The format of floating-point numbers can be either base 16 S/390® hexadecimal format, base 2 IEEE-754 binary format, or base 10 IEEE-754 decimal format. The formats are based on three operand lengths for hexadecimal and binary: short (32 bits), long (64 bits), and extended (128 bits). The formats are also based on three operand lengths for decimal: _Decimal32 (32 bits), _Decimal64 (64 bits), and _Decimal128 (128 bits).
A floating-point operand may be numeric or, for binary and decimal floating-point only, positive or negative infinity, or nonnumeric (Not a Number, or NaN). A floating-point number, has three components: a sign bit, a signed binary exponent, and a significand. The significand consists of an implicit unit digit to the left of an implied radix point, and an explicit fraction field to the right. The significand digits are based on the radix, 2 (for binary floating-point), 10 (for decimal floating-point), or 16 (for hexadecimal floating-point). The magnitude (an unsigned value) of the number is the product of the significand and the radix raised to the power of the exponent. The number is positive or negative depending on whether the sign bit is zero or one, respectively. A nonnumeric binary or decimal floating-point operand also has a sign bit, signed exponent, and fraction field.
Hexadecimal floating-point operands have formats that provide for exponents that specify powers of the radix 16 and significands that are hexadecimal numbers. The exponent range is the same for the short, long, and extended formats. The results of most operations on hexadecimal floating-point data are truncated to fit into the target format, but there are instructions available to round the result when converting to a narrower format. For hexadecimal floating-point operands, the implicit unit digit of the significand is always zero. Because the value if the significand and fraction are the same, hexadecimal floating-point operations are described in terms of the fraction, and the term significand is not used.
Binary floating-point operands have formats which provide for exponents that specify powers of the radix 2 and significands that are binary numbers. The exponent range differs for different formats, the range being greater for the longer formats. In the long and extended formats, the exponent range is significantly greater for binary floating-point data than for hexadecimal floating-point data. The results of operations performed on binary floating-point data are rounded automatically to fit into the target format; the manner of rounding is determined by a program-settable rounding mode.
Decimal floating-point operands have formats that provide for exponents that specify powers of the radix 10 and significands that are decimal numbers. The exponent range differs for different formats, the range being greater for the longer formats. The results of operations performed on decimal floating-point data are rounded automatically to fit into the target format; the manner of rounding is determined by a program-settable rounding mode.