mirror of https://github.com/python/cpython
Rewrite two sections
This commit is contained in:
Andrew M. Kuchling
parent
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@ -2,6 +2,10 @@
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\usepackage{distutils}
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% $Id$
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% Don't write extensive text for new sections; I'll do that.
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% Feel free to add commented-out reminders of things that need
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% to be covered. --amk
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\title{What's New in Python 2.4}
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\release{0.0}
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\author{A.M.\ Kuchling}
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@ -89,73 +93,61 @@ Greg Wilson and ultimately implemented by Raymond Hettinger.}
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XXX write this.
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%======================================================================
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\section{PEP 229: Generator Expressions}
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\section{PEP 289: Generator Expressions}
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Now, simple generators can be coded succinctly as expressions using a syntax
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like list comprehensions but with parentheses instead of brackets. These
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expressions are designed for situations where the generator is used right
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away by an enclosing function. Generator expressions are more compact but
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less versatile than full generator definitions and they tend to be more memory
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friendly than equivalent list comprehensions.
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The iterator feature introduced in Python 2.2 makes it easier to write
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programs that loop through large data sets without having the entire
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data set in memory at one time. Programmers can use iterators and the
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\module{itertools} module to write code in a fairly functional style.
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The fly in the ointment has been list comprehensions, because they
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produce a Python list object containing all of the items, unavoidably
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pulling them all into memory. When trying to write a program using the functional approach, it would be natural to write something like:
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\begin{verbatim}
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g = (tgtexp for var1 in exp1 for var2 in exp2 if exp3)
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links = [link for link in get_all_links() if not link.followed]
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for link in links:
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...
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\end{verbatim}
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is equivalent to:
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instead of
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\begin{verbatim}
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def __gen(exp):
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for var1 in exp:
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for var2 in exp2:
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if exp3:
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yield tgtexp
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g = __gen(iter(exp1))
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del __gen
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for link in get_all_links():
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if link.followed:
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continue
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...
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\end{verbatim}
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The advantage over full generator definitions is in economy of
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expression. Their advantage over list comprehensions is in saving
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memory by creating data only when it is needed rather than forming
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a whole list is memory all at once. Applications using memory
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friendly generator expressions may scale-up to high volumes of data
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more readily than with list comprehensions.
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The first form is more concise and perhaps more readable, but if
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you're dealing with a large number of link objects the second form
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would have to be used.
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Generator expressions are best used in functions that consume their
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data all at once and would not benefit from having a full list instead
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of a generator as an input:
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Generator expressions work similarly to list comprehensions but don't
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materialize the entire list; instead they create a generator that will
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return elements one by one. The above example could be written as:
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\begin{verbatim}
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>>> sum(i*i for i in range(10))
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285
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>>> sorted(set(i*i for i in xrange(-20, 20) if i%2==1)) # odd squares
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[1, 9, 25, 49, 81, 121, 169, 225, 289, 361]
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>>> from itertools import izip
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>>> xvec = [10, 20, 30]
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>>> yvec = [7, 5, 3]
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>>> sum(x*y for x,y in izip(xvec, yvec)) # dot product
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260
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>>> from math import pi, sin
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>>> sine_table = dict((x, sin(x*pi/180)) for x in xrange(0, 91))
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>>> unique_words = set(word for line in page for word in line.split())
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>>> valedictorian = max((student.gpa, student.name) for student in graduates)
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links = (link for link in get_all_links() if not link.followed)
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for link in links:
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...
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\end{verbatim}
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For more complex uses of generators, it is strongly recommended that
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the traditional full generator definitions be used instead. In a
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generator expression, the first for-loop expression is evaluated
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as soon as the expression is defined while the other expressions do
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not get evaluated until the generator is run. This nuance is never
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an issue when the generator is used immediately; however, if it is not
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used right away, a full generator definition would be much more clear
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about when the sub-expressions are evaluated and would be more obvious
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about the visibility and lifetime of the variables.
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Generator expressions always have to be written inside parentheses, as
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in the above example. The parentheses signalling a function call also
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count, so if you want to create a iterator that will be immediately
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passed to a function you could write:
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\begin{verbatim}
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print sum(obj.count for obj in list_all_objects())
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\end{verbatim}
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There are some small differences from list comprehensions. Most
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notably, the loop variable (\var{obj} in the above example) is not
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accessible outside of the generator expression. List comprehensions
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leave the variable assigned to its last value; future versions of
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Python will change this, making list comprehensions match generator
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expressions in this respect.
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\begin{seealso}
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\seepep{289}{Generator Expressions}{Proposed by Raymond Hettinger and
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@ -203,62 +195,222 @@ root:*:0:0:System Administrator:/var/root:/bin/tcsh
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%======================================================================
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\section{PEP 327: Decimal Data Type}
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A new module, \module{decimal}, offers a \class{Decimal} data type for
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decimal floating point arithmetic. Compared to the built-in \class{float}
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type implemented with binary floating point, the new class is especially
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useful for financial applications and other uses which require exact
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decimal representation, control over precision, control over rounding
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to meet legal or regulatory requirements, tracking of significant
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decimal places, or for applications where the user expects the results
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to match hand calculations done the way they were taught in school.
