I will never understand float point arithmetic… julia> a = 10000 * 7 /100 700.0 julia> b = 10000 * 0.07 700.0000000000001 julia> c = 1000 * 0.69999999999999999 700.0 (but at list I am aware of the danger…)

[image] sylvaticus: (but at list I am aware of the danger…) As we say in France: “un homme averti en vaut 1.999999999999999” (Literally, the saying says something like “a forewarned person is worth two”)

Also, I’m not sure you were really looking for an explanation, but maybe it will help to note that: julia> 7/100 0.07 So this is merely an example of non-associativity of the floating-point operations: julia> 10000 * (7 / 100) 700.0000000000001 julia> (10000 * 7) / 100 700.0

Look at this excellent presentation by Avik Sengupta Everything You Wanted to Know About Floating Point Numbers, And Didn't Know... Everything You Wanted to Know About Floating Point Numbers, And Didn't Know Who to Ask - JuliaHub

[image] ffevotte: julia> 7/100 0.07 Part of the confusion is that, although this is printed as 0.07, it’s actually a slightly different number. (Binary) floating-point values are integers times powers of two, so 7/100 is not exactly representable and has to be rounded to: julia> big(7/100) …

It’s not so hard to understand floating-point arithmetic, actually! Trefethen and Bau’s book “Numerical Linear Algebra” covers the essentials in a couple lectures (each 4 or 5 pages of text). It’ll change your reaction to the above from “Wha…?” to “Yep, that’s how it works, no mystery about it.” Wel…

[image] stevengj: when you compute 10000 * 7 / 100 it is parsed as (10000 * 7) / 100, and each of these operations can be performed exactly (the result of each operation is an integer value) so there is no rounding What is the rule here, is for a / b, when both a and b (or at least b) is an i…

If you want that calculation, I recommend to use rational number representation: julia> 10000*7//100 700//1

To complement a bit, IEEE754 Float64 are stored as M × 2E, where M is the 53-bit integer mantissa and E the 11-bit exponent (some further details omitted). 700.0 becomes M=700 and E=0, as integer values between and -2^52 and 2^52-1 are stored with E=0. 0.07 becomes M=6157265115545601 and E=-43, …

[image] Palli: What is the rule here, is for a / b, when both a and b (or at least b) is an integer (or non-approx), and the result should be, then you get exact, i.e. integer? Yes. The result of each elementary fp operation (+,-,*,/) is as if you had done that operation exactly and then roun…

[image] stephancb: BTW, is there a package for Julia that would reveal mantissa and exponent of IEEE754 floats? There are built-in functions: How to get the significand and the exponent of a floating point number?

I will never understand floating-point arithmetic

Offtopic

and March 8, 2024, 4:05pm 19

Ha! Please look at my only message on this forum, with three likes by the way! But keep in mind, in fact, I don’t fully understand either, but I hope that when it comes down to it, I’ll turn to this lesson and definitely understand!

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I will never understand floating-point arithmetic

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