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:
s sign (±1)
b base or radix of exponent representation (an integer >1)
e exponent (an integer between a minimum emin and a maximum emax)
p precision (the number of base-b digits in the significand)
fk 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.
The accuracy of the library functions in math.h(3HEAD) and complex.h(3HEAD) that return floating-point results is defined on the libm(3LIB) manual page.
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:
0 Toward zero.
1 To nearest.
2 Toward positive infinity.
3 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:
0 Evaluate all operations and constants just to the range and precision of the type.
1 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.
2 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, b **1 - p .
FLT_EPSILON DBL_EPSILON LDBL_EPSILON
• Minimum normalized positive floating-point number, b **emin **-1 .
FLT_MIN DBL_MIN LDBL_MIN
See attributes(5) for descriptions of the following attributes:
|ATTRIBUTE TYPE||ATTRIBUTE VALUE|
complex.h(3HEAD), math.h(3HEAD), attributes(5), standards(5)