#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Python wrapper around the C extension for the angular correlation function
:math:`\\omega(\\theta)`. Corresponding C routines are in
``mocks/DDtheta_mocks/``, while the python interface is
:py:mod:`Corrfunc.mocks.DDtheta_mocks`
"""
from __future__ import (division, print_function, absolute_import,
unicode_literals)
import warnings
__author__ = ('Manodeep Sinha', 'Kris Akira Stern')
__all__ = ('DDtheta_mocks', 'find_fastest_DDtheta_mocks_bin_refs')
[docs]
def DDtheta_mocks(autocorr, nthreads, binfile,
RA1, DEC1, weights1=None,
RA2=None, DEC2=None, weights2=None,
link_in_dec=True, link_in_ra=True,
verbose=False, output_thetaavg=False,
fast_acos=False, ra_refine_factor=2,
dec_refine_factor=2, max_cells_per_dim=100,
copy_particles=True, enable_min_sep_opt=True,
c_api_timer=False, isa=r'fastest', weight_type=None):
"""
Function to compute the angular correlation function for points on
the sky (i.e., mock catalogs or observed galaxies).
Returns a numpy structured array containing the pair counts for the
specified angular bins.
If ``weights`` are provided, the resulting pair counts are weighted. The
weighting scheme depends on ``weight_type``.
.. note:: This module only returns pair counts and not the actual
correlation function :math:`\\omega(\\theta)`. See
:py:mod:`Corrfunc.utils.convert_3d_counts_to_cf` for computing
:math:`\\omega(\\theta)` from the pair counts returned.
Parameters
-----------
autocorr : boolean, required
Boolean flag for auto/cross-correlation. If autocorr is set to 1,
then the second set of particle positions are not required.
nthreads : integer
Number of threads to use.
binfile: string or an list/array of floats. Units: degrees.
For string input: filename specifying the ``theta`` bins for
``DDtheta_mocks``. The file should contain white-space separated values
of (thetamin, thetamax) for each ``theta`` wanted. The bins need to be
contiguous and sorted in increasing order (smallest bins come first).
For array-like input: A sequence of ``theta`` values that provides the
bin-edges. For example,
``np.logspace(np.log10(0.1), np.log10(10.0), 15)`` is a valid
input specifying **14** (logarithmic) bins between 0.1 and 10.0
degrees. This array does not need to be sorted.
RA1 : array-like, real (float/double)
The array of Right Ascensions for the first set of points. RA's
are expected to be in [0.0, 360.0], but the code will try to fix cases
where the RA's are in [-180, 180.0]. For peace of mind, always supply
RA's in [0.0, 360.0].
Calculations are done in the precision of the supplied arrays.
DEC1 : array-like, real (float/double)
Array of Declinations for the first set of points. DEC's are expected
to be in the [-90.0, 90.0], but the code will try to fix cases where
the DEC's are in [0.0, 180.0]. Again, for peace of mind, always supply
DEC's in [-90.0, 90.0].
Must be of same precision type as RA1.
weights1 : array_like, real (float/double), optional
A scalar, or an array of weights of shape (n_weights, n_positions) or
(n_positions,). `weight_type` specifies how these weights are used;
results are returned in the `weightavg` field. If only one of weights1
and weights2 is specified, the other will be set to uniform weights.
RA2 : array-like, real (float/double)
The array of Right Ascensions for the second set of points. RA's
are expected to be in [0.0, 360.0], but the code will try to fix cases
where the RA's are in [-180, 180.0]. For peace of mind, always supply
RA's in [0.0, 360.0].
Must be of same precision type as RA1/DEC1.
DEC2 : array-like, real (float/double)
Array of Declinations for the second set of points. DEC's are expected
to be in the [-90.0, 90.0], but the code will try to fix cases where
the DEC's are in [0.0, 180.0]. Again, for peace of mind, always supply
DEC's in [-90.0, 90.0].
Must be of same precision type as RA1/DEC1.
weights2 : array-like, real (float/double), optional
Same as weights1, but for the second set of positions
link_in_dec : boolean (default True)
Boolean flag to create lattice in Declination. Code runs faster with
this option. However, if the angular separations are too small, then
linking in declination might produce incorrect results. When running
for the first time, check your results by comparing with the output
of the code for ``link_in_dec=False`` and ``link_in_ra=False``.
link_in_ra : boolean (default True)
Boolean flag to create lattice in Right Ascension. Setting this option
implies ``link_in_dec=True``. Similar considerations as ``link_in_dec``
described above.
