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831 lines
16 KiB
831 lines
16 KiB
# pylint: disable=unused-argument
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from __future__ import absolute_import
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import itertools
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import math as _math
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import operator
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import random
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from functions.info import ISNUMBER, ISLOGICAL
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import roman
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# Iterates through elements of iterable arguments, or through individual args when not iterable.
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def _chain(*values_or_iterables):
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for v in values_or_iterables:
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try:
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for x in v:
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yield x
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except TypeError:
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yield v
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# Iterates through iterable or other arguments, skipping non-numeric ones.
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def _chain_numeric(*values_or_iterables):
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for v in _chain(*values_or_iterables):
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if ISNUMBER(v) and not ISLOGICAL(v):
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yield v
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# Iterates through iterable or other arguments, replacing non-numeric ones with 0 (or True with 1).
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def _chain_numeric_a(*values_or_iterables):
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for v in _chain(*values_or_iterables):
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yield int(v) if ISLOGICAL(v) else v if ISNUMBER(v) else 0
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def _round_toward_zero(value):
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return _math.floor(value) if value >= 0 else _math.ceil(value)
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def _round_away_from_zero(value):
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return _math.ceil(value) if value >= 0 else _math.floor(value)
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def ABS(value):
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"""
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Returns the absolute value of a number.
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>>> ABS(2)
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2
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>>> ABS(-2)
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2
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>>> ABS(-4)
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4
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"""
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return abs(value)
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def ACOS(value):
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"""
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Returns the inverse cosine of a value, in radians.
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>>> round(ACOS(-0.5), 9)
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2.094395102
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>>> round(ACOS(-0.5)*180/PI(), 10)
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120.0
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"""
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return _math.acos(value)
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def ACOSH(value):
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"""
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Returns the inverse hyperbolic cosine of a number.
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>>> ACOSH(1)
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0.0
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>>> round(ACOSH(10), 7)
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2.9932228
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"""
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return _math.acosh(value)
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def ARABIC(roman_numeral):
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"""
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Computes the value of a Roman numeral.
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>>> ARABIC("LVII")
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57
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>>> ARABIC('mcmxii')
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1912
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"""
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return roman.fromRoman(roman_numeral.upper())
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def ASIN(value):
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"""
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Returns the inverse sine of a value, in radians.
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>>> round(ASIN(-0.5), 9)
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-0.523598776
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>>> round(ASIN(-0.5)*180/PI(), 10)
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-30.0
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>>> round(DEGREES(ASIN(-0.5)), 10)
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-30.0
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"""
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return _math.asin(value)
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def ASINH(value):
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"""
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Returns the inverse hyperbolic sine of a number.
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>>> round(ASINH(-2.5), 9)
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-1.647231146
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>>> round(ASINH(10), 9)
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2.99822295
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"""
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return _math.asinh(value)
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def ATAN(value):
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"""
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Returns the inverse tangent of a value, in radians.
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>>> round(ATAN(1), 9)
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0.785398163
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>>> ATAN(1)*180/PI()
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45.0
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>>> DEGREES(ATAN(1))
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45.0
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"""
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return _math.atan(value)
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def ATAN2(x, y):
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"""
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Returns the angle between the x-axis and a line segment from the origin (0,0) to specified
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coordinate pair (`x`,`y`), in radians.
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>>> round(ATAN2(1, 1), 9)
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0.785398163
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>>> round(ATAN2(-1, -1), 9)
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-2.35619449
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>>> ATAN2(-1, -1)*180/PI()
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-135.0
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>>> DEGREES(ATAN2(-1, -1))
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-135.0
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>>> round(ATAN2(1,2), 9)
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1.107148718
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"""
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return _math.atan2(y, x)
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def ATANH(value):
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"""
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Returns the inverse hyperbolic tangent of a number.
