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|
# -*- coding: utf-8 -*-
# This is the test of all C++ lib/high-precision/MathFunctions.hpp exported to python via py/high-precision/_math.cpp
# (C) 2015 Anton Gladky <gladk@debian.org>
# (C) 2019 Janek Kozicki
import unittest, math, sys
import yade
from yade import math as mth
import testMathHelper
if (yade.config.highPrecisionMpmath):
print('\n\033[92m' + "Using " + str(yade.math.getRealHPPythonDigits10()) + " decimal digits in python. Importing mpmath" + '\033[0m\n')
import mpmath
class SimpleTests(unittest.TestCase):
def needsMpmathAtN(self, N):
return yade.math.needsMpmathAtN(N)
def incompleteComplex(self):
return ('COMPLEX_MP' not in yade.config.features)
def hasMpfr(self):
return ('MPFR' in yade.config.features)
# flags: -Ofast -march=native -mtune=native -fno-associative-math -fno-finite-math-only -fsigned-zeros
def isFastNative(self):
return ('FAST_NATIVE' in yade.config.features)
def nowUsesBoostBinFloat(self, N):
return (not self.hasMpfr()) and ((yade.math.RealHPConfig.getDigits10(N) > 33) or (yade.math.RealHPConfig.getDigits10(N) in [24, 30]))
def setUp(self):
self.testRecordingMode = False # if 'True' then it will record 'self.newTolerances' maximum errors encountered, to be put later in place of 'self.defaultTolerances'. See function tearDown() below.
self.printedAlready = set()
self.nonBoostMPFR = False # I was testing non-boost MPFR before: /usr/include/eigen3/unsupported/Eigen/MPRealSupport. Might come handy later.
# If failures appear and function is not broken then increase tolerance a little.
# yapf: disable
self.defaultTolerances={
# function decimal places : tolerance factor. Each "10" corresponds to single wrong decimal place. But they are approximate and rounded up.
#
# float double long double float128 MPFR_100 MPFR_150 cpp_bin_float_100 cpp_bin_float_150
# Real C++ functions
"acos" : {"6": 100 , "15": 100 , "18": 100 , "33": 1000 , "100": 1000 , "150" : 1000 , "100_b" : 1000 , "150_b" : 1000 }
, "atanh" : {"6": 100 , "15": 100 , "18": 100 , "33": 1000 , "100": 1000 , "150" : 1000 , "100_b" : 1000 , "150_b" : 1000 }
, "atan" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 50 }
, "atan2" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 50 }
, "acosh" : {"6": 100 , "15": 100 , "18": 100 , "33": 1000 , "100": 1000 , "150" : 1000 , "100_b" : 1000 , "150_b" : 1000 }
, "asin" : {"6": 100 , "15": 100 , "18": 100 , "33": 1000 , "100": 1000 , "150" : 1000 , "100_b" : 1000 , "150_b" : 1000 }
, "asinh" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 50 }
# maybe the error lies in mpmath, because everything is compared with it.
, "sin" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "cos" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "tan" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "tanh" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 50 }
, "exp" : {"6": 10 , "15": 10 , "18": 10 , "33": 10 , "100": 10 , "150" : 10 , "100_b" : 100 , "150_b" : 100 }
, "exp2" : {"6": 10 , "15": 10 , "18": 10 , "33": 10 , "100": 10 , "150" : 10 , "100_b" : 100 , "150_b" : 100 }
, "expm1" : {"6": 10 , "15": 10 , "18": 10 , "33": 10 , "100": 10 , "150" : 10 , "100_b" : 100 , "150_b" : 100 }
, "cosh" : {"6": 10 , "15": 10 , "18": 10 , "33": 10 , "100": 10 , "150" : 10 , "100_b" : 100 , "150_b" : 100 }
, "sinh" : {"6": 10 , "15": 10 , "18": 10 , "33": 10 , "100": 10 , "150" : 10 , "100_b" : 100 , "150_b" : 100 }
, "log" : {"6": 1000, "15": 1000, "18": 100 , "33": 100 , "100": 100 , "150" : 100 , "100_b" : 100 , "150_b" : 100 }
, "log10" : {"6": 1000, "15": 1000, "18": 100 , "33": 100 , "100": 100 , "150" : 100 , "100_b" : 100 , "150_b" : 100 }
, "log1p" : {"6": 1000, "15": 1000, "18": 100 , "33": 100 , "100": 100 , "150" : 100 , "100_b" : 100 , "150_b" : 100 }
, "log2" : {"6": 1000, "15": 1000, "18": 100 , "33": 100 , "100": 100 , "150" : 100 , "100_b" : 100 , "150_b" : 100 }
, "pow" : {"6": 5 , "15": 10 , "18": 50 , "33": 50 , "100": 50 , "150" : 50 , "100_b" : 50 , "150_b" : 50 }
, "sqrt" : {"6": 5 , "15": 10 , "18": 50 , "33": 50 , "100": 50 , "150" : 50 , "100_b" : 50 , "150_b" : 50 }
, "lgamma" : {"6": 100 , "15": 500 , "18": 1000 , "33": 10000 , "100": 100000, "150" : 100000, "100_b" : 1000000 , "150_b" : 1000000}
, "tgamma" : {"6": 100 , "15": 100 , "18": 1000 , "33": 10000 , "100": 100000, "150" : 100000, "100_b" : 1000000 , "150_b" : 1000000}
, "erfc" : {"6": 100 , "15": 100 , "18": 2000 , "33": 20000 , "100": 200000, "150" : 200000, "100_b" : 4000000 , "150_b" : 8000000}
, "erf" : {"6": 100 , "15": 100 , "18": 5 , "33": 5 , "100": 100 , "150" : 100 , "100_b" : 100 , "150_b" : 100 }
, "modf" : {"6": 10 , "15": 100 , "18": 5000 , "33": 300000 , "100": 10000 , "150" : 100000, "100_b" : 10000 , "150_b" : 10000 }
, "fmod" : {"6": 10 , "15": 100 , "18": 5000 , "33": 10000 , "100": 10000 , "150" : 100000, "100_b" : 10000 , "150_b" : 10000 }
, "remainder" : {"6": 100 , "15": 5000, "18": 5000 , "33": 10000 , "100": 10000 , "150" : 100000, "100_b" : 10000 , "150_b" : 10000 }
, "remquo" : {"6": 100 , "15": 5000, "18": 5000 , "33": 10000 , "100": 10000 , "150" : 100000, "100_b" : 10000 , "150_b" : 10000 }
, "fma" : {"6": 10 , "15": 100 , "18": 10 , "33": 10 , "100": 100 , "150" : 100 , "100_b" : 100 , "150_b" : 1000 }
# Same order of functions as in #include <lib/high-precision/MathComplexFunctions.hpp>
# Complex C++ functions. Start names with "Complex " so that they can sit in the same defaultTolerances dictionary
, "Complex conj" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 1 }
, "Complex real" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 1 }
, "Complex imag" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 1 }
, "Complex abs" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 1 }
, "Complex arg" : {"6": 1 , "15": 1 , "18": 2 , "33": 4 , "100": 8 , "150" : 8 , "100_b" : 8 , "150_b" : 8 }
, "Complex norm" : {"6": 1 , "15": 1 , "18": 2 , "33": 4 , "100": 8 , "150" : 8 , "100_b" : 8 , "150_b" : 8 }
, "Complex proj" : {"6": 1 , "15": 1 , "18": 2 , "33": 4 , "100": 8 , "150" : 8 , "100_b" : 8 , "150_b" : 8 }
, "Complex polar": {"6": 1 , "15": 1 , "18": 2 , "33": 4 , "100": 8 , "150" : 8 , "100_b" : 8 , "150_b" : 8 }
, "Complex sin" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex sinh" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex cos" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex cosh" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex tan" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex tanh" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex asin" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex asinh": {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex acos" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex acosh": {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex atan" : {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex atanh": {"6": 100 , "15": 100 , "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "Complex exp" : {"6": 10 , "15": 10 , "18": 10 , "33": 10 , "100": 10 , "150" : 10 , "100_b" : 100 , "150_b" : 100 }
