Import Upstream version 3a1upstream/3a1

1 files changed, 7 insertions, 7 deletions

diff --git a/root.scm b/root.scm
index 144a4af..0a56bc9 100644
--- a/root.scm
+++ b/root.scm
@@ -8,7 +8,7 @@
 ;1.  Any copy made of this software must include this copyright notice
 ;in full.
 ;
-;2.  I have made no warrantee or representation that the operation of
+;2.  I have made no warranty or representation that the operation of
 ;this software will be error-free, and I am under no obligation to
 ;provide any services, by way of maintenance, update, or otherwise.
 ;
@@ -23,7 +23,7 @@
 ;;; D. E. Knuth, "The Art of Computer Programming", Vol 2 /
 ;;; Seminumerical Algorithms, Reading Massachusetts, Addison-Wesley
 ;;; Publishing Company, 2nd Edition, p. 510
-
+;@
 (define (newton:find-integer-root f df/dx x_0)
   (let loop ((x x_0) (fx (f x_0)))
     (cond
@@ -40,12 +40,12 @@
 		 (next-fx (f next-x)))
 	    (cond ((>= (abs next-fx) (abs fx)) x)
 		  (else (loop next-x next-fx)))))))))))
-
+;@
 (define (integer-sqrt y)
   (newton:find-integer-root (lambda (x) (- (* x x) y))
 			    (lambda (x) (* 2 x))
 			    (ash 1 (quotient (integer-length y) 2))))
-
+;@
 (define (newton:find-root f df/dx x_0 prec)
   (if (and (negative? prec) (integer? prec))
       (let loop ((x x_0) (fx (f x_0)) (count prec))
@@ -71,7 +71,7 @@
 ;;; H. J. Orchard, "The Laguerre Method for Finding the Zeros of
 ;;; Polynomials", IEEE Transactions on Circuits and Systems, Vol. 36,
 ;;; No. 11, November 1989, pp 1377-1381.
-
+;@
 (define (laguerre:find-root f df/dz ddf/dz^2 z_0 prec)
   (if (and (negative? prec) (integer? prec))
       (let loop ((z z_0) (fz (f z_0)) (count prec))
@@ -114,7 +114,7 @@
 			     ((and delta-z (>= next-delta-z delta-z)) z)
 			     (else
 			      (loop next-z (f next-z) next-delta-z)))))))))))
-
+;@
 (define (laguerre:find-polynomial-root deg f df/dz ddf/dz^2 z_0 prec)
   (if (and (negative? prec) (integer? prec))
       (let loop ((z z_0) (fz (f z_0)) (count prec))
@@ -210,7 +210,7 @@
 			     (fnew (f xnew))
 			     (fmax (max (abs f1) (abs fnew))))
 			(secant-iter x1 f1 xnew fnew (+ count 1)))))))))))
-
+;@
 (define (secant:find-root f x0 x1 prec)
   (secant:find-root-1 f x0 x1 prec #f))
 (define (secant:find-bracketed-root f x0 x1 prec)