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These macro definitions can be accessed by including the header file float.h in your program.
Macro names starting with ‘FLT_’ refer to the float
type,
while names beginning with ‘DBL_’ refer to the double
type
and names beginning with ‘LDBL_’ refer to the long double
type. (If GCC does not support long double
as a distinct data
type on a target machine then the values for the ‘LDBL_’ constants
are equal to the corresponding constants for the double
type.)
Of these macros, only FLT_RADIX
is guaranteed to be a constant
expression. The other macros listed here cannot be reliably used in
places that require constant expressions, such as ‘#if’
preprocessing directives or in the dimensions of static arrays.
Although the ISO C standard specifies minimum and maximum values for most of these parameters, the GNU C implementation uses whatever values describe the floating point representation of the target machine. So in principle GNU C actually satisfies the ISO C requirements only if the target machine is suitable. In practice, all the machines currently supported are suitable.
FLT_ROUNDS
This value characterizes the rounding mode for floating point addition. The following values indicate standard rounding modes:
-1
The mode is indeterminable.
0
Rounding is towards zero.
1
Rounding is to the nearest number.
2
Rounding is towards positive infinity.
3
Rounding is towards negative infinity.
Any other value represents a machine-dependent nonstandard rounding mode.
On most machines, the value is 1
, in accordance with the IEEE
standard for floating point.
Here is a table showing how certain values round for each possible value
of FLT_ROUNDS
, if the other aspects of the representation match
the IEEE single-precision standard.
0 1 2 3 1.00000003 1.0 1.0 1.00000012 1.0 1.00000007 1.0 1.00000012 1.00000012 1.0 -1.00000003 -1.0 -1.0 -1.0 -1.00000012 -1.00000007 -1.0 -1.00000012 -1.0 -1.00000012
FLT_RADIX
This is the value of the base, or radix, of the exponent representation. This is guaranteed to be a constant expression, unlike the other macros described in this section. The value is 2 on all machines we know of except the IBM 360 and derivatives.
FLT_MANT_DIG
This is the number of base-FLT_RADIX
digits in the floating point
mantissa for the float
data type. The following expression
yields 1.0
(even though mathematically it should not) due to the
limited number of mantissa digits:
float radix = FLT_RADIX; 1.0f + 1.0f / radix / radix / … / radix
where radix
appears FLT_MANT_DIG
times.
DBL_MANT_DIG
LDBL_MANT_DIG
This is the number of base-FLT_RADIX
digits in the floating point
mantissa for the data types double
and long double
,
respectively.
FLT_DIG
This is the number of decimal digits of precision for the float
data type. Technically, if p and b are the precision and
base (respectively) for the representation, then the decimal precision
q is the maximum number of decimal digits such that any floating
point number with q base 10 digits can be rounded to a floating
point number with p base b digits and back again, without
change to the q decimal digits.
The value of this macro is supposed to be at least 6
, to satisfy
ISO C.
DBL_DIG
LDBL_DIG
These are similar to FLT_DIG
, but for the data types
double
and long double
, respectively. The values of these
macros are supposed to be at least 10
.
FLT_MIN_EXP
This is the smallest possible exponent value for type float
.
More precisely, is the minimum negative integer such that the value
FLT_RADIX
raised to this power minus 1 can be represented as a
normalized floating point number of type float
.
DBL_MIN_EXP
LDBL_MIN_EXP
These are similar to FLT_MIN_EXP
, but for the data types
double
and long double
, respectively.
FLT_MIN_10_EXP
This is the minimum negative integer such that 10
raised to this
power minus 1 can be represented as a normalized floating point number
of type float
. This is supposed to be -37
or even less.
DBL_MIN_10_EXP
LDBL_MIN_10_EXP
These are similar to FLT_MIN_10_EXP
, but for the data types
double
and long double
, respectively.
FLT_MAX_EXP
This is the largest possible exponent value for type float
. More
precisely, this is the maximum positive integer such that value
FLT_RADIX
raised to this power minus 1 can be represented as a
floating point number of type float
.
DBL_MAX_EXP
LDBL_MAX_EXP
These are similar to FLT_MAX_EXP
, but for the data types
double
and long double
, respectively.
FLT_MAX_10_EXP
This is the maximum positive integer such that 10
raised to this
power minus 1 can be represented as a normalized floating point number
of type float
. This is supposed to be at least 37
.
DBL_MAX_10_EXP
LDBL_MAX_10_EXP
These are similar to FLT_MAX_10_EXP
, but for the data types
double
and long double
, respectively.
FLT_MAX
The value of this macro is the maximum number representable in type
float
. It is supposed to be at least 1E+37
. The value
has type float
.
The smallest representable number is - FLT_MAX
.
DBL_MAX
LDBL_MAX
These are similar to FLT_MAX
, but for the data types
double
and long double
, respectively. The type of the
macro’s value is the same as the type it describes.
FLT_MIN
The value of this macro is the minimum normalized positive floating
point number that is representable in type float
. It is supposed
to be no more than 1E-37
.
DBL_MIN
LDBL_MIN
These are similar to FLT_MIN
, but for the data types
double
and long double
, respectively. The type of the
macro’s value is the same as the type it describes.
FLT_EPSILON
This is the difference between 1 and the smallest floating point
number of type float
that is greater than 1. It’s supposed to
be no greater than 1E-5
.
DBL_EPSILON
LDBL_EPSILON
These are similar to FLT_EPSILON
, but for the data types
double
and long double
, respectively. The type of the
macro’s value is the same as the type it describes. The values are not
supposed to be greater than 1E-9
.
Next: IEEE Floating Point, Previous: Floating Point Concepts, Up: Floating Type Macros [Contents][Index]