, "Complex log" : {"6": 1000, "15": 1000, "18": 100 , "33": 100 , "100": 100 , "150" : 100 , "100_b" : 100 , "150_b" : 100 }
, "Complex log10": {"6": 1000, "15": 1000, "18": 100 , "33": 100 , "100": 100 , "150" : 100 , "100_b" : 100 , "150_b" : 100 }
, "Complex pow" : {"6": 1000, "15": 1000, "18": 100 , "33": 100 , "100": 100 , "150" : 100 , "100_b" : 100 , "150_b" : 100 }
, "Complex sqrt" : {"6": 1000, "15": 1000, "18": 100 , "33": 100 , "100": 100 , "150" : 100 , "100_b" : 100 , "150_b" : 100 }
# MathSpecialFunctions
, "cylBesselJ" : {"6": 1000, "15": 1000, "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "factorial" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 50 }
, "laguerre" : {"6": 1000, "15": 1000, "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
, "sphericalHarmonic" : {"6": 1000, "15": 1000, "18": 20000, "33": 4000 , "100": 80000 , "150" : 80000 , "100_b" : 800000 , "150_b" : 800000 }
# these are not tolerances. These are EigenCostRealHP from lib/high-precision/EigenNumTraits.hpp
, "read" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 10000 , "150" : 10000 , "100_b" : 10000 , "150_b" : 10000 }
, "add" : {"6": 1 , "15": 1 , "18": 1 , "33": 2 , "100": 10000 , "150" : 10000 , "100_b" : 10000 , "150_b" : 10000 }
, "mul" : {"6": 1 , "15": 1 , "18": 1 , "33": 2 , "100": 10000 , "150" : 10000 , "100_b" : 10000 , "150_b" : 10000 }
, "cread" : {"6": 2 , "15": 2 , "18": 2 , "33": 2 , "100": 20000 , "150" : 20000 , "100_b" : 20000 , "150_b" : 20000 }
, "cadd" : {"6": 2 , "15": 2 , "18": 2 , "33": 4 , "100": 20000 , "150" : 20000 , "100_b" : 20000 , "150_b" : 20000 }
, "cmul" : {"6": 6 , "15": 6 , "18": 6 , "33": 12 , "100": 60000 , "150" : 60000 , "100_b" : 60000 , "150_b" : 60000 }
# Euler–Mascheroni and Pi constants need higher tolerance in boost cpp_bin_float at very high precisions
, "euler" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 50 }
, "pi" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 50 }
, "logE2" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 50 }
, "catalan" : {"6": 1 , "15": 1 , "18": 1 , "33": 1 , "100": 1 , "150" : 1 , "100_b" : 1 , "150_b" : 50 }
}
# yapf: enable
if (yade.libVersions.getArchitecture() in ['arm64', 's390x']):
for a in ["read", "add", "mul", "cread", "cadd", "cmul"]:
for b in ["18", "33"]:
self.defaultTolerances[a][b] = self.defaultTolerances[a]["100"]
if (yade.libVersions.getArchitecture() == 'ppc64el'):
self.defaultTolerances["asinh"]["100"] = 1e14 # NOTE: something seems to be off with asinh on ppc64el architecture
self.defaultTolerances["asinh"]["150"] = 1e14
self.testLevelsHP = mth.RealHPConfig.getSupportedByMinieigen()
self.baseDigits = mth.RealHPConfig.getDigits10(1)
self.use33or30 = (33 if mth.RealHPConfig.isFloat128Present else 30)
self.builtinHP = {
6: [6, 15, 18, 24, self.use33or30],
15: [15, self.use33or30]
} # higher precisions are multiplies of baseDigits, see NthLevelRealHP in lib/high-precision/RealHP.hpp
if (self.testRecordingMode):
self.startRecordingErrors()
def tearDown(self):
if (self.testRecordingMode):
if (self.totalCount != 0):
import pickle
fname = "/tmp/" + str(
self.id().split('.')[-1] + "_dig" + str(self.baseDigits) + self.extraName + "_ex" +
str(mth.RealHPConfig.extraStringDigits10) + "__" + str(self.totalCount)
) + ".pickle"
print(str(self.newTolerances) + "\n\n saving: " + fname)
pickle.dump(self.newTolerances, open(fname, "wb"))
# this is how I sort by error, to find the worst performing functions:
# d=pickle.load( open( "testMathFunctions_dig33_ex4__18000.pickle", "rb" ) );sorted([(d[key]['33'][0],key) for key in d], key=lambda tup: tup[0])
def getDefaultTolerance(self, name, multiplyByTolerance=True):
mult = self.tolerance
key = str(self.digs0) + self.extraName
if (self.testRecordingMode):
if (name in self.newTolerances and key in self.newTolerances[name] and self.getMpmath().isfinite(self.newTolerances[name][key][0])):
return self.newTolerances[name][key][0] * mult
if (not multiplyByTolerance):
mult = 1
dictForThisFunc = self.defaultTolerances[name]
if (key in dictForThisFunc):
return dictForThisFunc[key] * mult
## lower than 33 digits are all hardware precision: 6, 15, 18, 33 digits. But 4*float is 24 digits, and it can be achieved by MPFR only so add exception for 24 also.
if (yade.libVersions.getArchitecture() == 'ppc64el'): # long double on ppc64el has 31 digits10
self.assertTrue(self.digs0 > 33 or self.digs0 in [24, 30, 31])
else:
self.assertTrue(self.digs0 > 33 or self.digs0 in [24, 30]) ## 33 was here before
low = dictForThisFunc["100" + self.extraName]
high = dictForThisFunc["150" + self.extraName]
import numpy
return numpy.interp(self.digs0, [100, 150], [low, high]) * mult
def storeArgs(self, args):
self.storedArgs = args
def storeDefaultTolerance(self, error, name):
newFactor = (error / self.tolerance) * self.getMpmath().mpf(1.01)
oldFactor = newFactor
key = str(self.digs0) + self.extraName
if (name in self.newTolerances):
if (key in self.newTolerances[name] and self.getMpmath().isfinite(self.newTolerances[name][key][0])):
oldFactor = self.newTolerances[name][key][0]
else:
self.newTolerances[name] = {}
if (newFactor >= oldFactor):
self.newTolerances[name][key] = (newFactor, self.storedArgs)
def lgamma(self, r):
mpmath.mp.dps = mth.RealHPConfig.getDigits10(self.maxN) + mth.RealHPConfig.extraStringDigits10
return mpmath.log(abs(mpmath.gamma(r)))
def startRecordingErrors(self):
self.newTolerances = {}
self.maxN = mth.RealHPConfig.getSupportedByMinieigen()[-1]
if (mth.RealHPConfig.getDigits10(self.maxN) < 490):
print(
"\n*****\nWarning: recording errors uses less than 490 digits precision. See commits ef1fed55f 015292c0a, they were removed afer this error search was finished.\n*****\n"
)
self.maxHPn = getattr(mth, "HP" + str(self.maxN))
# make maxHPn very similar to mpmath - emulate it.
self.maxHPn.mpf = mpmath.mpf
self.maxHPn.mpc = mpmath.mpc
self.maxHPn.power = self.maxHPn.pow
self.maxHPn.pi = self.maxHPn.Pi()
self.maxHPn.euler = self.maxHPn.Euler()
self.maxHPn.catalan = self.maxHPn.Catalan()
if (
self.maxN > mth.RealHPConfig.workaroundSlowBoostBinFloat
): # these functions are unavailable in C++ (because 'import minieigenHP' is too slow for cpp_bin_float), so emulate them
self.maxHPn.lgamma = self.lgamma
self.maxHPn.tgamma = mpmath.gamma
self.maxHPn.gamma = mpmath.gamma
self.maxHPn.erf = mpmath.erf
self.maxHPn.erfc = mpmath.erfc
else:
self.maxHPn.gamma = self.maxHPn.tgamma
self.storeArgs((mpmath.mpf('nan'),))
self.totalCount = 0
def testBasicHP(self):
if (self.testRecordingMode):
return # skip this test if recording.
