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- Newsgroups: comp.sources.misc
- From: daveg@synaptics.com (David Gillespie)
- Subject: v24i069: gnucalc - GNU Emacs Calculator, v2.00, Part21/56
- Message-ID: <1991Oct31.072644.17973@sparky.imd.sterling.com>
- X-Md4-Signature: 935912531147058885be56ee6ad9de74
- Date: Thu, 31 Oct 1991 07:26:44 GMT
- Approved: kent@sparky.imd.sterling.com
-
- Submitted-by: daveg@synaptics.com (David Gillespie)
- Posting-number: Volume 24, Issue 69
- Archive-name: gnucalc/part21
- Environment: Emacs
- Supersedes: gmcalc: Volume 13, Issue 27-45
-
- ---- Cut Here and unpack ----
- #!/bin/sh
- # do not concatenate these parts, unpack them in order with /bin/sh
- # file calc-mat.el continued
- #
- if test ! -r _shar_seq_.tmp; then
- echo 'Please unpack part 1 first!'
- exit 1
- fi
- (read Scheck
- if test "$Scheck" != 21; then
- echo Please unpack part "$Scheck" next!
- exit 1
- else
- exit 0
- fi
- ) < _shar_seq_.tmp || exit 1
- if test ! -f _shar_wnt_.tmp; then
- echo 'x - still skipping calc-mat.el'
- else
- echo 'x - continuing file calc-mat.el'
- sed 's/^X//' << 'SHAR_EOF' >> 'calc-mat.el' &&
- X (nth j (nth k lu))))
- X k (1+ k)))
- X (setcar (nthcdr j (nth i lu)) sum)
- X (let ((dum (math-abs-approx sum)))
- X (if (Math-lessp big dum)
- X (setq big dum
- X imax i)))
- X (setq i (1+ i)))
- X (if (> imax j)
- X (setq lu (math-swap-rows lu j imax)
- X d (- d)))
- X (setq index (cons imax index))
- X (let ((pivot (nth j (nth j lu))))
- X (if (math-zerop pivot)
- X (throw 'singular nil)
- X (setq i j)
- X (while (<= (setq i (1+ i)) n)
- X (setcar (nthcdr j (nth i lu))
- X (math-div (nth j (nth i lu)) pivot)))))
- X (setq j (1+ j)))
- X (list lu (nreverse index) d))
- )
- X
- (defun math-swap-rows (m r1 r2)
- X (or (= r1 r2)
- X (let* ((r1prev (nthcdr (1- r1) m))
- X (row1 (cdr r1prev))
- X (r2prev (nthcdr (1- r2) m))
- X (row2 (cdr r2prev))
- X (r2next (cdr row2)))
- X (setcdr r2prev row1)
- X (setcdr r1prev row2)
- X (setcdr row2 (cdr row1))
- X (setcdr row1 r2next)))
- X m
- )
- X
- X
- (defun math-lud-solve (lud b &optional need)
- X (if lud
- X (let* ((x (math-copy-matrix b))
- X (n (1- (length x)))
- X (m (1- (length (nth 1 x))))
- X (lu (car lud))
- X (col 1)
- X i j ip ii index sum)
- X (while (<= col m)
- X (math-working "LUD solver step" col)
- X (setq i 1
- X ii nil
- X index (nth 1 lud))
- X (while (<= i n)
- X (setq ip (car index)
- X index (cdr index)
- X sum (nth col (nth ip x)))
- X (setcar (nthcdr col (nth ip x)) (nth col (nth i x)))
- X (if (null ii)
- X (or (math-zerop sum)
- X (setq ii i))
- X (setq j ii)
- X (while (< j i)
- X (setq sum (math-sub sum (math-mul (nth j (nth i lu))
- X (nth col (nth j x))))
- X j (1+ j))))
- X (setcar (nthcdr col (nth i x)) sum)
- X (setq i (1+ i)))
- X (while (>= (setq i (1- i)) 1)
- X (setq sum (nth col (nth i x))
- X j i)
- X (while (<= (setq j (1+ j)) n)
- X (setq sum (math-sub sum (math-mul (nth j (nth i lu))
- X (nth col (nth j x))))))
- X (setcar (nthcdr col (nth i x))
- X (math-div sum (nth i (nth i lu)))))
- X (setq col (1+ col)))
- X x)
- X (and need
- X (math-reject-arg need "*Singular matrix")))
- )
- X
- (defun calcFunc-lud (m)
- X (if (math-square-matrixp m)
- X (or (math-with-extra-prec 2
- X (let ((lud (math-matrix-lud m)))
- X (and lud
- X (let* ((lmat (math-copy-matrix (car lud)))
- X (umat (math-copy-matrix (car lud)))
- X (n (1- (length (car lud))))
- X (perm (calcFunc-idn 1 n))
- X i (j 1))
- X (while (<= j n)
- X (setq i 1)
- X (while (< i j)
- X (setcar (nthcdr j (nth i lmat)) 0)
- X (setq i (1+ i)))
- X (setcar (nthcdr j (nth j lmat)) 1)
- X (while (<= (setq i (1+ i)) n)
- X (setcar (nthcdr j (nth i umat)) 0))
- X (setq j (1+ j)))
- X (while (>= (setq j (1- j)) 1)
- X (let ((pos (nth (1- j) (nth 1 lud))))
- X (or (= pos j)
- X (setq perm (math-swap-rows perm j pos)))))
- X (list 'vec perm lmat umat)))))
- X (math-reject-arg m "*Singular matrix"))
- X (math-reject-arg m 'square-matrixp))
- )
- X
- SHAR_EOF
- echo 'File calc-mat.el is complete' &&
- chmod 0644 calc-mat.el ||
- echo 'restore of calc-mat.el failed'
- Wc_c="`wc -c < 'calc-mat.el'`"
- test 10372 -eq "$Wc_c" ||
- echo 'calc-mat.el: original size 10372, current size' "$Wc_c"
- rm -f _shar_wnt_.tmp
- fi
- # ============= calc-math.el ==============
- if test -f 'calc-math.el' -a X"$1" != X"-c"; then
- echo 'x - skipping calc-math.el (File already exists)'
- rm -f _shar_wnt_.tmp
- else
- > _shar_wnt_.tmp
- echo 'x - extracting calc-math.el (Text)'
- sed 's/^X//' << 'SHAR_EOF' > 'calc-math.el' &&
- ;; Calculator for GNU Emacs, part II [calc-math.el]
- ;; Copyright (C) 1990, 1991 Free Software Foundation, Inc.
- ;; Written by Dave Gillespie, daveg@csvax.cs.caltech.edu.
- X
- ;; This file is part of GNU Emacs.
- X
- ;; GNU Emacs is distributed in the hope that it will be useful,
- ;; but WITHOUT ANY WARRANTY. No author or distributor
- ;; accepts responsibility to anyone for the consequences of using it
- ;; or for whether it serves any particular purpose or works at all,
- ;; unless he says so in writing. Refer to the GNU Emacs General Public
- ;; License for full details.
- X
- ;; Everyone is granted permission to copy, modify and redistribute
- ;; GNU Emacs, but only under the conditions described in the
- ;; GNU Emacs General Public License. A copy of this license is
- ;; supposed to have been given to you along with GNU Emacs so you
- ;; can know your rights and responsibilities. It should be in a
- ;; file named COPYING. Among other things, the copyright notice
- ;; and this notice must be preserved on all copies.
- X
- X
- X
- ;; This file is autoloaded from calc-ext.el.
