341 lines
16 KiB
Python
341 lines
16 KiB
Python
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# Part of Odoo. See LICENSE file for full copyright and licensing details.
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import builtins
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import math
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__all__ = [
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"float_compare",
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"float_is_zero",
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"float_repr",
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"float_round",
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"float_split",
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"float_split_str",
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]
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def round(f):
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# P3's builtin round differs from P2 in the following manner:
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# * it rounds half to even rather than up (away from 0)
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# * round(-0.) loses the sign (it returns -0 rather than 0)
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# * round(x) returns an int rather than a float
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#
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# this compatibility shim implements Python 2's round in terms of
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# Python 3's so that important rounding error under P3 can be
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# trivially fixed, assuming the P2 behaviour to be debugged and
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# correct.
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roundf = builtins.round(f)
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if builtins.round(f + 1) - roundf != 1:
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return f + math.copysign(0.5, f)
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# copysign ensures round(-0.) -> -0 *and* result is a float
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return math.copysign(roundf, f)
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def _float_check_precision(precision_digits=None, precision_rounding=None):
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if precision_rounding is not None and precision_digits is None:
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assert precision_rounding > 0,\
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f"precision_rounding must be positive, got {precision_rounding}"
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elif precision_digits is not None and precision_rounding is None:
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# TODO: `int`s will also get the `is_integer` method starting from python 3.12
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assert float(precision_digits).is_integer() and precision_digits >= 0,\
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f"precision_digits must be a non-negative integer, got {precision_digits}"
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precision_rounding = 10 ** -precision_digits
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else:
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msg = "exactly one of precision_digits and precision_rounding must be specified"
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raise AssertionError(msg)
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return precision_rounding
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def float_round(value, precision_digits=None, precision_rounding=None, rounding_method='HALF-UP'):
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"""Return ``value`` rounded to ``precision_digits`` decimal digits,
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minimizing IEEE-754 floating point representation errors, and applying
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the tie-breaking rule selected with ``rounding_method``, by default
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HALF-UP (away from zero).
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Precision must be given by ``precision_digits`` or ``precision_rounding``,
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not both!
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:param float value: the value to round
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:param int precision_digits: number of fractional digits to round to.
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:param float precision_rounding: decimal number representing the minimum
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non-zero value at the desired precision (for example, 0.01 for a
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2-digit precision).
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:param rounding_method: the rounding method used:
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- 'HALF-UP' will round to the closest number with ties going away from zero.
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- 'HALF-DOWN' will round to the closest number with ties going towards zero.
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- 'HALF_EVEN' will round to the closest number with ties going to the closest
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even number.
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- 'UP' will always round away from 0.
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- 'DOWN' will always round towards 0.
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:return: rounded float
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"""
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rounding_factor = _float_check_precision(precision_digits=precision_digits,
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precision_rounding=precision_rounding)
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if rounding_factor == 0 or value == 0:
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return 0.0
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# NORMALIZE - ROUND - DENORMALIZE
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# In order to easily support rounding to arbitrary 'steps' (e.g. coin values),
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# we normalize the value before rounding it as an integer, and de-normalize
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# after rounding: e.g. float_round(1.3, precision_rounding=.5) == 1.5
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def normalize(val):
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return val / rounding_factor
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def denormalize(val):
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return val * rounding_factor
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# inverting small rounding factors reduces rounding errors
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if rounding_factor < 1:
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rounding_factor = float_invert(rounding_factor)
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normalize, denormalize = denormalize, normalize
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normalized_value = normalize(value)
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# Due to IEEE-754 float/double representation limits, the approximation of the
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# real value may be slightly below the tie limit, resulting in an error of
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# 1 unit in the last place (ulp) after rounding.
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# For example 2.675 == 2.6749999999999998.
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# To correct this, we add a very small epsilon value, scaled to the
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# the order of magnitude of the value, to tip the tie-break in the right
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# direction.
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# Credit: discussion with OpenERP community members on bug 882036
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epsilon_magnitude = math.log2(abs(normalized_value))
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# `2**(epsilon_magnitude - 52)` would be the minimal size, but we increase it to be
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# more tolerant of inaccuracies accumulated after multiple floating point operations
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epsilon = 2**(epsilon_magnitude - 50)
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match rounding_method:
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case 'HALF-UP': # 0.5 rounds away from 0
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result = round(normalized_value + math.copysign(epsilon, normalized_value))
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case 'HALF-EVEN': # 0.5 rounds towards closest even number
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integral = math.floor(normalized_value)
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remainder = abs(normalized_value - integral)
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is_half = abs(0.5 - remainder) < epsilon
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# if is_half & integral is odd, add odd bit to make it even
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result = integral + (integral & 1) if is_half else round(normalized_value)
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case 'HALF-DOWN': # 0.5 rounds towards 0
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result = round(normalized_value - math.copysign(epsilon, normalized_value))
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case 'UP': # round to number furthest from zero
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result = math.trunc(normalized_value + math.copysign(1 - epsilon, normalized_value))
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case 'DOWN': # round to number closest to zero
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result = math.trunc(normalized_value + math.copysign(epsilon, normalized_value))
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case _:
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msg = f"unknown rounding method: {rounding_method}"
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raise ValueError(msg)
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return denormalize(result)
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def float_is_zero(value, precision_digits=None, precision_rounding=None):
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"""Returns true if ``value`` is small enough to be treated as
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zero at the given precision (smaller than the corresponding *epsilon*).
