This is not correct wrt J.
For historical and practical (time and space) reasons,
by default numbers are 64-bit IEEE floating point numbers
("machine numbers"), which gives 16 decimal digits of precision.
In J, if you want more digits, you can use rational numbers,
and that has infinite precision. All you need to do is
to make your input numbers extended precision,
and the interpreter will try to carry through your
computations in extended precision. For example:
% 1 + +/~ i.10 NB. Hilbert matrix
1 0.5 0.333333 0.25 0.2 0.166667 0.142857 0.125
0.111111 0.1
0.5 0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111
0.1 0.0909091
0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111 0.1
0.0909091 0.0833333
0.25 0.2 0.166667 0.142857 0.125 0.111111 0.1 0.0909091
0.0833333 0.0769231
0.2 0.166667 0.142857 0.125 0.111111 0.1 0.0909091 0.0833333
0.0769231 0.0714286
0.166667 0.142857 0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231
0.0714286 0.0666667
0.142857 0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231 0.0714286
0.0666667 0.0625
0.125 0.111111 0.1 0.0909091 0.0833333 0.0769231 0.0714286 0.0666667
0.0625 0.0588235
0.111111 0.1 0.0909091 0.0833333 0.0769231 0.0714286 0.0666667 0.0625
0.0588235 0.0555556
0.1 0.0909091 0.0833333 0.0769231 0.0714286 0.0666667 0.0625 0.0588235
0.0555556 0.0526316
The above calculation has 16 decimal digits of precision.
The output is 6 decimal digits because that is the default
for the session. (You can change the print precision for
the session.)
% 1 + +/~ i.10x
1 1r2 1r3 1r4 1r5 1r6 1r7 1r8 1r9 1r10
1r2 1r3 1r4 1r5 1r6 1r7 1r8 1r9 1r10 1r11
1r3 1r4 1r5 1r6 1r7 1r8 1r9 1r10 1r11 1r12
1r4 1r5 1r6 1r7 1r8 1r9 1r10 1r11 1r12 1r13
1r5 1r6 1r7 1r8 1r9 1r10 1r11 1r12 1r13 1r14
1r6 1r7 1r8 1r9 1r10 1r11 1r12 1r13 1r14 1r15
1r7 1r8 1r9 1r10 1r11 1r12 1r13 1r14 1r15 1r16
1r8 1r9 1r10 1r11 1r12 1r13 1r14 1r15 1r16 1r17
1r9 1r10 1r11 1r12 1r13 1r14 1r15 1r16 1r17 1r18
1r10 1r11 1r12 1r13 1r14 1r15 1r16 1r17 1r18 1r19
The only difference between the two input sentences
is the trailing 10 (machine number) and 10x (extended
precision number).
m +/ .* %. m=: % 1 + +/~ i.10
1.00047 _0.00619721 0.0133228 0.00179932 _0.00673962 _0.00755167
_0.00690055 _0.000172734 0.00353628 0.00956631
_0.00620086 1.0811 _0.174345 _0.0235263 0.0882211 0.0988431
0.0903749 0.00217986 _0.0462107 _0.125206
0.0133312 _0.174349 1.37482 0.0506763 _0.190106 _0.21133
_0.196193 _0.00288332 0.0984164 0.269389
0.00179848 _0.0235348 0.0506859 1.00591 _0.0213178 _0.0402455
_0.00748849 _0.0185254 0.0227113 0.0343037
_0.00674288 0.0882262 _0.190103 _0.0213129 1.07596 0.161627
0.0106583 0.0861107 _0.0938043 _0.126691
_0.00756361 0.098839 _0.211326 _0.0402408 0.161622 0.974321
0.34696 _0.223546 0.06125 _0.178329
_0.00690331 0.090379 _0.196192 _0.00748292 0.0106608 0.346969
0.71698 0.368988 _0.242016 _0.0978327
_0.000171363 0.00217855 _0.00288343 _0.0185248 0.0861086 _0.223544
0.368986 0.649903 0.18074 _0.0432134
0.003535 _0.0462151 0.0984225 0.0227093 _0.0938085 0.0612454
_0.24202 0.180739 0.931766 0.0920672
0.00957343 _0.125208 0.269389 0.0342936 _0.126692 _0.178331
_0.0978323 _0.0432161 0.0920641 1.18877
x +/ .* %. x=: % 1 + +/~ i.10x
1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1
The preceding are two expressions of the product of the
Hilbert matrix and its inverse. The first uses machine numbers;
the second uses extended precision numbers.
----- Original Message -----
From: DIETER ENSSLEN <[email protected]>
Date: Sunday, August 9, 2009 13:43
Subject: Re: [Jgeneral] Array Based Languages
To: General forum <[email protected]>
> so unfortunately for the moment or for a very long time we are
> in this at the level of all ipod touch / i phones: 16
> significant digits, and one level above windows excel's 15, and
> quite a few levels below several i pod Apps
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