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Python has always supported floating-point (FP) numbers as a data
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type, based on the underlying C \ctype{double} type. However, while
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most programming languages provide a floating-point type, most people
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(even programmers) are unaware that computing with floating-point
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numbers entails certain unavoidable inaccuracies. The new decimal
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type provides a way to avoid these inaccuracies.
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For example, calculating a 5% tax on a 70 cent phone charge gives
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different results in decimal floating point and binary floating point
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with the difference being significant when rounding to the nearest
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cent:
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\subsection{Why is Decimal needed?}
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The limitations arise from the representation used for floating-point numbers.
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FP numbers are made up of three components:
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\begin{itemize}
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\item The sign, which is -1 or +1.
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\item The mantissa, which is a single-digit binary number
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followed by a fractional part. For example, \code{1.01} in base-2 notation
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is \code{1 + 0/2 + 1/4}, or 1.25 in decimal notation.
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\item The exponent, which tells where the decimal point is located in the number represented.
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\end{itemize}
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For example, the number 1.25 has sign +1, mantissa 1.01 (in binary),
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and exponent of 0 (the decimal point doesn't need to be shifted). The
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number 5 has the same sign and mantissa, but the exponent is 2
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because the mantissa is multiplied by 4 (2 to the power of the exponent 2).
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Modern systems usually provide floating-point support that conforms to
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a relevant standard called IEEE 754. C's \ctype{double} type is
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usually implemented as a 64-bit IEEE 754 number, which uses 52 bits of
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space for the mantissa. This means that numbers can only be specified
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to 52 bits of precision. If you're trying to represent numbers whose
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expansion repeats endlessly, the expansion is cut off after 52 bits.
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Unfortunately, most software needs to produce output in base 10, and
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base 10 often gives rise to such repeating decimals. For example, 1.1
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decimal is binary \code{1.0001100110011 ...}; .1 = 1/16 + 1/32 + 1/256
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plus an infinite number of additional terms. IEEE 754 has to chop off
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that infinitely repeated decimal after 52 digits, so the
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representation is slightly inaccurate.
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Sometimes you can see this inaccuracy when the number is printed:
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\begin{verbatim}
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>>> from decimal import *
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>>> Decimal('0.70') * Decimal('1.05')
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Decimal("0.7350")
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>>> .70 * 1.05
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0.73499999999999999
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>>> 1.1
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1.1000000000000001
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\end{verbatim}
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Note that the \class{Decimal} result keeps a trailing zero, automatically
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inferring four place significance from two digit mulitiplicands. A key
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goal is to reproduce the mathematics we do by hand and avoid the tricky
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issues that arise when decimal numbers cannot be represented exactly in
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binary floating point.
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The inaccuracy isn't always visible when you print the number because
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the FP-to-decimal-string conversion is provided by the C library, and
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most C libraries try to produce sensible output, but the inaccuracy is
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still there and subsequent operations can magnify the error.
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Exact representation enables the \class{Decimal} class to perform
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modulo calculations and equality tests that would fail in binary
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floating point:
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For many applications this doesn't matter. If I'm plotting points and
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displaying them on my monitor, the difference between 1.1 and
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1.1000000000000001 is too small to be visible. Reports often limit
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output to a certain number of decimal places, and if you round the
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number to two or three or even eight decimal places, the error is
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never apparent. However, for applications where it does matter,
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it's a lot of work to implement your own custom arithmetic routines.
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\subsection{The \class{Decimal} type}
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A new module, \module{decimal}, was added to Python's standard library.
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It contains two classes, \class{Decimal} and \class{Context}.
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\class{Decimal} instances represent numbers, and
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\class{Context} instances are used to wrap up various settings such as the precision and default rounding mode.
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\class{Decimal} instances, like regular Python integers and FP numbers, are immutable; once they've been created, you can't change the value it represents.
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\class{Decimal} instances can be created from integers or strings:
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\begin{verbatim}
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>>> Decimal('1.00') % Decimal('.10')
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Decimal("0.00")
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>>> 1.00 % 0.10
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0.09999999999999995
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>>> sum([Decimal('0.1')]*10) == Decimal('1.0')
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True
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>>> sum([0.1]*10) == 1.0
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False
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>>> import decimal
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>>> decimal.Decimal(1972)
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Decimal("1972")
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>>> decimal.Decimal("1.1")
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Decimal("1.1")
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\end{verbatim}
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The \module{decimal} module also allows arbitrarily large precisions to be
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set for calculation:
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You can also provide tuples containing the sign, mantissa represented
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as a tuple of decimal digits, and exponent:
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\begin{verbatim}
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>>> getcontext().prec = 24
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>>> Decimal(1) / Decimal(7)
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Decimal("0.142857142857142857142857")
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>>> decimal.Decimal((1, (1, 4, 7, 5), -2))
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Decimal("-14.75")
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\end{verbatim}
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Cautionary note: the sign bit is a Boolean value, so 0 is positive and 1 is negative.
