Mathematical Constants

Definitions

See D Goldberg, What Every Computer Scientist Should Know About Floating Point Arithmetic.

Floating-point : real number type stored as sign, exponent and significand. Unlike integer types, most floating-point values cannot be stored exactly.
See D Goldberg.
Exponent : power of radix by which to multiply the significand. (radix, or base, returned by std::numeric_limits< floating_point_type>::radix, usually 2). Exponent is always signed, using one bit, and often offset or biased for storage convenience.
Mantissa: deprecated term - see significand.
Radix : base for exponent, usually 2, (decimal and hexadecimal radix systems exist, but are not yet supported by this package).
Significand: binary fraction where most significant bit represents 0.5, next 0.25, then 0.125 … The most significant bit (0.5) is usually not stored and is implicitly assumed to be set, so the significand always represents a fraction greater than 0.5, (but just less than 1). std::numeric_limits<floating_point_type>::digits returns the number if significant bits, including any implicit bit.
Least Significant bit: of significand – also called “unit in last place” ulp. (decimal or hexadecimal if radix or base is 10 or 16).
nextafter functions: (C99 float, double and long double versions) changes the least significant bit by adding or subtracting 1 to the binary significand.
ULP “unit in last place” can be a binary, decimal or hexadecimal digit.