Floating-point conversions

The standard rule for converting between real floating-point types 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
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 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.

Implicit conversions of decimal floating-point types (IBM extension)

The compiler has the following decimal floating-point types:
  • _Decimal32
  • _Decimal64
  • _Decimal128
The following implicit conversions are always supported:
  • Implicit conversions between decimal floating-point types:
    • _Decimal32 to _Decimal64
    • _Decimal32 to _Decimal128
    • _Decimal64 to _Decimal32
    • _Decimal64 to _Decimal128
    • _Decimal128 to _Decimal32
    • _Decimal128 to _Decimal64
  • Implicit conversions between decimal floating-point types and the following integer types:
    • signed char, unsigned char
    • signed short int, unsigned short int
    • signed int, unsigned int
    • signed long int, unsigned long int
    • signed long long int, unsigned long long int
  • Implicit conversions between decimal floating-point types and Boolean types bool or _Bool.
Implicit conversions between decimal floating-point types and the following generic floating-point types are supported conditionally. It is supported through assignment operation using the simple assignment operator =, initialization, function argument passing and function return statements.
  • float
  • double
  • long double
The following examples demonstrate the implicit conversion from a generic floating-point type to a decimal floating-point type. In this example, variable f1 is implicitly converted from type float to type _Decimal32 in the initialization.
float f1;
_Decimal32 d1 = f1;
C++ only begins
float f1;
_Decimal32 d1(f1);
C++ only ends
Restriction: You cannot mix decimal floating-point types with generic floating-point types or complex floating-point types in arithmetic expressions unless you use explicit conversions. Here is an example:
_Decimal32 d1;
float f1;
float f2 = f1 + d1;         // Incorrect
float f3 = f1 + (float)d1;  // Correct

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.
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.