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Floating-point numbers posed a bit of a problem: should the FP number
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representing 1.1 turn into the decimal number for exactly 1.1, or for
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1.1 plus whatever inaccuracies are introduced? The decision was to
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leave such a conversion out of the API. Instead, you should convert
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the floating-point number into a string using the desired precision and
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pass the string to the \class{Decimal} constructor:
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\begin{verbatim}
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>>> f = 1.1
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>>> decimal.Decimal(str(f))
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Decimal("1.1")
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>>> decimal.Decimal(repr(f))
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Decimal("1.1000000000000001")
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\end{verbatim}
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Once you have \class{Decimal} instances, you can perform the usual
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mathematical operations on them. One limitation: exponentiation
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requires an integer exponent:
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\begin{verbatim}
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>>> a = decimal.Decimal('35.72')
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>>> b = decimal.Decimal('1.73')
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>>> a+b
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Decimal("37.45")
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>>> a-b
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Decimal("33.99")
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>>> a*b
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Decimal("61.7956")
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>>> a/b
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Decimal("20.6473988")
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>>> a ** 2
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Decimal("1275.9184")
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>>> a ** b
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Decimal("NaN")
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\end{verbatim}
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You can combine \class{Decimal} instances with integers, but not with
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floating-point numbers:
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\begin{verbatim}
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>>> a + 4
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Decimal("39.72")
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>>> a + 4.5
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Traceback (most recent call last):
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...
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TypeError: You can interact Decimal only with int, long or Decimal data types.
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>>>
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\end{verbatim}
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\class{Decimal} numbers can be used with the \module{math} and
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\module{cmath} modules, though you'll get back a regular
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floating-point number and not a \class{Decimal}. Instances also have a \method{sqrt()} method:
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\begin{verbatim}
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>>> import math, cmath
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>>> d = decimal.Decimal('123456789012.345')
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>>> math.sqrt(d)
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351364.18288201344
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>>> cmath.sqrt(-d)
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351364.18288201344j
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>>> d.sqrt()
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Decimal(``351364.1828820134592177245001'')
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\end{verbatim}
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\subsection{The \class{Context} type}
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Instances of the \class{Context} class encapsulate several settings for
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decimal operations:
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\begin{itemize}
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\item \member{prec} is the precision, the number of decimal places.
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\item \member{rounding} specifies the rounding mode. The \module{decimal}
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module has constants for the various possibilities:
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\constant{ROUND_DOWN}, \constant{ROUND_CEILING}, \constant{ROUND_HALF_EVEN}, and various others.
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\item \member{trap_enablers} is a dictionary specifying what happens on
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encountering certain error conditions: either an exception is raised or
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a value is returned. Some examples of error conditions are
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division by zero, loss of precision, and overflow.
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\end{itemize}
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There's a thread-local default context available by calling
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\function{getcontext()}; you can change the properties of this context
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to alter the default precision, rounding, or trap handling.
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\begin{verbatim}
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>>> decimal.getcontext().prec
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28
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>>> decimal.Decimal(1) / decimal.Decimal(7)
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Decimal(``0.1428571428571428571428571429'')
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>>> decimal.getcontext().prec = 9
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>>> decimal.Decimal(1) / decimal.Decimal(7)
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Decimal(``0.142857143'')
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\end{verbatim}
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The default action for error conditions is to return a special value
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such as infinity or not-a-number, but you can request that exceptions
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be raised:
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\begin{verbatim}
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>>> decimal.Decimal(1) / decimal.Decimal(0)
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Decimal(``Infinity'')
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>>> decimal.getcontext().trap_enablers[decimal.DivisionByZero] = True
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>>> decimal.Decimal(1) / decimal.Decimal(0)
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Traceback (most recent call last):
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...
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decimal.DivisionByZero: x / 0
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>>>
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\end{verbatim}
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The \class{Context} instance also has various methods for formatting
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numbers such as \method{to_eng_string()} and \method{to_sci_string()}.
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\begin{seealso}
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\seepep{327}{Decimal Data Type}{Written by Facundo Batista and implemented
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by Eric Price, Facundo Bastista, Raymond Hettinger, Aahz, and Tim Peters.}
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by Facundo Batista, Eric Price, Raymond Hettinger, Aahz, and Tim Peters.}
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\seeurl{http://research.microsoft.com/~hollasch/cgindex/coding/ieeefloat.html}
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{A more detailed overview of the IEEE-754 representation.}
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\seeurl{http://www.lahey.com/float.htm}
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{The article uses Fortran code to illustrate many of the problems
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that floating-point inaccuracy can cause.}
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\seeurl{http://www2.hursley.ibm.com/decimal/}
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{A description of a decimal-based representation. This representation
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is being proposed as a standard, and underlies the new Python decimal
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type. Much of this material was written by Mike Cowlishaw, designer of the
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REXX language.}
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\end{seealso}
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