- (require 'calc-ext)
- X
- (require 'calc-macs)
- X
- (defun calc-Need-calc-math () nil)
- X
- X
- (defun calc-sqrt (arg)
- X (interactive "P")
- X (calc-slow-wrapper
- X (if (calc-is-inverse)
- X (calc-unary-op "^2" 'calcFunc-sqr arg)
- X (calc-unary-op "sqrt" 'calcFunc-sqrt arg)))
- )
- X
- (defun calc-isqrt (arg)
- X (interactive "P")
- X (calc-slow-wrapper
- X (if (calc-is-inverse)
- X (calc-unary-op "^2" 'calcFunc-sqr arg)
- X (calc-unary-op "isqt" 'calcFunc-isqrt arg)))
- )
- X
- X
- (defun calc-hypot (arg)
- X (interactive "P")
- X (calc-slow-wrapper
- X (calc-binary-op "hypt" 'calcFunc-hypot arg))
- )
- X
- (defun calc-ln (arg)
- X (interactive "P")
- X (calc-invert-func)
- X (calc-exp arg)
- )
- X
- (defun calc-log10 (arg)
- X (interactive "P")
- X (calc-hyperbolic-func)
- X (calc-ln arg)
- )
- X
- (defun calc-log (arg)
- X (interactive "P")
- X (calc-slow-wrapper
- X (if (calc-is-inverse)
- X (calc-binary-op "alog" 'calcFunc-alog arg)
- X (calc-binary-op "log" 'calcFunc-log arg)))
- )
- X
- (defun calc-ilog (arg)
- X (interactive "P")
- X (calc-slow-wrapper
- X (if (calc-is-inverse)
- X (calc-binary-op "alog" 'calcFunc-alog arg)
- X (calc-binary-op "ilog" 'calcFunc-ilog arg)))
- )
- X
- (defun calc-lnp1 (arg)
- X (interactive "P")
- X (calc-invert-func)
- X (calc-expm1 arg)
- )
- X
- (defun calc-exp (arg)
- X (interactive "P")
- X (calc-slow-wrapper
- X (if (calc-is-hyperbolic)
- X (if (calc-is-inverse)
- X (calc-unary-op "lg10" 'calcFunc-log10 arg)
- X (calc-unary-op "10^" 'calcFunc-exp10 arg))
- X (if (calc-is-inverse)
- X (calc-unary-op "ln" 'calcFunc-ln arg)
- X (calc-unary-op "exp" 'calcFunc-exp arg))))
- )
- X
- (defun calc-expm1 (arg)
- X (interactive "P")
- X (calc-slow-wrapper
- X (if (calc-is-inverse)
- X (calc-unary-op "ln+1" 'calcFunc-lnp1 arg)
- X (calc-unary-op "ex-1" 'calcFunc-expm1 arg)))
- )
- X
- (defun calc-pi ()
- X (interactive)
- X (calc-slow-wrapper
- X (if (calc-is-inverse)
- X (if (calc-is-hyperbolic)
- X (if calc-symbolic-mode
- X (calc-pop-push-record 0 "phi" '(var phi var-phi))
- X (calc-pop-push-record 0 "phi" (math-phi)))
- X (if calc-symbolic-mode
- X (calc-pop-push-record 0 "gmma" '(var gamma var-gamma))
- X (calc-pop-push-record 0 "gmma" (math-gamma-const))))
- X (if (calc-is-hyperbolic)
- X (if calc-symbolic-mode
- X (calc-pop-push-record 0 "e" '(var e var-e))
- X (calc-pop-push-record 0 "e" (math-e)))
- X (if calc-symbolic-mode
- X (calc-pop-push-record 0 "pi" '(var pi var-pi))
- X (calc-pop-push-record 0 "pi" (math-pi))))))
- )
- X
- (defun calc-sin (arg)
- X (interactive "P")
- X (calc-slow-wrapper
- X (if (calc-is-hyperbolic)
- X (if (calc-is-inverse)
- X (calc-unary-op "asnh" 'calcFunc-arcsinh arg)
- X (calc-unary-op "sinh" 'calcFunc-sinh arg))
- X (if (calc-is-inverse)
- X (calc-unary-op "asin" 'calcFunc-arcsin arg)
- X (calc-unary-op "sin" 'calcFunc-sin arg))))
- )
- X
- (defun calc-arcsin (arg)
- X (interactive "P")
- X (calc-invert-func)
- X (calc-sin arg)
- )
- X
- (defun calc-sinh (arg)
- X (interactive "P")
- X (calc-hyperbolic-func)
- X (calc-sin arg)
- )
- X
- (defun calc-arcsinh (arg)
- X (interactive "P")
- X (calc-invert-func)
- X (calc-hyperbolic-func)
- X (calc-sin arg)
- )
- X
- (defun calc-cos (arg)
- X (interactive "P")
- X (calc-slow-wrapper
- X (if (calc-is-hyperbolic)
- X (if (calc-is-inverse)
- X (calc-unary-op "acsh" 'calcFunc-arccosh arg)
- X (calc-unary-op "cosh" 'calcFunc-cosh arg))
- X (if (calc-is-inverse)
- X (calc-unary-op "acos" 'calcFunc-arccos arg)
- X (calc-unary-op "cos" 'calcFunc-cos arg))))
- )
- X
- (defun calc-arccos (arg)
- X (interactive "P")
- X (calc-invert-func)
- X (calc-cos arg)
- )
- X
- (defun calc-cosh (arg)
- X (interactive "P")
- X (calc-hyperbolic-func)
- X (calc-cos arg)
- )
- X
- (defun calc-arccosh (arg)
- X (interactive "P")
- X (calc-invert-func)
- X (calc-hyperbolic-func)
- X (calc-cos arg)
- )
- X
- (defun calc-sincos ()
- X (interactive)
- X (calc-slow-wrapper
- X (if (calc-is-inverse)
- X (calc-enter-result 1 "asnc" (list 'calcFunc-arcsincos (calc-top-n 1)))
- X (calc-enter-result 1 "sncs" (list 'calcFunc-sincos (calc-top-n 1)))))
- )
- X
- (defun calc-tan (arg)
- X (interactive "P")
- X (calc-slow-wrapper
- X (if (calc-is-hyperbolic)
- X (if (calc-is-inverse)
- X (calc-unary-op "atnh" 'calcFunc-arctanh arg)
- X (calc-unary-op "tanh" 'calcFunc-tanh arg))
- X (if (calc-is-inverse)
- X (calc-unary-op "atan" 'calcFunc-arctan arg)
- X (calc-unary-op "tan" 'calcFunc-tan arg))))
- )
- X
- (defun calc-arctan (arg)
- X (interactive "P")
- X (calc-invert-func)
- X (calc-tan arg)
- )
- X
- (defun calc-tanh (arg)
- X (interactive "P")
- X (calc-hyperbolic-func)
- X (calc-tan arg)
- )
- X
- (defun calc-arctanh (arg)
- X (interactive "P")
- X (calc-invert-func)
- X (calc-hyperbolic-func)
- X (calc-tan arg)
- )
- X
- (defun calc-arctan2 ()
- X (interactive)
- X (calc-slow-wrapper
- X (calc-enter-result 2 "atn2" (cons 'calcFunc-arctan2 (calc-top-list-n 2))))
- )
- X
- (defun calc-conj (arg)
- X (interactive "P")
- X (calc-wrapper
- X (calc-unary-op "conj" 'calcFunc-conj arg))
- )
- X
- (defun calc-imaginary ()
- X (interactive)
- X (calc-slow-wrapper
- X (calc-pop-push-record 1 "i*" (math-imaginary (calc-top-n 1))))
- )
- X
- X
- X
- (defun calc-to-degrees (arg)
- X (interactive "P")
- X (calc-wrapper
- X (calc-unary-op ">deg" 'calcFunc-deg arg))
- )
- X
- (defun calc-to-radians (arg)
- X (interactive "P")
- X (calc-wrapper
- X (calc-unary-op ">rad" 'calcFunc-rad arg))
- )
- X
- X
- (defun calc-degrees-mode ()
- X (interactive)
- X (calc-wrapper
- X (calc-change-mode 'calc-angle-mode 'deg)
- X (message "Angles measured in degrees."))
- )
- X
- (defun calc-radians-mode ()
- X (interactive)
- X (calc-wrapper
- X (calc-change-mode 'calc-angle-mode 'rad)
- X (message "Angles measured in radians."))
- )
- X
- X
- ;;; Compute the integer square-root floor(sqrt(A)). A > 0. [I I] [Public]
- ;;; This method takes advantage of the fact that Newton's method starting
- ;;; with an overestimate always works, even using truncating integer division!
- (defun math-isqrt (a)
- X (cond ((Math-zerop a) a)
- X ((not (math-natnump a))
- X (math-reject-arg a 'natnump))
- X ((integerp a)
- X (math-isqrt-small a))
- X (t
- X (math-normalize (cons 'bigpos (cdr (math-isqrt-bignum (cdr a)))))))
- )
- X
- (defun calcFunc-isqrt (a)
- X (if (math-realp a)
- X (math-isqrt (math-floor a))
- X (math-floor (math-sqrt a)))
- )
- X
- X
- ;;; This returns (flag . result) where the flag is T if A is a perfect square.
- (defun math-isqrt-bignum (a) ; [P.l L]
- X (let ((len (length a)))
- X (if (= (% len 2) 0)
- X (let* ((top (nthcdr (- len 2) a)))
- X (math-isqrt-bignum-iter
- X a
- X (math-scale-bignum-3
- X (math-bignum-big
- X (1+ (math-isqrt-small
- X (+ (* (nth 1 top) 1000) (car top)))))
- X (1- (/ len 2)))))
- X (let* ((top (nth (1- len) a)))
- X (math-isqrt-bignum-iter
- X a
- X (math-scale-bignum-3
- X (list (1+ (math-isqrt-small top)))
- X (/ len 2))))))
- )
- X
- (defun math-isqrt-bignum-iter (a guess) ; [l L l]
- X (math-working "isqrt" (cons 'bigpos guess))
- X (let* ((q (math-div-bignum a guess))
- X (s (math-add-bignum (car q) guess))
- X (g2 (math-div2-bignum s))
- X (comp (math-compare-bignum g2 guess)))
- X (if (< comp 0)
- X (math-isqrt-bignum-iter a g2)
- X (cons (and (= comp 0)
- X (math-zerop-bignum (cdr q))
- X (= (% (car s) 2) 0))
- X guess)))
- )
- X
- (defun math-zerop-bignum (a)
- X (and (eq (car a) 0)
- X (progn
- X (while (eq (car (setq a (cdr a))) 0))
- X (null a)))
- )
- X
- (defun math-scale-bignum-3 (a n) ; [L L S]
- X (while (> n 0)
- X (setq a (cons 0 a)
- X n (1- n)))
- X a
- )
- X
- (defun math-isqrt-small (a) ; A > 0. [S S]
- X (let ((g (cond ((>= a 10000) 1000)
- X ((>= a 100) 100)
- X (t 10)))
- X g2)
- X (while (< (setq g2 (/ (+ g (/ a g)) 2)) g)
- X (setq g g2))
- X g)
- )
- X
- X
- X
- X
- ;;; Compute the square root of a number.
