<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META content="text/html; charset=iso-8859-1" http-equiv=Content-Type> <META name=GENERATOR content="MSHTML 8.00.6001.18854"> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT size=2 face="Courier New">#lang scheme</FONT></DIV> <DIV><FONT size=2 face="Courier New"></FONT> </DIV> <DIV><FONT size=2 face="Courier New">; I do not understand the difference between the following two:</FONT></DIV> <DIV><FONT size=2 face="Courier New"></FONT> </DIV> <DIV><FONT size=2 face="Courier New">(let loop ((x 0))<BR> (let ((d (- 1.0 (+ 1.0 (expt 2 x)))))<BR>  (if (= d 0) x</FONT></DIV> <DIV><FONT size=2 face="Courier New">   ; d is an inexact real number.</FONT></DIV> <DIV><FONT size=2 face="Courier New">   ; well, all reals are inexact I think.</FONT></DIV> <DIV><FONT size=2 face="Courier New">   ; an exact real would have to be an exact ranional, is it not?<BR>   (loop (sub1 x))))) ; --> 54</FONT></DIV> <DIV><FONT size=2 face="Courier New">; flonum arithmetic I think.</FONT></DIV> <DIV><FONT size=2 face="Courier New"></FONT> </DIV> <DIV><FONT size=2 face="Courier New">(let loop ((x 0))<BR> (let ((d (exact->inexact (- 1 (+ 1 (expt 2 x))))))</FONT></DIV> <DIV><FONT size=2 face="Courier New">  ; d is an inexact rational number.<BR>  (if (= d 0) x<BR>   (loop (sub1 x))))) ; --> -1075</FONT></DIV> <DIV><FONT size=2 face="Courier New">; where does this high though finite precision come from?</FONT></DIV> <DIV><FONT size=2 face="Courier New"></FONT> </DIV> <DIV><FONT size=2 face="Courier New">This is with:</FONT></DIV> <DIV><FONT size=2 face="Courier New">Welcome to DrScheme, version 4.2.3.12-svn16jan2010 [3m].<BR>Language: Module custom; memory limit: 800 megabytes.</FONT></DIV> <DIV><FONT size=2 face="Courier New"></FONT> </DIV> <DIV><FONT size=2 face="Courier New">I cannot make head or tail of it.</FONT></DIV> <DIV><FONT size=2 face="Courier New"></FONT> </DIV> <DIV><FONT size=2 face="Courier New">Thanks, Jos</FONT></DIV> <DIV><FONT size=2 face="Courier New"></FONT> </DIV></BODY></HTML>