if (mth.RealHPConfig.isEnabledRealHP):
ec = (1, 2, 3, 4, 8, 10, 20) # (1,2,3,4,5,6,7,8,9,10,20) #
mn = (1, 2) # ec # use these if changed something in lib/high-precision/RealHPConfig.hpp
self.assertEqual(ec, mth.RealHPConfig.getSupportedByEigenCgal())
self.assertEqual(mn, mth.RealHPConfig.getSupportedByMinieigen())
if (not self.hasMpfr()):
self.assertEqual(2, mth.RealHPConfig.workaroundSlowBoostBinFloat)
else:
self.assertEqual(ec[-1], mth.RealHPConfig.workaroundSlowBoostBinFloat)
else:
self.assertEqual((1,), mth.RealHPConfig.getSupportedByEigenCgal())
self.assertEqual((1,), mth.RealHPConfig.getSupportedByMinieigen())
self.assertEqual(1, mth.RealHPConfig.workaroundSlowBoostBinFloat)
def getDigitsHP(self, N):
ret = None
if (self.baseDigits in self.builtinHP) and (N <= len(self.builtinHP[self.baseDigits])):
ret = self.builtinHP[self.baseDigits][N - 1]
else:
ret = self.baseDigits * N
self.assertEqual(ret, mth.RealHPConfig.getDigits10(N))
return ret
def adjustDigs0(self, N, HPn, MPn):
self.HPnHelper = HPn
self.digs0 = self.getDigitsHP(N)
# tolerance = 1.2×10⁻ᵈ⁺¹, where ᵈ==self.digs0
# so basically we store one more decimal digit, and expect one less decimal digit. That amounts to ignoring one (two, if the extra one is counted) least significant digits.
self.tolerance = HPn.Real((MPn.mpf(10)**(-self.digs0 + 1)) * MPn.mpf("1.2"))
#self.bits = MPn.ceil(MPn.mpf(self.digs0)/(MPn.log(2)/MPn.log(10)))+1 # Maybe a bug report against MPFR + cpp_bin_float? They don't use this formula for number of bits
self.bits = MPn.ceil(
MPn.mpf(self.digs0) / (0.301)
) + 1 # it is reproducing MPFR's formula for number of bits. Discovered by experiments. Adjustments are possible.
mpmathVsMpfrBits = int(
self.bits / 2085
) # adjust discrepency between mpmath and MPFR due to incorrect log10/log2 value (above line). The 2085 was found empirically.
# mpmath has 5 more internal bits, use its mechanisms to extract epsilon
self.getMpmath().mp.dps = self.digs0 + 1
self.expectedEpsilon = (2**5) * self.getMpmath().eps() / (2**mpmathVsMpfrBits)
# now go back to using extraStringDigits10
self.getMpmath().mp.dps = self.digs0 + mth.RealHPConfig.extraStringDigits10
if (self.digs0 == 6): # float case
self.bits = 24
self.expectedEpsilon = 1.1920928955078125e-07
if (self.digs0 == 15): # double case
self.bits = 53
self.expectedEpsilon = 2.220446049250313e-16
if (self.digs0 == 18): # long double case
self.bits = 64
self.expectedEpsilon = MPn.mpf('1.084202172485504433993e-19')
if ((self.digs0 == 31) and (yade.libVersions.getArchitecture() == 'ppc64el')): # long double on ppc64el
self.bits = 106
#self.expectedEpsilon = MPn.mpf('2.465190328815661891911651766508706967e-32') # value for 1 + epsilon
self.expectedEpsilon = MPn.mpf(
'4.9406564584124654417656879286822137013e-324'
) # note: ppc64el uses 0+epsilon, not 1+epsilon. This can be misleading.
if (self.digs0 == 33): # float128 case
self.bits = 113
self.expectedEpsilon = MPn.mpf('1.925929944387235853055977942584926994e-34')
if (self.needsMpmathAtN(N)):
self.maxval = (MPn.mpf(1) - self.expectedEpsilon) * MPn.power(2, HPn.max_exp2)
else:
import sys
self.maxval = sys.float_info.max
if (self.nowUsesBoostBinFloat(N)):
self.extraName = "_b"
else:
self.extraName = ""
def getMpmath(self):
if (self.needsMpmathAtN(self.currentN)):
return mpmath
else:
return testMathHelper
def runCheck(self, N, func):
if (self.testRecordingMode and N == self.maxN):
return # no need to test maxN against itself. It is for testing lower precisions against it.
self.currentN = N
# the same as the line 'std::string name = "HP" + boost::lexical_cast<std::string>(N)' in function registerInScope in _math.cpp
HPn = getattr(mth, "HP" + str(N))
if (not self.testRecordingMode):
MPn = self.getMpmath()
else:
MPn = self.maxHPn # we are recording the errors, do all the tests against the max precision available
if (N == 1):
self.adjustDigs0(N, mth, MPn)
func(N, mth, MPn) # test global scope functions with RealHP<1>
self.adjustDigs0(N, HPn, MPn)
func(N, HPn, MPn) # test scopes HP1, HP2, etc
def printOnce(self, functionName, a):
MPn = self.getMpmath()
if (functionName and (functionName not in self.printedAlready) and (not MPn.isnan(abs(a)))):
self.printedAlready.add(functionName)
print(functionName.ljust(15) + " : " + a.__repr__())
def checkRelativeError(self, a, b, tol=None, functionName=None, isComplex=False):
if (functionName and self.incompleteComplex() and functionName[0:7] == "Complex"):
# don't check complex functions
return
MPn = self.getMpmath()
prevDps = MPn.mp.dps
if (self.testRecordingMode):
MPn.mp.dps = mth.RealHPConfig.getDigits10(self.maxN) + mth.RealHPConfig.extraStringDigits10
denominator = max(abs(a), abs(b)) # avoid division by zero
if (denominator == 0): # they are both equal to zero
error = 0
else:
if isComplex:
error = abs((MPn.mpc(a) - MPn.mpc(b)) / MPn.mpc(denominator))
else:
error = abs((MPn.mpf(a) - MPn.mpf(b)) / MPn.mpf(denominator))
if (abs(b) <= self.maxval and abs(b) >= self.HPnHelper.smallest_positive()):
#print("a= ",a," b= ",b," smallest=",self.HPnHelper.smallest_positive(), " maxval=",self.maxval)
self.printOnce(functionName, a)
if ((not MPn.isfinite(a)) or (not MPn.isfinite(b))):
if ((functionName != "lgamma") and (not self.testRecordingMode)): # lgamma triggers this warning too often.
print(
"\033[93m Warning: \033[0m got NaN or Inf, cannot verify if: ", a, " == ", b,
" that was for function: \033[93m ", functionName, " \033[0m"
)
else:
if (tol != None):
#print("a=",a," b=",b," tol=",tol)
self.assertLessEqual(error, tol)
else:
if (functionName in self.defaultTolerances):
if (self.testRecordingMode):
self.storeDefaultTolerance(error, functionName)
defaultToleranceForThisFunction = self.getDefaultTolerance(functionName)
#print(defaultToleranceForThisFunction," ---- ",functionName)
self.assertLessEqual(error, defaultToleranceForThisFunction)
else:
self.assertLessEqual(error, self.tolerance)
elif (not self.testRecordingMode):
print(
"Skipping ", functionName, " check, the builtin number: ", a, " cannot have value outside of its possible repesentation: ", b,
", because it has only ", self.digs0, " digits."
