For a given IEEE-754 floating point number X, if 2^E <= abs(X) < 2^(E+1) then the distance from X to the next largest representable floating point number (epsilon) is: epsilon = 2^(E-52) % For a 64-bit float (double precision) epsilon = 2^(E-23) % For a 32-bit float (single precision) epsilon = 2^(E-10) % For a … Read more
Huge difference. As the name implies, a double has 2x the precision of float[1]. In general a double has 15 decimal digits of precision, while float has 7. Here’s how the number of digits are calculated: double has 52 mantissa bits + 1 hidden bit: log(253)÷log(10) = 15.95 digits float has 23 mantissa bits + … Read more
2mantissa bits + 1 + 1 The +1 in the exponent (mantissa bits + 1) is because, if the mantissa contains abcdef… the number it represents is actually 1.abcdef… × 2^e, providing an extra implicit bit of precision. Therefore, the first integer that cannot be accurately represented and will be rounded is: For float, 16,777,217 … Read more
The biggest/largest integer that can be stored in a double without losing precision is the same as the largest possible value of a double. That is, DBL_MAX or approximately 1.8 × 10308 (if your double is an IEEE 754 64-bit double). It’s an integer. It’s represented exactly. What more do you want? Go on, ask me what … Read more
You’re overflowing the capacity of JavaScript’s number type, see §8.5 of the spec for details. Those IDs will need to be strings. IEEE-754 double-precision floating point (the kind of number JavaScript uses) can’t precisely represent all numbers (of course). Famously, 0.1 + 0.2 == 0.3 is false. That can affect whole numbers just like it … Read more
I was a member of the IEEE-754 committee, I’ll try to help clarify things a bit. First off, floating-point numbers are not real numbers, and floating-point arithmetic does not satisfy the axioms of real arithmetic. Trichotomy is not the only property of real arithmetic that does not hold for floats, nor even the most important. … Read more