- ;;; [T N] if possible, else [F N] if possible, else [C N]. [Public]
- (defun math-sqrt (a)
- X (or
- X (and (Math-zerop a) a)
- X (and (math-known-nonposp a)
- X (math-imaginary (math-sqrt (math-neg a))))
- X (and (integerp a)
- X (let ((sqrt (math-isqrt-small a)))
- X (if (= (* sqrt sqrt) a)
- X sqrt
- X (if calc-symbolic-mode
- X (list 'calcFunc-sqrt a)
- X (math-sqrt-float (math-float a) (math-float sqrt))))))
- X (and (eq (car-safe a) 'bigpos)
- X (let* ((res (math-isqrt-bignum (cdr a)))
- X (sqrt (math-normalize (cons 'bigpos (cdr res)))))
- X (if (car res)
- X sqrt
- X (if calc-symbolic-mode
- X (list 'calcFunc-sqrt a)
- X (math-sqrt-float (math-float a) (math-float sqrt))))))
- X (and (eq (car-safe a) 'frac)
- X (let* ((num-res (math-isqrt-bignum (cdr (Math-bignum-test (nth 1 a)))))
- X (num-sqrt (math-normalize (cons 'bigpos (cdr num-res))))
- X (den-res (math-isqrt-bignum (cdr (Math-bignum-test (nth 2 a)))))
- X (den-sqrt (math-normalize (cons 'bigpos (cdr den-res)))))
- X (if (and (car num-res) (car den-res))
- X (list 'frac num-sqrt den-sqrt)
- X (if calc-symbolic-mode
- X (if (or (car num-res) (car den-res))
- X (math-div (if (car num-res)
- X num-sqrt (list 'calcFunc-sqrt (nth 1 a)))
- X (if (car den-res)
- X den-sqrt (list 'calcFunc-sqrt (nth 2 a))))
- X (list 'calcFunc-sqrt a))
- X (math-sqrt-float (math-float a)
- X (math-div (math-float num-sqrt) den-sqrt))))))
- X (and (eq (car-safe a) 'float)
- X (if calc-symbolic-mode
- X (if (= (% (nth 2 a) 2) 0)
- X (let ((res (math-isqrt-bignum
- X (cdr (Math-bignum-test (nth 1 a))))))
- X (if (car res)
- X (math-make-float (math-normalize
- X (cons 'bigpos (cdr res)))
- X (/ (nth 2 a) 2))
- X (signal 'inexact-result nil)))
- X (signal 'inexact-result nil))
- X (math-sqrt-float a)))
- X (and (eq (car-safe a) 'cplx)
- X (math-with-extra-prec 2
- X (let* ((d (math-abs a))
- X (imag (math-sqrt (math-mul (math-sub d (nth 1 a))
- X '(float 5 -1)))))
- X (list 'cplx
- X (math-sqrt (math-mul (math-add d (nth 1 a)) '(float 5 -1)))
- X (if (math-negp (nth 2 a)) (math-neg imag) imag)))))
- X (and (eq (car-safe a) 'polar)
- X (list 'polar
- X (math-sqrt (nth 1 a))
- X (math-mul (nth 2 a) '(float 5 -1))))
- X (and (eq (car-safe a) 'sdev)
- X (let ((sqrt (math-sqrt (nth 1 a))))
- X (math-make-sdev sqrt
- X (math-div (nth 2 a) (math-mul sqrt 2)))))
- X (and (eq (car-safe a) 'intv)
- X (not (math-negp (nth 2 a)))
- X (math-make-intv (nth 1 a) (math-sqrt (nth 2 a)) (math-sqrt (nth 3 a))))
- X (and (eq (car-safe a) '*)
- X (or (math-known-nonnegp (nth 1 a))
- X (math-known-nonnegp (nth 2 a)))
- X (math-mul (math-sqrt (nth 1 a)) (math-sqrt (nth 2 a))))
- X (and (eq (car-safe a) '/)
- X (or (and (math-known-nonnegp (nth 2 a))
- X (math-div (math-sqrt (nth 1 a)) (math-sqrt (nth 2 a))))
- X (and (math-known-nonnegp (nth 1 a))
- X (not (math-equal-int (nth 1 a) 1))
- X (math-mul (math-sqrt (nth 1 a))
- X (math-sqrt (math-div 1 (nth 2 a)))))))
- X (and (eq (car-safe a) '^)
- X (math-known-evenp (nth 2 a))
- X (math-known-realp (nth 1 a))
- X (math-abs (math-pow (nth 1 a) (math-div (nth 2 a) 2))))
- X (let ((inf (math-infinitep a)))
- X (and inf
- X (math-mul (math-sqrt (math-infinite-dir a inf)) inf)))
- X (progn
- X (calc-record-why 'numberp a)
- X (list 'calcFunc-sqrt a)))
- )
- (fset 'calcFunc-sqrt (symbol-function 'math-sqrt))
- X
- (defun math-infinite-dir (a &optional inf)
- X (or inf (setq inf (math-infinitep a)))
- X (math-normalize (math-expr-subst a inf 1))
- )
- X
- (defun math-sqrt-float (a &optional guess) ; [F F F]
- X (if calc-symbolic-mode
- X (signal 'inexact-result nil)
- X (math-with-extra-prec 1 (math-sqrt-raw a guess)))
- )
- X
- (defun math-sqrt-raw (a &optional guess) ; [F F F]
- X (if (not (Math-posp a))
- X (math-sqrt a)
- X (if (null guess)
- X (let ((ldiff (- (math-numdigs (nth 1 a)) 6)))
- X (or (= (% (+ (nth 2 a) ldiff) 2) 0) (setq ldiff (1+ ldiff)))
- X (setq guess (math-make-float (math-isqrt-small
- X (math-scale-int (nth 1 a) (- ldiff)))
- X (/ (+ (nth 2 a) ldiff) 2)))))
- X (math-sqrt-float-iter a guess))
- )
- X
- (defun math-sqrt-float-iter (a guess) ; [F F F]
- X (math-working "sqrt" guess)
- X (let ((g2 (math-mul-float (math-add-float guess (math-div-float a guess))
- X '(float 5 -1))))
- X (if (math-nearly-equal-float g2 guess)
- X g2
- X (math-sqrt-float-iter a g2)))
- )
- X
- ;;; True if A and B differ only in the last digit of precision. [P F F]
- (defun math-nearly-equal-float (a b)
- X (let ((ediff (- (nth 2 a) (nth 2 b))))
- X (cond ((= ediff 0) ;; Expanded out for speed
- X (setq ediff (math-add (Math-integer-neg (nth 1 a)) (nth 1 b)))
- X (or (eq ediff 0)
- X (and (not (consp ediff))
- X (< ediff 10)
- X (> ediff -10)
- X (= (math-numdigs (nth 1 a)) calc-internal-prec))))
- X ((= ediff 1)
- X (setq ediff (math-add (Math-integer-neg (nth 1 b))
- X (math-scale-int (nth 1 a) 1)))
- X (and (not (consp ediff))
- X (< ediff 10)
- X (> ediff -10)
- X (= (math-numdigs (nth 1 b)) calc-internal-prec)))
- X ((= ediff -1)
- X (setq ediff (math-add (Math-integer-neg (nth 1 a))
- X (math-scale-int (nth 1 b) 1)))
- X (and (not (consp ediff))
- X (< ediff 10)
- X (> ediff -10)
- X (= (math-numdigs (nth 1 a)) calc-internal-prec)))))
- )
- X
- (defun math-nearly-equal (a b) ; [P N N] [Public]
- X (setq a (math-float a))
- X (setq b (math-float b))
- X (if (eq (car a) 'polar) (setq a (math-complex a)))
- X (if (eq (car b) 'polar) (setq b (math-complex b)))
- X (if (eq (car a) 'cplx)
- X (if (eq (car b) 'cplx)
- X (and (or (math-nearly-equal-float (nth 1 a) (nth 1 b))
- X (and (math-nearly-zerop-float (nth 1 a) (nth 2 a))
- X (math-nearly-zerop-float (nth 1 b) (nth 2 b))))
- X (or (math-nearly-equal-float (nth 2 a) (nth 2 b))
- X (and (math-nearly-zerop-float (nth 2 a) (nth 1 a))
- X (math-nearly-zerop-float (nth 2 b) (nth 1 b)))))
- X (and (math-nearly-equal-float (nth 1 a) b)
- X (math-nearly-zerop-float (nth 2 a) b)))
- X (if (eq (car b) 'cplx)
- X (and (math-nearly-equal-float a (nth 1 b))
- X (math-nearly-zerop-float a (nth 2 b)))
- X (math-nearly-equal-float a b)))
- )
- X
- ;;; True if A is nearly zero compared to B. [P F F]
- (defun math-nearly-zerop-float (a b)
- X (or (eq (nth 1 a) 0)
- X (<= (+ (math-numdigs (nth 1 a)) (nth 2 a))
- X (1+ (- (+ (math-numdigs (nth 1 b)) (nth 2 b)) calc-internal-prec))))
- )
- X
- (defun math-nearly-zerop (a b) ; [P N R] [Public]
- X (setq a (math-float a))
- X (setq b (math-float b))
- X (if (eq (car a) 'cplx)
- X (and (math-nearly-zerop-float (nth 1 a) b)
- X (math-nearly-zerop-float (nth 2 a) b))
- X (if (eq (car a) 'polar)
- X (math-nearly-zerop-float (nth 1 a) b)
- X (math-nearly-zerop-float a b)))
- )
- X
- ;;; This implementation could be improved, accuracy-wise.