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>>> round(ATANH(0.76159416), 9)
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1.00000001
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>>> round(ATANH(-0.1), 9)
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-0.100335348
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"""
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return _math.atanh(value)
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def CEILING(value, factor=1):
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"""
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Rounds a number up to the nearest multiple of factor, or the nearest integer if the factor is
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omitted or 1.
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>>> CEILING(2.5, 1)
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3
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>>> CEILING(-2.5, -2)
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-4
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>>> CEILING(-2.5, 2)
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-2
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>>> CEILING(1.5, 0.1)
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1.5
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>>> CEILING(0.234, 0.01)
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0.24
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"""
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return int(_math.ceil(float(value) / factor)) * factor
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def COMBIN(n, k):
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"""
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Returns the number of ways to choose some number of objects from a pool of a given size of
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objects.
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>>> COMBIN(8,2)
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28
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>>> COMBIN(4,2)
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6
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>>> COMBIN(10,7)
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120
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"""
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# From http://stackoverflow.com/a/4941932/328565
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k = min(k, n-k)
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if k == 0:
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return 1
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numer = reduce(operator.mul, xrange(n, n-k, -1))
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denom = reduce(operator.mul, xrange(1, k+1))
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return numer//denom
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def COS(angle):
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"""
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Returns the cosine of an angle provided in radians.
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>>> round(COS(1.047), 7)
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0.5001711
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>>> round(COS(60*PI()/180), 10)
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0.5
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>>> round(COS(RADIANS(60)), 10)
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0.5
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"""
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return _math.cos(angle)
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def COSH(value):
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"""
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Returns the hyperbolic cosine of any real number.
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>>> round(COSH(4), 6)
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27.308233
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>>> round(COSH(EXP(1)), 7)
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7.6101251
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"""
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return _math.cosh(value)
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def DEGREES(angle):
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"""
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Converts an angle value in radians to degrees.
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>>> round(DEGREES(ACOS(-0.5)), 10)
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120.0
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>>> DEGREES(PI())
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180.0
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"""
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return _math.degrees(angle)
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def EVEN(value):
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"""
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Rounds a number up to the nearest even integer, rounding away from zero.
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>>> EVEN(1.5)
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2
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>>> EVEN(3)
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4
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>>> EVEN(2)
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2
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>>> EVEN(-1)
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-2
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"""
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return int(_round_away_from_zero(float(value) / 2)) * 2
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def EXP(exponent):
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"""
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Returns Euler's number, e (~2.718) raised to a power.
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>>> round(EXP(1), 8)
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2.71828183
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>>> round(EXP(2), 7)
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7.3890561
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"""
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return _math.exp(exponent)
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def FACT(value):
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"""
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Returns the factorial of a number.
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>>> FACT(5)
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120
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>>> FACT(1.9)
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1
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>>> FACT(0)
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1
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>>> FACT(1)
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1
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>>> FACT(-1)
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Traceback (most recent call last):
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...
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ValueError: factorial() not defined for negative values
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"""
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return _math.factorial(int(value))
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def FACTDOUBLE(value):
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"""
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Returns the "double factorial" of a number.
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>>> FACTDOUBLE(6)
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48
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>>> FACTDOUBLE(7)
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105
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>>> FACTDOUBLE(3)
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3
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>>> FACTDOUBLE(4)
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8
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"""
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return reduce(operator.mul, xrange(value, 1, -2))
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def FLOOR(value, factor=1):
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"""
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Rounds a number down to the nearest integer multiple of specified significance.
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>>> FLOOR(3.7,2)
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2
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>>> FLOOR(-2.5,-2)
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-2
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>>> FLOOR(2.5,-2)
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Traceback (most recent call last):
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...
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ValueError: factor argument invalid
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>>> FLOOR(1.58,0.1)
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1.5
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>>> FLOOR(0.234,0.01)
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0.23
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"""
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if (factor < 0) != (value < 0):
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raise ValueError("factor argument invalid")
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return int(_math.floor(float(value) / factor)) * factor
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def _gcd(a, b):
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while a != 0:
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if a > b:
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a, b = b, a
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a, b = b % a, a
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return b
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def GCD(value1, *more_values):
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"""
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Returns the greatest common divisor of one or more integers.