)
MPn.mp.dps = prevDps
def checkRelativeComplexError(self, a, b, tol=None, functionName=None):
self.printOnce(functionName, a)
self.checkRelativeError(abs(a), abs(b), tol, functionName, True)
def oneArgMathCheck(self, N, HPn, MPn, r):
# note: cos, tan, sin, lgamma, tgamma get wildly inaccurrate when |arg| > 20. Errors are in the range log₁₀(8000000)≈7 decimal places for most of RealHP<…> types.
# these functions become more or less useless. So better to measure error in a usable range. I arbitrarily set it to 4*Pi and 20.
# This strange behavior is explained by the error in the remainder(…) for which I do not restrict arguments (so you can look up its error in the table). These trig
# functions try to remove periodicity by calculating remainder from division by Pi, but they can only be as good as the remainder calculation itself. And this calculation
# cannot produce more precision than the number already has, after its first few digits are cut-off by the remainder calculation.
cut1 = HPn.roundTrip(r % HPn.Real(self.getMpmath().pi * 4)) # the HPn.identity(…) call is to cut the digits to those representible in HPn
cut2 = HPn.roundTrip(r % 20)
self.checkRelativeError(HPn.sin(cut1), MPn.sin(cut1), functionName="sin")
self.checkRelativeError(HPn.sinh(r), MPn.sinh(r), functionName="sinh")
self.checkRelativeError(HPn.cos(cut1), MPn.cos(cut1), functionName="cos")
self.checkRelativeError(HPn.cosh(r), MPn.cosh(r), functionName="cosh")
self.checkRelativeError(HPn.tan(cut1), MPn.tan(cut1), functionName="tan")
self.checkRelativeError(HPn.tanh(r), MPn.tanh(r), functionName="tanh")
# check math functions, but ensure that input arguments produce real (not complex) results
self.checkRelativeError(HPn.abs(r), abs(r), functionName="abs")
self.checkRelativeError(HPn.acos(r % 1), MPn.acos(r % 1), functionName="acos")
self.checkRelativeError(HPn.acosh(abs(r) + 1), MPn.acosh(abs(r) + 1), functionName="acosh")
self.checkRelativeError(HPn.asin(r % 1), MPn.asin(r % 1), functionName="asin")
self.checkRelativeError(HPn.asinh(r), MPn.asinh(r), functionName="asinh")
self.checkRelativeError(HPn.atan(r), MPn.atan(r), functionName="atan")
self.checkRelativeError(HPn.atanh(r % 1), MPn.atanh(r % 1), functionName="atanh")
self.checkRelativeError(HPn.cbrt(abs(r)), MPn.cbrt(abs(r)), functionName="cbrt")
self.assertEqual(HPn.ceil(r), MPn.ceil(r))
self.checkRelativeError(HPn.exp(r), MPn.exp(r), functionName="exp")
self.checkRelativeError(HPn.sqrt(abs(r)), MPn.sqrt(abs(r)), functionName="sqrt")
self.checkRelativeError(HPn.exp2(r), MPn.power(2, r), functionName="exp2")
self.checkRelativeError(HPn.expm1(r), MPn.expm1(r), functionName="expm1")
self.assertEqual(HPn.floor(r), MPn.floor(r))
#print(HPn.ilogb(r).__repr__()) # ilogb is not present in mpmath
if (N <= mth.RealHPConfig.workaroundSlowBoostBinFloat):
#print(" N=",N , " digits10=", yade.math.RealHPConfig.getDigits10(N) ," self.expectedEpsilon = ",self.expectedEpsilon, " r=",r)
if (self.testRecordingMode):
self.checkRelativeError(HPn.lgamma(cut2), self.maxHPn.lgamma(cut2), functionName="lgamma")
self.checkRelativeError(HPn.tgamma(cut2), self.maxHPn.tgamma(cut2), functionName="tgamma")
else:
self.checkRelativeError(HPn.lgamma(cut2), MPn.log(abs(MPn.gamma(cut2))), functionName="lgamma")
self.checkRelativeError(HPn.tgamma(cut2), MPn.gamma(cut2), functionName="tgamma")
self.checkRelativeError(HPn.erf(r), MPn.erf(r), functionName="erf")
self.checkRelativeError(HPn.erfc(r), MPn.erfc(r), functionName="erfc")
self.checkRelativeError(HPn.log(abs(r) + self.tolerance), MPn.log(abs(r) + self.tolerance), functionName="log")
self.checkRelativeError(HPn.log10(abs(r) + self.tolerance), MPn.log10(abs(r) + self.tolerance), functionName="log10")
self.checkRelativeError(HPn.log1p(abs(r) + self.tolerance), MPn.log(1 + abs(r) + self.tolerance), functionName="log1p")
self.checkRelativeError(HPn.log2(abs(r) + self.tolerance), MPn.log(abs(r) + self.tolerance) / MPn.log(2), functionName="log2")
#print(HPn.logb(r).__repr__()) # logb is not present in mpmath
self.assertEqual(HPn.rint(r), round(r))
self.assertTrue((HPn.round(r) == round(r)) or (r % 1 == 0.5)) # ignore rounding 0.5 up or down.
