ #'(lambda (n) (- (* z (+ a n))))))))))

+;; Series expansion for incomplete gamma. Intended for |a|<1 and +;; |z|<1. The series is +;; +;; g(a,z) = z^a * sum((-z)^k/k!/(a+k), k, 0, inf) +(defun s-incomplete-gamma (a z) + (let ((-z (- z)) + (eps (epsilon z))) + (loop for k from 0 + for term = 1 then (* term (/ -z k)) + for sum = (/ a) then (+ sum (/ term (+ a k))) + when (< (abs term) (* (abs sum) eps)) + return (* sum (expt z a))))) + + + ;; Tail of the incomplete gamma function. (defun incomplete-gamma-tail (a z) "Tail of the incomplete gamma function defined by: @@ -276,9 +291,9 @@ (if (and (realp a) (realp z)) ;; For real values, we split the result to compute either the ;; tail directly or from gamma(a) - incomplete-gamma - (if (> z (- a 1)) + (if (> (abs z) (abs (- a 1))) (cf-incomplete-gamma-tail a z) - (- (gamma a) (cf-incomplete-gamma a z))) + (- (gamma a) (incomplete-gamma a z))) (cf-incomplete-gamma-tail a z))))

(defun incomplete-gamma (a z) @@ -288,13 +303,18 @@ (let* ((prec (float-contagion a z)) (a (apply-contagion a prec)) (z (apply-contagion z prec))) - (if (and (realp a) (realp z)) - (if (< z (- a 1)) - (cf-incomplete-gamma a z) - (- (gamma a) (cf-incomplete-gamma-tail a z))) - (if (< (abs z) (abs a)) - (cf-incomplete-gamma a z) - (- (gamma a) (cf-incomplete-gamma-tail a z)))))) + (if (and (< (abs a) 1) (< (abs z) 1)) + (s-incomplete-gamma a z) + (if (and (realp a) (realp z)) + (if (< z (- a 1)) + (cf-incomplete-gamma a z) + (- (gamma a) (cf-incomplete-gamma-tail a z))) + ;; The continued fraction doesn't converge very fast if a + ;; and z are small. In this case, use the series + ;; expansion instead, which converges quite rapidly. + (if (< (abs z) (abs a)) + (cf-incomplete-gamma a z) + (- (gamma a) (cf-incomplete-gamma-tail a z)))))))

(defun erf (z) "Error function: @@ -405,9 +425,20 @@ (- (log -iz) (log iz))))))) (if (realp z) - (if (< z 0) - (- (sin-integral (- z))) - (si z)) + ;; Si is odd and real for real z. In this case, we have + ;; + ;; Si(x) = %i/2*(gamma_inc_tail(0, -%i*x) - gamma_inc_tail(0, %i*x) - %i*%pi) + ;; = %pi/2 + %i/2*(gamma_inc_tail(0, -%i*x) - gamma_inc_tail(0, %i*x)) + ;; But gamma_inc_tail(0, conjugate(z)) = conjugate(gamma_inc_tail(0, z)), so + ;; + ;; Si(x) = %pi/2 + imagpart(gamma_inc_tail(0, %i*x)) + (cond ((< z 0) + (- (sin-integral (- z)))) + ((= z 0) + (* 0 z)) + (t + (+ (* 1/2 (float-pi z)) + (imagpart (incomplete-gamma-tail 0 (complex 0 z)))))) (si z))))

(defun cos-integral (z)

commit 50fc6412a3effd9bea8f3e481f7c35c3c911f856 Author: Raymond Toy toy.raymond@gmail.com Date: Thu Mar 17 23:12:30 2011 -0400

Implement Si and Ci, sin and cos integrals.

diff --git a/qd-gamma.lisp b/qd-gamma.lisp index dfc87a6..a6fc7cf 100644 --- a/qd-gamma.lisp +++ b/qd-gamma.lisp @@ -387,4 +387,49 @@ (- (realpart (fs (- z)))) (realpart (fs z))) (fs z))))) - \ No newline at end of file + +(defun sin-integral (z) + "Sin integral: + + Si(z) = integrate(sin(t)/t, t, 0, z)" + ;; Wolfram has + ;; + ;; Si(z) = %i/2*(gamma_inc_tail(0, -%i*z) - gamma_inc_tail(0, %i*z) + log(-%i*z)-log(%i*z)) + ;; + (flet ((si (z) + (* #c(0 1/2) + (let ((iz (* #c(0 1) z)) + (-iz (* #c(0 -1) z))) + (+ (- (incomplete-gamma-tail 0 -iz) + (incomplete-gamma-tail 0 iz)) + (- (log -iz) + (log iz))))))) + (if (realp z) + (if (< z 0) + (- (sin-integral (- z))) + (si z)) + (si z)))) + +(defun cos-integral (z) + "Cos integral: + + Ci(z) = integrate((cos(t) - 1)/t, t, 0, z) + log(z) + gamma + + where gamma is Euler-Mascheroni constant" + ;; Wolfram has + ;; + ;; Ci(z) = log(z) - 1/2*(gamma_inc_tail(0, -%i*z) + gamma_inc_tail(0, %i*z) + log(-%i*z)+log(%i*z)) + ;; + (flet ((ci (z) + (- (log z) + (* 1/2 + (let ((iz (* #c(0 1) z)) + (-iz (* #c(0 -1) z))) + (+ (+ (incomplete-gamma-tail 0 -iz) + (incomplete-gamma-tail 0 iz)) + (+ (log -iz) + (log iz)))))))) + (if (and (realp z) (plusp z)) + (realpart (ci z)) + (ci z)))) + \ No newline at end of file

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

Summary of changes: qd-gamma.lisp | 96 +++++++++++++++++++++++++++++++++++++++++++++++++------ qd-methods.lisp | 6 +++ qd-package.lisp | 4 ++ qd.lisp | 39 +++++++++++----------- 4 files changed, 115 insertions(+), 30 deletions(-)

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