## Numerical Definitions

Numerical Definitions — mathematical constants, and floating point decomposition

## Synopsis

    #include <glib.h>

    #define             G_IEEE754_FLOAT_BIAS
    #define             G_IEEE754_DOUBLE_BIAS
    union               GFloatIEEE754;
    union               GDoubleIEEE754;

    #define             G_E
    #define             G_LN2
    #define             G_LN10
    #define             G_PI
    #define             G_PI_2
    #define             G_PI_4
    #define             G_SQRT2
    #define             G_LOG_2_BASE_10

## Description

GLib offers mathematical constants such as G_PI for the value of pi; many platforms have these in the C library, but some don't, the GLib versions always exist.

The GFloatIEEE754 and GDoubleIEEE754 unions are used to access the sign, mantissa and exponent of IEEE floats and doubles. These unions are defined as appropriate for a given platform. IEEE floats and doubles are supported (used for storage) by at least Intel, PPC and Sparc. See IEEE 754-2008 for more information about IEEE number formats.

## Details

### G_IEEE754_FLOAT_BIAS

    #define G_IEEE754_FLOAT_BIAS (127)

The bias by which exponents in single-precision floats are offset.

### G_IEEE754_DOUBLE_BIAS

    #define G_IEEE754_DOUBLE_BIAS (1023)

The bias by which exponents in double-precision floats are offset.

### union GFloatIEEE754

    union _GFloatIEEE754
    {
      gfloat v_float;
      struct {
        guint mantissa : 23;
        guint biased_exponent : 8;
        guint sign : 1;
      } mpn;
    };

The GFloatIEEE754 and GDoubleIEEE754 unions are used to access the sign, mantissa and exponent of IEEE floats and doubles. These unions are defined as appropriate for a given platform. IEEE floats and doubles are supported (used for storage) by at least Intel, PPC and Sparc.

gfloat `v_float`; | the double value

### union GDoubleIEEE754

    union _GDoubleIEEE754
    {
      gdouble v_double;
      struct {
        guint mantissa_low : 32;
        guint mantissa_high : 20;
        guint biased_exponent : 11;
        guint sign : 1;
      } mpn;
    };

The GFloatIEEE754 and GDoubleIEEE754 unions are used to access the sign, mantissa and exponent of IEEE floats and doubles. These unions are defined as appropriate for a given platform. IEEE floats and doubles are supported (used for storage) by at least Intel, PPC and Sparc.

gdouble `v_double`; | the double value

### G_E

    #define G_E     2.7182818284590452353602874713526624977572470937000

The base of natural logarithms.

### G_LN2

    #define G_LN2   0.69314718055994530941723212145817656807550013436026

The natural logarithm of 2.

### G_LN10

    #define G_LN10  2.3025850929940456840179914546843642076011014886288

The natural logarithm of 10.

### G_PI

    #define G_PI    3.1415926535897932384626433832795028841971693993751

The value of pi (ratio of circle's circumference to its diameter).

### G_PI_2

    #define G_PI_2  1.5707963267948966192313216916397514420985846996876

Pi divided by 2.

### G_PI_4

    #define G_PI_4  0.78539816339744830961566084581987572104929234984378

Pi divided by 4.

### G_SQRT2

    #define G_SQRT2 1.4142135623730950488016887242096980785696718753769

The square root of two.

### G_LOG_2_BASE_10

    #define G_LOG_2_BASE_10		(0.30102999566398119521)

Multiplying the base 2 exponent by this number yields the base 10 exponent.