If you disable both ``link_in_dec`` and ``link_in_ra``, then
the code reduces to a brute-force pair counter. No lattices are created
at all. For very small angular separations, the brute-force method
might be the most numerically stable method.
verbose : boolean (default false)
Boolean flag to control output of informational messages
output_thetaavg : boolean (default false)
Boolean flag to output the average ``\\theta`` for each bin. Code will
run slower if you set this flag.
If you are calculating in single-precision, ``thetaavg`` will
suffer from numerical loss of precision and can not be trusted. If you
need accurate ``thetaavg`` values, then pass in double precision arrays
for ``RA/DEC``.
Code will run significantly slower if you enable this option.
Use the keyword ``fast_acos`` if you can tolerate some loss of
precision.
fast_acos : boolean (default false)
Flag to use numerical approximation for the ``arccos`` - gives better
performance at the expense of some precision. Relevant only if
``output_thetaavg==True``.
Developers: Two versions already coded up in ``utils/fast_acos.h``,
so you can choose the version you want. There are also notes on how
to implement faster (and less accurate) functions, particularly
relevant if you know your ``theta`` range is limited. If you implement
a new version, then you will have to reinstall the entire Corrfunc
package.
Note: Tests will fail if you run the tests with``fast_acos=True``.
(radec)_refine_factor : integer, default is (2,2); typically within [1-5]
Controls the refinement on the cell sizes. Can have up to a 20% impact
on runtime.
Only two refine factors are to be specified and these
correspond to ``ra`` and ``dec`` (rather, than the usual three of
``(xyz)bin_refine_factor`` for all other correlation functions).
max_cells_per_dim : integer, default is 100, typical values in [50-300]
Controls the maximum number of cells per dimension. Total number of
cells can be up to (max_cells_per_dim)^2. Only increase if ``thetamax``
is too small relative to the boxsize (and increasing helps the
runtime).
copy_particles: boolean (default True)
Boolean flag to make a copy of the particle positions
If set to False, the particles will be re-ordered in-place
.. versionadded:: 2.3.0
enable_min_sep_opt: boolean (default true)
Boolean flag to allow optimizations based on min. separation between
pairs of cells. Here to allow for comparison studies.
.. versionadded:: 2.3.0
c_api_timer : boolean (default false)
Boolean flag to measure actual time spent in the C libraries. Here
to allow for benchmarking and scaling studies.
isa: string, case-insensitive (default ``fastest``)
Controls the runtime dispatch for the instruction set to use. Options
are: [``fastest``, ``avx512f``, ``avx``, ``sse42``, ``fallback``]
Setting isa to ``fastest`` will pick the fastest available instruction
set on the current computer. However, if you set ``isa`` to, say,
``avx`` and ``avx`` is not available on the computer, then the code
will revert to using ``fallback`` (even though ``sse42`` might be
available).
Unless you are benchmarking the different instruction sets, you should
always leave ``isa`` to the default value. And if you *are*
benchmarking, then the string supplied here gets translated into an
``enum`` for the instruction set defined in ``utils/defs.h``.
weight_type : string, optional (default None)
The type of weighting to apply. One of ["pair_product", None].
Returns
--------
results : Numpy structured array
A numpy structured array containing [thetamin, thetamax, thetaavg,
npairs, weightavg] for each angular bin specified in the ``binfile``.
If ``output_thetaavg`` is not set then ``thetavg`` will be set to 0.0
for all bins; similarly for ``weightavg``. ``npairs`` contains the
number of pairs in that bin.
api_time : float, optional
Only returned if ``c_api_timer`` is set. ``api_time`` measures only
the time spent within the C library and ignores all python overhead.
