Replace floating point math with integer in sigmoid transfer function

Question

I would like to replace floating point math in these function without losing much precision, because I have no FPU. Is this possible? I think 3 numbers after comma is enough.

inline float smaller_f(float value, float bias) {
  return value < bias ? value : bias;
}

inline float pow2_f(float fVal) {
  return fVal * fVal;
}

float sigm_f(float fX, float fSlope) {
  float fVal = (180.f - smaller_f(fabs(fSlope * fX), 179.9f) ) / 180.f;
  return fVal / sqrt(1.f + pow2_f(fVal) );
}

Answer 1

A fixed-point math library is what you need. My preferred solution for this is Anthony Williams' fixed-Point math C++ library. Because it is in C++ and defines a fixed class with extensive function and operator overloading, it can largely be used simply by replacing float or double in your existing code with fixed. It uses int64_t as the underlying integer data type, with 34 integer bits and 28 fractional bits (34Q28), so is good for about 8 decimal places and a wider range than int32_t.

If your compiler supports C++, you can still essentially write your code using the essentially C subset if you prefer, using C++ only to support this library.

On 32bit ARM this library performs about 5 times faster than software-floating point and is comparable in performance to ARM's VFP unit for C code.

Note that the sqrt() function in this library has poor precision performance for very small values as it looses lower-order bits in intermediate calculations that can be preserved. It can be improved by replacing it with the code the version I presented in this question.

There are no doubt C libraries for fixed-point math but they will lack the simplicity and convenience of a "real" fixed-point data type provided by this library, and this library has a complete set of standard library math function equivalents, while many fixed point solutions just provide basic arithmetic operators.