- (defun math-hypot (a b)
- X (cond ((Math-zerop a) (math-abs b))
- X ((Math-zerop b) (math-abs a))
- X ((not (Math-scalarp a))
- X (if (math-infinitep a)
- X (if (math-infinitep b)
- X (if (equal a b)
- X a
- X '(var nan var-nan))
- X a)
- X (calc-record-why 'scalarp a)
- X (list 'calcFunc-hypot a b)))
- X ((not (Math-scalarp b))
- X (if (math-infinitep b)
- X b
- X (calc-record-why 'scalarp b)
- X (list 'calcFunc-hypot a b)))
- X ((and (Math-numberp a) (Math-numberp b))
- X (math-with-extra-prec 1
- X (math-sqrt (math-add (calcFunc-abssqr a) (calcFunc-abssqr b)))))
- X ((eq (car-safe a) 'hms)
- X (if (eq (car-safe b) 'hms) ; this helps sdev's of hms forms
- X (math-to-hms (math-hypot (math-from-hms a 'deg)
- X (math-from-hms b 'deg)))
- X (math-to-hms (math-hypot (math-from-hms a 'deg) b))))
- X ((eq (car-safe b) 'hms)
- X (math-to-hms (math-hypot a (math-from-hms b 'deg))))
- X (t nil))
- )
- (fset 'calcFunc-hypot (symbol-function 'math-hypot))
- X
- (defun calcFunc-sqr (x)
- X (math-pow x 2)
- )
- X
- X
- X
- (defun math-nth-root (a n)
- X (cond ((= n 2) (math-sqrt a))
- X ((Math-zerop a) a)
- X ((Math-negp a) nil)
- X ((Math-integerp a)
- X (let ((root (math-nth-root-integer a n)))
- X (if (car root)
- X (cdr root)
- X (and (not calc-symbolic-mode)
- X (math-nth-root-float (math-float a) n
- X (math-float (cdr root)))))))
- X ((eq (car-safe a) 'frac)
- X (let* ((num-root (math-nth-root-integer (nth 1 a) n))
- X (den-root (math-nth-root-integer (nth 2 a) n)))
- X (if (and (car num-root) (car den-root))
- X (list 'frac (cdr num-root) (cdr den-root))
- X (and (not calc-symbolic-mode)
- X (math-nth-root-float
- X (math-float a) n
- X (math-div-float (math-float (cdr num-root))
- X (math-float (cdr den-root))))))))
- X ((eq (car-safe a) 'float)
- X (and (not calc-symbolic-mode)
- X (math-nth-root-float a n)))
- X ((eq (car-safe a) 'polar)
- X (let ((root (math-nth-root (nth 1 a) n)))
- X (and root (list 'polar root (math-div (nth 2 a) n)))))
- X (t nil))
- )
- X
- (defun math-nth-root-float (a n &optional guess)
- X (math-inexact-result)
- X (math-with-extra-prec 1
- X (let ((nf (math-float n))
- X (nfm1 (math-float (1- n))))
- X (math-nth-root-float-iter a (or guess
- X (math-make-float
- X 1 (/ (+ (math-numdigs (nth 1 a))
- X (nth 2 a)
- X (/ n 2))
- X n))))))
- )
- X
- (defun math-nth-root-float-iter (a guess) ; uses "n", "nf", "nfm1"
- X (math-working "root" guess)
- X (let ((g2 (math-div-float (math-add-float (math-mul nfm1 guess)
- X (math-div-float
- X a (math-ipow guess (1- n))))
- X nf)))
- X (if (math-nearly-equal-float g2 guess)
- X g2
- X (math-nth-root-float-iter a g2)))
- )
- X
- (defun math-nth-root-integer (a n &optional guess) ; [I I S]
- X (math-nth-root-int-iter a (or guess
- X (math-scale-int 1 (/ (+ (math-numdigs a)
- X (1- n))
- X n))))
- )
- X
- (defun math-nth-root-int-iter (a guess) ; uses "n"
- X (math-working "root" guess)
- X (let* ((q (math-idivmod a (math-ipow guess (1- n))))
- X (s (math-add (car q) (math-mul (1- n) guess)))
- X (g2 (math-idivmod s n)))
- X (if (Math-natnum-lessp (car g2) guess)
- X (math-nth-root-int-iter a (car g2))
- X (cons (and (equal (car g2) guess)
- X (eq (cdr q) 0)
- X (eq (cdr g2) 0))
- X guess)))
- )
- X
- (defun calcFunc-nroot (x n)
- X (calcFunc-pow x (if (integerp n)
- X (math-make-frac 1 n)
- X (math-div 1 n)))
- )
- X
- X
- X
- X
- ;;;; Transcendental functions.
- X
- ;;; All of these functions are defined on the complex plane.
- ;;; (Branch cuts, etc. follow Steele's Common Lisp book.)
- X
- ;;; Most functions increase calc-internal-prec by 2 digits, then round
- ;;; down afterward. "-raw" functions use the current precision, require
- ;;; their arguments to be in float (or complex float) format, and always
- ;;; work in radians (where applicable).
- X
- (defun math-to-radians (a) ; [N N]
- X (cond ((eq (car-safe a) 'hms)
- X (math-from-hms a 'rad))
- X ((memq calc-angle-mode '(deg hms))
- X (math-mul a (math-pi-over-180)))
- X (t a))
- )
- X
- (defun math-from-radians (a) ; [N N]
- X (cond ((eq calc-angle-mode 'deg)
- X (if (math-constp a)
- X (math-div a (math-pi-over-180))
- X (list 'calcFunc-deg a)))
- X ((eq calc-angle-mode 'hms)
- X (math-to-hms a 'rad))
- X (t a))
- )
- X
- (defun math-to-radians-2 (a) ; [N N]
- X (cond ((eq (car-safe a) 'hms)
- X (math-from-hms a 'rad))
- X ((memq calc-angle-mode '(deg hms))
- X (if calc-symbolic-mode
- X (math-div (math-mul a '(var pi var-pi)) 180)
- X (math-mul a (math-pi-over-180))))
- X (t a))
- )
- X
- (defun math-from-radians-2 (a) ; [N N]
- X (cond ((memq calc-angle-mode '(deg hms))
- X (if calc-symbolic-mode
- X (math-div (math-mul 180 a) '(var pi var-pi))
- X (math-div a (math-pi-over-180))))
- X (t a))
- )
- X
- X
- X
- ;;; Sine, cosine, and tangent.
- X
- (defun calcFunc-sin (x) ; [N N] [Public]
- X (cond ((and (integerp x)
- X (if (eq calc-angle-mode 'deg)
- X (= (% x 90) 0)
- X (= x 0)))
- X (aref [0 1 0 -1] (math-mod (/ x 90) 4)))
- X ((Math-scalarp x)
- X (math-with-extra-prec 2
- X (math-sin-raw (math-to-radians (math-float x)))))
- X ((eq (car x) 'sdev)
- X (if (math-constp x)
- X (math-with-extra-prec 2
- X (let* ((xx (math-to-radians (math-float (nth 1 x))))
- X (xs (math-to-radians (math-float (nth 2 x))))
- X (sc (math-sin-cos-raw xx)))
- X (math-make-sdev (car sc) (math-mul xs (cdr sc)))))
- X (math-make-sdev (calcFunc-sin (nth 1 x))
- X (math-mul (nth 2 x) (calcFunc-cos (nth 1 x))))))
- X ((and (eq (car x) 'intv) (math-intv-constp x))
- X (calcFunc-cos (math-sub x (math-quarter-circle nil))))
- X ((equal x '(var nan var-nan))
- X x)
- X (t (calc-record-why 'scalarp x)
- X (list 'calcFunc-sin x)))
- )
- X
- (defun calcFunc-cos (x) ; [N N] [Public]
- X (cond ((and (integerp x)
- X (if (eq calc-angle-mode 'deg)
- X (= (% x 90) 0)
- X (= x 0)))
- X (aref [1 0 -1 0] (math-mod (/ x 90) 4)))
- X ((Math-scalarp x)
- X (math-with-extra-prec 2
- X (math-cos-raw (math-to-radians (math-float x)))))
- X ((eq (car x) 'sdev)
- X (if (math-constp x)
- X (math-with-extra-prec 2
- X (let* ((xx (math-to-radians (math-float (nth 1 x))))
- X (xs (math-to-radians (math-float (nth 2 x))))
- X (sc (math-sin-cos-raw xx)))
- X (math-make-sdev (cdr sc) (math-mul xs (car sc)))))
- X (math-make-sdev (calcFunc-cos (nth 1 x))
- X (math-mul (nth 2 x) (calcFunc-sin (nth 1 x))))))
- X ((and (eq (car x) 'intv) (math-intv-constp x))
- X (math-with-extra-prec 2
- X (let* ((xx (math-to-radians (math-float x)))
- X (na (math-floor (math-div (nth 2 xx) (math-pi))))
- X (nb (math-floor (math-div (nth 3 xx) (math-pi))))
- X (span (math-sub nb na)))
- X (if (memq span '(0 1))
- X (let ((int (math-sort-intv (nth 1 x)
- X (math-cos-raw (nth 2 xx))
- X (math-cos-raw (nth 3 xx)))))
- X (if (eq span 1)
- X (if (math-evenp na)
- X (math-make-intv (logior (nth 1 x) 2)
- X -1
- X (nth 3 int))
- X (math-make-intv (logior (nth 1 x) 1)
- X (nth 2 int)
- X 1))
- X int))
- X (list 'intv 3 -1 1)))))
- X ((equal x '(var nan var-nan))
- X x)
- X (t (calc-record-why 'scalarp x)
- X (list 'calcFunc-cos x)))
