Sollya User's Manual

Name:

~ floating-point evaluation of a constant expression

Usage:

~ expression : function -> constant ~ something : any type -> any type

Parameters:

expression stands for an expression that is a constant
something stands for some language element that is not a constant expression

Description:

~ expression evaluates the expression that is a constant term to a floating-point constant. The evaluation may involve a rounding. If expression is not a constant, the evaluated constant is a faithful rounding of expression with precision bits, unless the expression is exactly 0 as a result of cancellation. In the latter case, a floating-point approximation of some (unknown) accuracy is returned.
~ does not do anything on all language elements that are not a constant expression. In other words, it behaves like the identity function on any type that is not a constant expression. It can hence be used in any place where one wants to be sure that expressions are simplified using floating-point computations to constants of a known precision, regardless of the type of actual language elements.
~ error evaluates to error and provokes a warning.
~ is a prefix operator not requiring parentheses. Its precedence is the same as for the unary + and - operators. It cannot be repeatedly used without brackets.

Example 1:

   > print(exp(5));
   exp(5)
   > print(~ exp(5));
   1.48413159102576603421115580040552279623487667593878e2

Example 2:

> autosimplify = off!;

Example 3:

> print(~sin(5 * pi));
0

Example 4:

   > print(~exp(x));
   exp(x)
   > print(~ "Hello");
   Hello

Example 5:

   > print(~exp(x*5*Pi));
   exp((pi) * 5 * x)
   > print(exp(x* ~(5*Pi)));
   exp(x * 1.57079632679489661923132169163975144209858469968757e1)

Example 6:

   > print(~exp(5)*x);
   1.48413159102576603421115580040552279623487667593878e2 * x
   > print( (~exp(5))*x);
   1.48413159102576603421115580040552279623487667593878e2 * x
   > print(~(exp(5)*x));
   exp(5) * x