in reply to Re^5: Euler's identity in Raku
in thread Euler's identity in Raku
There may be a world where a language can do identity / symbol math - indeed there are cpan packages for this kind of thing. But core Raku does not attempt to do that. Raku is (fortunately) pretty simplistic: you get Ints, Rats and Nums (well and Complex but that's another topic). This aligns to mathematics number spaces Integers, Rational and Irrational numbers. Some operations (eg. sqrt(2)) will make an irrational number. Without symbolic math, you lose a little precision in any machine with finite word size and cannot fully restore the initial state with a round trip. Rounding can hide this.
sooooo You are plumbing the edges of IEEE754 here ... and very small numbers are subject to all kinds of influences ... here is a good write up ...https://randomascii.wordpress.com/2013/07/16/floating-point-determinism/ Back in the day many FPUs did random seed guess for division/sqrt ... even if that practice has become standardised to make the result deterministic (every pass is the same), it certainly will not require each FPU design to guess the same seed. And this ignores the fact that FPU designers will often shortcut full IEEE754 to save on transistors, various compiler settings. Not to rule out frequent chip logic design errors that do not get caught since the test sw will judge any of the near '0' as zero.> my $t=sqrt(2) 1.4142135623730951 > $t ** 2 2.0000000000000004
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Re^7: Euler's identity in Raku
by syphilis (Archbishop) on Jun 08, 2021 at 01:32 UTC
In Section Seekers of Perl Wisdom