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Custom Float
This crate adds a custom floating point number type, Fp<U, EXP_SIZE, INT_SIZE, FRAC_SIZE, EXP_BASE>, where the bit size of the exponent and mantissa can be set separately.
U is the underlying unsigned integer type which is used to represent the number.
EXP_SIZE is the size of the exponent in bits.
INT_SIZE is the size of the integer part of the mantissa in bits. If zero, then the integer bit is implicit.
FRAC_SIZE is the size of the fractional part of the mantissa in bits.
EXP_BASE is the base of the exponent.
The total bit size of U must be greater or equal to EXP_SIZE + INT_SIZE + FRAC_SIZE + 1 to contain the entire number.
The number then automatically implements num::Float, and supports all ordinary floating point operations.
This allows simple implementation of special floating point types, such as TensorFloat, IEEE754 Quadruple/binary128, Fp80, and BFloat16.
The accuracy of all of the floating point operations are not perfect, but work well enough to be usable. Various plots showing the accuracy of basic functions are shown in the plots subfolder.
All floats can be converted into each other painlessly, though the conversion may produce rounding errors or unbounded outputs when converting to a float with lesser resolution.