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From: Raymond Toy <rtoy@us...>  20021008 17:06:29

Update of /cvsroot/maxima/maxima/src In directory uswprcvs1:/tmp/cvsserv12070/src Modified Files: float.lisp Log Message: o Fix bug in fpshift wherein right shifts of negative numbers were not truncated properly o Add some comments on the algorithm used by fplog. o Move the multiplication by 2 that was inside the loop to outside the loop. Index: float.lisp =================================================================== RCS file: /cvsroot/maxima/maxima/src/float.lisp,v retrieving revision 1.3 retrieving revision 1.4 diff u d r1.3 r1.4  float.lisp 27 Jun 2002 17:37:20 0000 1.3 +++ float.lisp 8 Oct 2002 17:06:25 0000 1.4 @@ 575,13 +575,22 @@ FPPREC)) (RETURN (FPSHIFT L (MINUS *M))))))) +;; Compute (* L (expt d n)) where D is 2 or 10 depending on +;; *decfp. Throw away an fractional part by truncating to zero. (DEFUN FPSHIFT (L N)  ;; It seems that BIGLSH is broken so we replace it by ASH  ;(COND ((NULL *DECFP) (BIGLSH L N))  (COND ((NULL *DECFP) (ASH L N))  ((GREATERP N 0.) (TIMES L (EXPT 10. N)))  ((LESSP N 0.) (QUOTIENT L (EXPT 10. (MINUS N))))  (T L))) + (COND ((NULL *DECFP) + (cond ((and (minusp n) (minusp l)) + ;; Left shift of negative number requires some + ;; care. (That is, (truncate l (expt 2 n)), but use + ;; shifts instead.) + ( (ash ( l) n))) + (t + (ash l n)))) + ((GREATERP N 0.) + (TIMES L (EXPT 10. N))) + ((LESSP N 0.) + (QUOTIENT L (EXPT 10. (MINUS N)))) + (T L))) ;; Bignum LSH  N is assumed (and declared above) to be a fixnum. ;; This isn't really LSH, since the sign bit isn't propagated when @@ 1005,11 +1014,38 @@ (COND (MINUS (ADD A (MUL '$%I ($BFLOAT '$%PI)))) (T A))) NIL)) +;;; Computes the log of a bigfloat number. +;;; +;;; Uses the series +;;; +;;; log(1+x) = sum((x/(x+2))^(2*n+1)/(2*n+1),n,0,inf); +;;; +;;; +;;; INF x 2 n + 1 +;;; ==== () +;;; \ x + 2 +;;; = 2 >  +;;; / 2 n + 1 +;;; ==== +;;; n = 0 +;;; +;;; +;;; which converges for x > 0. +;;; +;;; Note that FPLOG is given 1+X, not X. +;;; +;;; However, to aid convergence of the series, we scale 1+x until 1/e +;;; < 1+x <= e. +;;; (DEFUN FPLOG (X) (PROG (OVER TWO ANS OLDANS TERM E) (IF (NOT (GREATERP (CAR X) 0)) (MERROR "Nonpositive argument to FPLOG"))  (SETQ E (FPE) OVER (FPQUOTIENT (FPONE) E) ANS 0) + (SETQ E (FPE) + OVER (FPQUOTIENT (FPONE) E) + ANS 0) + ;; Scale X until 1/e < X <= E. ANS keeps track of how + ;; many factors of E were used. Set X to NIL if X is E. (DO () (NIL) (COND ((EQUAL X E) (SETQ X NIL) (RETURN NIL)) ((AND (FPLESSP X E) (FPLESSP OVER X)) @@ 1020,21 +1056,27 @@ (T (SETQ ANS (ADD1 ANS)) (SETQ X (FPQUOTIENT X e))))) (COND ((NULL X) (RETURN (INTOFP (ADD1 ANS)))))  (SETQ X (FPDIFFERENCE X (FPONE)) ANS (INTOFP ANS)) + ;; Prepare X for the series. The series is for 1 + x, so + ;; get x from our X. TERM is (x/(x+2)). X becomes + ;; (x/(x+2))^2. + (SETQ X (FPDIFFERENCE X (FPONE)) + ANS (INTOFP ANS)) (SETQ X (FPEXPT (SETQ TERM (FPQUOTIENT X (FPPLUS X (SETQ TWO (INTOFP 2))))) 2))  (DO ((N 0 (f1+ N))) ((EQUAL ANS OLDANS)) + ;; Sum the series until the sum (in ANS) doesn't change + ;; anymore. + (DO ((N 1 (+ N 2))) + ((EQUAL ANS OLDANS)) (SETQ OLDANS ANS)  (SETQ  ANS  (FPPLUS  ANS  (FPTIMES* TWO (FPQUOTIENT TERM (INTOFP (f1+ (f* 2 N))))))) + (SETQ ANS + (FPPLUS + ANS + (FPQUOTIENT TERM (INTOFP N)))) (SETQ TERM (FPTIMES* TERM X)))  (RETURN ANS))) + (RETURN (fptimes* two ANS)))) (DEFUN MABSBIGFLOAT (L) (PROG (R) 