Floating point conversions

The standard rule for converting between real floating point types (binary to binary, decimal to decimal and decimal to binary) is as follows:

If the value being converted can be represented exactly in the new type, it is unchanged. If the value being converted is in the range of values that can be represented but cannot be represented exactly, the result is rounded, according to the current compile-time or runtime rounding mode in effect. If the value being converted is outside the range of values that can be represented, the result is dependent on the rounding mode.

Integer to floating point (binary or decimal)
If the value being converted can be represented exactly in the new type, it is unchanged. If the value being converted is in the range of values that can be represented but cannot be represented exactly, the result is correctly rounded. If the value being converted is outside the range of values that can be represented, the result is quiet NaN.
Floating point (binary or decimal) to integer
The fractional part is discarded (i.e., the value is truncated toward zero). If the value of the integral part cannot be represented by the integer type, the result is one of the following:
  • If the integer type is unsigned, the result is the largest representable number if the floating point number is positive, or 0 otherwise.
  • If the integer type is signed, the result is the most negative or positive representable number according to the sign of the floating point number.

Complex conversions

Complex to complex
If the types are identical, there is no change. If the types are of a different size, and the value can be represented by the new type, the value is not changed; if the value cannot be represented by the new type, both real and imaginary parts are converted according to the standard conversion rule given above.
Complex to real (binary)
The imaginary part of the complex value is discarded. If necessary, the value of the real part is converted according to the standard conversion rule given above.
Complex to real (decimal)
The imaginary part of the complex value is discarded. The value of the real part is converted from binary to decimal floating point, according to the standard conversion rule given above.
Real (binary) to complex
The source value is used as the real part of the complex value, and converted, if necessary, according to the standard conversion rule given above. The value of the imaginary part is zero.
Real (decimal) to complex
The source value is converted from decimal to binary floating point, according to the standard conversion rule given above, and used as the real part of the complex value. The value of the imaginary part is zero.