I know of no way to way to make normal floating points deterministic in .net. The JITter is allowed to create code that behaves differently on different platforms(or between different versions of .net). So using normal floats in deterministic .net code is not possible. The workarounds I considered: Implement FixedPoint32 in C#. While this is … Read more
The simple answer is because 3*0.1 != 0.3 due to quantization (roundoff) error (whereas 4*0.1 == 0.4 because multiplying by a power of two is usually an “exact” operation). Python tries to find the shortest string that would round to the desired value, so it can display 4*0.1 as 0.4 as these are equal, but … 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 32-bit floats, … Read more
The Wikipedia page on it is a good place to start. To sum up: float is represented in 32 bits, with 1 sign bit, 8 bits of exponent, and 23 bits of the significand (or what follows from a scientific-notation number: 2.33728*1012; 33728 is the significand). double is represented in 64 bits, with 1 sign … 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
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
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