Example
-------
>>> from __future__ import print_function
>>> import numpy as np
>>> import time
>>> from math import pi
>>> from os.path import dirname, abspath, join as pjoin
>>> import Corrfunc
>>> from Corrfunc.mocks.DDtheta_mocks import DDtheta_mocks
>>> binfile = pjoin(dirname(abspath(Corrfunc.__file__)),
... "../mocks/tests/", "angular_bins")
>>> N = 100000
>>> nthreads = 4
>>> seed = 42
>>> np.random.seed(seed)
>>> RA = np.random.uniform(0.0, 2.0*pi, N)*180.0/pi
>>> cos_theta = np.random.uniform(-1.0, 1.0, N)
>>> DEC = 90.0 - np.arccos(cos_theta)*180.0/pi
>>> weights = np.ones_like(RA)
>>> autocorr = 1
>>> for isa in ['AVX', 'SSE42', 'FALLBACK']:
... for link_in_dec in [False, True]:
... for link_in_ra in [False, True]:
... results = DDtheta_mocks(autocorr, nthreads, binfile,
... RA, DEC, output_thetaavg=True,
... weights1=weights, weight_type='pair_product',
... link_in_dec=link_in_dec, link_in_ra=link_in_ra,
... isa=isa, verbose=True)
>>> for r in results:
... print("{0:10.6f} {1:10.6f} {2:10.6f} {3:10d} {4:10.6f}".
... format(r['thetamin'], r['thetamax'],
... r['thetaavg'], r['npairs'], r['weightavg']))
... # doctest: +NORMALIZE_WHITESPACE
0.010000 0.014125 0.012272 62 1.000000
0.014125 0.019953 0.016978 172 1.000000
0.019953 0.028184 0.024380 298 1.000000
0.028184 0.039811 0.034321 598 1.000000
0.039811 0.056234 0.048535 1164 1.000000
0.056234 0.079433 0.068385 2438 1.000000
0.079433 0.112202 0.096631 4658 1.000000
0.112202 0.158489 0.136834 9414 1.000000
0.158489 0.223872 0.192967 19098 1.000000
0.223872 0.316228 0.272673 37848 1.000000
0.316228 0.446684 0.385344 75520 1.000000
0.446684 0.630957 0.543973 150938 1.000000
0.630957 0.891251 0.768406 301854 1.000000
0.891251 1.258925 1.085273 599896 1.000000
1.258925 1.778279 1.533461 1200238 1.000000
1.778279 2.511886 2.166009 2396338 1.000000
2.511886 3.548134 3.059159 4775162 1.000000
3.548134 5.011872 4.321445 9532582 1.000000
5.011872 7.079458 6.104214 19001930 1.000000
7.079458 10.000000 8.622400 37842502 1.000000
"""
try:
from Corrfunc._countpairs_mocks import countpairs_theta_mocks as\
DDtheta_mocks_extn
except ImportError:
msg = "Could not import the C extension for the angular "\
"correlation function for mocks."
raise ImportError(msg)
import numpy as np
from Corrfunc.utils import translate_isa_string_to_enum, fix_ra_dec,\
return_file_with_rbins, convert_to_native_endian,\
sys_pipes, process_weights
from future.utils import bytes_to_native_str
if autocorr == 0:
if RA2 is None or DEC2 is None:
msg = "Must pass valid arrays for RA2/DEC2 for "\
"computing cross-correlation"
raise ValueError(msg)
else:
RA2 = np.empty(1)
DEC2 = np.empty(1)
weights1, weights2 = process_weights(weights1, weights2,
RA1, RA2, weight_type, autocorr)
# Ensure all input arrays are native endian
RA1, DEC1, weights1, RA2, DEC2, weights2 = [
convert_to_native_endian(arr, warn=True) for arr in
[RA1, DEC1, weights1, RA2, DEC2, weights2]]
fix_ra_dec(RA1, DEC1)
if autocorr == 0:
fix_ra_dec(RA2, DEC2)
if link_in_ra:
link_in_dec = True
# Passing None parameters breaks the parsing code, so avoid this
kwargs = {}
for k in ['weights1', 'weights2', 'weight_type', 'RA2', 'DEC2']:
v = locals()[k]
if v is not None:
kwargs[k] = v
integer_isa = translate_isa_string_to_enum(isa)
rbinfile, delete_after_use = return_file_with_rbins(binfile)
warn_small_theta(rbinfile,
RA1.dtype, # RA and DEC are checked to be the same dtype
)
with sys_pipes():
extn_results = DDtheta_mocks_extn(autocorr, nthreads, rbinfile,
RA1, DEC1,
verbose=verbose,
link_in_dec=link_in_dec,
link_in_ra=link_in_ra,
output_thetaavg=output_thetaavg,
fast_acos=fast_acos,
ra_refine_factor=ra_refine_factor,
dec_refine_factor=dec_refine_factor,
max_cells_per_dim=max_cells_per_dim,
copy_particles=copy_particles,
enable_min_sep_opt=enable_min_sep_opt,
c_api_timer=c_api_timer,
isa=integer_isa, **kwargs)