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>>> GCD(5, 2)
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1
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>>> GCD(24, 36)
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12
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>>> GCD(7, 1)
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1
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>>> GCD(5, 0)
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5
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>>> GCD(0, 5)
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5
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>>> GCD(5)
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5
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>>> GCD(14, 42, 21)
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7
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"""
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values = [v for v in (value1,) + more_values if v]
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if not values:
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return 0
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if any(v < 0 for v in values):
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raise ValueError("gcd requires non-negative values")
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return reduce(_gcd, map(int, values))
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def INT(value):
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"""
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Rounds a number down to the nearest integer that is less than or equal to it.
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>>> INT(8.9)
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8
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>>> INT(-8.9)
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-9
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>>> 19.5-INT(19.5)
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0.5
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"""
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return int(_math.floor(value))
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def _lcm(a, b):
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return a * b / _gcd(a, b)
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def LCM(value1, *more_values):
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"""
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Returns the least common multiple of one or more integers.
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>>> LCM(5, 2)
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10
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>>> LCM(24, 36)
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72
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>>> LCM(0, 5)
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0
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>>> LCM(5)
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5
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>>> LCM(10, 100)
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100
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>>> LCM(12, 18)
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36
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>>> LCM(12, 18, 24)
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72
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"""
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values = (value1,) + more_values
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if any(v < 0 for v in values):
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raise ValueError("gcd requires non-negative values")
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if any(v == 0 for v in values):
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return 0
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return reduce(_lcm, map(int, values))
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def LN(value):
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"""
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Returns the the logarithm of a number, base e (Euler's number).
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>>> round(LN(86), 7)
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4.4543473
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>>> round(LN(2.7182818), 7)
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1.0
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>>> round(LN(EXP(3)), 10)
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3.0
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"""
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return _math.log(value)
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def LOG(value, base=10):
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"""
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Returns the the logarithm of a number given a base.
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>>> LOG(10)
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1.0
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>>> LOG(8, 2)
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3.0
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>>> round(LOG(86, 2.7182818), 7)
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4.4543473
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"""
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return _math.log(value, base)
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def LOG10(value):
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"""
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Returns the the logarithm of a number, base 10.
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>>> round(LOG10(86), 9)
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1.934498451
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>>> LOG10(10)
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1.0
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>>> LOG10(100000)
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5.0
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>>> LOG10(10**5)
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5.0
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"""
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return _math.log10(value)
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def MOD(dividend, divisor):
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"""
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Returns the result of the modulo operator, the remainder after a division operation.
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>>> MOD(3, 2)
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1
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>>> MOD(-3, 2)
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1
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>>> MOD(3, -2)
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-1
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>>> MOD(-3, -2)
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-1
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"""
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return dividend % divisor
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def MROUND(value, factor):
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"""
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Rounds one number to the nearest integer multiple of another.
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>>> MROUND(10, 3)
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9
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>>> MROUND(-10, -3)
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-9
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>>> round(MROUND(1.3, 0.2), 10)
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1.4
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>>> MROUND(5, -2)
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Traceback (most recent call last):
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...
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ValueError: factor argument invalid
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"""
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if (factor < 0) != (value < 0):
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raise ValueError("factor argument invalid")
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return int(_round_toward_zero(float(value) / factor + 0.5)) * factor
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def MULTINOMIAL(value1, *more_values):
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"""
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Returns the factorial of the sum of values divided by the product of the values' factorials.
