## 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, for reference: http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html

## Details

### G_IEEE754_FLOAT_BIAS

```#define G_IEEE754_FLOAT_BIAS (127)
```

### G_IEEE754_DOUBLE_BIAS

```#define G_IEEE754_DOUBLE_BIAS (1023)
```

### 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, for reference: http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html

### 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, for reference: http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html

### 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)
```

Used for fooling around with float formats, see http://cch.loria.fr/documentation/IEEE754/numerical_comp_guide/ncg_math.doc.html