self.assertEqual(HPn.trunc(abs(r)), int(abs(r)))
self.checkRelativeError(HPn.fabs(r), abs(r), functionName="fabs")
pair = HPn.frexp(abs(r))
self.checkRelativeError(abs(r), pair[0] * MPn.power(2, pair[1]), functionName="frexp")
pair = HPn.modf(abs(r))
self.checkRelativeError(pair[0], (abs(r)) % 1, functionName="modf")
self.assertEqual(pair[1], int(abs(r)))
#self.assertEqual(HPn.frexp(abs(r)),HPn.frexp_c_test(abs(r)))
#self.assertEqual(HPn.modf(abs(r)),HPn.modf_c_test(abs(r)))
if (r == 0):
self.assertEqual(HPn.sgn(r), 0)
self.assertEqual(HPn.sign(r), 0)
if (r > 0):
self.assertEqual(HPn.sgn(r), 1)
self.assertEqual(HPn.sign(r), 1)
if (r < 0):
self.assertEqual(HPn.sgn(r), -1)
self.assertEqual(HPn.sign(r), -1)
self.checkCgalNumTraits(HPn, MPn, r)
# One arg MathSpecialFunctions
self.checkRelativeError(HPn.factorial(int(abs(r))), MPn.factorial(int(abs(r))), functionName="factorial")
def checkCgalNumTraits(self, HPn, MPn, r):
if (HPn.testCgalNumTraits == False):
print("Skipping test of CgalNumTraits")
return
self.assertEqual(HPn.CGAL_Is_valid(r), True)
if (r != 0):
self.checkRelativeError(HPn.CGAL_Square(r), MPn.power(r, 2), functionName="pow")
self.checkRelativeError(HPn.CGAL_Sqrt(abs(r)), MPn.sqrt(abs(r)), functionName="sqrt")
for kk in range(5):
k = kk + 1
self.checkRelativeError(HPn.CGAL_Kth_root(k, abs(r)), MPn.power(abs(r), 1 / MPn.mpf(k)), functionName="pow")
# CGAL uses double for intervals
interval = HPn.CGAL_To_interval(r)
self.checkRelativeError(r, interval[0], 1e-14)
self.checkRelativeError(r, interval[1], 1e-14)
self.assertEqual(HPn.CGAL_Is_finite(r), True)
if (r == 0):
self.assertEqual(HPn.CGAL_Sgn(r), 0)
if (r > 0):
self.assertEqual(HPn.CGAL_Sgn(r), 1)
if (r < 0):
self.assertEqual(HPn.CGAL_Sgn(r), -1)
self.assertEqual(HPn.CGAL_Sgn(0), 0)
self.assertEqual(HPn.CGAL_Sgn(2.5), 1)
self.assertEqual(HPn.CGAL_Sgn(-2.3), -1)
def testInfinityNaN(self):
for N in self.testLevelsHP:
self.runCheck(N, self.HPtestInfinityNaN)
def HPtestInfinityNaN(self, N, HPn, MPn):
if (HPn.hasInfinityNan == False):
print("Skipping inf,nan regular test\n")
print("\033[91m *** Warning: usually YADE needs Inf and NaN for most of the calculations. *** \033[0m")
return
self.assertEqual(HPn.isinf(HPn.Real(1)), False)
self.assertEqual(HPn.isinf(HPn.Real('nan')), False)
self.assertEqual(HPn.isinf(HPn.Real('inf')), True)
self.assertEqual(HPn.isnan(HPn.Real(1)), False)
self.assertEqual(HPn.isnan(HPn.Real('nan')), True)
self.assertEqual(HPn.isnan(HPn.Real('inf')), False)
self.assertEqual(HPn.isfinite(HPn.Real(1)), True)
self.assertEqual(HPn.isfinite(HPn.Real('nan')), False)
self.assertEqual(HPn.isfinite(HPn.Real('inf')), False)
def testRealHPDiagnostics(self):
for N in self.testLevelsHP:
self.runCheck(N, self.HPtestRealHPDiagnostics)
def HPtestRealHPDiagnostics(self, N, HPn, MPn):
import random
source = '1'
for i in range(mth.getDigits2(N) - 1):
source += random.choice(['0', '1'])
for m in (
list(self.testLevelsHP) + list(reversed(self.testLevelsHP))
): # goes both directions, because that's how I discovered a small mistake in ToFromPythonConverter.hpp
if (m >= N):
HPm = getattr(mth, "HP" + str(m))
toHPn = getattr(HPm, "toHP" + str(N))
testNum = HPm.fromBits(source)
if (m == N):
source2 = source[:-1] + '1'
testNum2 = HPm.fromBits(source2)
self.assertLessEqual(HPm.getFloatDistanceULP(testNum, testNum2), 1)
source3 = source[:-2] + '11'
testNum3 = HPm.fromBits(source3)
self.assertLessEqual(HPm.getFloatDistanceULP(testNum, testNum3), 3)
if (mth.getDigits2(m) in [24, 53, 64, 113]): # don't check MPFR, cpp_bin_float.
self.assertTrue(
source in HPm.getRawBits(testNum)
) # checks only 'in', because sign+exponent (usually in front of raw bits) are architecture-specific.
self.assertEqual(HPm.getDecomposedReal(testNum)['bits'], source.ljust(mth.getDigits2(m), '0'))
self.assertEqual(HPn.fromBits(source), toHPn(testNum))
if (mth.getDigits2(N) == 24):
self.assertEqual(HPn.getDemangledName(), 'float')
if (mth.getDigits2(N) == 53):
self.assertEqual(HPn.getDemangledName(), 'double')
if (mth.getDigits2(N) == 64):
self.assertTrue('long double' in HPn.getDemangledName())
if (mth.getDigits2(N) in [113, 106]):
if (yade.libVersions.getArchitecture() == 'arm64'):
self.assertTrue('long double' in HPn.getDemangledName())
else:
self.assertTrue('float128' in HPn.getDemangledName())
def bitsToLevelHP(self, bits):
N = -1
for nn in self.testLevelsHP:
if (mth.getDigits2(nn) == bits):
N = nn
break
return N
def testRealHPErrors(self):
if (len(self.testLevelsHP) < 2):
return
testUlpRandom = yade.math.getRealHPErrors(
list(self.testLevelsHP), testCount=2000, minX=-100, maxX=100, useRandomArgs=True, printEveryNth=100000, extraChecks=False
)
testUlpLinear = yade.math.getRealHPErrors(
list(self.testLevelsHP), testCount=2000, minX=-100, maxX=100, useRandomArgs=False, printEveryNth=100000, extraChecks=False
)
self.showRealHPResults(testUlpRandom)
self.showRealHPResults(testUlpLinear)
self.processRealHPResults(testUlpRandom)
self.processRealHPResults(testUlpLinear)
def showRealHPResults(self, testULP):
#print(testULP)
for func in testULP:
for bits in testULP[func]:
ulp = testULP[func][bits][1]
if (ulp > 4):
N = self.bitsToLevelHP(bits)
print(
"\033[93mWarning:\033[0m ULP error of\033[91m", func, "\033[0musing RealHP<", N, ">, ", bits, "bits, with arg:",
testULP[func][bits][0], "is ULP=\033[93m", ulp, "\033[0m"
)
def getBoostComplexTolerance(self, func, tol, bits):
# g++ flags: -Ofast -march=native -mtune=native -fno-associative-math -fno-finite-math-only -fsigned-zeros
isFast = self.isFastNative()
mpfr = not self.nowUsesBoostBinFloat(self.bitsToLevelHP(bits))
longDouble = (bits == 64) # C++ double has 53
# The self.defaultTolerances is about errors found on python side. This one is more precise about ULP errors found on C++ side.
complexTolerancesInUnitsOfULP = {
"complex acos imag": 1e5,
"complex acos real": 3e5,
"complex asin imag": 3e5,
"complex asin real": 3e5,
"complex asinh imag": 3e5,
"complex asinh real": 1e5,
"complex atan imag": 6e6,
"complex atanh real": 5e5 if mpfr else 8e8, # boost::cpp_bin_float has larger error
"complex cos imag": 8 if mpfr else 4e5,
"complex cos real": 8 if mpfr else 2e5,
"complex cosh imag": 8 if mpfr else 6e5,
"complex cosh real": 8 if mpfr else 7e5,
"complex exp imag": 8 if mpfr else 4e5,
"complex exp real": 8 if mpfr else 7e5,
"complex polar imag": 8 if mpfr else 5e5,
"complex polar real": 8 if mpfr else 1e6,
"complex pow imag": 3e7 if isFast else
(9e6 if longDouble else
(4e6 if mpfr else 7e8)), # std::complex<double> -Ofast has 3e7 error then std::complex<long double> has 9e6.
"complex pow real": 5e7 if self.incompleteComplex() else (4e6 if mpfr else 2e7),
"complex sin imag": 8 if mpfr else 2e5,
"complex sin real": 8 if mpfr else 4e5,
"complex sinh imag": 8 if mpfr else 6e5,
"complex sinh real": 8 if mpfr else 7e5,
"complex tan imag": 8 if mpfr else 520,
"complex tan real": 8 if mpfr else 500,
"complex tanh imag": 8 if mpfr else 500,
"complex tanh real": 8 if mpfr else 500,
}
# FIXME: These tolerances ↑ also need to be reported to boost. But that's a smaller error anyway. the complex tan, tanh had error 1e38 ULP.