if extn_results is None:
msg = "RuntimeError occurred"
raise RuntimeError(msg)
else:
extn_results, api_time = extn_results
if delete_after_use:
import os
os.remove(rbinfile)
results_dtype = np.dtype([(bytes_to_native_str(b'thetamin'), np.float64),
(bytes_to_native_str(b'thetamax'), np.float64),
(bytes_to_native_str(b'thetaavg'), np.float64),
(bytes_to_native_str(b'npairs'), np.uint64),
(bytes_to_native_str(b'weightavg'), np.float64)])
results = np.array(extn_results, dtype=results_dtype)
if not c_api_timer:
return results
else:
return results, api_time
def find_fastest_DDtheta_mocks_bin_refs(autocorr, nthreads, binfile,
RA1, DEC1, RA2=None, DEC2=None,
link_in_dec=True, link_in_ra=True,
verbose=False, output_thetaavg=False,
max_cells_per_dim=100,
isa=r'fastest',
maxbinref=3, nrepeats=3,
return_runtimes=False):
"""
Parameters
----------
autocorr : boolean, required
Boolean flag for auto/cross-correlation. If autocorr is set to 1,
then the second set of particle positions are not required.
nthreads : integer
Number of threads to use.
binfile: string or an list/array of floats. Units: degrees.
For string input: filename specifying the ``theta`` bins for
``DDtheta_mocks``. The file should contain white-space separated values
of (thetamin, thetamax) for each ``theta`` wanted. The bins need to be
contiguous and sorted in increasing order (smallest bins come first).
For array-like input: A sequence of ``theta`` values that provides the
bin-edges. For example,
``np.logspace(np.log10(0.1), np.log10(10.0), 15)`` is a valid
input specifying **14** (logarithmic) bins between 0.1 and 10.0
degrees. This array does not need to be sorted.
RA1 : array-like, real (float/double)
The array of Right Ascensions for the first set of points. RA1's
are expected to be in [0.0, 360.0], but the code will try to fix cases
where the RA1's are in [-180, 180.0]. For peace of mind, always supply
RA1's in [0.0, 360.0].
Calculations are done in the precision of the supplied arrays.
DEC1 : array-like, real (float/double)
Array of Declinations for the first set of points. DEC1's are expected
to be in the [-90.0, 90.0], but the code will try to fix cases where
the DEC1's are in [0.0, 180.0]. Again, for peace of mind, always supply
DEC1's in [-90.0, 90.0].
Must be of same precision type as RA1.
RA2 : array-like, real (float/double)
The array of Right Ascensions for the second set of points. RA2's
are expected to be in [0.0, 360.0], but the code will try to fix cases
where the RA2's are in [-180, 180.0]. For peace of mind, always supply
RA2's in [0.0, 360.0].
Must be of same precision type as RA1/DEC1.
DEC2 : array-like, real (float/double)
Array of Declinations for the second set of points. DEC2's are expected
to be in the [-90.0, 90.0], but the code will try to fix cases where
the DEC2's are in [0.0, 180.0]. Again, for peace of mind, always supply
DEC2's in [-90.0, 90.0].
Must be of same precision type as RA1/DEC1.
verbose : boolean (default false)
Boolean flag to control output of informational messages
output_thetaavg : boolean (default false)
Boolean flag to output the average ``\\theta`` for each bin. Code will
run slower if you set this flag.
If you are calculating in single-precision, ``thetaavg`` will
suffer from numerical loss of precision and can not be trusted. If you
need accurate ``thetaavg`` values, then pass in double precision arrays
for ``RA/DEC``.
isa: string, case-insensitive (default ``fastest``)
Controls the runtime dispatch for the instruction set to use. Options
are: [``fastest``, ``avx512f``, ``avx``, ``sse42``, ``fallback``]
Setting isa to ``fastest`` will pick the fastest available instruction
set on the current computer. However, if you set ``isa`` to, say,
``avx`` and ``avx`` is not available on the computer, then the code
will revert to using ``fallback`` (even though ``sse42`` might be
available).