- )
- X
- (defun calcFunc-sincos (x) ; [V N] [Public]
- X (if (Math-scalarp x)
- X (math-with-extra-prec 2
- X (let ((sc (math-sin-cos-raw (math-to-radians (math-float x)))))
- X (list 'vec (cdr sc) (car sc)))) ; the vector [cos, sin]
- X (list 'vec (calcFunc-sin x) (calcFunc-cos x)))
- )
- X
- (defun calcFunc-tan (x) ; [N N] [Public]
- X (cond ((and (integerp x)
- X (if (eq calc-angle-mode 'deg)
- X (= (% x 180) 0)
- X (= x 0)))
- X 0)
- X ((Math-scalarp x)
- X (math-with-extra-prec 2
- X (math-tan-raw (math-to-radians (math-float x)))))
- X ((eq (car x) 'sdev)
- X (if (math-constp x)
- X (math-with-extra-prec 2
- X (let* ((xx (math-to-radians (math-float (nth 1 x))))
- X (xs (math-to-radians (math-float (nth 2 x))))
- X (sc (math-sin-cos-raw xx)))
- X (if (and (math-zerop (cdr sc)) (not calc-infinite-mode))
- X (progn
- X (calc-record-why "*Division by zero")
- X (list 'calcFunc-tan x))
- X (math-make-sdev (math-div-float (car sc) (cdr sc))
- X (math-div-float xs (math-sqr (cdr sc)))))))
- X (math-make-sdev (calcFunc-tan (nth 1 x))
- X (math-div (nth 2 x)
- X (math-sqr (calcFunc-cos (nth 1 x)))))))
- X ((and (eq (car x) 'intv) (math-intv-constp x))
- X (or (math-with-extra-prec 2
- X (let* ((xx (math-to-radians (math-float x)))
- X (na (math-floor (math-div (math-sub (nth 2 xx)
- X (math-pi-over-2))
- X (math-pi))))
- X (nb (math-floor (math-div (math-sub (nth 3 xx)
- X (math-pi-over-2))
- X (math-pi)))))
- X (and (equal na nb)
- X (math-sort-intv (nth 1 x)
- X (math-tan-raw (nth 2 xx))
- X (math-tan-raw (nth 3 xx))))))
- X '(intv 3 (neg (var inf var-inf)) (var inf var-inf))))
- X ((equal x '(var nan var-nan))
- X x)
- X (t (calc-record-why 'scalarp x)
- X (list 'calcFunc-tan x)))
- )
- X
- (defun math-sin-raw (x) ; [N N]
- X (cond ((eq (car x) 'cplx)
- X (let* ((expx (math-exp-raw (nth 2 x)))
- X (expmx (math-div-float '(float 1 0) expx))
- X (sc (math-sin-cos-raw (nth 1 x))))
- X (list 'cplx
- X (math-mul-float (car sc)
- X (math-mul-float (math-add-float expx expmx)
- X '(float 5 -1)))
- X (math-mul-float (cdr sc)
- X (math-mul-float (math-sub-float expx expmx)
- X '(float 5 -1))))))
- X ((eq (car x) 'polar)
- X (math-polar (math-sin-raw (math-complex x))))
- X ((Math-integer-negp (nth 1 x))
- X (math-neg-float (math-sin-raw (math-neg-float x))))
- X ((math-lessp-float '(float 7 0) x) ; avoid inf loops due to roundoff
- X (math-sin-raw (math-mod x (math-two-pi))))
- X (t (math-sin-raw-2 x x)))
- )
- X
- (defun math-cos-raw (x) ; [N N]
- X (if (eq (car-safe x) 'polar)
- X (math-polar (math-cos-raw (math-complex x)))
- X (math-sin-raw (math-sub (math-pi-over-2) x)))
- )
- X
- ;;; This could use a smarter method: Reduce x as in math-sin-raw, then
- ;;; compute either sin(x) or cos(x), whichever is smaller, and compute
- ;;; the other using the identity sin(x)^2 + cos(x)^2 = 1.
- (defun math-sin-cos-raw (x) ; [F.F F] (result is (sin x . cos x))
- X (cons (math-sin-raw x) (math-cos-raw x))
- )
- X
- (defun math-tan-raw (x) ; [N N]
- X (cond ((eq (car x) 'cplx)
- X (let* ((x (math-mul x '(float 2 0)))
- X (expx (math-exp-raw (nth 2 x)))
- X (expmx (math-div-float '(float 1 0) expx))
- X (sc (math-sin-cos-raw (nth 1 x)))
- X (d (math-add-float (cdr sc)
- X (math-mul-float (math-add-float expx expmx)
- X '(float 5 -1)))))
- X (and (not (eq (nth 1 d) 0))
- X (list 'cplx
- X (math-div-float (car sc) d)
- X (math-div-float (math-mul-float (math-sub-float expx
- X expmx)
- X '(float 5 -1)) d)))))
- X ((eq (car x) 'polar)
- X (math-polar (math-tan-raw (math-complex x))))
- X (t
- X (let ((sc (math-sin-cos-raw x)))
- X (if (eq (nth 1 (cdr sc)) 0)
- X (math-div (car sc) 0)
- X (math-div-float (car sc) (cdr sc))))))
- )
- X
- (defun math-sin-raw-2 (x orgx) ; This avoids poss of inf recursion. [F F]
- X (let ((xmpo2 (math-sub-float (math-pi-over-2) x)))
- X (cond ((Math-integer-negp (nth 1 xmpo2))
- X (math-neg-float (math-sin-raw-2 (math-sub-float x (math-pi))
- X orgx)))
- X ((math-lessp-float (math-pi-over-4) x)
- X (math-cos-raw-2 xmpo2 orgx))
- X ((math-lessp-float x (math-neg (math-pi-over-4)))
- X (math-neg (math-cos-raw-2 (math-add (math-pi-over-2) x) orgx)))
- X ((math-nearly-zerop-float x orgx) '(float 0 0))
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X (t (math-sin-series x 6 4 x (math-neg-float (math-sqr-float x))))))
- )
- X
- (defun math-cos-raw-2 (x orgx) ; [F F]
- X (cond ((math-nearly-zerop-float x orgx) '(float 1 0))
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X (t (let ((xnegsqr (math-neg-float (math-sqr-float x))))
- X (math-sin-series
- X (math-add-float '(float 1 0)
- X (math-mul-float xnegsqr '(float 5 -1)))
- X 24 5 xnegsqr xnegsqr))))
- )
- X
- (defun math-sin-series (sum nfac n x xnegsqr)
- X (math-working "sin" sum)
- X (let* ((nextx (math-mul-float x xnegsqr))
- X (nextsum (math-add-float sum (math-div-float nextx
- X (math-float nfac)))))
- X (if (math-nearly-equal-float sum nextsum)
- X sum
- X (math-sin-series nextsum (math-mul nfac (* n (1+ n)))
- X (+ n 2) nextx xnegsqr)))
- )
- X
- X
- ;;; Inverse sine, cosine, tangent.
- X
- (defun calcFunc-arcsin (x) ; [N N] [Public]
- X (cond ((eq x 0) 0)
- X ((and (eq x 1) (eq calc-angle-mode 'deg)) 90)
- X ((and (eq x -1) (eq calc-angle-mode 'deg)) -90)
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X ((Math-numberp x)
- X (math-with-extra-prec 2
- X (math-from-radians (math-arcsin-raw (math-float x)))))
- X ((eq (car x) 'sdev)
- X (math-make-sdev (calcFunc-arcsin (nth 1 x))
- X (math-from-radians
- X (math-div (nth 2 x)
- X (math-sqrt
- X (math-sub 1 (math-sqr (nth 1 x))))))))
- X ((eq (car x) 'intv)
- X (math-sort-intv (nth 1 x)
- X (calcFunc-arcsin (nth 2 x))
- X (calcFunc-arcsin (nth 3 x))))
- X ((equal x '(var nan var-nan))
- X x)
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-arcsin x)))
- )
- X
- (defun calcFunc-arccos (x) ; [N N] [Public]
- X (cond ((eq x 1) 0)
- X ((and (eq x 0) (eq calc-angle-mode 'deg)) 90)
- X ((and (eq x -1) (eq calc-angle-mode 'deg)) 180)
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X ((Math-numberp x)
- X (math-with-extra-prec 2
- X (math-from-radians (math-arccos-raw (math-float x)))))
- X ((eq (car x) 'sdev)
- X (math-make-sdev (calcFunc-arccos (nth 1 x))
- X (math-from-radians
- X (math-div (nth 2 x)
- X (math-sqrt
- X (math-sub 1 (math-sqr (nth 1 x))))))))
- X ((eq (car x) 'intv)
- X (math-sort-intv (nth 1 x)
- X (calcFunc-arccos (nth 2 x))
- X (calcFunc-arccos (nth 3 x))))
- X ((equal x '(var nan var-nan))
- X x)
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-arccos x)))
- )
- X
- (defun calcFunc-arctan (x) ; [N N] [Public]
- X (cond ((eq x 0) 0)
- X ((and (eq x 1) (eq calc-angle-mode 'deg)) 45)
- X ((and (eq x -1) (eq calc-angle-mode 'deg)) -45)
- X ((Math-numberp x)
- X (math-with-extra-prec 2
- X (math-from-radians (math-arctan-raw (math-float x)))))
- X ((eq (car x) 'sdev)
- X (math-make-sdev (calcFunc-arctan (nth 1 x))
- X (math-from-radians
- X (math-div (nth 2 x)
- X (math-add 1 (math-sqr (nth 1 x)))))))
