From: Jeff M.
Subject: Logarithms of bignums
Date: Sat, 13 Jun 2009 19:34:13 +0000
Message-ID: <b7b1eba5-a589-4630-92a9-ee0a5d8a40ef@y17g2000yqn.googlegroups.com>

(log (fac 1000) 10)

On SBCL, this returns properly:
2567.6047

On LispWorks (which is my Lisp of choice), I sadly get returned:
+1F++0 #| +1F++0 is single-float plus-infinity |#

Just wondering if anyone is aware of either (a) another way to get
this (been a long time since college) or (b) some way of getting
LispWorks to not choke? ;-)

Thanks!

Jeff M.

• Re: Logarithms of bignums Pillsy
• Re: Logarithms of bignums Pascal J. Bourguignon

From: Pillsy
Subject: Re: Logarithms of bignums
Date: Sun, 14 Jun 2009 03:33:33 +0000
Message-ID: <3ea4d78d-c95a-40ff-9356-2be0775fcbd9@x3g2000yqa.googlegroups.com>

On Jun 13, 3:34 pm, "Jeff M." <·······@gmail.com> wrote:
> (log (fac 1000) 10)

> On SBCL, this returns properly:
> 2567.6047

> On LispWorks (which is my Lisp of choice), I sadly get returned:
> +1F++0 #| +1F++0 is single-float plus-infinity |#

> Just wondering if anyone is aware of either (a) another way to get
> this (been a long time since college)

Well, you can also just calculate it by using the fact that log ab =
log a + log b:

* (loop :for x :from 1d0 :to 1000d0 :summing (log x 10))
2567.6046442221304d0

This has the advantage of being pretty accurate (not perfect because
of the vagaries of adding floating point numbers, but pretty
accurate).

If you can tolerate a little less accuracy, there's also Stirling's
approximation, which will do a good job for ln (n!) if n >> 1.

http://mathworld.wolfram.com/StirlingsApproximation.html

* (defun stirling (x)
    (+ (* (+ x 0.5) (log x)) (- x) (/ (log (* 2 pi)) 2)))
STIRLING

* (stirling 1000)
5912.128411189455d0

* (/ * (log 10))
2567.60470962732d0

Cheers,
Pillsy

From: Pascal J. Bourguignon
Subject: Re: Logarithms of bignums
Date: Sat, 13 Jun 2009 19:44:47 +0000
Message-ID: <8763ez3ols.fsf@galatea.local>

"Jeff M." <·······@gmail.com> writes:

> (log (fac 1000) 10)
>
> On SBCL, this returns properly:
> 2567.6047
>
> On LispWorks (which is my Lisp of choice), I sadly get returned:
> +1F++0 #| +1F++0 is single-float plus-infinity |#
>
> Just wondering if anyone is aware of either (a) another way to get
> this (been a long time since college) 

integer-length = ceiling log2

so (/ (1- (integer-length x)) (log 10 2)) <= (log x 10) < (/ (integer-length x) (log 10 2)) 

(/ (integer-length (ext:! 1000)) (log 10 2)) --> 2567.786


And since I don't see any reason to get the log10 of a number other
than to know the number of base-ten digits needed to display it, the
above expression must be precise enough for this purpose.


> (b) some way of getting LispWorks to not choke? ;-)

-- 
__Pascal Bourguignon__