def getNthSquareTriangularNumber( n ):
neededPrecision = int( real_int( n ) * 3.5 ) # determined by experimentation
if mp.dps < neededPrecision:
setAccuracy( neededPrecision )
sqrt2 = sqrt( 2 )
return nint( power( fdiv( fsub( power( fadd( 1, sqrt2 ), fmul( 2, n ) ),
power( fsub( 1, sqrt2 ), fmul( 2, n ) ) ),
fmul( 4, sqrt2 ) ), 2 ) )
def parseInputValue( term, inputRadix ):
if isinstance( term, mpf ):
return term
innerChars = term[ 1 : -1 ]
# this helps us parse dates
if '/' in innerChars:
term = term.replace( '/', '-' )
innerChars = term[ 1 : -1 ]
# 'e' implies scientific notation, which isn't a date regardless
if ( 'e' not in innerChars ):
# 'd' means a dice expression, '[' means a build_number expression, so don't treat it as a date
if ( ( '-' in innerChars ) or ( ':' in innerChars ) ) and ( 'd' not in term ) and ( '[' not in term ):
# try:
datetime = arrow.get( term )
datetime = RPNDateTime( datetime.year, datetime.month, datetime.day,
datetime.hour, datetime.minute, datetime.second,
datetime.microsecond )
# except:
# raise ValueError( 'error parsing datetime' )
return datetime
if term == '0':
return mpmathify( 0 )
# ignore commas
term = ''.join( [ i for i in term if i not in ',' ] )
if term[ 0 ] == '\\':
term = term[ 1 : ]
ignoreSpecial = True
else:
ignoreSpecial = False
if '.' in term:
if inputRadix == 10:
newPrecision = len( term ) + 1
if mp.dps < newPrecision:
setAccuracy( newPrecision )
return mpmathify( term )
decimal = term.find( '.' )
else:
decimal = len( term )
negative = term[ 0 ] == '-'
if negative:
start = 1
else:
if term[ 0 ] == '+':
start = 1
else:
start = 0
integer = term[ start : decimal ]
mantissa = term[ decimal + 1 : ]
# check for hex, then binary, then octal, otherwise a plain old decimal integer
if not ignoreSpecial and mantissa == '':
if integer[ 0 ] == '0':
if len( integer ) == 1:
return mpmathify( 0 )
if integer[ 1 ] in 'Xx':
# set the precision big enough to handle this value
newPrecision = math.ceil( ( math.log10( 16 ) * ( len( integer ) - 2 ) ) ) + 1
if mp.dps < newPrecision:
setAccuracy( newPrecision )
return mpmathify( int( integer[ 2 : ], 16 ) )
elif integer[ -1 ] in 'bB':
# set the precision big enough to handle this value
newPrecision = math.ceil( math.log10( 2 ) * ( len( integer ) - 1 ) ) + 1
if mp.dps < newPrecision:
setAccuracy( newPrecision )
integer = integer[ : -1 ]
return mpmathify( int( integer, 2 ) * ( -1 if negative else 1 ) )
else:
integer = integer[ 1 : ]
return mpmathify( int( integer, 8 ) )
if integer[ 0 ] == '1' and integer[ -1 ] in 'bB':
# set the precision big enough to handle this value
newPrecision = math.ceil( math.log10( 2 ) * ( len( integer ) - 1 ) ) + 1
if mp.dps < newPrecision:
setAccuracy( newPrecision )
integer = integer[ : -1 ]
return mpmathify( int( integer, 2 ) * ( -1 if negative else 1 ) )
elif inputRadix == 10:
newPrecision = len( integer ) + 1
if mp.dps < newPrecision:
setAccuracy( newPrecision )
return fneg( integer ) if negative else mpmathify( integer )
# finally, we have a non-radix 10 number to parse
result = convertToBase10( integer, mantissa, inputRadix )
return fneg( result ) if negative else mpmathify( result )
def getFactors( n ):
'''
A factorization of *Nptr into prime and q-prime factors is first obtained.
Selfridge's primality test is then applied to any q-prime factors; the test
is applied repeatedly until either a q-prime is found to be composite or
likely to be composite (in which case the initial factorization is doubtful
and an extra base should be used in Miller's test) or we run out of q-primes,
in which case every q-prime factor of *Nptr is certified as prime.