- X ((eq (car x) 'intv)
- X (math-sort-intv (nth 1 x)
- X (calcFunc-arctan (nth 2 x))
- X (calcFunc-arctan (nth 3 x))))
- X ((equal x '(var inf var-inf))
- X (math-quarter-circle t))
- X ((equal x '(neg (var inf var-inf)))
- X (math-neg (math-quarter-circle t)))
- X ((equal x '(var nan var-nan))
- X x)
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-arctan x)))
- )
- X
- (defun math-arcsin-raw (x) ; [N N]
- X (let ((a (math-sqrt-raw (math-sub '(float 1 0) (math-sqr x)))))
- X (if (or (memq (car x) '(cplx polar))
- X (memq (car a) '(cplx polar)))
- X (math-with-extra-prec 2 ; use extra precision for difficult case
- X (math-mul '(cplx 0 -1)
- X (math-ln-raw (math-add (math-mul '(cplx 0 1) x) a))))
- X (math-arctan2-raw x a)))
- )
- X
- (defun math-arccos-raw (x) ; [N N]
- X (math-sub (math-pi-over-2) (math-arcsin-raw x))
- )
- X
- (defun math-arctan-raw (x) ; [N N]
- X (cond ((memq (car x) '(cplx polar))
- X (math-with-extra-prec 2 ; extra-extra
- X (math-div (math-sub
- X (math-ln-raw (math-add 1 (math-mul '(cplx 0 1) x)))
- X (math-ln-raw (math-add 1 (math-mul '(cplx 0 -1) x))))
- X '(cplx 0 2))))
- X ((Math-integer-negp (nth 1 x))
- X (math-neg-float (math-arctan-raw (math-neg-float x))))
- X ((math-zerop x) x)
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X ((math-equal-int x 1) (math-pi-over-4))
- X ((math-equal-int x -1) (math-neg (math-pi-over-4)))
- X ((math-lessp-float '(float 414214 -6) x) ; if x > sqrt(2) - 1, reduce
- X (if (math-lessp-float '(float 1 0) x)
- X (math-sub-float (math-mul-float (math-pi) '(float 5 -1))
- X (math-arctan-raw (math-div-float '(float 1 0) x)))
- X (math-sub-float (math-mul-float (math-pi) '(float 25 -2))
- X (math-arctan-raw (math-div-float
- X (math-sub-float '(float 1 0) x)
- X (math-add-float '(float 1 0)
- X x))))))
- X (t (math-arctan-series x 3 x (math-neg-float (math-sqr-float x)))))
- )
- X
- (defun math-arctan-series (sum n x xnegsqr)
- X (math-working "arctan" sum)
- X (let* ((nextx (math-mul-float x xnegsqr))
- X (nextsum (math-add-float sum (math-div-float nextx (math-float n)))))
- X (if (math-nearly-equal-float sum nextsum)
- X sum
- X (math-arctan-series nextsum (+ n 2) nextx xnegsqr)))
- )
- X
- (defun calcFunc-arctan2 (y x) ; [F R R] [Public]
- X (if (Math-anglep y)
- X (if (Math-anglep x)
- X (math-with-extra-prec 2
- X (math-from-radians (math-arctan2-raw (math-float y)
- X (math-float x))))
- X (calc-record-why 'anglep x)
- X (list 'calcFunc-arctan2 y x))
- X (if (and (or (math-infinitep x) (math-anglep x))
- X (or (math-infinitep y) (math-anglep y)))
- X (progn
- X (if (math-posp x)
- X (setq x 1)
- X (if (math-negp x)
- X (setq x -1)
- X (or (math-zerop x)
- X (setq x nil))))
- X (if (math-posp y)
- X (setq y 1)
- X (if (math-negp y)
- X (setq y -1)
- X (or (math-zerop y)
- X (setq y nil))))
- X (if (and y x)
- X (calcFunc-arctan2 y x)
- X '(var nan var-nan)))
- X (calc-record-why 'anglep y)
- X (list 'calcFunc-arctan2 y x)))
- )
- X
- (defun math-arctan2-raw (y x) ; [F R R]
- X (cond ((math-zerop y)
- X (if (math-negp x) (math-pi)
- X (if (or (math-floatp x) (math-floatp y)) '(float 0 0) 0)))
- X ((math-zerop x)
- X (if (math-posp y)
- X (math-pi-over-2)
- X (math-neg (math-pi-over-2))))
- X ((math-posp x)
- X (math-arctan-raw (math-div-float y x)))
- X ((math-posp y)
- X (math-add-float (math-arctan-raw (math-div-float y x))
- X (math-pi)))
- X (t
- X (math-sub-float (math-arctan-raw (math-div-float y x))
- X (math-pi))))
- )
- X
- (defun calcFunc-arcsincos (x) ; [V N] [Public]
- X (if (and (Math-vectorp x)
- X (= (length x) 3))
- X (calcFunc-arctan2 (nth 2 x) (nth 1 x))
- X (math-reject-arg x "*Two-element vector expected"))
- )
- X
- X
- X
- ;;; Exponential function.
- X
- (defun calcFunc-exp (x) ; [N N] [Public]
- X (cond ((eq x 0) 1)
- X ((and (memq x '(1 -1)) calc-symbolic-mode)
- X (if (eq x 1) '(var e var-e) (math-div 1 '(var e var-e))))
- X ((Math-numberp x)
- X (math-with-extra-prec 2 (math-exp-raw (math-float x))))
- X ((eq (car-safe x) 'sdev)
- X (let ((ex (calcFunc-exp (nth 1 x))))
- X (math-make-sdev ex (math-mul (nth 2 x) ex))))
- X ((eq (car-safe x) 'intv)
- X (math-make-intv (nth 1 x) (calcFunc-exp (nth 2 x))
- X (calcFunc-exp (nth 3 x))))
- X ((equal x '(var inf var-inf))
- X x)
- X ((equal x '(neg (var inf var-inf)))
- X 0)
- X ((equal x '(var nan var-nan))
- X x)
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-exp x)))
- )
- X
- (defun calcFunc-expm1 (x) ; [N N] [Public]
- X (cond ((eq x 0) 0)
- X ((math-zerop x) '(float 0 0))
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X ((Math-numberp x)
- X (math-with-extra-prec 2
- X (let ((x (math-float x)))
- X (if (and (eq (car x) 'float)
- X (math-lessp-float x '(float 1 0))
- X (math-lessp-float '(float -1 0) x))
- X (math-exp-minus-1-raw x)
- X (math-add (math-exp-raw x) -1)))))
- X ((eq (car-safe x) 'sdev)
- X (if (math-constp x)
- X (let ((ex (calcFunc-expm1 (nth 1 x))))
- X (math-make-sdev ex (math-mul (nth 2 x) (math-add ex 1))))
- X (math-make-sdev (calcFunc-expm1 (nth 1 x))
- X (math-mul (nth 2 x) (calcFunc-exp (nth 1 x))))))
- X ((eq (car-safe x) 'intv)
- X (math-make-intv (nth 1 x)
- X (calcFunc-expm1 (nth 2 x))
- X (calcFunc-expm1 (nth 3 x))))
- X ((equal x '(var inf var-inf))
- X x)
- X ((equal x '(neg (var inf var-inf)))
- X -1)
- X ((equal x '(var nan var-nan))
- X x)
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-expm1 x)))
- )
- X
- (defun calcFunc-exp10 (x) ; [N N] [Public]
- X (if (eq x 0)
- X 1
- X (math-pow '(float 1 1) x))
- )
- X
- (defun math-exp-raw (x) ; [N N]
- X (cond ((math-zerop x) '(float 1 0))
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X ((eq (car x) 'cplx)
- X (let ((expx (math-exp-raw (nth 1 x)))
- X (sc (math-sin-cos-raw (nth 2 x))))
- X (list 'cplx
- X (math-mul-float expx (cdr sc))
- X (math-mul-float expx (car sc)))))
- X ((eq (car x) 'polar)
- X (let ((xc (math-complex x)))
- X (list 'polar
- X (math-exp-raw (nth 1 xc))
- X (math-from-radians (nth 2 xc)))))
- X ((or (math-lessp-float '(float 5 -1) x)
- X (math-lessp-float x '(float -5 -1)))
- X (if (math-lessp-float '(float 921035 1) x)
- X (math-overflow)
- X (if (math-lessp-float x '(float -921035 1))
- X (math-underflow)))
- X (let* ((two-x (math-mul-float x '(float 2 0)))
- X (hint (math-scale-int (nth 1 two-x) (nth 2 two-x)))
- X (hfrac (math-sub-float x (math-mul-float (math-float hint)
- X '(float 5 -1)))))
- X (math-mul-float (math-ipow (math-sqrt-e) hint)
- X (math-add-float '(float 1 0)
- X (math-exp-minus-1-raw hfrac)))))
- X (t (math-add-float '(float 1 0) (math-exp-minus-1-raw x))))
- )
- X
- (defun math-exp-minus-1-raw (x) ; [F F]
- X (math-exp-series x 2 3 x x)
- )
- X
- (defun math-exp-series (sum nfac n xpow x)
- X (math-working "exp" sum)
- X (let* ((nextx (math-mul-float xpow x))
- X (nextsum (math-add-float sum (math-div-float nextx
- X (math-float nfac)))))
- X (if (math-nearly-equal-float sum nextsum)
- X sum
- X (math-exp-series nextsum (math-mul nfac n) (1+ n) nextx x)))
- )
- X
- X
- X
- ;;; Logarithms.
