pyQuadp

Python interface to gcc's libquadmath for quad (128-bit) precision maths.

Build

This project must be compiled with GCC/GFortran toolchain (gcc, g++, gfortran). Do not use clang for builds.

CC=gcc CXX=g++ FC=gfortran python -m build
python -m pip install .

For editable installs, also force the same toolchain:

CC=gcc CXX=g++ FC=gfortran python -m pip install -e . --no-build-isolation

If your shell should always use GCC/GFortran for local development:

export CC=gcc
export CXX=g++
export FC=gfortran
python -m build
python -m pip install .

This package requires quadmath.h and libquadmath.so. This might come installed with your installation of gcc/gfortran from your package manager. Or it might require a separate installation. This should be installed before trying to install the Python package.

Fedora

sudo dnf install libquadmath libquadmath-devel

Usage

qfloat

A quad precision number is created by passing either a int, float, or string to qfloat:

import pyquadp

q = pyquadp.qfloat(1)
q = pyquadp.qfloat(1.0)
q = pyquadp.qfloat('1')

A qfloat implements Python's NumberProtocol, thus it can be used like any other number, either with basic math operations or in rich comparisons:

q1 = pyquadp.qfloat(1)
q2 = pyquadp.qfloat(2)

q1+q2 # pyquadp.qfloat(3)
q1*q2  # pyquadp.qfloat(2)
q1+=q2 # pyquadp.qfloat(3)

q1 <= q2 # True
q1 == q2 # False

str(q) # "1.000000000000000000000000000000000000e+00"

Scalar utility methods are also available:

q = pyquadp.qfloat("1.5")

q.as_integer_ratio()  # (3, 2)
q.is_integer()        # False
round(q)              # qfloat('2')
q.__floor__()         # qfloat('1')
q.__ceil__()          # qfloat('2')
q.__trunc__()         # qfloat('1')

For ctypes compatibility, scalar from_param methods return packed bytes:

param = pyquadp.qfloat.from_param("1.25")
isinstance(param, bytes)  # True

qint

qint is a signed 128-bit integer scalar type with full arithmetic and bitwise operators.

import pyquadp

x = pyquadp.qint("13")

x.bit_length()   # 4
x.bit_count()    # 3
x.__index__()    # 13

param = pyquadp.qint.from_param(x)
isinstance(param, bytes)  # True

qarray

qarray provides NumPy-compatible arrays of quad-precision (128-bit) values. It registers a custom NumPy dtype so arrays behave like any other NumPy array where supported.

import pyquadp
import numpy as np

# creation
arr = pyquadp.qarray.zeros(4)           # array of four zeros
arr = pyquadp.qarray.ones(3)            # array of three ones
arr = pyquadp.qarray.from_list([1, 2.5, "3.141592653589793238"])  # from Python sequence
arr = pyquadp.qarray.from_array(np.linspace(0, 1, 5))  # from any NumPy array

# dtype handle for asarray / casting
dt = pyquadp.qarray.dtype

# casting to/from standard NumPy dtypes
out64 = np.asarray(arr, dtype=np.float64)          # qarray → float64
back  = np.asarray(out64, dtype=pyquadp.qarray.dtype)  # float64 → qarray

Arithmetic ufuncs

All standard element-wise binary and unary arithmetic ufuncs work directly:

a = pyquadp.qarray.from_list([1.0, 2.0, 3.0])
b = pyquadp.qarray.from_list([0.5, 1.5, 2.5])

np.add(a, b)       # qarray([1.5, 3.5, 5.5])
np.subtract(a, b)  # qarray([0.5, 0.5, 0.5])
np.multiply(a, b)  # qarray([0.5, 3.0, 7.5])
np.divide(a, b)    # qarray([2.0, 1.333..., 1.2])
np.negative(a)     # qarray([-1.0, -2.0, -3.0])
np.absolute(a)     # qarray([1.0,  2.0,  3.0])
np.square(a)       # qarray([1.0,  4.0,  9.0])

Operands can be mixed with float64 arrays; the output dtype is always qarray:

d = np.array([10.0, 20.0, 30.0], dtype=np.float64)
np.add(a, d)       # qarray([11.0, 22.0, 33.0])
np.multiply(d, a)  # qarray([10.0, 40.0, 90.0])

Math ufuncs

np.sqrt(a)   # quad-precision square root
np.exp(a)    # quad-precision exponential
np.log(a)    # quad-precision natural log
np.sin(a)    # quad-precision sine
np.cos(a)    # quad-precision cosine

Platform requirements

qarray requires GCC's libquadmath and a NumPy ≥ 2.0 installation.

qiarray

qiarray provides NumPy-compatible arrays of signed __int128 values through a custom NumPy dtype.

import pyquadp
import numpy as np

arr = pyquadp.qiarray.arange(5)
arr = pyquadp.qiarray.from_list([1, "2", -3])
arr = np.asarray(np.array([4, 5, 6], dtype=np.int64), dtype=pyquadp.qiarray.dtype)

np.add(arr, arr)
np.multiply(arr, 3)
np.bitwise_and(arr, np.array([1, 1, 1], dtype=np.int64))
np.asarray(arr, dtype=np.int64)

The surface includes constructors, casts to and from signed fixed-width integer dtypes, and core arithmetic, division, shift, and bitwise ufuncs.

qcmplx

A quad precision number is created by passing either a complex variable or two ints, floats, strs, or qfloats to qcmplx:

import pyquadp

q = pyquadp.qcmplx(complex(1,1))
q = pyquadp.qcmplx(1,1.0)
q = pyquadp.qcmplx('1',1.0)
q = pyquadp.qcmplx('1','1')
q = pyquadp.qcmplx(pyquadp.qfloat(1), pyquadp.qfloat('1'))

qcmplx also accepts a single complex string in Python complex notation:

q = pyquadp.qcmplx('1+1j')
q = pyquadp.qcmplx('1-1j')
q = pyquadp.qcmplx('-2.5j')
q = pyquadp.qcmplx('3.25')

Both one-string and two-argument forms are supported.

For ctypes compatibility, qcmplx.from_param returns packed bytes.

Math libraries

The qmath provides the union of math operations from Python's math library and the routines provided in libquadmath. qmath provides routines for qfloat, while complex numbers are handled by qcmath versions.

Where possible functions accessed via the Python name follows Python's conventions regarding behavior of exceptional values. While routines from libquadmath (those ending in q) follows libquadmath's conventions.

Routines from Python's math library

Routines from gcc's libquadthmath library

Routines from Python's complex math cmath library

These are available from qcmath

Routines from complex math libquadthmath library

These are available from qcmath

Constants from libquadthmath library.

The following constants are availbe both in qmath and qcmath