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The precision (``10**-precision_digits`` or ``precision_rounding``)
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is used as the zero *epsilon*: values less than that are considered
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to be zero.
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Precision must be given by ``precision_digits`` or ``precision_rounding``,
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not both!
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Warning: ``float_is_zero(value1-value2)`` is not equivalent to
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``float_compare(value1,value2) == 0``, as the former will round after
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computing the difference, while the latter will round before, giving
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different results for e.g. 0.006 and 0.002 at 2 digits precision.
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:param int precision_digits: number of fractional digits to round to.
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:param float precision_rounding: decimal number representing the minimum
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non-zero value at the desired precision (for example, 0.01 for a
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2-digit precision).
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:param float value: value to compare with the precision's zero
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:return: True if ``value`` is considered zero
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"""
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epsilon = _float_check_precision(precision_digits=precision_digits,
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precision_rounding=precision_rounding)
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return value == 0.0 or abs(float_round(value, precision_rounding=epsilon)) < epsilon
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def float_compare(value1, value2, precision_digits=None, precision_rounding=None):
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"""Compare ``value1`` and ``value2`` after rounding them according to the
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given precision. A value is considered lower/greater than another value
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if their rounded value is different. This is not the same as having a
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non-zero difference!
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Precision must be given by ``precision_digits`` or ``precision_rounding``,
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not both!
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Example: 1.432 and 1.431 are equal at 2 digits precision,
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so this method would return 0
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However 0.006 and 0.002 are considered different (this method returns 1)
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because they respectively round to 0.01 and 0.0, even though
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0.006-0.002 = 0.004 which would be considered zero at 2 digits precision.
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Warning: ``float_is_zero(value1-value2)`` is not equivalent to
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``float_compare(value1,value2) == 0``, as the former will round after
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computing the difference, while the latter will round before, giving
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different results for e.g. 0.006 and 0.002 at 2 digits precision.
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:param float value1: first value to compare
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:param float value2: second value to compare
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:param int precision_digits: number of fractional digits to round to.
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:param float precision_rounding: decimal number representing the minimum
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non-zero value at the desired precision (for example, 0.01 for a
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2-digit precision).
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:return: (resp.) -1, 0 or 1, if ``value1`` is (resp.) lower than,
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equal to, or greater than ``value2``, at the given precision.
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"""
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rounding_factor = _float_check_precision(precision_digits=precision_digits,
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precision_rounding=precision_rounding)
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# equal numbers round equally, so we can skip that step
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# doing this after _float_check_precision to validate parameters first
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if value1 == value2:
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return 0
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value1 = float_round(value1, precision_rounding=rounding_factor)
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value2 = float_round(value2, precision_rounding=rounding_factor)
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delta = value1 - value2
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if float_is_zero(delta, precision_rounding=rounding_factor):
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return 0
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return -1 if delta < 0.0 else 1
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def float_repr(value, precision_digits):
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"""Returns a string representation of a float with the
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given number of fractional digits. This should not be
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used to perform a rounding operation (this is done via
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:func:`~.float_round`), but only to produce a suitable
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string representation for a float.
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:param float value:
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:param int precision_digits: number of fractional digits to include in the output
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"""
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# Can't use str() here because it seems to have an intrinsic
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# rounding to 12 significant digits, which causes a loss of
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# precision. e.g. str(123456789.1234) == str(123456789.123)!!
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return "%.*f" % (precision_digits, value)
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def float_split_str(value, precision_digits):
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"""Splits the given float 'value' in its unitary and decimal parts,
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returning each of them as a string, rounding the value using
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the provided ``precision_digits`` argument.
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The length of the string returned for decimal places will always
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be equal to ``precision_digits``, adding zeros at the end if needed.
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In case ``precision_digits`` is zero, an empty string is returned for
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the decimal places.
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Examples:
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1.432 with precision 2 => ('1', '43')
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1.49 with precision 1 => ('1', '5')
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1.1 with precision 3 => ('1', '100')
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1.12 with precision 0 => ('1', '')
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:param float value: value to split.
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:param int precision_digits: number of fractional digits to round to.
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:return: returns the tuple(<unitary part>, <decimal part>) of the given value
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:rtype: tuple(str, str)
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"""
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value = float_round(value, precision_digits=precision_digits)
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value_repr = float_repr(value, precision_digits)
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return tuple(value_repr.split('.')) if precision_digits else (value_repr, '')
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def float_split(value, precision_digits):
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""" same as float_split_str() except that it returns the unitary and decimal
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parts as integers instead of strings. In case ``precision_digits`` is zero,
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0 is always returned as decimal part.
