Ambiguity

A language should define the semantics precisely enough to prove statements about the programs. Common points of ambiguity:

• x=3.0/10.0 FP number, it is usually not specified that all occurrences of 10.0*x must have the same value.
• what happens during exceptions.
• interpretation of parenthesis.
• evaluation of subexpressions. If x real and m,n integers, in the expression x+m/n is the division integer or FP? For example, we can compute all the operations in the highest precision present in the expression; or we can assign from bottom up in the expression graph tentative precisions based on the operands, and then from top down assign the maximum of the tentative and the expected precision.
• defining the exponential consistently. Ex: (-3)**3 = -27 but (-3.0)**(3.0) is problematic, as it is defined via logarithm. Goldberg proposes to consider , as . If for all then . For example, , but since but .