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>>> MULTINOMIAL(2, 3, 4)
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1260
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>>> MULTINOMIAL(3)
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1
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>>> MULTINOMIAL(1,2,3)
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60
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>>> MULTINOMIAL(0,2,4,6)
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13860
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"""
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s = value1
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res = 1
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for v in more_values:
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s += v
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res *= COMBIN(s, v)
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return res
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def ODD(value):
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"""
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Rounds a number up to the nearest odd integer.
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>>> ODD(1.5)
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3
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>>> ODD(3)
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3
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>>> ODD(2)
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3
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>>> ODD(-1)
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-1
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>>> ODD(-2)
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-3
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"""
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return int(_round_away_from_zero(float(value + 1) / 2)) * 2 - 1
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def PI():
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"""
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Returns the value of Pi to 14 decimal places.
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>>> round(PI(), 9)
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3.141592654
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>>> round(PI()/2, 9)
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1.570796327
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>>> round(PI()*9, 8)
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28.27433388
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"""
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return _math.pi
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def POWER(base, exponent):
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"""
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Returns a number raised to a power.
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>>> POWER(5,2)
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25.0
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>>> round(POWER(98.6,3.2), 3)
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2401077.222
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>>> round(POWER(4,5.0/4), 9)
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5.656854249
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"""
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return _math.pow(base, exponent)
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def PRODUCT(factor1, *more_factors):
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"""
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Returns the result of multiplying a series of numbers together. Each argument may be a number or
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an array.
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>>> PRODUCT([5,15,30])
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2250
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>>> PRODUCT([5,15,30], 2)
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4500
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>>> PRODUCT(5,15,[30],[2])
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4500
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More tests:
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>>> PRODUCT([2, True, None, "", False, "0", 5])
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10
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>>> PRODUCT([2, True, None, "", False, 0, 5])
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0
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"""
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return reduce(operator.mul, _chain_numeric(factor1, *more_factors))
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def QUOTIENT(dividend, divisor):
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"""
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Returns one number divided by another.
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>>> QUOTIENT(5, 2)
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2
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>>> QUOTIENT(4.5, 3.1)
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1
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>>> QUOTIENT(-10, 3)
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-3
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"""
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return TRUNC(float(dividend) / divisor)
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def RADIANS(angle):
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"""
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Converts an angle value in degrees to radians.
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>>> round(RADIANS(270), 6)
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4.712389
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"""
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return _math.radians(angle)
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def RAND():
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"""
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Returns a random number between 0 inclusive and 1 exclusive.
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"""
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return random.random()
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def RANDBETWEEN(low, high):
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"""
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Returns a uniformly random integer between two values, inclusive.
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"""
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return random.randrange(low, high + 1)
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def ROMAN(number, form_unused=None):
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"""
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|
Formats a number in Roman numerals. The second argument is ignored in this implementation.
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>>> ROMAN(499,0)
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'CDXCIX'
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>>> ROMAN(499.2,0)
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'CDXCIX'
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>>> ROMAN(57)
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'LVII'
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>>> ROMAN(1912)
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'MCMXII'
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"""
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# TODO: Maybe we should support the second argument.
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return roman.toRoman(int(number))
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def ROUND(value, places=0):
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"""
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Rounds a number to a certain number of decimal places according to standard rules.
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>>> ROUND(2.15, 1) # Excel actually gives the more correct 2.2
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2.1
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>>> ROUND(2.149, 1)
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2.1
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>>> ROUND(-1.475, 2)
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-1.48
|
|
>>> ROUND(21.5, -1)
|
|
20.0
|
|
>>> ROUND(626.3,-3)
|
|
1000.0
|
|
>>> ROUND(1.98,-1)
|
|
0.0
|
|
>>> ROUND(-50.55,-2)
|
|
-100.0
|
|
"""
|
|
# TODO: Excel manages to round 2.15 to 2.2, but Python sees 2.149999... and rounds to 2.1
|
|
# (see Python notes in documentation of `round()`).
|
|
return round(value, places)
|
|
|
|
def ROUNDDOWN(value, places=0):
|
|
"""
|
|
Rounds a number to a certain number of decimal places, always rounding down towards zero.