Unless you are benchmarking the different instruction sets, you should
always leave ``isa`` to the default value. And if you *are*
benchmarking, then the string supplied here gets translated into an
``enum`` for the instruction set defined in ``utils/defs.h``.
max_cells_per_dim: integer, default is 100, typical values in [50-300]
Controls the maximum number of cells per dimension. Total number of
cells can be up to (max_cells_per_dim)^2. Only increase if ``rpmax`` is
too small relative to the boxsize (and increasing helps the runtime).
maxbinref: integer (default 3)
The maximum ``bin refine factor`` to use along each dimension.
Runtime of module scales as ``maxbinref^2``, so change the value of
``maxbinref`` with caution.
Note that ``max_cells_per_dim`` might need to be increased
to accommodate really large ``maxbinref``.
nrepeats: integer (default 3)
Number of times to repeat the timing for an individual run. Accounts
for the dispersion in runtimes on computers with multiple user
processes.
return_runtimes: boolean (default ``false``)
If set, also returns the array of runtimes.
Returns
-------
(nRA, nDEC) : tuple of integers
The combination of ``bin refine factors`` along each dimension that
produces the fastest code.
runtimes : numpy structured array
Only returned if ``return_runtimes`` is set, then the return value
is a tuple containing ((nRA, nDEC), runtimes). ``runtimes`` is a
``numpy`` structured array containing the fields, [``nRA``, ``nDEC``,
``avg_runtime``, ``sigma_time``]. Here, ``avg_runtime`` is the
average time, measured over ``nrepeats`` invocations, spent in
the python extension. ``sigma_time`` is the dispersion of the
run times across those ``nrepeats`` invocations.
Example
-------
>>> from __future__ import print_function
>>> import numpy as np
>>> import time
>>> from math import pi
>>> from os.path import dirname, abspath, join as pjoin
>>> import Corrfunc
>>> from Corrfunc.mocks.DDtheta_mocks \
import find_fastest_DDtheta_mocks_bin_refs
>>> binfile = pjoin(dirname(abspath(Corrfunc.__file__)),
... "../mocks/tests/", "angular_bins")
>>> N = 100000
>>> nthreads = 4
>>> seed = 42
>>> np.random.seed(seed)
>>> RA1 = np.random.uniform(0.0, 2.0*pi, N)*180.0/pi
>>> cos_theta = np.random.uniform(-1.0, 1.0, N)
>>> DEC1 = 90.0 - np.arccos(cos_theta)*180.0/pi
>>> autocorr = 1
>>> best, _ = find_fastest_DDtheta_mocks_bin_refs(autocorr, nthreads,\
... binfile, RA1, DEC1,\
... return_runtimes=True)
>>> print(best) # doctest:+SKIP
(2, 1)
.. note:: Since the result might change depending on the computer,
doctest is skipped for this function.
"""
weights1 = None
weights2 = None
weight_type = None
try:
from Corrfunc._countpairs_mocks import countpairs_theta_mocks as\
DDtheta_mocks_extn
except ImportError:
msg = "Could not import the C extension for the angular "\
"correlation function for mocks."
raise ImportError(msg)
import numpy as np
from Corrfunc.utils import translate_isa_string_to_enum, fix_ra_dec,\
return_file_with_rbins, convert_to_native_endian, process_weights
from future.utils import bytes_to_native_str
import itertools
import time
weights1, weights2 = process_weights(weights1, weights2, RA1, RA2,
weight_type, autocorr)
# Ensure all input arrays are native endian
RA1, DEC1, weights1, RA2, DEC2, weights2 = [
convert_to_native_endian(arr, warn=True) for arr in
[RA1, DEC1, weights1, RA2, DEC2, weights2]]
fix_ra_dec(RA1, DEC1)
if autocorr == 0:
fix_ra_dec(RA2, DEC2)
# Passing None parameters breaks the parsing code, so avoid this
kwargs = {}
for k in ['weights1', 'weights2', 'weight_type', 'RA2', 'DEC2']:
v = locals()[k]
if v is not None:
kwargs[k] = v
integer_isa = translate_isa_string_to_enum(isa)
rbinfile, delete_after_use = return_file_with_rbins(binfile)
bin_refs = np.arange(1, maxbinref + 1)
if link_in_ra:
bin_ref_perms = itertools.product(bin_refs, bin_refs)
nperms = maxbinref ** 2
else:
bin_ref_perms = [(1, binref) for binref in bin_refs]
nperms = maxbinref
dtype = np.dtype([(bytes_to_native_str(b'nRA'), np.int),
(bytes_to_native_str(b'nDEC'), np.int),
(bytes_to_native_str(b'avg_time'), np.float64),
(bytes_to_native_str(b'sigma_time'), np.float64)])
all_runtimes = np.zeros(nperms, dtype=dtype)
all_runtimes[:] = np.inf
if autocorr == 0:
if RA2 is None or DEC2 is None:
msg = "Must pass valid arrays for RA2/DEC2 for "\
"computing cross-correlation."
