;;; calc-math.el --- mathematical functions for Calc
;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
-;; 2005, 2006, 2007 Free Software Foundation, Inc.
+;; 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
;; This file is part of GNU Emacs.
-;; GNU Emacs is free software; you can redistribute it and/or modify
+;; GNU Emacs is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
-;; the Free Software Foundation; either version 3, or (at your option)
-;; any later version.
+;; the Free Software Foundation, either version 3 of the License, or
+;; (at your option) any later version.
;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; GNU General Public License for more details.
;; You should have received a copy of the GNU General Public License
-;; along with GNU Emacs; see the file COPYING. If not, write to the
-;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
-;; Boston, MA 02110-1301, USA.
+;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
;;; Commentary:
;;; is an Emacs float, for acceptable d.dddd....
(defvar math-largest-emacs-expt
- (let ((x 1))
- (while (condition-case nil
- (expt 10.0 x)
- (error nil))
- (setq x (* 2 x)))
- (setq x (/ x 2))
- (while (condition-case nil
- (expt 10.0 x)
- (error nil))
- (setq x (1+ x)))
- (- x 2))
+ (let ((x 1)
+ (pow 1e2))
+ ;; The following loop is for efficiency; it should stop when
+ ;; 10^(2x) is too large. This could be indicated by a range
+ ;; error when computing 10^(2x) or an infinite value for 10^(2x).
+ (while (and
+ pow
+ (< pow 1.0e+INF))
+ (setq x (* 2 x))
+ (setq pow (condition-case nil
+ (expt 10.0 (* 2 x))
+ (error nil))))
+ ;; The following loop should stop when 10^(x+1) is too large.
+ (setq pow (condition-case nil
+ (expt 10.0 (1+ x))
+ (error nil)))
+ (while (and
+ pow
+ (< pow 1.0e+INF))
+ (setq x (1+ x))
+ (setq pow (condition-case nil
+ (expt 10.0 (1+ x))
+ (error nil))))
+ (1- x))
"The largest exponent which Calc will convert to an Emacs float.")
(defvar math-smallest-emacs-expt
(let ((x -1))
(while (condition-case nil
- (expt 10.0 x)
+ (> (expt 10.0 x) 0.0)
(error nil))
(setq x (* 2 x)))
(setq x (/ x 2))
(while (condition-case nil
- (expt 10.0 x)
+ (> (expt 10.0 x) 0.0)
(error nil))
(setq x (1- x)))
(+ x 2))
(defun math-sqrt-raw (a &optional guess) ; [F F F]
(if (not (Math-posp a))
(math-sqrt a)
- (if (null guess)
- (let ((ldiff (- (math-numdigs (nth 1 a)) 6)))
- (or (= (% (+ (nth 2 a) ldiff) 2) 0) (setq ldiff (1+ ldiff)))
- (setq guess (math-make-float (math-isqrt-small
- (math-scale-int (nth 1 a) (- ldiff)))
- (/ (+ (nth 2 a) ldiff) 2)))))
- (math-sqrt-float-iter a guess)))
+ (cond
+ ((math-use-emacs-fn 'sqrt a))
+ (t
+ (if (null guess)
+ (let ((ldiff (- (math-numdigs (nth 1 a)) 6)))
+ (or (= (% (+ (nth 2 a) ldiff) 2) 0) (setq ldiff (1+ ldiff)))
+ (setq guess (math-make-float (math-isqrt-small
+ (math-scale-int (nth 1 a) (- ldiff)))
+ (/ (+ (nth 2 a) ldiff) 2)))))
+ (math-sqrt-float-iter a guess)))))
(defun math-sqrt-float-iter (a guess) ; [F F F]
(math-working "sqrt" guess)
(t (calc-record-why 'scalarp x)
(list 'calcFunc-cot x))))
-(defun math-sin-raw (x) ; [N N]
+(defun math-sin-raw (x &optional orgx) ; [N N]
(cond ((eq (car x) 'cplx)
