Widening of values

  double f(float x) {...}
  double g(float y, float z) {
      return f(y + z);
  }

1. Compute the sum of y and z to long double.
   
2. Convert the sum to type float
   
3. Pass the float value parameter to f.
   
4. Within f, convert the parameter to long double in a register for use.
   

For almost all numerical programs, strict adherence to the types specified by declared variables is unnecessary and possibly wasteful. Strict type adherence produced a less accurate result in the case of y = y + (x * x) and a slower computation in the case of f(y + z). However, some algorithms do depend critically on the rounding of intermediate values to a specified precision.

FPCE defines compiler pragmas for these situations:

• fp_wide_function_parameters permits a float or double parameter to be passed as a wider value (perhaps in a hardware register).
• fp_wide_function_returns permits a float or double function to return a wider value.
• fp_wide_variables permits automatic variables declared float or double to be kept as wider values.

NOTE For most portable results, use intermediate values of type float_t and double_t. They allow the compiler to do what's best for the hardware. In the (rare) circumstance that a float or double value must be rounded to exactly the precision of the type, use an explicit cast.