TLFloat - C++ template library for floating point operations

Original distribution site : https://github.com/shibatch/tlfloat

Doxygen-generated reference : https://shibatch.github.io/tlfloat-doxygen/

Introduction

This library implements C++ classes with which half, single, double, quadruple and octuple precision IEEE 754 floating point numbers can be operated.

Internally, these classes are implemented as class templates on top of arbitrary-precision integer class templates so that the templates are expanded as arbitrary precision floating-point operations by just changing the template parameters, rather than implementing each floating-point operation for each precision. The arbitrary-precision integer class templates are also included in this library.

Features

• Truly constexpr functions

  • Compilable with C++20 standard
  • Most of the functions are implemented as templates
    • Completely inlinable functions
    • The functions can be evaluated at compile time
  • No malloc required
  • Works without libstdc++

• IEEE 754 compliant

  • Supports subnormal numbers, NaN, infinity, and signed zero

• Supports a wide range of precisions

  • Half, float, double, quad, and octuple precisions
  • Returns correctly rounded results for arithmetic oprations, fma and sqrt
  • Returns 1-ulp accuracy results for other math.h functions
    • All functions, including trigonometric functions, return 1ulp-accuracy results for all input range

• Portable

  • Compatible with Linux, Windows, microcontrollers, wasm, CUDA (version 12 or later)
  • Constexpr functions can be called from CUDA devices with --expt-relaxed-constexpr compiler option

• C/C++11 API with libquadmath emulation

  • Most of libquadmath functions can be used on x86_64 clang and MSVC
  • 128-bit integer types can be used on MSVC
  • C++11 FP and int classes with overloaded operators are provided
    • C++11 functions in TLFloat are not constexpr

• Moderately optimized

  • Optimized for each architecture using intrinsics, etc.
  • Library design allows compilers to fully inline operations
  • All functions are thread-safe and reentrant

• Implements most of the math.h functions

  • Arithmetic operations, comparison, cast operations
  • fma, sqrt, hypot, cbrt, fmod, remainder, remquo
  • sin, cos, tan, sinpi, cospi, tanpi
  • asin, acos, atan, atan2
  • log, log2, log10, log1p
  • exp, exp2, exp10, expm1, pow
  • sinh, cosh, tanh, asinh, acosh, atanh
  • erf, erfc, tgamma
  • trunc, floor, ceil, round, rint
  • fabs, copysign, fmax, fmin, fdim
  • ldexp, frexp, modf, nextafter
  • isnan, isinf, finite, fpclassify, signbit

• Implements I/O functions

  • Conversion to/from C strings
  • printf-family functions

• Provides BigInt template classes in addition to the FP classes

  • It provides operations for integers of artibrary length (2^N bits)
  • They can be used in the similar way to the ordinary int/uint types
  • Data formats are the same as ordinary int/uint
  • These classes are internally used to implement the FP classes in TLFloat

How to build

1. Check out the source code from our GitHub repository : git clone https://github.com/shibatch/tlfloat

2. Make a separate directory to create an out-of-source build : cd tlfloat && mkdir build && cd build

3. Run cmake to configure the project : cmake .. -DCMAKE_INSTALL_PREFIX=../../install

4. Run make to build and install the project : make && make install

Compiling hello world example

Below is a simple C++ source code utilizing TLFloat.

#include <iostream>
#include <iomanip>
#include <tlfloat/tlmath.hpp>

using namespace tlfloat;

Octuple machin() {
  return 4 * (4 * atan(1 / Octuple(5)) - atan(1 / Octuple(239)));
}

int main(int argc, char **argv) {
  std::cout << std::setprecision(70) << machin() << std::endl;
}

To compile this source code, use the following command.

g++ -std=c++20 -I./install/include hello.cpp

You have to specify C++20 standard. Note that you do not need to link any library in this example. This program computes PI in octuple precision and shows it.

$ ./a.out
3.141592653589793238462643383279502884197169399375105820974944592307816

Libquadmath emulation

In gcc/g++ on x86_64 architecture, libquadmath provides math functions for quadruple precision floating point numbers. However, libquadmath is not available with clang or Visual Studio. By using the libquadmath emulation feature of TLFloat library, it is possible to use most of the features of libquadmath with clang and Visual Studio.

Below is a simple C source code utilizing this feature.