(let* ((expx (math-exp-raw (nth 2 x)))
(expmx (math-div-float '(float 1 0) expx))
((eq (car x) 'polar)
(math-polar (math-sin-raw (math-complex x))))
((Math-integer-negp (nth 1 x))
- (math-neg-float (math-sin-raw (math-neg-float x))))
+ (math-neg-float (math-sin-raw (math-neg-float x) (if orgx orgx x))))
((math-lessp-float '(float 7 0) x) ; avoid inf loops due to roundoff
- (math-sin-raw (math-mod x (math-two-pi))))
- (t (math-sin-raw-2 x x))))
+ (math-sin-raw (math-mod x (math-two-pi)) (if orgx orgx x)))
+ (t (math-sin-raw-2 x (if orgx orgx x)))))
(defun math-cos-raw (x) ; [N N]
(if (eq (car-safe x) 'polar)
(math-polar (math-cos-raw (math-complex x)))
- (math-sin-raw (math-sub (math-pi-over-2) x))))
+ (math-sin-raw (math-sub (math-pi-over-2) x) x)))
(defun math-sec-raw (x) ; [N N]
(cond ((eq (car x) 'cplx)
(math-cos-raw-2 xmpo2 orgx))
((math-lessp-float x (math-neg (math-pi-over-4)))
(math-neg (math-cos-raw-2 (math-add (math-pi-over-2) x) orgx)))
- ((math-nearly-zerop-float x orgx) '(float 0 0))
+ ((math-with-extra-prec -1 (math-nearly-zerop-float x orgx))
+ '(float 0 0))
+ ((math-use-emacs-fn 'sin x))
(calc-symbolic-mode (signal 'inexact-result nil))
(t (math-sin-series x 6 4 x (math-neg-float (math-sqr-float x)))))))
(defun math-cos-raw-2 (x orgx) ; [F F]
- (cond ((math-nearly-zerop-float x orgx) '(float 1 0))
+ (cond ((math-with-extra-prec -1 (math-nearly-zerop-float x orgx))
+ '(float 1 0))
+ ((math-use-emacs-fn 'cos x))
(calc-symbolic-mode (signal 'inexact-result nil))
(t (let ((xnegsqr (math-neg-float (math-sqr-float x))))
(math-sin-series
((Math-integer-negp (nth 1 x))
(math-neg-float (math-arctan-raw (math-neg-float x))))
((math-zerop x) x)
+ ((math-use-emacs-fn 'atan x))
(calc-symbolic-mode (signal 'inexact-result nil))
((math-equal-int x 1) (math-pi-over-4))
((math-equal-int x -1) (math-neg (math-pi-over-4)))
'(float 0 0))
(calc-symbolic-mode (signal 'inexact-result nil))
((math-posp (nth 1 x)) ; positive and real
- (let ((xdigs (1- (math-numdigs (nth 1 x)))))
- (math-add-float (math-ln-raw-2 (list 'float (nth 1 x) (- xdigs)))
- (math-mul-float (math-float (+ (nth 2 x) xdigs))
- (math-ln-10)))))
+ (cond
+ ((math-use-emacs-fn 'log x))
+ (t
+ (let ((xdigs (1- (math-numdigs (nth 1 x)))))
+ (math-add-float (math-ln-raw-2 (list 'float (nth 1 x) (- xdigs)))
+ (math-mul-float (math-float (+ (nth 2 x) xdigs))
+ (math-ln-10)))))))
((math-zerop x)
(math-reject-arg x "*Logarithm of zero"))
((eq calc-complex-mode 'polar) ; negative and real
(math-lnp1-series nextsum (1+ n) nextx x))))
(defconst math-approx-ln-10
- (eval-when-compile
- (math-read-number-simple "2.302585092994045684018"))
+ (math-read-number-simple "2.302585092994045684018")
"An approximation for ln(10).")
(math-defcache math-ln-10 math-approx-ln-10
(math-ln-raw-2 '(float 1 1)))
(defconst math-approx-ln-2
- (eval-when-compile
- (math-read-number-simple "0.693147180559945309417"))
+ (math-read-number-simple "0.693147180559945309417")
"An approximation for ln(2).")
(math-defcache math-ln-2 math-approx-ln-2
(provide 'calc-math)
-;;; arch-tag: c7367e8e-d0b8-4f70-8577-2fb3f31dbb4c
+;; arch-tag: c7367e8e-d0b8-4f70-8577-2fb3f31dbb4c
;;; calc-math.el ends here
HCoop / bpt / emacs.git / blobdiff