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

Name	Implemented	Descritpion
ceil	:heavy_check_mark:
comb	:x:
copysign	:heavy_check_mark:
fabs	:heavy_check_mark:
factorial	:x:
floor	:heavy_check_mark:
fmod	:heavy_check_mark:
frexp	:heavy_check_mark:
fsum	:x:
gcd	:x:
isclose	:x:
isfinite	:x:
isinf	:heavy_check_mark:
isnan	:heavy_check_mark:
isqrt	:x:
lcm	:x:
ldexp	:heavy_check_mark:
modf	:heavy_check_mark:
nextafter	:heavy_check_mark:
perm	:x:
prod	:x:
remainder	:heavy_check_mark:
trunc	:heavy_check_mark:
ulp	:x:
cbrt	:heavy_check_mark:
exp	:heavy_check_mark:
exp2	:heavy_check_mark:
expm1	:heavy_check_mark:
log	:heavy_check_mark:
log1p	:heavy_check_mark:
log2	:heavy_check_mark:
log10	:heavy_check_mark:
pow	:heavy_check_mark:
sqrt	:heavy_check_mark:
acos	:heavy_check_mark:
asin	:heavy_check_mark:
atan	:heavy_check_mark:
atan2	:heavy_check_mark:
cos	:heavy_check_mark:
dist	:heavy_check_mark:
hypot	:heavy_check_mark:
sin	:heavy_check_mark:
tan	:heavy_check_mark:
degress	:heavy_check_mark:
radians	:heavy_check_mark:
acosh	:heavy_check_mark:
asinh	:heavy_check_mark:
atanh	:heavy_check_mark:
cosh	:heavy_check_mark:
sinh	:heavy_check_mark:
tanh	:heavy_check_mark:
erf	:heavy_check_mark:
erfc	:heavy_check_mark:
gamma	:heavy_check_mark:
lgamma	:heavy_check_mark:
pi	:heavy_check_mark:
e	:heavy_check_mark:
tau	:heavy_check_mark:
inf	:heavy_check_mark:
nan	:heavy_check_mark:

Routines from gcc's libquadthmath library

Name	Implemented
acosq	:heavy_check_mark:
acoshq	:heavy_check_mark:
asinq	:heavy_check_mark:
asinhq	:heavy_check_mark:
atanq	:heavy_check_mark:
atanhq	:heavy_check_mark:
atan2q	:heavy_check_mark:
cbrtq	:heavy_check_mark:
ceilq	:heavy_check_mark:
copysignq	:heavy_check_mark:
coshq	:heavy_check_mark:
cosq	:heavy_check_mark:
erfq	:heavy_check_mark:
erfcq	:heavy_check_mark:
exp2q	:heavy_check_mark:
expq	:heavy_check_mark:
expm1q	:heavy_check_mark:
fabsq	:heavy_check_mark:
fdimq	:heavy_check_mark:
finiteq	:heavy_check_mark:
floorq	:heavy_check_mark:
fmaq	:heavy_check_mark:
fmaxq	:heavy_check_mark:
fminq	:heavy_check_mark:
fmodq	:heavy_check_mark:
frexpq	:heavy_check_mark:
hypotq	:heavy_check_mark:
ilogbq	:heavy_check_mark:
isinfq	:heavy_check_mark:
isnanq	:heavy_check_mark:
issignalingq	:heavy_check_mark:
j0q	:heavy_check_mark:
j1q	:heavy_check_mark:
jnq	:heavy_check_mark:
ldexpq	:heavy_check_mark:
lgammaq	:heavy_check_mark:
llrintq	:heavy_check_mark:
llroundq	:heavy_check_mark:
logbq	:heavy_check_mark:
logq	:heavy_check_mark:
log10q	:heavy_check_mark:
log1pq	:heavy_check_mark:
log2q	:heavy_check_mark:
lrintq	:heavy_check_mark:
lroundq	:heavy_check_mark:
modfq	:heavy_check_mark:
nanq	:heavy_check_mark:
nearbyintq	:heavy_check_mark:
nextafterq	:heavy_check_mark:
powq	:heavy_check_mark:
remainderq	:heavy_check_mark:
remquoq	:heavy_check_mark:
rintq	:heavy_check_mark:
roundq	:heavy_check_mark:
scalblnq	:heavy_check_mark:
scalbnq	:heavy_check_mark:
signbitq	:heavy_check_mark:
sincosq	:heavy_check_mark:
sinhq	:heavy_check_mark:
sinq	:heavy_check_mark:
sqrtq	:heavy_check_mark:
tanq	:heavy_check_mark:
tanhq	:heavy_check_mark:
tgammaq	:heavy_check_mark:
truncq	:heavy_check_mark:
y0q	:heavy_check_mark:
y1q	:heavy_check_mark:
ynq	:heavy_check_mark:

