- floating types
The characteristics of floating types are defined in terms of a model that describes a representation of floating-point numbers and values that provide information about an implementation's floating-point arithmetic.
The following parameters are used to define the model for each floating-point type:
base or radix of exponent representation (an integer >1)
exponent (an integer between a minimum emin and a maximum emax)
precision (the number of base-b digits in the significand)
non-negative integers less than b (the significand digits)
In addition to normalized floating-point numbers (f1>0 if x≠0), floating types might be able to contain other kinds of floating-point numbers, such as subnormal floating-point numbers (x≠0, e=emin, f1=0) and unnormalized floating-point numbers (x≠0, e=emin, f1=0), and values that are not floating-point numbers, such as infinities and NaNs. A NaN is an encoding signifying Not-a-Number. A quiet NaN propagates through almost every arithmetic operation without raising a floating-point exception; a signaling NaN generally raises a floating-point exception when occurring as an arithmetic operand.
All integer values in the <float.h> header, except FLT_ROUNDS, are constant expressions suitable for use in #if preprocessing directives; all floating values are constant expressions. All except DECIMAL_DIG, FLT_EVAL_METHOD, FLT_RADIX, and FLT_ROUNDS have separate names for all three floating-point types. The floating-point model representation is provided for all values except FLT_EVAL_METHOD and FLT_ROUNDS.
The rounding mode for floating-point addition is characterized by the value of FLT_ROUNDS:
Toward positive infinity.
Toward negative infinity.
The values of operations with floating operands and values subject to the usual arithmetic conversions and of floating constants are evaluated to a format whose range and precision might be greater than required by the type. The use of evaluation formats is characterized by the architecture-dependent value of FLT_EVAL_METHOD:
Evaluate all operations and constants just to the range and precision of the type.
Evaluate operations and constants of type float and double to the range and precision of the double type; evaluate long double operations and constants to the range and precision of the long double type.
Evaluate all operations and constants to the range and precision of the long double type.
The values given in the following list are defined as constants.
Radix of exponent representation, b.
Number of base-FLT_RADIX digits in the floating-point significand, p.
FLT_MANT_DIG DBL_MANT_DIG LDBL_MANT_DIG
Number of decimal digits, n, such that any floating-point number in the widest supported floating type with pmax radix b digits can be rounded to a floating-point number with n decimal digits and back again without change to the value.
Number of decimal digits, q, such that any floating-point number with q decimal digits can be rounded into a floating-point number with p radix b digits and back again without change to the q decimal digits.
FLT_DIG DBL_DIG LDBL_DIG
Minimum negative integer such that FLT_RADIX raised to that power minus 1 is a normalized floating-point number, emin.
FLT_MIN_EXP DBL_MIN_EXP LDBL_MIN_EXP
Minimum negative integer such that 10 raised to that power is in the range of normalized floating-point numbers.
FLT_MIN_10_EXP DBL_MIN_10_EXP LDBL_MIN_10_EXP
Maximum integer such that FLT_RADIX raised to that power minus 1 is a representable finite floating-point number, emax.
FLT_MAX_EXP DBL_MAX_EXP LDBL_MAX_EXP
Maximum integer such that 10 raised to that power is in the range of representable finite floating-point numbers.
FLT_MAX_10_EXP DBL_MAX_10_EXP LDBL_MAX_10_EXP
The values given in the following list are defined as constant expressions with values that are greater than or equal to those shown:
Maximum representable finite floating-point number.
FLT_MAX DBL_MAX LDBL_MAX
The values given in the following list are defined as constant expressions with implementation-defined (positive) values that are less than or equal to those shown:
The difference between 1 and the least value greater than 1 that is representable in the given floating-point type, b1 - p.
FLT_EPSILON DBL_EPSILON LDBL_EPSILON
Minimum normalized positive floating-point number, bemin-1.
FLT_MIN DBL_MIN LDBL_MIN
See attributes(5) for descriptions of the following attributes: