author | martin.trojer@nokia.com |
Fri, 31 Jul 2009 15:01:17 +0100 | |
changeset 1 | 2fb8b9db1c86 |
permissions | -rw-r--r-- |
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:mod:`math` --- Mathematical functions |
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====================================== |
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.. module:: math |
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:synopsis: Mathematical functions (sin() etc.). |
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This module is always available. It provides access to the mathematical |
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functions defined by the C standard. |
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These functions cannot be used with complex numbers; use the functions of the |
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same name from the :mod:`cmath` module if you require support for complex |
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numbers. The distinction between functions which support complex numbers and |
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those which don't is made since most users do not want to learn quite as much |
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mathematics as required to understand complex numbers. Receiving an exception |
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instead of a complex result allows earlier detection of the unexpected complex |
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number used as a parameter, so that the programmer can determine how and why it |
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was generated in the first place. |
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The following functions are provided by this module. Except when explicitly |
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noted otherwise, all return values are floats. |
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Number-theoretic and representation functions: |
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.. function:: ceil(x) |
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Return the ceiling of *x* as a float, the smallest integer value greater than or |
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equal to *x*. |
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.. function:: copysign(x, y) |
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Return *x* with the sign of *y*. ``copysign`` copies the sign bit of an IEEE |
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754 float, ``copysign(1, -0.0)`` returns *-1.0*. |
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.. versionadded:: 2.6 |
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.. function:: fabs(x) |
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Return the absolute value of *x*. |
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.. function:: factorial(x) |
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Return *x* factorial. Raises :exc:`ValueError` if *x* is not integral or |
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is negative. |
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.. versionadded:: 2.6 |
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.. function:: floor(x) |
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Return the floor of *x* as a float, the largest integer value less than or equal |
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to *x*. |
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.. versionchanged:: 2.6 |
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Added :meth:`__floor__` delegation. |
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.. function:: fmod(x, y) |
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Return ``fmod(x, y)``, as defined by the platform C library. Note that the |
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Python expression ``x % y`` may not return the same result. The intent of the C |
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standard is that ``fmod(x, y)`` be exactly (mathematically; to infinite |
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precision) equal to ``x - n*y`` for some integer *n* such that the result has |
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the same sign as *x* and magnitude less than ``abs(y)``. Python's ``x % y`` |
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returns a result with the sign of *y* instead, and may not be exactly computable |
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for float arguments. For example, ``fmod(-1e-100, 1e100)`` is ``-1e-100``, but |
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the result of Python's ``-1e-100 % 1e100`` is ``1e100-1e-100``, which cannot be |
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represented exactly as a float, and rounds to the surprising ``1e100``. For |
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this reason, function :func:`fmod` is generally preferred when working with |
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floats, while Python's ``x % y`` is preferred when working with integers. |
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.. function:: frexp(x) |
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Return the mantissa and exponent of *x* as the pair ``(m, e)``. *m* is a float |
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and *e* is an integer such that ``x == m * 2**e`` exactly. If *x* is zero, |
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returns ``(0.0, 0)``, otherwise ``0.5 <= abs(m) < 1``. This is used to "pick |
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apart" the internal representation of a float in a portable way. |
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.. function:: fsum(iterable) |
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Return an accurate floating point sum of values in the iterable. Avoids |
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loss of precision by tracking multiple intermediate partial sums. The |
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algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the |
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typical case where the rounding mode is half-even. |
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.. note:: |
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The accuracy of fsum() may be impaired on builds that use |
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extended precision addition and then double-round the results. |
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.. versionadded:: 2.6 |
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.. function:: isinf(x) |
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Checks if the float *x* is positive or negative infinite. |
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.. versionadded:: 2.6 |
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.. function:: isnan(x) |
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Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
109 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
110 |
Checks if the float *x* is a NaN (not a number). NaNs are part of the |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
111 |
IEEE 754 standards. Operation like but not limited to ``inf * 0``, |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
112 |
``inf / inf`` or any operation involving a NaN, e.g. ``nan * 1``, return |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
113 |
a NaN. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
114 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
115 |
.. versionadded:: 2.6 |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
116 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
117 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
118 |
.. function:: ldexp(x, i) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
119 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
120 |
Return ``x * (2**i)``. This is essentially the inverse of function |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
121 |
:func:`frexp`. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