Routines from Python's complex math cmath library

These are available from qcmath

Name	Implemented	Descritpion
phase	:heavy_check_mark:
polar	:heavy_check_mark:
rect	:heavy_check_mark:
exp	:heavy_check_mark:
log	:heavy_check_mark:
log10	:heavy_check_mark:
sqrt	:heavy_check_mark:
acos	:heavy_check_mark:
asin	:heavy_check_mark:
atan	:heavy_check_mark:
cos	:heavy_check_mark:
sin	:heavy_check_mark:
tan	:heavy_check_mark:
acosh	:heavy_check_mark:
asinh	:heavy_check_mark:
atanh	:heavy_check_mark:
cosh	:heavy_check_mark:
sinh	:heavy_check_mark:
tanh	:heavy_check_mark:
isfinite	:heavy_check_mark:
isinf	:heavy_check_mark:
isnan	:heavy_check_mark:
isclose	:x:
pi	:heavy_check_mark:
e	:heavy_check_mark:
tau	:heavy_check_mark:
inf	:heavy_check_mark:
infj	:heavy_check_mark:
nan	:heavy_check_mark:
nanj	:heavy_check_mark:

Routines from complex math libquadthmath library

These are available from qcmath

Name	Implemented	Descritpion
cabsq	:heavy_check_mark:	complex absolute value function
cargq	:heavy_check_mark:	calculate the argument
cimagq	:heavy_check_mark:	imaginary part of complex number
crealq	:heavy_check_mark:	real part of complex number
cacoshq	:heavy_check_mark:	complex arc hyperbolic cosine function
cacosq	:heavy_check_mark:	complex arc cosine function
casinhq	:heavy_check_mark:	complex arc hyperbolic sine function
casinq	:heavy_check_mark:	complex arc sine function
catanhq	:heavy_check_mark:	complex arc hyperbolic tangent function
catanq	:heavy_check_mark:	complex arc tangent function
ccosq:	:heavy_check_mark:	complex cosine function
ccoshq	:heavy_check_mark:	complex hyperbolic cosine function
cexpq	:heavy_check_mark:	complex exponential function
cexpiq	:heavy_check_mark:	computes the exponential function of i times a real value
clogq	:heavy_check_mark:	complex natural logarithm
clog10q	:heavy_check_mark:	complex base 10 logarithm
conjq	:heavy_check_mark:	complex conjugate function
cpowq	:heavy_check_mark:	complex power function
cprojq	:heavy_check_mark:	project into Riemann Sphere
csinq	:heavy_check_mark:	complex sine function
csinhq	:heavy_check_mark:	complex hyperbolic sine function
csqrtq	:heavy_check_mark:	complex square root
ctanq	:heavy_check_mark:	complex tangent function
ctanhq	:heavy_check_mark:	complex hyperbolic tangent function

Constants from libquadthmath library.

The following constants are availbe both in qmath and qcmath

Name	Implemented	Descritpion
FLT128_MAX	:heavy_check_mark:	largest finite number
FLT128_MIN	:heavy_check_mark:	smallest positive number with full precision
FLT128_EPSILON	:heavy_check_mark:	difference between 1 and the next larger representable number
FLT128_DENORM_MIN	:heavy_check_mark:	smallest positive denormalized number
FLT128_MANT_DIG	:heavy_check_mark:	number of digits in the mantissa (bit precision)
FLT128_MIN_EXP	:heavy_check_mark:	maximal negative exponent
FLT128_MAX_EXP	:heavy_check_mark:	maximal positive exponent
FLT128_DIG	:heavy_check_mark:	number of decimal digits in the mantissa
FLT128_MIN_10_EXP	:heavy_check_mark:	maximal negative decimal exponent
FLT128_MAX_10_EXP	:heavy_check_mark:	maximal positive decimal exponent
M_Eq	:heavy_check_mark:	the constant e (Euler’s number)
M_LOG2Eq	:heavy_check_mark:	binary logarithm of 2
M_LOG10Eq	:heavy_check_mark:	common, decimal logarithm of 2
M_LN2q	:heavy_check_mark:	natural logarithm of 2
M_LN10q	:heavy_check_mark:	natural logarithm of 10
M_PIq	:heavy_check_mark:	pi
M_PI_2q	:heavy_check_mark:	pi divided by two
M_PI_4q	:heavy_check_mark:	pi divided by four
M_1_PIq	:heavy_check_mark:	one over pi
M_2_PIq	:heavy_check_mark:	one over two pi
M_2_SQRTPIq	:heavy_check_mark:	two over square root of pi
M_SQRT2q	:heavy_check_mark:	square root of 2
M_SQRT1_2q	:heavy_check_mark:	one over square root of 2