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:rtype: tuple(int, int)
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"""
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units, cents = float_split_str(value, precision_digits)
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if not cents:
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return int(units), 0
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return int(units), int(cents)
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def json_float_round(value, precision_digits, rounding_method='HALF-UP'):
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"""Not suitable for float calculations! Similar to float_repr except that it
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returns a float suitable for json dump
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This may be necessary to produce "exact" representations of rounded float
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values during serialization, such as what is done by `json.dumps()`.
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Unfortunately `json.dumps` does not allow any form of custom float representation,
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nor any custom types, everything is serialized from the basic JSON types.
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:param int precision_digits: number of fractional digits to round to.
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:param rounding_method: the rounding method used: 'HALF-UP', 'UP' or 'DOWN',
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the first one rounding up to the closest number with the rule that
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number>=0.5 is rounded up to 1, the second always rounding up and the
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latest one always rounding down.
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:return: a rounded float value that must not be used for calculations, but
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is ready to be serialized in JSON with minimal chances of
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representation errors.
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"""
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rounded_value = float_round(value, precision_digits=precision_digits, rounding_method=rounding_method)
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rounded_repr = float_repr(rounded_value, precision_digits=precision_digits)
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# As of Python 3.1, rounded_repr should be the shortest representation for our
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# rounded float, so we create a new float whose repr is expected
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# to be the same value, or a value that is semantically identical
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# and will be used in the json serialization.
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# e.g. if rounded_repr is '3.1750', the new float repr could be 3.175
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# but not 3.174999999999322452.
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# Cfr. bpo-1580: https://bugs.python.org/issue1580
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return float(rounded_repr)
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_INVERTDICT = {
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1e-1: 1e+1, 1e-2: 1e+2, 1e-3: 1e+3, 1e-4: 1e+4, 1e-5: 1e+5,
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1e-6: 1e+6, 1e-7: 1e+7, 1e-8: 1e+8, 1e-9: 1e+9, 1e-10: 1e+10,
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2e-1: 5e+0, 2e-2: 5e+1, 2e-3: 5e+2, 2e-4: 5e+3, 2e-5: 5e+4,
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2e-6: 5e+5, 2e-7: 5e+6, 2e-8: 5e+7, 2e-9: 5e+8, 2e-10: 5e+9,
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5e-1: 2e+0, 5e-2: 2e+1, 5e-3: 2e+2, 5e-4: 2e+3, 5e-5: 2e+4,
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5e-6: 2e+5, 5e-7: 2e+6, 5e-8: 2e+7, 5e-9: 2e+8, 5e-10: 2e+9,
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}
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def float_invert(value):
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"""Inverts a floating point number with increased accuracy.
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:param float value: value to invert.
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:param bool store: whether store the result in memory for future calls.
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:return: rounded float.
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"""
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result = _INVERTDICT.get(value)
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if result is None:
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coefficient, exponent = f'{value:.15e}'.split('e')
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# invert exponent by changing sign, and coefficient by dividing by its square
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result = float(f'{coefficient}e{-int(exponent)}') / float(coefficient)**2
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return result
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if __name__ == "__main__":
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import time
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start = time.time()
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count = 0
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def try_round(amount, expected, precision_digits=3):
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result = float_repr(float_round(amount, precision_digits=precision_digits),
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precision_digits=precision_digits)
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if result != expected:
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print('###!!! Rounding error: got %s , expected %s' % (result, expected))
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return complex(1, 1)
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return 1
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# Extended float range test, inspired by Cloves Almeida's test on bug #882036.
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fractions = [.0, .015, .01499, .675, .67499, .4555, .4555, .45555]
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expecteds = ['.00', '.02', '.01', '.68', '.67', '.46', '.456', '.4556']
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precisions = [2, 2, 2, 2, 2, 2, 3, 4]
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for magnitude in range(7):
|
||
|
|
for frac, exp, prec in zip(fractions, expecteds, precisions):
|
||
|
|
for sign in [-1, 1]:
|
||
|
|
for x in range(0, 10000, 97):
|
||
|
|
n = x * 10**magnitude
|
||
|
|
f = sign * (n + frac)
|
||
|
|
f_exp = ('-' if f != 0 and sign == -1 else '') + str(n) + exp
|
||
|
|
count += try_round(f, f_exp, precision_digits=prec)
|
||
|
|
|
||
|
|
stop = time.time()
|
||
|
|
count, errors = int(count.real), int(count.imag)
|
||
|
|
|
||
|
|
# Micro-bench results:
|
||
|
|
# 47130 round calls in 0.422306060791 secs, with Python 2.6.7 on Core i3 x64
|
||
|
|
# with decimal:
|
||
|
|
# 47130 round calls in 6.612248100021 secs, with Python 2.6.7 on Core i3 x64
|
||
|
|
print(count, " round calls, ", errors, "errors, done in ", (stop-start), 'secs')
|