#include <stdio.h>
#include <stdlib.h>

#define TLFLOAT_LIBQUADMATH_EMULATION
#include <tlfloat/tlfloat.h>

int main(int argc, char **argv) {
  if (argc < 3) exit(-1);

  __float128 q1 = strtoflt128(argv[1], NULL);
  __float128 q2 = strtoflt128(argv[2], NULL);

  char str[256];
  quadmath_snprintf(str, sizeof(str), "%.30Qg", powq(q1, q2));
  puts(str);
}

To compile this source code, use the following command.

clang quad.c -I./install/include -L./install/lib -ltlfloat -lm

Below is an example of executing this program.

$ ./a.out 1.234 2.345
1.63732181977903314975233575019

In order to use the libquadmath emulation feature, define TLFLOAT_LIBQUADMATH_EMULATION macro, include tlfloat/tlfloat.h instead of quadmath.h, and link with -ltlfloat -lm. If you need portability, replace __float128 with tlfloat_quad.

C++11 API

Besides the C++20 API, TLFloat provides classes that can be used with C++11 standard.

Below is a simple C++ source code utilizing this feature.

#include <iostream>
#include <tlfloat/tlfloat.h>

tlfloat_octuple AGM(int N) {
  tlfloat_octuple y = tlfloat_sqrto(2) - 1;
  tlfloat_octuple a = y * y * 2;

  for(int k=0;k<N;k++) {
    y = 1.0 - tlfloat_powo(y, 4);
    y = tlfloat_powo(y, 1.0/4);
    y = (1 - y) / (1 + y);
    a *= tlfloat_powo(1 + y, 4);
    a -= tlfloat_ldexpo(((y + 1) * y + 1) * y, 2 * k + 3);
  }

  return 1 / a;
}

int main(int argc, char **argv) {
  std::cout << tlfloat::to_string(AGM(3), 70) << std::endl;
}

To compile this source code, use the following command.

g++ cpp11.cpp -std=c++11 -I./install/include -L./install/lib -ltlfloat

Below is an example of executing this program.

$ ./a.out
3.141592653589793238462643383279502884197169399375105820974944592307818

Benchmark results

This software package includes a benchmark tool. This can be built by specifying -DBUILD_BENCH=True cmake option. Below are some results of the benchmarks.

CPU: AMD Ryzen 9 7950X (running at 4.5GHz)

Compiler: gcc version 12.3.0 (Ubuntu 12.3.0-17ubuntu1)

TLFloat Quad

TLFloat version      : 1.10.0
Config               : tlfloat quad
Measurement time     : 10 sec
Addition             : 124.091 Mops/second
Multiplication       : 99.8746 Mops/second
Division             : 50.3795 Mops/second
Cast to/from double  : 163.924 Mops/second
Compare              : 296.318 Mops/second
FMA                  : 67.8103 Mops/second
Square root          : 15.7953 Mops/second
Rint                 : 192.819 Mops/second
Sin                  : 2.11886 Mops/second
Atan                 : 1.30871 Mops/second
Exp                  : 1.46121 Mops/second
Log                  : 1.58222 Mops/second
Pow                  : 0.887895 Mops/second

GNU libquadmath

TLFloat version      : 1.10.0
Config               : Libquadmath
Measurement time     : 10 sec
Addition             : 87.8567 Mops/second
Multiplication       : 74.334 Mops/second
Division             : 70.8784 Mops/second
Cast to/from double  : 64.6601 Mops/second
Compare              : 222.737 Mops/second
FMA                  : 1.92256 Mops/second
Square root          : 9.58719 Mops/second
Rint                 : 40.1336 Mops/second
Sin                  : 1.72235 Mops/second
Atan                 : 2.87544 Mops/second
Exp                  : 1.78155 Mops/second
Log                  : 1.77996 Mops/second
Pow                  : 1.27151 Mops/second

Development plan

• The following features will be added in future releases
  • Further documentation
  • More testing
    • Add more testers for I/O functions
  • Interoperability with SLEEF
  • Remaining math functions in math.h
  • BFloat16 support
  • Better microcontroller support
    • All-integer sqrt
    • Selectable rpi table size
  • Further optimization

License

The software is distributed under the Boost Software License, Version 1.0. See accompanying file LICENSE.txt or copy at : http://www.boost.org/LICENSE_1_0.txt.

Contributions to this project are accepted under the same license.

The fact that this software is released under an open source license only means that you can use the current version of the software for free. If you want this software to be maintained, you need to financially support the project. Please see CODE_OF_CONDUCT.md.

Copyright Naoki Shibata 2024.