Package: apcalc
Version: 2.12.3.3-1
Severity: normal
Hi,
I noticed something I cannot understand.
I wanted to compute a base 10 logarithm with increasing precision, but
it seems that the precision does not increase beyond some sort of limit
value:
$ calc
C-style arbitrary precision calculator (version 2.12.3.3)
Calc is open software. For license details type: help copyright
[Type "exit" to exit, or "help" for help.]
; display(70)
20
; for (n = 4 ; n <= 70 ; n += 4) { epsilon(10^(-n)) ; print n, log(10^0.5) ; }
4 0.5
8 ~0.4999967645270563710588030921566924346391036219925301832710848605923738
12 ~0.4999967630057326500477720837314340310952835924606966038391383653261530
16 ~0.4999967630057425518978545991487883262399027186658559888821332406844437
20 ~0.4999967630057425701424476678537305654477547120646226005385216711543473
24 ~0.4999967630057425701420116390167636584730304872752540606271171718926431
28 ~0.4999967630057425701420115205854251715452097628767480239729001997741683
32 ~0.4999967630057425701420115206037435941978632849821940415182836793190307
36 ~0.4999967630057425701420115206037445079475375662294797185789976548249805
40 ~0.4999967630057425701420115206037445078609398071744983931208199426734995
44 ~0.4999967630057425701420115206037445078609184139668201163901676365847303
48 ~0.4999967630057425701420115206037445078609184158403543820029531833579432
52 ~0.4999967630057425701420115206037445078609184158405222357335186311126553
56 ~0.4999967630057425701420115206037445078609184158405222305307044210892035
60 ~0.4999967630057425701420115206037445078609184158405222305292556240771302
64 ~0.4999967630057425701420115206037445078609184158405222305292556025796925
68 ~0.4999967630057425701420115206037445078609184158405222305292556025726483
Awkwardly enough, it seems that the exact value is computed, when epsilon
is set to 10^-4, but, when I set epsilon to 10^-8 or less, the absolute
error (with respect to the exact value of 0.5) does not seem to lower
significantly.
Indeed, the absolute error seem to be stay almost unchanged:
; for (n = 4 ; n <= 70 ; n += 4) { epsilon(10^(-n)) ; print n, 0.5 -
log(10^0.5) ; }
4 0
8 ~0.0000032354729436289411969078433075653608963780074698167289151394076262
12 ~0.0000032369942673499522279162685659689047164075393033961608616346738470
16 ~0.0000032369942574481021454008512116737600972813341440111178667593155563
20 ~0.0000032369942574298575523321462694345522452879353773994614783288456527
24 ~0.0000032369942574298579883609832363415269695127247459393728828281073569
28 ~0.0000032369942574298579884794145748284547902371232519760270998002258317
32 ~0.0000032369942574298579884793962564058021367150178059584817163206809693
36 ~0.0000032369942574298579884793962554920524624337705202814210023451750195
40 ~0.0000032369942574298579884793962554921390601928255016068791800573265005
44 ~0.0000032369942574298579884793962554921390815860331798836098323634152697
48 ~0.0000032369942574298579884793962554921390815841596456179970468166420568
52 ~0.0000032369942574298579884793962554921390815841594777642664813688873447
56 ~0.0000032369942574298579884793962554921390815841594777694692955789107965
60 ~0.0000032369942574298579884793962554921390815841594777694707443759228698
64 ~0.0000032369942574298579884793962554921390815841594777694707443974203075
68 ~0.0000032369942574298579884793962554921390815841594777694707443974273517
;
I seem to get reasonable results with, say, the computation of sqrt(2),
where the absolute error really decreases exponentially (as I think
it should).
Why does the computation of log(10^0.5) fail to increase in precision?
What did I fail to understand?
Could you please explain if I missed something in the documentation
(I tried to read various "help" documents) or if this is an actual
bug?
Thanks for your time.
-- System Information:
Debian Release: squeeze/sid
APT prefers testing
APT policy: (800, 'testing'), (500, 'unstable')
Architecture: amd64 (x86_64)
Kernel: Linux 2.6.32-5-amd64 (SMP w/2 CPU cores)
Locale: LANG=en_US.UTF-8, LC_CTYPE=en_US.UTF-8 (charmap=UTF-8)
Shell: /bin/sh linked to /bin/bash
Versions of packages apcalc depends on:
ii apcalc-common 2.12.3.3-1 Arbitrary precision calculator (co
ii libc6 2.11.2-6+squeeze1 Embedded GNU C Library: Shared lib
ii libreadline5 5.2-7 GNU readline and history libraries
apcalc recommends no packages.
apcalc suggests no packages.
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