FOUNDATION SERVICES - Expression evaluation

Expression evaluation

The way in which a compiler on a platform issues code to evaluate expressions depends intimately on the underlying hardware architecture. Recall this code idiom, extracted from the example "Inner products using wide accumulators" on page 189:

  float  x = ...;
  double y = ...;
  y = y + (x * x);

On three different systems this can be evaluated three different ways. FPCE simplifies the discussion with its characterization of platforms by their minimum evaluation format--the narrowest type to which results (other than assignments) are computed. From this point of view:

PA-RISC has a minimum evaluation format of float. It supports both float and double evaluation in hardware. For speed, a compiler probably issues code to evaluate the square (x * x) to float before converting it to double for the add to y.
PowerPC, by convention, has a minimum evaluation format of double. A typical compiler promotes x to double to compute its square and then adds y.
X86 has a minimum evaluation format of long double. It evaluates the entire expression using extra range and precision, before assigning to the double variable y.

A cast ensures at least double evaluation on all platforms:

  float  x = ...;
  double y = ...;
  y = y + ((double_t) x * x);

To guarantee the evaluation of narrow inner subexpressions to a wider type across all platforms, use explicit casting. You can determine the minimum evaluation format of an FPCE-compliant compiler on a particular platform from the macro _MIN_EVAL_FORMAT, which evaluates to 0, 1, or 2 according to whether the format is float, double, or long double.

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