- X
- (defun calcFunc-ln (x) ; [N N] [Public]
- X (cond ((math-zerop x)
- X (if calc-infinite-mode
- X '(neg (var inf var-inf))
- X (math-reject-arg x "*Logarithm of zero")))
- X ((eq x 1) 0)
- X ((Math-numberp x)
- X (math-with-extra-prec 2 (math-ln-raw (math-float x))))
- X ((eq (car-safe x) 'sdev)
- X (math-make-sdev (calcFunc-ln (nth 1 x))
- X (math-div (nth 2 x) (nth 1 x))))
- X ((and (eq (car-safe x) 'intv) (or (Math-posp (nth 2 x))
- X (Math-zerop (nth 2 x))
- X (not (math-intv-constp x))))
- X (let ((calc-infinite-mode t))
- X (math-make-intv (nth 1 x) (calcFunc-ln (nth 2 x))
- X (calcFunc-ln (nth 3 x)))))
- X ((equal x '(var e var-e))
- X 1)
- X ((and (eq (car-safe x) '^)
- X (equal (nth 1 x) '(var e var-e))
- X (math-known-realp (nth 2 x)))
- X (nth 2 x))
- X ((math-infinitep x)
- X (if (equal x '(var nan var-nan))
- X x
- X '(var inf var-inf)))
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-ln x)))
- )
- X
- (defun calcFunc-log10 (x) ; [N N] [Public]
- X (cond ((math-equal-int x 1)
- X (if (math-floatp x) '(float 0 0) 0))
- X ((and (Math-integerp x)
- X (math-posp x)
- X (let ((res (math-integer-log x 10)))
- X (and (car res)
- X (setq x (cdr res)))))
- X x)
- X ((and (eq (car-safe x) 'frac)
- X (eq (nth 1 x) 1)
- X (let ((res (math-integer-log (nth 2 x) 10)))
- X (and (car res)
- X (setq x (- (cdr res))))))
- X x)
- X ((math-zerop x)
- X (if calc-infinite-mode
- X '(neg (var inf var-inf))
- X (math-reject-arg x "*Logarithm of zero")))
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X ((Math-numberp x)
- X (math-with-extra-prec 2
- X (let ((xf (math-float x)))
- X (if (eq (nth 1 xf) 0)
- X (math-reject-arg x "*Logarithm of zero"))
- X (if (Math-integer-posp (nth 1 xf))
- X (if (eq (nth 1 xf) 1) ; log10(1*10^n) = n
- X (math-float (nth 2 xf))
- X (let ((xdigs (1- (math-numdigs (nth 1 xf)))))
- X (math-add-float
- X (math-div-float (math-ln-raw-2
- X (list 'float (nth 1 xf) (- xdigs)))
- X (math-ln-10))
- X (math-float (+ (nth 2 xf) xdigs)))))
- X (math-div (calcFunc-ln xf) (math-ln-10))))))
- X ((eq (car-safe x) 'sdev)
- X (math-make-sdev (calcFunc-log10 (nth 1 x))
- X (math-div (nth 2 x)
- X (math-mul (nth 1 x) (math-ln-10)))))
- X ((and (eq (car-safe x) 'intv) (or (Math-posp (nth 2 x))
- X (not (math-intv-constp x))))
- X (math-make-intv (nth 1 x)
- X (calcFunc-log10 (nth 2 x))
- X (calcFunc-log10 (nth 3 x))))
- X ((math-infinitep x)
- X (if (equal x '(var nan var-nan))
- X x
- X '(var inf var-inf)))
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-log10 x)))
- )
- X
- (defun calcFunc-log (x &optional b) ; [N N N] [Public]
- X (cond ((or (null b) (equal b '(var e var-e)))
- X (math-normalize (list 'calcFunc-ln x)))
- X ((or (eq b 10) (equal b '(float 1 1)))
- X (math-normalize (list 'calcFunc-log10 x)))
- X ((math-zerop x)
- X (if calc-infinite-mode
- X (math-div (calcFunc-ln x) (calcFunc-ln b))
- X (math-reject-arg x "*Logarithm of zero")))
- X ((math-zerop b)
- X (if calc-infinite-mode
- X (math-div (calcFunc-ln x) (calcFunc-ln b))
- X (math-reject-arg b "*Logarithm of zero")))
- X ((math-equal-int b 1)
- X (if calc-infinite-mode
- X (math-div (calcFunc-ln x) 0)
- X (math-reject-arg b "*Logarithm base one")))
- X ((math-equal-int x 1)
- X (if (or (math-floatp a) (math-floatp b)) '(float 0 0) 0))
- X ((and (Math-ratp x) (Math-ratp b)
- X (math-posp x) (math-posp b)
- X (let* ((sign 1) (inv nil)
- X (xx (if (Math-lessp 1 x)
- X x
- X (setq sign -1)
- X (math-div 1 x)))
- X (bb (if (Math-lessp 1 b)
- X b
- X (setq sign (- sign))
- X (math-div 1 b)))
- X (res (if (Math-lessp xx bb)
- X (setq inv (math-integer-log bb xx))
- X (math-integer-log xx bb))))
- X (and (car res)
- X (setq x (if inv
- X (math-div 1 (* sign (cdr res)))
- X (* sign (cdr res)))))))
- X x)
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X ((and (Math-numberp x) (Math-numberp b))
- X (math-with-extra-prec 2
- X (math-div (math-ln-raw (math-float x))
- X (math-log-base-raw b))))
- X ((and (eq (car-safe x) 'sdev)
- X (Math-numberp b))
- X (math-make-sdev (calcFunc-log (nth 1 x) b)
- X (math-div (nth 2 x)
- X (math-mul (nth 1 x)
- X (math-log-base-raw b)))))
- X ((and (eq (car-safe x) 'intv) (or (Math-posp (nth 2 x))
- X (not (math-intv-constp x)))
- X (math-realp b))
- X (math-make-intv (nth 1 x)
- X (calcFunc-log (nth 2 x) b)
- X (calcFunc-log (nth 3 x) b)))
- X ((or (eq (car-safe x) 'intv) (eq (car-safe b) 'intv))
- X (math-div (calcFunc-ln x) (calcFunc-ln b)))
- X ((or (math-infinitep x)
- X (math-infinitep b))
- X (math-div (calcFunc-ln x) (calcFunc-ln b)))
- X (t (if (Math-numberp b)
- X (calc-record-why 'numberp x)
- X (calc-record-why 'numberp b))
- X (list 'calcFunc-log x b)))
- )
- X
- (defun calcFunc-alog (x &optional b)
- X (cond ((or (null b) (equal b '(var e var-e)))
- X (math-normalize (list 'calcFunc-exp x)))
- X (t (math-pow b x)))
- )
- X
- (defun calcFunc-ilog (x b)
- X (if (and (math-natnump x) (not (eq x 0))
- X (math-natnump b) (not (eq b 0)))
- X (if (eq b 1)
- X (math-reject-arg x "*Logarithm base one")
- X (if (Math-natnum-lessp x b)
- X 0
- X (cdr (math-integer-log x b))))
- X (math-floor (calcFunc-log x b)))
- )
- X
- (defun math-integer-log (x b)
- X (let ((pows (list b))
- X (pow (math-sqr b))
- X next
- X sum n)
- X (while (not (Math-lessp x pow))
- X (setq pows (cons pow pows)
- X pow (math-sqr pow)))
- X (setq n (lsh 1 (1- (length pows)))
- X sum n
- X pow (car pows))
- X (while (and (setq pows (cdr pows))
- X (Math-lessp pow x))
- X (setq n (/ n 2)
- X next (math-mul pow (car pows)))
- X (or (Math-lessp x next)
- X (setq pow next
- X sum (+ sum n))))
- X (cons (equal pow x) sum))
- )
- X
- X
- (defun math-log-base-raw (b) ; [N N]
- X (if (not (and (equal (car math-log-base-cache) b)
- X (eq (nth 1 math-log-base-cache) calc-internal-prec)))
- X (setq math-log-base-cache (list b calc-internal-prec
- X (math-ln-raw (math-float b)))))
- X (nth 2 math-log-base-cache)
- )
- (setq math-log-base-cache nil)
- X
- (defun calcFunc-lnp1 (x) ; [N N] [Public]
- X (cond ((Math-equal-int x -1)
- X (if calc-infinite-mode
- X '(neg (var inf var-inf))
- X (math-reject-arg x "*Logarithm of zero")))
- X ((eq x 0) 0)
- X ((math-zerop x) '(float 0 0))
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X ((Math-numberp x)
- X (math-with-extra-prec 2
- X (let ((x (math-float x)))
- X (if (and (eq (car x) 'float)
- X (math-lessp-float x '(float 5 -1))
- X (math-lessp-float '(float -5 -1) x))
- X (math-ln-plus-1-raw x)
- X (math-ln-raw (math-add-float x '(float 1 0)))))))
- X ((eq (car-safe x) 'sdev)
- X (math-make-sdev (calcFunc-lnp1 (nth 1 x))
- X (math-div (nth 2 x) (math-add (nth 1 x) 1))))
- X ((and (eq (car-safe x) 'intv) (or (Math-posp (nth 2 x))
- X (not (math-intv-constp x))))
- X (math-make-intv (nth 1 x)
- X (calcFunc-lnp1 (nth 2 x))
- X (calcFunc-lnp1 (nth 3 x))))
- X ((math-infinitep x)
- X (if (equal x '(var nan var-nan))
- X x
- X '(var inf var-inf)))
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-lnp1 x)))
- )
- X
- (defun math-ln-raw (x) ; [N N] --- must be float format!