raise ValueError(msg)
else:
RA2 = np.empty(1)
DEC2 = np.empty(1)
if link_in_ra:
link_in_dec = True
if not link_in_dec:
msg = "Error: Brute-force calculation without any gridding " \
"is forced, as link_in_dec and link_in_ra are both set " \
"to False. Please set at least one of link_in_dec, link_in_ra=True " \
"to enable gridding along DEC or along both RA and DEC."
raise ValueError(msg)
if verbose and not link_in_ra:
msg = "INFO: Since ``link_in_ra`` is not set, only gridding in declination " \
"Checking with refinements in declination ranging from [1, {}] and a " \
"maximum of {} bins".format(maxbinref, max_cells_per_dim)
print(msg)
for ii, (nRA, nDEC) in enumerate(bin_ref_perms):
total_runtime = 0.0
total_sqr_runtime = 0.0
for _ in range(nrepeats):
t0 = time.perf_counter()
extn_results = DDtheta_mocks_extn(autocorr, nthreads, rbinfile,
RA1, DEC1, RA2, DEC2,
link_in_dec=link_in_dec,
link_in_ra=link_in_ra,
verbose=verbose,
output_thetaavg=output_thetaavg,
ra_refine_factor=nRA,
dec_refine_factor=nDEC,
max_cells_per_dim=max_cells_per_dim,
isa=integer_isa)
t1 = time.perf_counter()
if extn_results is None:
msg = "RuntimeError occurred with perms = ({0}, {1})".\
format(nRA, nDEC)
raise ValueError(msg)
dt = (t1 - t0)
total_runtime += dt
total_sqr_runtime += dt * dt
avg_runtime = total_runtime / nrepeats
# variance = E(X^2) - E^2(X)
# disp = sqrt(variance)
runtime_disp = np.sqrt(total_sqr_runtime / nrepeats -
avg_runtime * avg_runtime)
all_runtimes[ii]['nRA'] = nRA
all_runtimes[ii]['nDEC'] = nDEC
all_runtimes[ii]['avg_time'] = avg_runtime
all_runtimes[ii]['sigma_time'] = runtime_disp
if delete_after_use:
import os
os.remove(rbinfile)
all_runtimes.sort(order=('avg_time', 'sigma_time'))
results = (all_runtimes[0]['nRA'],
all_runtimes[0]['nDEC'])
optional_returns = return_runtimes
if not optional_returns:
ret = results
else:
ret = (results,)
if return_runtimes:
ret += (all_runtimes,)
return ret
def warn_small_theta(thetabinfile, dtype):
'''
Small theta values underfloat float32. Warn the user.
Context: https://github.com/manodeep/Corrfunc/issues/296 (see also #297)
'''
if dtype.itemsize > 4:
return
import numpy as np
try:
bins = np.loadtxt(thetabinfile)
except RuntimeError:
warnings.warn("""
Could not load binfile "{}". Be aware that small angular pair separations
will suffer from loss of floating-point precision, as the input data is in
float32 precision or lower. The loss of precision is 0.5% in theta at
separations of 0.2 degrees, and larger at smaller separations.
For more information, see:
https://github.com/manodeep/Corrfunc/issues/296 (see also #297)
""".format(thetabinfile)
)
return
if bins.min() <= 0.2:
warnings.warn("""
A binning with a minimum angular separation of 0.2 degrees or less was
requested, and the input data is in float32 precision or lower. Be aware that
small angular pair separations will suffer from loss of floating-point
precision. In float32, the loss of precision is 0.5% in theta at separations of
0.2 degrees, and larger at smaller separations.
For more information, see:
https://github.com/manodeep/Corrfunc/issues/296 (see also #297)
"""
)
if __name__ == '__main__':
import doctest
doctest.testmod()
