IEEE Floating Point

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Here is an example showing how the floating type measurements come out for the most common floating point representation, specified by the IEEE Standard for Binary Floating Point Arithmetic (ANSI/IEEE Std 754-1985). Nearly all computers designed since the 1980s use this format.

The IEEE single-precision float representation uses a base of 2. There is a sign bit, a mantissa with 23 bits plus one hidden bit (so the total precision is 24 base-2 digits), and an 8-bit exponent that can represent values in the range -125 to 128, inclusive.

So, for an implementation that uses this representation for the float data type, appropriate values for the corresponding parameters are:

FLT_RADIX                             2
FLT_MANT_DIG                         24
FLT_DIG                               6
FLT_MIN_EXP                        -125
FLT_MIN_10_EXP                      -37
FLT_MAX_EXP                         128
FLT_MAX_10_EXP                      +38
FLT_MIN                 1.17549435E-38F
FLT_MAX                 3.40282347E+38F
FLT_EPSILON             1.19209290E-07F

Here are the values for the double data type:

DBL_MANT_DIG                         53
DBL_DIG                              15
DBL_MIN_EXP                       -1021
DBL_MIN_10_EXP                     -307
DBL_MAX_EXP                        1024
DBL_MAX_10_EXP                      308
DBL_MAX         1.7976931348623157E+308
DBL_MIN         2.2250738585072014E-308
DBL_EPSILON     2.2204460492503131E-016