<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; charset=iso-8859-7"> <META content="MSHTML 6.00.6000.16939" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT face="Courier New" size=2>Hi Phil,</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>Yes, that is an exact method (provided b is exact) and the code is straight forward indeed. </FONT><FONT face="Courier New" size=2>As you say, it takes a while. That's why I try to use primitive log. </FONT><FONT face="Courier New" size=2>In fact I use a method that computes the logarithms (base 10) of the numerator and nominator of rationals separately such as to avoid -inf.0 for (positive) rational numbers very close to zero (not shown in my example)</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT size=2><FONT face="Courier New">We have something like <SPAN title="Provided from: scheme/base, scheme"><SPAN class=ScmSym><A class=ScmValLink href="file:///C:/Program%20Files/PLT-FULL-4.2.2.4/doc/reference/numbers.html#(def._((quote._~23~25kernel)._integer-sqrt/remainder))">integer-sqrt/remainder</A> for square roots. It would be nice to have something like (integer-log-base-10/remainder n) --> p r </SPAN></SPAN></FONT></FONT><FONT size=2><FONT face="Courier New"><SPAN title="Provided from: scheme/base, scheme"><SPAN class=ScmSym>such that (+ (expt 10 p) r) exactly equals n, where n, p and r are positive exact integer numbers and p is computed to be maximal.</SPAN></SPAN></FONT></FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>Jos</FONT></DIV> <BLOCKQUOTE style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B> <A title=pbewig@gmail.com href="mailto:pbewig@gmail.com">Phil Bewig</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A title=jos.koot@telefonica.net href="mailto:jos.koot@telefonica.net">Jos Koot</A> </DIV> <DIV style="FONT: 10pt arial"><B>Cc:</B> <A title=plt-scheme@list.cs.brown.edu href="mailto:plt-scheme@list.cs.brown.edu">plt-scheme@list.cs.brown.edu</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Thursday, November 05, 2009 4:02 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [plt-scheme] order of magnitude</DIV> <DIV><BR></DIV><CODE style="FONT-FAMILY: courier new,monospace">(define (ilog b n)<BR>Ā  (let loop ((n n) (i -1))<BR>Ā Ā Ā  (if (zero? n) i<BR>Ā Ā Ā Ā Ā  (loop (quotient n b) (+ i 1)))))<BR><BR>(ilog 10 #e1000e1000000) => 1000003<BR></CODE><BR style="FONT-FAMILY: courier new,monospace"> <DIV class=gmail_quote><SPAN style="FONT-FAMILY: courier new,monospace">It does take a while....</SPAN><BR><BR>On Thu, Nov 5, 2009 at 5:04 AM, Jos Koot <SPAN dir=ltr><<A href="mailto:jos.koot@telefonica.net" target=_blank>jos.koot@telefonica.net</A>></SPAN> wrote:<BR> <BLOCKQUOTE class=gmail_quote style="PADDING-LEFT: 1ex; MARGIN: 0pt 0pt 0pt 0.8ex; BORDER-LEFT: rgb(204,204,204) 1px solid"> <DIV bgcolor="#ffffff"><FONT face="Courier New" size=2>Some browsing did not lead me to finding a function that accepts an exact positive rational number and returns its order of magnitude (an exact integer number) Something like:<BR><BR>(define log10 (inexact->exact (log 10)))<BR>(define (order-of-magnitude q) (floor (/ (inexact->exact (log q)) log10)))<BR><BR>However, due to inexactness of function log we find:<BR><BR>(/ (inexact->exact (log #e1000e1000000)) log10) --> close to but sligtly less than 1000003<BR><BR>and hence:<BR><BR>(order-of-magnitude #e1000e1000000) ; --> 1000002 <BR><BR>The wanted answer is 1000003. So I did the following:<BR><BR>(define order-of-magnitude<BR>Ā (let*<BR>Ā  ((log10 (inexact->exact (log 10)))<BR>Ā Ā  (10log (Ī» (q) (/ (inexact->exact (log q)) log10))))<BR>Ā  (Ī» (q)<BR>Ā Ā  (unless (and (rational? q) (exact? q) (positive? q))<BR>Ā Ā Ā  (raise-type-error 'magnitude "positive exact rational number" q))<BR>Ā Ā  (let* ((m (floor (10log q))) (k (expt 10 m)))<BR>Ā Ā Ā  ; >From now on all arithmetic operations and their operands are exact.<BR>Ā Ā Ā  (let loop ((m m) (lower (* k 1/10)) (middle k) (upper (* k 10)))<BR>Ā Ā Ā Ā  (cond<BR>Ā Ā Ā Ā Ā  ((<= q lower) (loop (sub1 m) (* lower 1/10) lower middle))<BR>Ā Ā Ā Ā Ā  ((>= q upper) (loop (add1 m) middle upper (* upper 10)))<BR>Ā Ā Ā Ā Ā  (else m)))))))<BR><BR>(order-of-magnitude #e1000e1000000) ; --> 1000003<BR><BR>However, this seems rather complicated. Does someone have or know of a simpler and faster function for this purpose?<BR><BR>Thanks, Jos</FONT></DIV><BR>_________________________________________________<BR>Ā For list-related administrative tasks:<BR>Ā <A href="http://list.cs.brown.edu/mailman/listinfo/plt-scheme" target=_blank>http://list.cs.brown.edu/mailman/listinfo/plt-scheme</A><BR><BR></BLOCKQUOTE></DIV><BR></BLOCKQUOTE></BODY></HTML>