Returns a list of tuples where each tuple is a prime factor and an exponent.
'''
verbose = g.verbose
if real( n ) < -1:
return [ ( -1, 1 ) ] + getFactors( fneg( n ) )
elif n == -1:
return [ ( -1, 1 ) ]
elif n == 0:
return [ ( 0, 1 ) ]
elif n == 1:
return [ ( 1, 1 ) ]
target = int( n )
dps = ceil( log( n ) )
if dps > mp.dps:
setAccuracy( dps )
if target > g.minValueToCache:
if g.factorCache is None:
loadFactorCache( )
if target in g.factorCache:
if verbose:
print( 'cache hit:', target )
return g.factorCache[ target ]
smallFactors, largeFactors, qPrimes = getPrimeFactors( int( n ), verbose )
if qPrimes:
if verbose:
print( 'testing q-primes for primality' )
print( '--' )
i = 0
for qPrime in qPrimes:
t = doSelfridgeTest( qPrime[ 0 ], verbose )
if not t:
print( 'do FACTOR() again with an extra base' )
return 0
if verbose:
print( 'all q-primes are primes:', n, 'has the following factorization:' )
print( )
for i in smallFactors:
print( 'prime factor:', i[ 0 ], 'exponent:', i[ 1 ] )
for i in largeFactors:
print( 'prime factor:', i[ 0 ], 'exponent:', i[ 1 ] )
else:
if verbose:
print( 'NO Q-PRIMES:' )
print( )
print( n, 'has the following factorization:' )
for i in smallFactors:
print( 'prime factor:', i[ 0 ], 'exponent:', i[ 1 ] )
for i in largeFactors:
print( 'prime factor:', i[ 0 ], 'exponent:', i[ 1 ] )
result = [ ]
result.extend( smallFactors )
result.extend( largeFactors )
if g.factorCache is not None:
product = int( fprod( [ power( i[ 0 ], i[ 1 ] ) for i in largeFactors ] ) )
if product not in g.factorCache:
g.factorCache[ product ] = largeFactors
g.factorCacheIsDirty = True
if n > g.minValueToCache and n not in g.factorCache:
g.factorCache[ n ] = result
g.factorCacheIsDirty = True
return result
def getFactors( n ):
verbose = g.verbose
if real( n ) < -1:
return [ ( -1, 1 ) ] + getFactors( fneg( n ) )
elif n == -1:
return [ ( -1, 1 ) ]
elif n == 0:
return [ ( 0, 1 ) ]
elif n == 1:
return [ ( 1, 1 ) ]
target = int( n )
dps = ceil( log( n ) )
if dps > mp.dps:
setAccuracy( dps )
if target > g.minValueToCache:
if g.factorCache is None:
loadFactorCache( )
if target in g.factorCache:
if verbose:
print( 'cache hit:', target )
return g.factorCache[ target ]
smallFactors, largeFactors, qPrimes = getPrimeFactors( int( n ), verbose )
if qPrimes:
if verbose:
print( 'testing q-primes for primality' )
print( '--' )
i = 0
for qPrime in qPrimes:
t = doSelfridgeTest( qPrime[ 0 ], verbose )
if not t:
print( 'do FACTOR() again with an extra base' )
return 0
if verbose:
print( 'all q-primes are primes:', n, 'has the following factorization:' )
print( )
for i in smallFactors:
print( 'prime factor:', i[ 0 ], 'exponent:', i[ 1 ] )
for i in largeFactors:
print( 'prime factor:', i[ 0 ], 'exponent:', i[ 1 ] )
else:
if verbose:
print( 'NO Q-PRIMES:' )
print( )
print( n, 'has the following factorization:' )
for i in smallFactors:
print( 'prime factor:', i[ 0 ], 'exponent:', i[ 1 ] )
for i in largeFactors:
print( 'prime factor:', i[ 0 ], 'exponent:', i[ 1 ] )
result = [ ]
result.extend( smallFactors )
result.extend( largeFactors )
if g.factorCache is not None:
product = int( fprod( [ power( i[ 0 ], i[ 1 ] ) for i in largeFactors ] ) )
if product not in g.factorCache:
g.factorCache[ product ] = largeFactors
g.factorCacheIsDirty = True
if n > g.minValueToCache and n not in g.factorCache:
g.factorCache[ n ] = result
g.factorCacheIsDirty = True
return result