At 13:36 -0700 2009/08/09, Roger Hui wrote:
>J uses the C printf() routine to format 64-bit floating point
>numbers. The different outputs are perhaps due to the
>differences in the printf()'s on the different systems.
>In any case, only the first 16 decimal digits are significant;
>the rest are garbage.
>
"the rest are garbage." seems a little harsh. Especially in the case
of numbers that can be represented exactly in 64-bit floating point
e.g.
40":"0 ]2^120+4*i.5 NB. 64 bit floats
1329227995784915872903807060280344576
21267647932558653966460912964485513216
340282366920938463463374607431768211456
5444517870735015415413993718908291383296
****************************************
which is identical on my systems to -
40":"0 ]2^120+4*i.5x NB. extended integers
1329227995784915872903807060280344576
21267647932558653966460912964485513216
340282366920938463463374607431768211456
5444517870735015415413993718908291383296
****************************************
versus
40":"0 ]2^120+4*i.5
1329227995784915900000000000000000000
21267647932558654000000000000000000000
340282366920938460000000000000000000000
5444517870735015400000000000000000000000
****************************************
Somehow the 0s look more like garbage than the digits in the first
two. Since your other examples show the 0s, I'm assuming it is a
Windows issue since my environments are Linux and Darwin. Surely it
isn't AMD versus Intel thing.
I guess the "logic" in choosing the final 1 in the formatted pi is
that it is in the center of a sort of "guard band" -
3.14159265358979310 - 3.14159265358979280 3.14159265358979290
3.14159265358979300 3.14159265358979310 3.14159265358979320
3.14159265358979330 3.14159265358979340 NB. single long line will
undoubtedly be munged by mail...
4.44089e_16 0 0 0 0 0 _4.44089e_16
(j.15+i.5)":"0 o.1
3.141592653589793
3.1415926535897931
3.14159265358979312
3.141592653589793116
3.1415926535897931160
Certainly the last 1 in the default format of 0.1 is garbage since it
should be a 2 -
(j.15+i.5)":"0 pi 20
3.141592653589793
3.1415926535897932
3.14159265358979324
3.141592653589793238
3.1415926535897932385
I suppose I can count this as another reason I'm happy I don't use Windows....
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