|
|
|
|
>>> ROUNDDOWN(3.2, 0)
|
|
3
|
|
>>> ROUNDDOWN(76.9,0)
|
|
76
|
|
>>> ROUNDDOWN(3.14159, 3)
|
|
3.141
|
|
>>> ROUNDDOWN(-3.14159, 1)
|
|
-3.1
|
|
>>> ROUNDDOWN(31415.92654, -2)
|
|
31400
|
|
"""
|
|
factor = 10**-places
|
|
return int(_round_toward_zero(float(value) / factor)) * factor
|
|
|
|
def ROUNDUP(value, places=0):
|
|
"""
|
|
Rounds a number to a certain number of decimal places, always rounding up away from zero.
|
|
|
|
>>> ROUNDUP(3.2,0)
|
|
4
|
|
>>> ROUNDUP(76.9,0)
|
|
77
|
|
>>> ROUNDUP(3.14159, 3)
|
|
3.142
|
|
>>> ROUNDUP(-3.14159, 1)
|
|
-3.2
|
|
>>> ROUNDUP(31415.92654, -2)
|
|
31500
|
|
"""
|
|
factor = 10**-places
|
|
return int(_round_away_from_zero(float(value) / factor)) * factor
|
|
|
|
def SERIESSUM(x, n, m, a):
|
|
"""
|
|
Given parameters x, n, m, and a, returns the power series sum a_1*x^n + a_2*x^(n+m)
|
|
+ ... + a_i*x^(n+(i-1)m), where i is the number of entries in range `a`.
|
|
|
|
>>> SERIESSUM(1,0,1,1)
|
|
1
|
|
>>> SERIESSUM(2,1,0,[1,2,3])
|
|
12
|
|
>>> SERIESSUM(-3,1,1,[2,4,6])
|
|
-132
|
|
>>> round(SERIESSUM(PI()/4,0,2,[1,-1./FACT(2),1./FACT(4),-1./FACT(6)]), 6)
|
|
0.707103
|
|
"""
|
|
return sum(coef*pow(x, n+i*m) for i, coef in enumerate(_chain(a)))
|
|
|
|
def SIGN(value):
|
|
"""
|
|
Given an input number, returns `-1` if it is negative, `1` if positive, and `0` if it is zero.
|
|
|
|
>>> SIGN(10)
|
|
1
|
|
>>> SIGN(4.0-4.0)
|
|
0
|
|
>>> SIGN(-0.00001)
|
|
-1
|
|
"""
|
|
return 0 if value == 0 else int(_math.copysign(1, value))
|
|
|
|
def SIN(angle):
|
|
"""
|
|
Returns the sine of an angle provided in radians.
|
|
|
|
>>> round(SIN(PI()), 10)
|
|
0.0
|
|
>>> SIN(PI()/2)
|
|
1.0
|
|
>>> round(SIN(30*PI()/180), 10)
|
|
0.5
|
|
>>> round(SIN(RADIANS(30)), 10)
|
|
0.5
|
|
"""
|
|
return _math.sin(angle)
|
|
|
|
def SINH(value):
|
|
"""
|
|
Returns the hyperbolic sine of any real number.
|
|
|
|
>>> round(2.868*SINH(0.0342*1.03), 7)
|
|
0.1010491
|
|
"""
|
|
return _math.sinh(value)
|
|
|
|
def SQRT(value):
|
|
"""
|
|
Returns the positive square root of a positive number.
|
|
|
|
>>> SQRT(16)
|
|
4.0
|
|
>>> SQRT(-16)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: math domain error
|
|
>>> SQRT(ABS(-16))
|
|
4.0
|
|
"""
|
|
return _math.sqrt(value)
|
|
|
|
|
|
def SQRTPI(value):
|
|
"""
|
|
Returns the positive square root of the product of Pi and the given positive number.
