Floating point versus fixed point: what are the pros/cons?

Question

Floating point type represents a number by storing its significant digits and its exponent separately on separate binary words so it fits in 16, 32, 64 or 128 bits.

Fixe

Answer 1

That definition covers a very limited subset of fixed point implementations.

It would be more correct to say that in fixed point only the mantissa is stored and the exponent is a constant determined a-priori. There is no requirement for the binary point to fall inside the mantissa, and definitely no requirement that it fall on a word boundary. For example, all of the following are "fixed point":

• 64 bit mantissa, scaled by 2^-32 (this fits the definition listed in the question)
• 64 bit mantissa, scaled by 2^-33 (now the integer and fractional parts cannot be separated by an octet boundary)
• 32 bit mantissa, scaled by 2⁴ (now there is no fractional part)
• 32 bit mantissa, scaled by 2^-40 (now there is no integer part)

GPUs tend to use fixed point with no integer part (typically 32-bit mantissa scaled by 2^-32). Therefore APIs such as OpenGL and Direct3D often use floating-point types which are capable of holding these values. However, manipulating the integer mantissa is often more efficient so these APIs allow specifying coordinates (in texture space, color space, etc) this way as well.

As for your claim that C++ doesn't have a fixed point type, I disagree. All integer types in C++ are fixed point types. The exponent is often assumed to be zero, but this isn't required and I have quite a bit of fixed-point DSP code implemented in C++ this way.