# The values here are chosen only for std::complex<long double>, complex_adaptor<cpp_bin_float_45>, mpc_complex_150.
# Other precisions may vary slightly.
if ((func in complexTolerancesInUnitsOfULP)):
tol = complexTolerancesInUnitsOfULP[func]
return tol
def getMathSpecialTolerance(self, func, tol, bits):
# The self.defaultTolerances is about errors found on python side. This one is more precise about ULP errors found on C++ side.
mpfr = not self.nowUsesBoostBinFloat(self.bitsToLevelHP(bits))
tolerancesInUnitsOfULP = {
"cylBesselJ": 6e5,
"laguerre": 1e6,
"complex sphericalHarmonic imag": 5e7,
"complex sphericalHarmonic real": 3e7 if mpfr else 2e8,
}
if ((func in tolerancesInUnitsOfULP)):
tol = tolerancesInUnitsOfULP[func]
return tol
def processRealHPResults(self, testULP):
for func in testULP:
for bits in testULP[func]:
tolerateErrorULP = 8
if (self.nowUsesBoostBinFloat(self.bitsToLevelHP(bits))):
tolerateErrorULP = 256 # cpp_bin_float has larger errors
if (func in ["tgamma", "acos", "erfc"]):
tolerateErrorULP = 50000
elif (func == "lgamma"):
tolerateErrorULP = 1e10
elif (func in ["sin", "cos", "tan", "fma"]):
tolerateErrorULP = 2e8
boostVer = yade.libVersions.getVersion('boost')
tolerateErrorULP = self.getBoostComplexTolerance(func, tolerateErrorULP, bits)
tolerateErrorULP = self.getMathSpecialTolerance(func, tolerateErrorULP, bits)
# Architecture specific workarounds.
if (yade.libVersions.getArchitecture() == 'i386'):
if (func == 'acosh'): # the failing function name is printed in red.
tolerateErrorULP = 32
if (yade.libVersions.getArchitecture() in ['ppc64el', 's390x']):
if ('sphericalHarmonic' in func or func in ['complex tan real', 'complex tanh imag', 'cylBesselJ']):
tolerateErrorULP = 2e19 # TODO: these migh need a fix later. Or it may be just older boost library
if (yade.math.RealHPConfig.getDigits10(1) == 31): # ppc64el with long double
tolerateErrorULP = 40000
if (func in ['asinh']):
tolerateErrorULP = 4e15 # NOTE: something seems to be off with asinh on ppc64el
if (func in ['complex pow imag', 'complex pow real']):
tolerateErrorULP = 2e6
if ('sphericalHarmonic' in func or func in ['complex tan real', 'complex tanh imag']):
tolerateErrorULP = 4e34
# DONE: file a bug report about higher precision versions of these two functions. They have large error: log2(300000000)≈28.1 incorrect bits.
# https://github.com/boostorg/multiprecision/issues/262
# https://github.com/boostorg/multiprecision/issues/264
# when it's fixed we can check boost version and skip this line below.
if ((func in ["complex tan real", "complex tanh imag"]) and (boostVer < (1, 76, 0))):
# for older boost there's nothing we can do. We have a large error: 1e38 ULP
pass
else:
ulp = testULP[func][bits][1]
if (ulp > tolerateErrorULP):
print("\n\033[91mError with: ", func, "\033[0m having ULP=", ulp)
self.assertLessEqual(ulp, tolerateErrorULP)
def testCgalNumTraits(self):
for N in self.testLevelsHP:
self.runCheck(N, self.HPtestCgalNumTraits)
def HPtestCgalNumTraits(self, N, HPn, MPn):
if (HPn.testCgalNumTraits == False):
print("Skipping test of CgalNumTraits")
return
self.checkCgalNumTraits(HPn, MPn, 0)
self.checkCgalNumTraits(HPn, MPn, 0.5)
self.checkCgalNumTraits(HPn, MPn, -1.5)
self.checkCgalNumTraits(HPn, MPn, 55.5)
self.assertEqual(HPn.CGAL_Is_valid(HPn.Real(1)), True)
self.assertEqual(HPn.CGAL_Is_valid(HPn.Real('nan')), False)
self.assertEqual(HPn.CGAL_Is_valid(HPn.Real('inf')), True)
self.assertEqual(HPn.CGAL_Is_finite(HPn.Real(1)), True)
self.assertEqual(HPn.CGAL_Is_finite(HPn.Real('nan')), False)
self.assertEqual(HPn.CGAL_Is_finite(HPn.Real('inf')), False)
self.assertEqual(HPn.CGAL_simpleTest(), MPn.mpf("3.0"))
def twoArgMathCheck(self, HPn, MPn, r1, r2):
# same order of complex functions as in lib/high-precision/MathComplexFunctions.hpp , py/high-precision/_math.cpp
self.checkRelativeComplexError(HPn.conj(HPn.Complex(r1, r2)), MPn.conj(MPn.mpc(r1, r2)), functionName="Complex conj")
self.checkRelativeComplexError(HPn.real(HPn.Complex(r1, r2)), r1, functionName="Complex real")
self.checkRelativeComplexError(HPn.imag(HPn.Complex(r1, r2)), r2, functionName="Complex imag")
self.checkRelativeComplexError(HPn.abs(HPn.Complex(r1, r2)), abs(MPn.mpc(r1, r2)), functionName="Complex abs")
self.checkRelativeError(HPn.arg(HPn.Complex(r1, r2)), MPn.phase(MPn.mpc(r1, r2)), functionName="Complex arg")
self.checkRelativeError(
HPn.squaredNorm(HPn.Complex(r1, r2)), MPn.norm(MPn.mpc(r1, r2)) * MPn.norm(MPn.mpc(r1, r2)), functionName="Complex norm"
)
# for now skip testing C++ std::proj, see note in py/tests/testMathHelper.py
self.checkRelativeComplexError(HPn.polar(r1, r2), MPn.rect(r1, r2), functionName="Complex polar")
self.checkRelativeComplexError(HPn.sin(HPn.Complex(r1, r2)), MPn.sin(MPn.mpc(r1, r2)), functionName="Complex sin")
self.checkRelativeComplexError(HPn.sinh(HPn.Complex(r1, r2)), MPn.sinh(MPn.mpc(r1, r2)), functionName="Complex sinh")
self.checkRelativeComplexError(HPn.cos(HPn.Complex(r1, r2)), MPn.cos(MPn.mpc(r1, r2)), functionName="Complex cos")
self.checkRelativeComplexError(HPn.cosh(HPn.Complex(r1, r2)), MPn.cosh(MPn.mpc(r1, r2)), functionName="Complex cosh")
self.checkRelativeComplexError(HPn.tan(HPn.Complex(r1, r2)), MPn.tan(MPn.mpc(r1, r2)), functionName="Complex tan")
self.checkRelativeComplexError(HPn.tanh(HPn.Complex(r1, r2)), MPn.tanh(MPn.mpc(r1, r2)), functionName="Complex tanh")
self.checkRelativeComplexError(HPn.asin(HPn.Complex(r1, r2)), MPn.asin(MPn.mpc(r1, r2)), functionName="Complex asin")
self.checkRelativeComplexError(HPn.asinh(HPn.Complex(r1, r2)), MPn.asinh(MPn.mpc(r1, r2)), functionName="Complex asinh")
self.checkRelativeComplexError(HPn.acos(HPn.Complex(r1, r2)), MPn.acos(MPn.mpc(r1, r2)), functionName="Complex acos")
self.checkRelativeComplexError(HPn.acosh(HPn.Complex(r1, r2)), MPn.acosh(MPn.mpc(r1, r2)), functionName="Complex acosh")
self.checkRelativeComplexError(HPn.atan(HPn.Complex(r1, r2)), MPn.atan(MPn.mpc(r1, r2)), functionName="Complex atan")
self.checkRelativeComplexError(HPn.atanh(HPn.Complex(r1, r2)), MPn.atanh(MPn.mpc(r1, r2)), functionName="Complex atanh")
self.checkRelativeComplexError(HPn.exp(HPn.Complex(r1, r2)), MPn.exp(MPn.mpc(r1, r2)), functionName="Complex exp")
self.checkRelativeComplexError(HPn.log(HPn.Complex(r1, r2)), MPn.log(MPn.mpc(r1, r2)), functionName="Complex log")
self.checkRelativeComplexError(HPn.log10(HPn.Complex(r1, r2)), MPn.log10(MPn.mpc(r1, r2)), functionName="Complex log10")
self.checkRelativeComplexError(
HPn.pow(HPn.Complex(r1, r2), HPn.Complex(r1 + r2, r1 - r2)), (MPn.mpc(r1, r2)**MPn.mpc(r1 + r2, r1 - r2)), functionName="Complex pow"
)
self.checkRelativeComplexError(HPn.sqrt(HPn.Complex(r1, r2)), MPn.sqrt(MPn.mpc(r1, r2)), functionName="Complex sqrt")
# Two argument MathSpecialFunctions
if (self.needsMpmathAtN(self.currentN)): # can test Bessel only if mpmath is available.