|
|
|
|
>>> round(SQRTPI(1), 6)
|
|
1.772454
|
|
>>> round(SQRTPI(2), 6)
|
|
2.506628
|
|
"""
|
|
return _math.sqrt(_math.pi * value)
|
|
|
|
def SUBTOTAL(function_code, range1, range2):
|
|
"""
|
|
Returns a subtotal for a vertical range of cells using a specified aggregation function.
|
|
"""
|
|
raise NotImplementedError()
|
|
|
|
|
|
def SUM(value1, *more_values):
|
|
"""
|
|
Returns the sum of a series of numbers. Each argument may be a number or an array.
|
|
Non-numeric values are ignored.
|
|
|
|
>>> SUM([5,15,30])
|
|
50
|
|
>>> SUM([5.,15,30], 2)
|
|
52.0
|
|
>>> SUM(5,15,[30],[2])
|
|
52
|
|
|
|
More tests:
|
|
>>> SUM([10.25, None, "", False, "other", 20.5])
|
|
30.75
|
|
>>> SUM([True, "3", 4], True)
|
|
6
|
|
"""
|
|
return sum(_chain_numeric_a(value1, *more_values))
|
|
|
|
|
|
def SUMIF(records, criterion, sum_range):
|
|
"""
|
|
Returns a conditional sum across a range.
|
|
"""
|
|
raise NotImplementedError()
|
|
|
|
def SUMIFS(sum_range, criteria_range1, criterion1, *args):
|
|
"""
|
|
Returns the sum of a range depending on multiple criteria.
|
|
"""
|
|
raise NotImplementedError()
|
|
|
|
def SUMPRODUCT(array1, *more_arrays):
|
|
"""
|
|
Multiplies corresponding components in the given arrays, and returns the sum of those products.
|
|
|
|
>>> SUMPRODUCT([3,8,1,4,6,9], [2,6,5,7,7,3])
|
|
156
|
|
>>> SUMPRODUCT([], [], [])
|
|
0
|
|
>>> SUMPRODUCT([-0.25], [-2], [-3])
|
|
-1.5
|
|
>>> SUMPRODUCT([-0.25, -0.25], [-2, -2], [-3, -3])
|
|
-3.0
|
|
"""
|
|
return sum(reduce(operator.mul, values) for values in itertools.izip(array1, *more_arrays))
|
|
|
|
def SUMSQ(value1, value2):
|
|
"""
|
|
Returns the sum of the squares of a series of numbers and/or cells.
|
|
"""
|
|
raise NotImplementedError()
|
|
|
|
def TAN(angle):
|
|
"""
|
|
Returns the tangent of an angle provided in radians.
|
|
|
|
>>> round(TAN(0.785), 8)
|
|
0.99920399
|
|
>>> round(TAN(45*PI()/180), 10)
|
|
1.0
|
|
>>> round(TAN(RADIANS(45)), 10)
|
|
1.0
|
|
"""
|
|
return _math.tan(angle)
|
|
|
|
def TANH(value):
|
|
"""
|
|
Returns the hyperbolic tangent of any real number.
|
|
|
|
>>> round(TANH(-2), 6)
|
|
-0.964028
|
|
>>> TANH(0)
|
|
0.0
|
|
>>> round(TANH(0.5), 6)
|
|
0.462117
|
|
"""
|
|
return _math.tanh(value)
|
|
|
|
def TRUNC(value, places=0):
|
|
"""
|
|
Truncates a number to a certain number of significant digits by omitting less significant
|
|
digits.
|
|
|
|
>>> TRUNC(8.9)
|
|
8
|
|
>>> TRUNC(-8.9)
|
|
-8
|
|
>>> TRUNC(0.45)
|
|
0
|
|
"""
|
|
# TRUNC seems indistinguishable from ROUNDDOWN.
|
|
return ROUNDDOWN(value, places)
|