4.11.1 Conversion to floating-point numbers

The type float_format_t describes a floating-point format.

float_format_t float_format (uintE n)

Returns the smallest float format which guarantees at least n decimal digits in the mantissa (after the decimal point).

float_format_t float_format (const cl_F& x)

Returns the floating point format of x.

float_format_t default_float_format

Global variable: the default float format used when converting rational numbers to floats.

To convert a real number to a float, each of the types cl_R, cl_F, cl_I, cl_RA, int, unsigned int, float, double defines the following operations:

cl_F cl_float (const type&x, float_format_t f)

Returns x as a float of format f.

cl_F cl_float (const type&x, const cl_F& y)

Returns x in the float format of y.

cl_F cl_float (const type&x)

Returns x as a float of format default_float_format if it is an exact number, or x itself if it is already a float.

Of course, converting a number to a float can lose precision.

Every floating-point format has some characteristic numbers:

cl_F most_positive_float (float_format_t f)

Returns the largest (most positive) floating point number in float format f.

cl_F most_negative_float (float_format_t f)

Returns the smallest (most negative) floating point number in float format f.

cl_F least_positive_float (float_format_t f)

Returns the least positive floating point number (i.e. > 0 but closest to 0) in float format f.

cl_F least_negative_float (float_format_t f)

Returns the least negative floating point number (i.e. < 0 but closest to 0) in float format f.

cl_F float_epsilon (float_format_t f)

Returns the smallest floating point number e > 0 such that 1+e != 1.

cl_F float_negative_epsilon (float_format_t f)

Returns the smallest floating point number e > 0 such that 1-e != 1.

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