From The Floating-Point Guide: This is a bad way to do it because a fixed epsilon chosen because it “looks small” could actually be way too large when the numbers being compared are very small as well. The comparison would return “true” for numbers that are quite different. And when the numbers are very large, … Read more
Actually, using float.Epsilon may not make any significant difference here. float.Epsilon is the smallest possible float greater than zero (roughly 1.401298E-45), which does not mean that it’s the smallest difference between any two arbitrary floats. Since floating-point math is imprecise, the difference between two seemingly equal numbers can be much greater than float.Epsilon. For example: … Read more
Unfortunately, bc doesn’t support scientific notation. However, it can be translated into a format that bc can handle, using extended regex as per POSIX in sed: sed -E ‘s/([+-]?[0-9.]+)[eE]\+?(-?)([0-9]+)/(\1*10^\2\3)/g’ <<<“$value” you can replace the “e” (or “e+”, if the exponent is positive) with “*10^”, which bc will promptly understand. This works even if the exponent … Read more
If you are on a recent-ish x86 or x86-64 platform (and you probably are), use the bsr instruction which will return the position of the highest set bit in an unsigned integer. It turns out that this is exactly the same as log2(). Here is a short C or C++ function that invokes bsr using … Read more
Update(2019-08-19): BigInt is now part of Firefox and Chrome; you no longer need a library: const bigInt1 = 1111111111111111111111111111111n; const bigInt2 = BigInt(“1111111111111111111111111111111″) console.log((bigInt1 + bigInt2)+””) Original answer: If you need arbitrary-precision decimal numbers, use Javascript-bignum, as it is correct and fast.
decimal is not a magical do all the maths for me type. It’s still a floating point number – the main difference from float is that it’s a decimal floating point number, rather than binary. So you can easily represent 0.3 as a decimal (it’s impossible as a finite binary number), but you don’t have … Read more
Check out −0 (number) in Wikipedia Basically IEEE does actually define a negative zero. And by this definition for all purposes: -0.0 == +0.0 == 0 I agree with aaronasterling that -0.0 and +0.0 are different objects. Making them equal (equality operator) makes sure that subtle bugs are not introduced in the code. Think of … Read more
In the standard library, the decimal module may be what you’re looking for. Also, I have found mpmath to be quite helpful. The documentation has many great examples as well (unfortunately my office computer does not have mpmath installed; otherwise I would verify a few examples and post them). One caveat about the decimal module, … Read more
The question is confusingly worded. Let’s break it down into many smaller questions: Why is it that one tenth plus two tenths does not always equal three tenths in floating point arithmetic? Let me give you an analogy. Suppose we have a math system where all numbers are rounded off to exactly five decimal places. … Read more
(Flynn’s answer is the correct answer. This one addresses the problem more generally.) You seem to be assuming, OP, that the floating-point inaccuracy in your code is deterministic and predictably wrong (in a way, your approach is the polar opposite of that of people who don’t understand floating point yet). Although (as Ben points out) … Read more