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(libc.info)Floating Point Parameters


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Floating Point Parameters
.........................

   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 maximum positive floating point number of type `float'
     such that `1.0 + FLT_EPSILON != 1.0' is true.  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'.


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