# first is yade.math function here ↓ , next is mpmath function here ↓
self.checkRelativeComplexError(HPn.cylBesselJ(int(abs(r1)), r2), MPn.besselj(int(abs(r1)), r2), functionName="cylBesselJ")
# Other, non complex functions
self.checkRelativeError(HPn.atan2(r1, r2), MPn.atan2(r1, r2), functionName="atan2")
self.checkRelativeError(HPn.fmod(abs(r1), abs(r2)), MPn.fmod(abs(r1), abs(r2)), functionName="fmod")
self.checkRelativeError(HPn.hypot(r1, r2), MPn.hypot(r1, r2), functionName="hypot")
self.checkRelativeError(HPn.max(r1, r2), max(r1, r2), functionName="max")
self.checkRelativeError(HPn.min(r1, r2), min(r1, r2), functionName="min")
self.checkRelativeError(HPn.pow(abs(r1), r2), MPn.power(abs(r1), r2), functionName="pow")
self.checkRelativeError(HPn.remainder(abs(r1), abs(r2)), abs(r1) - round(abs(r1) / abs(r2)) * abs(r2), functionName="remainder")
pair = HPn.remquo(abs(r1), abs(r2))
self.checkRelativeError(pair[0], abs(r1) - round(abs(r1) / abs(r2)) * abs(r2), functionName="remquo")
self.assertEqual(pair[1] % 8, round(abs(r1 / r2)) % 8)
self.checkRelativeError(HPn.ldexp(r1, int(r2)), MPn.mpf(r1) * MPn.power(2, int(r2)), functionName="ldexp")
def threeArgMathCheck(self, HPn, MPn, r1, r2, r3):
self.checkRelativeError(HPn.fma(r1, r2, r3), (MPn.mpf(r1) * r2) + r3, functionName="fma")
# Three argument MathSpecialFunctions
if (yade.config.highPrecisionMpmath == True): # can test Bessel and sphericalHarmonic only if mpmath is available.
# first is yade.math function here ↓ , next is mpmath function here ↓
self.checkRelativeComplexError(
HPn.laguerre(int(abs(r1)), int(abs(r2)), r3), mpmath.laguerre(int(abs(r1)), int(abs(r2)), r3), functionName="laguerre"
)
theta = r2 % self.getMpmath().pi
phi = r2 % (self.getMpmath().pi * 2)
self.checkRelativeComplexError(
HPn.sphericalHarmonic(int(abs(r1)), int(abs(r1)), theta, phi),
mpmath.spherharm(int(abs(r1)), int(abs(r1)), theta, phi),
functionName="sphericalHarmonic"
)
def testMathFunctions(self):
for N in self.testLevelsHP:
self.printedAlready = set()
self.runCheck(N, self.HPtestMathFunctions)
def HPtestMathFunctions(self, N, HPn, MPn):
self.assertEqual(HPn.defprec, self.bits)
zz = MPn.acos(0)
#print(zz.__repr__())
#print("zz:",hex(id(zz)))
#print("mpmath:",hex(id(mpmath)))
a = HPn.Var()
if (type(a.val) != float):
a.val = zz
if (not self.testRecordingMode):
self.assertEqual(MPn.mp.dps, self.digs0 + mth.RealHPConfig.extraStringDigits10)
#print("---- a.val=",a.val.__repr__())
#print("---- zz =",zz .__repr__())
#print("---- DPS =",mpmath.mp.dps)
#print("---- abs =",abs(MPn.mpf(a.val-zz)))
#print("---- 10** =",self.tolerance)
self.checkRelativeError(a.val, zz)
self.assertEqual(HPn.IsInteger, 0)
self.assertEqual(HPn.IsSigned, 1)
self.assertEqual(HPn.IsComplex, 0)
if (self.bits >= 64):
self.assertEqual(HPn.RequireInitialization, 1)
else:
self.assertEqual(HPn.RequireInitialization, 0)
self.assertGreaterEqual(HPn.ReadCost, 1)
self.assertGreaterEqual(HPn.AddCost, 1)
self.assertGreaterEqual(HPn.MulCost, 1)
self.checkRelativeError(HPn.highest(), self.maxval, 2.1)
self.checkRelativeError(-HPn.lowest(), self.maxval, 2.1)
self.checkRelativeError(HPn.Pi(), MPn.pi, functionName="pi")
print("HPn.Euler() ", HPn.Euler(), " N=", N, " MPn.euler = ", str(MPn.euler))
self.checkRelativeError(HPn.Euler(), MPn.euler, functionName="euler")
self.checkRelativeError(HPn.Log2(), MPn.log(2), functionName="logE2")
self.checkRelativeError(HPn.Catalan(), MPn.catalan, functionName="catalan")
#print("HPn.epsilon() ",HPn.epsilon(), " N=",N ," self.expectedEpsilon = ",self.expectedEpsilon)
self.checkRelativeError(HPn.epsilon(), self.expectedEpsilon, 10)
if (self.digs0 == 6): # exception for float
self.assertLessEqual(HPn.dummy_precision(), 10e-6)
else:
self.checkRelativeError(MPn.log(HPn.dummy_precision() / HPn.epsilon()) / MPn.log(10), MPn.mpf(self.digs0) / 10, 1.5)
for x in range(50):
if (self.nonBoostMPFR): # this looks like a bug in /usr/include/eigen3/unsupported/Eigen/MPRealSupport !
self.assertLessEqual(abs(HPn.random() - 0.5), 0.5)
else:
self.assertLessEqual(abs(HPn.random()), 1.0)
for aa in range(1000000 if self.testRecordingMode else 20):
m = 100 if self.testRecordingMode else 20
r = HPn.random(-m, m)
r2 = HPn.random(-m, m)
r3 = HPn.random(-m, m)
if (self.testRecordingMode):
self.totalCount = self.totalCount + 1
self.storeArgs((r, r2, r3))
#print("random=",r)
self.assertLessEqual(r, m)
self.assertGreaterEqual(r, -m)
self.assertFalse(HPn.isMuchSmallerThan(r, 1, HPn.epsilon()))
# NOTE: Below is a very sensitive test. If it starts failing, then see in function adjustDigs0, how expectedEpsilon is calculated.
