Show HN: Floating point arithmetic types in C++ for any size and any base

fas is floating point arithmetic for arbitrary mantissa and exponent types in modern header-only C++. It lets you construct various different float types using template parameters for the mantissa, exponent and base.

The constructed float-types look and fell like a native float/double for arithmetic operations. Furthermore all methods are performed on the stack and do not require any heap space.

fas is header-only.

fas::Float<int16_t, int8_t> f;

This will result in a float using a signed 16 bit mantissa and a signed 8 bit exponent.

The arithmetical operations are supported using their corresponding operators + - * / += -= *= /= ++ --

fas::Float<int16_t, int8_t> f1 = 10;
auto f2 = f1;

f2 = -f1;     // => -10

f2 = f1 + 10; // => 20
f2 = f1 - f1; // => 0
f2 = f1 * f1; // => 100
f2 = f1 / 20; // => 0.5

f2 += 1;      // => 1.5
f2 -= 1;      // => 0.5
f2 *= 2;      // => 1
f2 /= 2;      // => 0.5

f1++;         // => 11
++f1;         // => 12
f1--;         // => 11
--f1;         // => 10

Each type knows its boundaries:

• MAX() returns the largest value
• MIN() returns the smallest positive value
• LOWEST() returns the smallest value The naming is the same as with internal float/double.

There are overloadings for std::numeric_limits available: fas::Float<int8_t, int8_t>::MAX() returns the same as std::numeric_limits<fas::Float<std::int16_t, std::int8_t>>::MAX() which is approx 2.16079e+40.

fas supports type traits:

is_fundamental<int16_t, int16_t>::value               // => true
is_floating_point<fas::Float<int16_t, int16_t>::value // => true
is_arithmetic<int16_t, int16_t>::value                // => true
is_scalar<int16_t, int16_t>::value                    // => true
is_object<int16_t, int16_t>::value                    // => true

constexpr c = fas::Float<std::int16_t, std::int8_t>(1);

Even the operations' results:

constexpr c1 = fas::Float<std::int16_t, std::int8_t>(1);
constexpr c2 = fas::Float<std::int16_t, std::int8_t>(2);

constexpr c3 = c1 + c2; // => 3

fas offers an output stream overload, which can be used for std::cout:

#include "fas/stream.hpp>

...

fas::Float<int8_t, int8_t> fas_float(1);
fas_float /= 3;
std::cout << fas_float << "\n"; // => 70 * 7 ^ fffffffd ≈ 0.32653061224489793313

Typical floats such as float or double are to the base of 2. fas allows to construct floats to any base:

fas::Float<int8_t, int8_t, 7> fas_float(0);
double cpp_float = 0;

for(auto i=0; i<7; ++i) {
	fas_float += fas::Float<int8_t, int8_t, 7>(1)/7;
	cpp_float += 1.0/7;
}

std::cout << std::setprecision(20);
std::cout << fas_float << "\n";    // => exaclty 1
std::cout << cpp_float << "\n";    // => 0.99999999999999977796

The setting of different bases allows to represent specific fractions exaclty. In this case the base is 7, so any fraction by 7 is represented exactly. Compare to the native double which is always to the base of 2, thus can not represent 1/7 exactly.

Download the float.hpp and include it in your source. Don't forget to add it in your include path.

To build and run unit tests type:

mkdir build; cd build; cmake ..; make && ./tests/tests

• The Stl's std::numeric_limits is required the limits of the specified types for mantissa and exponent.
• Catch2 is required to build the unit tests.

• (configurable) rounding support
• exp, sqrt, pow and other math.h functions
• string constructor
• string representation
• value constructor for all ints and other types
• a version without stl