- X (cond ((eq (car-safe x) 'cplx)
- X (list 'cplx
- X (math-mul-float (math-ln-raw
- X (math-add-float (math-sqr-float (nth 1 x))
- X (math-sqr-float (nth 2 x))))
- X '(float 5 -1))
- X (math-arctan2-raw (nth 2 x) (nth 1 x))))
- X ((eq (car x) 'polar)
- X (math-polar (list 'cplx
- X (math-ln-raw (nth 1 x))
- X (math-to-radians (nth 2 x)))))
- X ((Math-equal-int x 1)
- X '(float 0 0))
- X (calc-symbolic-mode (signal 'inexact-result nil))
- X ((math-posp (nth 1 x)) ; positive and real
- X (let ((xdigs (1- (math-numdigs (nth 1 x)))))
- X (math-add-float (math-ln-raw-2 (list 'float (nth 1 x) (- xdigs)))
- X (math-mul-float (math-float (+ (nth 2 x) xdigs))
- X (math-ln-10)))))
- X ((math-zerop x)
- X (math-reject-arg x "*Logarithm of zero"))
- X ((eq calc-complex-mode 'polar) ; negative and real
- X (math-polar
- X (list 'cplx ; negative and real
- X (math-ln-raw (math-neg-float x))
- X (math-pi))))
- X (t (list 'cplx ; negative and real
- X (math-ln-raw (math-neg-float x))
- X (math-pi))))
- )
- X
- (defun math-ln-raw-2 (x) ; [F F]
- X (cond ((math-lessp-float '(float 14 -1) x)
- X (math-add-float (math-ln-raw-2 (math-mul-float x '(float 5 -1)))
- X (math-ln-2)))
- X (t ; now .7 < x <= 1.4
- X (math-ln-raw-3 (math-div-float (math-sub-float x '(float 1 0))
- X (math-add-float x '(float 1 0))))))
- )
- X
- (defun math-ln-raw-3 (x) ; [F F]
- X (math-mul-float (math-ln-raw-series x 3 x (math-sqr-float x))
- X '(float 2 0))
- )
- X
- ;;; Compute ln((1+x)/(1-x))
- (defun math-ln-raw-series (sum n x xsqr)
- X (math-working "log" sum)
- X (let* ((nextx (math-mul-float x xsqr))
- X (nextsum (math-add-float sum (math-div-float nextx (math-float n)))))
- X (if (math-nearly-equal-float sum nextsum)
- X sum
- X (math-ln-raw-series nextsum (+ n 2) nextx xsqr)))
- )
- X
- (defun math-ln-plus-1-raw (x)
- X (math-lnp1-series x 2 x (math-neg x))
- )
- X
- (defun math-lnp1-series (sum n xpow x)
- X (math-working "lnp1" sum)
- X (let* ((nextx (math-mul-float xpow x))
- X (nextsum (math-add-float sum (math-div-float nextx (math-float n)))))
- X (if (math-nearly-equal-float sum nextsum)
- X sum
- X (math-lnp1-series nextsum (1+ n) nextx x)))
- )
- X
- (math-defcache math-ln-10 (float (bigpos 018 684 045 994 092 585 302 2) -21)
- X (math-ln-raw-2 '(float 1 1)))
- X
- (math-defcache math-ln-2 (float (bigpos 417 309 945 559 180 147 693) -21)
- X (math-ln-raw-3 (math-float '(frac 1 3))))
- X
- X
- X
- ;;; Hyperbolic functions.
- X
- (defun calcFunc-sinh (x) ; [N N] [Public]
- X (cond ((eq x 0) 0)
- X (math-expand-formulas
- X (math-normalize
- X (list '/ (list '- (list 'calcFunc-exp x)
- X (list 'calcFunc-exp (list 'neg x))) 2)))
- X ((Math-numberp x)
- X (if calc-symbolic-mode (signal 'inexact-result nil))
- X (math-with-extra-prec 2
- X (let ((expx (math-exp-raw (math-float x))))
- X (math-mul (math-add expx (math-div -1 expx)) '(float 5 -1)))))
- X ((eq (car-safe x) 'sdev)
- X (math-make-sdev (calcFunc-sinh (nth 1 x))
- X (math-mul (nth 2 x) (calcFunc-cosh (nth 1 x)))))
- X ((eq (car x) 'intv)
- X (math-sort-intv (nth 1 x)
- X (calcFunc-sinh (nth 2 x))
- X (calcFunc-sinh (nth 3 x))))
- X ((or (equal x '(var inf var-inf))
- X (equal x '(neg (var inf var-inf)))
- X (equal x '(var nan var-nan)))
- X x)
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-sinh x)))
- )
- (put 'calcFunc-sinh 'math-expandable t)
- X
- (defun calcFunc-cosh (x) ; [N N] [Public]
- X (cond ((eq x 0) 1)
- X (math-expand-formulas
- X (math-normalize
- X (list '/ (list '+ (list 'calcFunc-exp x)
- X (list 'calcFunc-exp (list 'neg x))) 2)))
- X ((Math-numberp x)
- X (if calc-symbolic-mode (signal 'inexact-result nil))
- X (math-with-extra-prec 2
- X (let ((expx (math-exp-raw (math-float x))))
- X (math-mul (math-add expx (math-div 1 expx)) '(float 5 -1)))))
- X ((eq (car-safe x) 'sdev)
- X (math-make-sdev (calcFunc-cosh (nth 1 x))
- X (math-mul (nth 2 x)
- X (calcFunc-sinh (nth 1 x)))))
- X ((and (eq (car x) 'intv) (math-intv-constp x))
- X (setq x (math-abs x))
- X (math-sort-intv (nth 1 x)
- X (calcFunc-cosh (nth 2 x))
- X (calcFunc-cosh (nth 3 x))))
- X ((or (equal x '(var inf var-inf))
- X (equal x '(neg (var inf var-inf)))
- X (equal x '(var nan var-nan)))
- X (math-abs x))
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-cosh x)))
- )
- (put 'calcFunc-cosh 'math-expandable t)
- X
- (defun calcFunc-tanh (x) ; [N N] [Public]
- X (cond ((eq x 0) 0)
- X (math-expand-formulas
- X (math-normalize
- X (let ((expx (list 'calcFunc-exp x))
- X (expmx (list 'calcFunc-exp (list 'neg x))))
- X (math-normalize
- X (list '/ (list '- expx expmx) (list '+ expx expmx))))))
- X ((Math-numberp x)
- X (if calc-symbolic-mode (signal 'inexact-result nil))
- X (math-with-extra-prec 2
- X (let* ((expx (calcFunc-exp (math-float x)))
- X (expmx (math-div 1 expx)))
- X (math-div (math-sub expx expmx)
- X (math-add expx expmx)))))
- X ((eq (car-safe x) 'sdev)
- X (math-make-sdev (calcFunc-tanh (nth 1 x))
- X (math-div (nth 2 x)
- X (math-sqr (calcFunc-cosh (nth 1 x))))))
- X ((eq (car x) 'intv)
- X (math-sort-intv (nth 1 x)
- X (calcFunc-tanh (nth 2 x))
- X (calcFunc-tanh (nth 3 x))))
- X ((equal x '(var inf var-inf))
- X 1)
- X ((equal x '(neg (var inf var-inf)))
- X -1)
- X ((equal x '(var nan var-nan))
- X x)
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-tanh x)))
- )
- (put 'calcFunc-tanh 'math-expandable t)
- X
- (defun calcFunc-arcsinh (x) ; [N N] [Public]
- X (cond ((eq x 0) 0)
- X (math-expand-formulas
- X (math-normalize
- X (list 'calcFunc-ln (list '+ x (list 'calcFunc-sqrt
- X (list '+ (list '^ x 2) 1))))))
- X ((Math-numberp x)
- X (if calc-symbolic-mode (signal 'inexact-result nil))
- X (math-with-extra-prec 2
- X (math-ln-raw (math-add x (math-sqrt-raw (math-add (math-sqr x)
- X '(float 1 0)))))))
- X ((eq (car-safe x) 'sdev)
- X (math-make-sdev (calcFunc-arcsinh (nth 1 x))
- X (math-div (nth 2 x)
- X (math-sqrt
- X (math-add (math-sqr (nth 1 x)) 1)))))
- X ((eq (car x) 'intv)
- X (math-sort-intv (nth 1 x)
- X (calcFunc-arcsinh (nth 2 x))
- X (calcFunc-arcsinh (nth 3 x))))
- X ((or (equal x '(var inf var-inf))
- X (equal x '(neg (var inf var-inf)))
- X (equal x '(var nan var-nan)))
- X x)
- X (t (calc-record-why 'numberp x)
- X (list 'calcFunc-arcsinh x)))
- )
- (put 'calcFunc-arcsinh 'math-expandable t)
- X
- (defun calcFunc-arccosh (x) ; [N N] [Public]
- X (cond ((eq x 1) 0)
- X ((and (eq x -1) calc-symbolic-mode)
- X '(var pi var-pi))
- X ((and (eq x 0) calc-symbolic-mode)
- X (math-div (math-mul '(var pi var-pi) '(var i var-i)) 2))
- X (math-expand-formulas
- X (math-normalize
- X (list 'calcFunc-ln (list '+ x (list 'calcFunc-sqrt
- X (list '- (list '^ x 2) 1))))))
- X ((Math-numberp x)
- X (if calc-symbolic-mode (signal 'inexact-result nil))
- X (if (Math-equal-int x -1)
- X (math-imaginary (math-pi))
- X (math-with-extra-prec 2
- X (if (or t ; need to do this even in the real case!
- X (memq (car-safe x) '(cplx polar)))
- X (let ((xp1 (math-add 1 x))) ; this gets the branch cuts right
- X (math-ln-raw
- X (math-add x (math-mul xp1
- X (math-sqrt-raw
- X (math-div (math-sub
- X x
- X '(float 1 0))
- X xp1))))))
- X (math-ln-raw
- X (math-add x (math-sqrt-raw (math-add (math-sqr x)
- X '(float -1 0)))))))))
- X ((eq (car-safe x) 'sdev)
- X (math-make-sdev (calcFunc-arccosh (nth 1 x))
- X (math-div (nth 2 x)
- X (math-sqrt
- X (math-add (math-sqr (nth 1 x)) -1)))))
- X ((eq (car x) 'intv)
- X (math-sort-intv (nth 1 x)
- X (calcFunc-arccosh (nth 2 x))
- X (calcFunc-arccosh (nth 3 x))))
- X ((or (equal x '(var inf var-inf))
- X (equal x '(neg (var inf var-inf)))
- X (equal x '(var nan var-nan)))
- SHAR_EOF
- true || echo 'restore of calc-math.el failed'
- fi
- echo 'End of part 21'
- echo 'File calc-math.el is continued in part 22'
- echo 22 > _shar_seq_.tmp
- exit 0
- exit 0 # Just in case...
- --
- Kent Landfield INTERNET: kent@sparky.IMD.Sterling.COM
- Sterling Software, IMD UUCP: uunet!sparky!kent
- Phone: (402) 291-8300 FAX: (402) 291-4362
- Please send comp.sources.misc-related mail to kent@uunet.uu.net.
-