<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; charset=iso-8859-1"> <META content="MSHTML 6.00.6000.16608" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY> <DIV><FONT face="Courier New" size=2>Hi</FONT></DIV> <DIV><FONT face="Courier New" size=2>I had a look in scheme/private/for.ss. If I understand the code correctly in-range computes subsequent values of the variable by accumulated addition of the step to the start. </FONT><FONT face="Courier New" size=2>When some decades ago do-loops with real variables were introduced in fortran, there was discussion about how to approach it:</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>1: accumulated addition of the step to the start.</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>2: compute the number of iterations in advance as</FONT></DIV> <DIV><FONT face="Courier New" size=2>   n=(inexact->exact (ceiling (/ (- finish start) step))))</FONT></DIV> <DIV><FONT face="Courier New" size=2>   and loop (for ((var (in-range 0 n 1))) (let ((var (+ start (* i step)))) etc))</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>The second method was choosen, because it was argued that accumulative addition also would accumulate error. The code below illustrates the difference:</FONT></DIV> <DIV><FONT face="Courier New" size=2>Kind regards, Jos</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>#lang scheme</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>(define start 1.0e10)<BR>(define finish 1.000001e10)<BR>(define step 0.01)</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>(define-values (nr-of-iterations-accumulated sum-accumulated)<BR> (let ((nr-of-iterations 0) (sum 0))<BR>  (for ((var (in-range start finish step)))<BR>   (set! nr-of-iterations (add1 nr-of-iterations))<BR>   (set! sum (+ sum var)))<BR>  (values nr-of-iterations sum)))</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>(define-values (nr-of-iterations-precomputed sum-precomputed)<BR> (let ((sum 0) (nr-of-iterations 0))<BR>  (for ((i (in-range 0 (inexact->exact (ceiling (/ (- finish start) step))) 1)))<BR>   (let ((var (+ start (* i step))))<BR>    (set! nr-of-iterations (add1 nr-of-iterations))<BR>    (set! sum (+ var sum))))<BR>  (values nr-of-iterations sum)))</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>(printf "nr-of-iterations precomputed: ~s~n" nr-of-iterations-precomputed)<BR>(printf "nr-of-iterations accumulated: ~s~n" nr-of-iterations-accumulated)<BR>(printf "difference: ~s~n~n"<BR> (- nr-of-iterations-precomputed nr-of-iterations-accumulated))</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>(printf "sum-precomputed: ~s~n" sum-precomputed)<BR>(printf "sum-accumulated: ~s~n" sum-accumulated)<BR>(printf "difference: ~s~n" (- sum-precomputed sum-accumulated))<BR>(printf "relative error: ~s~n"<BR> (* 2<BR>  (/<BR>   (- sum-precomputed sum-accumulated)<BR>   (+ sum-accumulated sum-precomputed))))</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>Welcome to DrScheme, version 3.99.0.13-svn27feb2008 [3m].<BR>Language: Module; memory limit: 750 megabytes.</FONT></DIV> <DIV><BR><FONT face="Courier New" size=2>nr-of-iterations precomputed: 1000000<BR>nr-of-iterations accumulated:  999978<BR>difference:                        22</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face=Arial size=2><FONT face="Courier New">sum-precomputed: 10000004999991172.0<BR>sum-accumulated:  9999784999889490.0</FONT></FONT></DIV> <DIV><FONT face=Arial size=2><FONT face="Courier New">difference:           220000101682.0<BR>relative error: 2.2000241170863566e-005</FONT><BR>> </FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>----- Original Message ----- </FONT> <DIV><FONT face=Arial size=2>From: "Noel Welsh" <</FONT><A href="mailto:noelwelsh@gmail.com"><FONT face=Arial size=2>noelwelsh@gmail.com</FONT></A><FONT face=Arial size=2>></FONT></DIV> <DIV><FONT face=Arial size=2>To: "Jos Koot" <</FONT><A href="mailto:jos.koot@telefonica.net"><FONT face=Arial size=2>jos.koot@telefonica.net</FONT></A><FONT face=Arial size=2>></FONT></DIV> <DIV><FONT face=Arial size=2>Cc: <</FONT><A href="mailto:plt-scheme@list.cs.brown.edu"><FONT face=Arial size=2>plt-scheme@list.cs.brown.edu</FONT></A><FONT face=Arial size=2>></FONT></DIV> <DIV><FONT face=Arial size=2>Sent: Friday, February 29, 2008 8:36 PM</FONT></DIV> <DIV><FONT face=Arial size=2>Subject: Re: [plt-scheme] redefinition in module</FONT></DIV></DIV> <DIV><FONT face=Arial><BR><FONT size=2></FONT></FONT></DIV><FONT face=Arial size=2>> On Fri, Feb 29, 2008 at 7:04 PM, Jos Koot <</FONT><A href="mailto:jos.koot@telefonica.net"><FONT face=Arial size=2>jos.koot@telefonica.net</FONT></A><FONT face=Arial size=2>> wrote:<BR>>> For example, I had my own nice and more general version of syntax 'for'. I<BR>>> no longer can import my own 'for' without renaming.<BR>> <BR>> If you have suggestions to improve the comprehension macros I, for<BR>> one, would like to hear them.  Designing such a system is very tricky,<BR>> and perhaps the existing system can be improved further.<BR>> <BR>> N.</FONT></BODY></HTML>