# Maybe MPFR or cpp_bin_float changed the number of bits or changed their internal approximation of log10/log2.
self.assertTrue(HPn.isMuchSmallerThan(self.expectedEpsilon, 1 + abs(r), HPn.epsilon()))
self.assertTrue(HPn.isEqualFuzzy(r + self.expectedEpsilon * 0.01, r, HPn.epsilon()))
self.checkRelativeError(HPn.toLongDouble(r), float(r), 1e-14) # FIXME - should be 1e-17, but python does not support that
self.checkRelativeError(HPn.toDouble(r), float(r), 1e-14)
self.checkRelativeError(HPn.toDouble(r), float(r), 1e-14)
self.assertEqual(HPn.toLong(r), int(r))
self.assertEqual(HPn.toInt(r), int(r))
#
#print(r.__repr__(),r2.__repr__(),r3.__repr__())
self.oneArgMathCheck(N, HPn, MPn, r)
self.oneArgMathCheck(N, HPn, MPn, r2)
self.oneArgMathCheck(N, HPn, MPn, r3)
self.twoArgMathCheck(HPn, MPn, r, r2)
self.twoArgMathCheck(HPn, MPn, r, r3)
self.twoArgMathCheck(HPn, MPn, r2, r3)
self.threeArgMathCheck(HPn, MPn, r, r2, r3)
if (self.testRecordingMode and (self.totalCount % 20000 == 0)):
self.tearDown() # save progress
def testConstantsPythonSide(self):
for N in self.testLevelsHP:
self.runCheck(N, self.HPtestConstants)
def HPtestConstants(self, N, HPn, MPn):
HPn.testConstants()
def testArray(self):
for N in self.testLevelsHP:
self.runCheck(N, self.HPtestArray)
def HPtestArray(self, N, HPn, MPn):
HPn.testArray()
def testConstantsCppSide(self):
mth.testLoopRealHP()
def testRealConstructors(self):
for N in self.testLevelsHP:
self.runCheck(N, self.HPtestRealConstructors)
def HPtestRealConstructors(self, N, HPn, MPn):
a = HPn.Var()
a.val = 1
a.val = 1.
if (type(a.val) != float):
a.val = "1."
a.val = yade.math.Real(1)
a.val = yade.math.Real(1.)
a.val = yade.math.Real("1.")
a.val = MPn.mpf(1)
a.val = MPn.mpf(1.)
a.val = MPn.mpf("1.")
a.val = HPn.Real(1)
a.val = HPn.Real(1.)
a.val = HPn.Real("1.")
def testBasicVariable(self):
for N in self.testLevelsHP:
self.runCheck(N, self.HPtestBasicVariable)
def HPtestBasicVariable(self, N, HPn, MPn):
a = HPn.Var()
self.checkRelativeError(a.val, -71.23, 0.01)
a.val = 10
self.checkRelativeError(a.val, 10)
a.val = 1
self.checkRelativeError(a.val, 1)
a.val = 1.5
self.checkRelativeError(a.val, 1.5)
if (type(a.val) != float):
a.val = "1.5"
self.checkRelativeError(a.val, 1.5)
a.val = HPn.Real("1.5")
self.checkRelativeError(a.val, MPn.mpf(1.5))
self.checkRelativeComplexError(a.cpl, -71.23 + 33.23j, 0.01)
if (type(a.cpl) != complex):
a.cpl = MPn.mpc("1", "-1")
self.checkRelativeComplexError(a.cpl, 1 - 1j, 1e-15)
self.checkRelativeComplexError(a.cpl, MPn.mpc("1", "-1"))
def thisTestsExceptionReal1(self):
a = self.HPnHelper.Var()
a.val = "13123-123123*123"
def thisTestsExceptionComplex1(self):
a = self.HPnHelper.Var()
a.cpl = "13123-123123*123-50j"
def thisTestsExceptionReal2(self):
a = self.HPnHelper.Var()
a.val = "wrong number"
def thisTestsExceptionComplex2(self):
a = self.HPnHelper.Var()
a.cpl = "wrong number"
def thisTestsExceptionReal3(self):
a = self.HPnHelper.Var()
a.val = "-1.0 wrong"
def thisTestsExceptionComplex3(self):
a = self.HPnHelper.Var()
a.cpl = "-1.0 wrong"
def thisTestsExceptionReal4(self):
a = self.HPnHelper.Var()
a.val = "-1wrong"
def thisTestsExceptionComplex4(self):
a = self.HPnHelper.Var()
a.cpl = "-1wrong"
def thisTestsExceptionReal1r(self):
a = self.HPnHelper.Var()
a.val = self.HPnHelper.Real("13123-123123*123")
def thisTestsExceptionComplex1c(self):
a = self.HPnHelper.Var()
a.cpl = self.HPnHelper.Complex("13123-123123*123-50j")
def thisTestsExceptionReal2r(self):
a = self.HPnHelper.Var()
a.val = self.HPnHelper.Real("wrong number")
def thisTestsExceptionComplex2c(self):
a = self.HPnHelper.Var()
a.cpl = self.HPnHelper.Complex("wrong number")
def thisTestsExceptionReal3r(self):
a = self.HPnHelper.Var()
a.val = self.HPnHelper.Real("-1.0 wrong")
def thisTestsExceptionComplex3c(self):
a = self.HPnHelper.Var()
a.cpl = self.HPnHelper.Complex("-1.0 wrong")
def thisTestsExceptionReal4r(self):
a = self.HPnHelper.Var()
a.val = self.HPnHelper.Real("-1wrong")
def thisTestsExceptionComplex4c(self):
a = self.HPnHelper.Var()
a.cpl = self.HPnHelper.Complex("-1wrong")
def testWrongInput(self):
for N in self.testLevelsHP:
self.runCheck(N, self.HPtestWrongInput)
def HPtestWrongInput(self, N, HPn, MPn):
if (self.nonBoostMPFR): # this looks like another bug in /usr/include/mpreal.h
print("skipping this test for non-boost /usr/include/mpreal.h")
return
# depending on backed Real use it throws TypeError or RuntimeError
self.HPnHelper = HPn
# TODO: this won't work. In ToFromPythonConverter.hpp the ArbitraryComplex_from_python has to be rewritten like ArbitraryReal_from_python was.
#a = self.HPnHelper.Var()
#a.cpl = "-1"
self.assertRaises(Exception, self.thisTestsExceptionReal1)
self.assertRaises(Exception, self.thisTestsExceptionComplex1)
self.assertRaises(Exception, self.thisTestsExceptionReal2)
self.assertRaises(Exception, self.thisTestsExceptionComplex2)
self.assertRaises(Exception, self.thisTestsExceptionReal3)
self.assertRaises(Exception, self.thisTestsExceptionComplex3)
self.assertRaises(Exception, self.thisTestsExceptionReal4)
self.assertRaises(Exception, self.thisTestsExceptionComplex4)
self.assertRaises(Exception, self.thisTestsExceptionReal1r)
self.assertRaises(Exception, self.thisTestsExceptionComplex1c)
self.assertRaises(Exception, self.thisTestsExceptionReal2r)
self.assertRaises(Exception, self.thisTestsExceptionComplex2c)
self.assertRaises(Exception, self.thisTestsExceptionReal3r)
self.assertRaises(Exception, self.thisTestsExceptionComplex3c)
self.assertRaises(Exception, self.thisTestsExceptionReal4r)
self.assertRaises(Exception, self.thisTestsExceptionComplex4c)
def testEigenCost(self):
for N in self.testLevelsHP:
self.runCheck(N, self.HPtestEigenCost)
def HPtestEigenCost(self, N, HPn, MPn):
self.assertEqual(self.getDefaultTolerance("read", False), HPn.ReadCost)
self.assertEqual(self.getDefaultTolerance("add", False), HPn.AddCost)
self.assertEqual(self.getDefaultTolerance("mul", False), HPn.MulCost)
self.assertEqual(self.getDefaultTolerance("cread", False), HPn.ComplexReadCost)
self.assertEqual(self.getDefaultTolerance("cadd", False), HPn.ComplexAddCost)
self.assertEqual(self.getDefaultTolerance("cmul", False), HPn.ComplexMulCost)
def testDefReadonly(self):
# boost::python def_readonly(…) has problems with higher precision Real
# types: https://yade-dem.org/doc/prog.html#custom-converters
# The solution (already applied almost everywhere in Serializable.hpp)
# is to use ::boost::python::return_by_value in def_readonly(…) when
# exposing Real member variable.
t = yade.TriaxialStressController()
p = t.porosity
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