122 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
123 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
124 |
.. function:: modf(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
125 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
126 |
Return the fractional and integer parts of *x*. Both results carry the sign of |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
127 |
*x*, and both are floats. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
128 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
129 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
130 |
.. function:: trunc(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
131 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
132 |
Return the :class:`Real` value *x* truncated to an :class:`Integral` (usually |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
133 |
a long integer). Delegates to ``x.__trunc__()``. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
134 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
135 |
.. versionadded:: 2.6 |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
136 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
137 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
138 |
Note that :func:`frexp` and :func:`modf` have a different call/return pattern |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
139 |
than their C equivalents: they take a single argument and return a pair of |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
140 |
values, rather than returning their second return value through an 'output |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
141 |
parameter' (there is no such thing in Python). |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
142 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
143 |
For the :func:`ceil`, :func:`floor`, and :func:`modf` functions, note that *all* |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
144 |
floating-point numbers of sufficiently large magnitude are exact integers. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
145 |
Python floats typically carry no more than 53 bits of precision (the same as the |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
146 |
platform C double type), in which case any float *x* with ``abs(x) >= 2**52`` |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
147 |
necessarily has no fractional bits. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
148 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
149 |
Power and logarithmic functions: |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
150 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
151 |
.. function:: exp(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
152 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
153 |
Return ``e**x``. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
154 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
155 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
156 |
.. function:: log(x[, base]) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
157 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
158 |
Return the logarithm of *x* to the given *base*. If the *base* is not specified, |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
159 |
return the natural logarithm of *x* (that is, the logarithm to base *e*). |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
160 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
161 |
.. versionchanged:: 2.3 |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
162 |
*base* argument added. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
163 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
164 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
165 |
.. function:: log1p(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
166 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
167 |
Return the natural logarithm of *1+x* (base *e*). The |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
168 |
result is calculated in a way which is accurate for *x* near zero. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
169 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
170 |
.. versionadded:: 2.6 |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
171 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
172 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
173 |
.. function:: log10(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
174 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
175 |
Return the base-10 logarithm of *x*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
176 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
177 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
178 |
.. function:: pow(x, y) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
179 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
180 |
Return ``x`` raised to the power ``y``. Exceptional cases follow |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
181 |
Annex 'F' of the C99 standard as far as possible. In particular, |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
182 |
``pow(1.0, x)`` and ``pow(x, 0.0)`` always return ``1.0``, even |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
183 |
when ``x`` is a zero or a NaN. If both ``x`` and ``y`` are finite, |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
184 |
``x`` is negative, and ``y`` is not an integer then ``pow(x, y)`` |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
185 |
is undefined, and raises :exc:`ValueError`. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
186 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
187 |
.. versionchanged:: 2.6 |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
188 |
The outcome of ``1**nan`` and ``nan**0`` was undefined. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
189 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
190 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
191 |
.. function:: sqrt(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
192 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
193 |
Return the square root of *x*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
194 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
195 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
196 |
Trigonometric functions: |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
197 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
198 |
.. function:: acos(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
199 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
200 |
Return the arc cosine of *x*, in radians. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
201 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
202 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
203 |
.. function:: asin(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
204 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
205 |
Return the arc sine of *x*, in radians. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
206 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
207 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
208 |
.. function:: atan(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
209 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
210 |
Return the arc tangent of *x*, in radians. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
211 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
212 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
213 |
.. function:: atan2(y, x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
214 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
215 |
Return ``atan(y / x)``, in radians. The result is between ``-pi`` and ``pi``. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
216 |
The vector in the plane from the origin to point ``(x, y)`` makes this angle |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
217 |
with the positive X axis. The point of :func:`atan2` is that the signs of both |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
218 |
inputs are known to it, so it can compute the correct quadrant for the angle. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
219 |
For example, ``atan(1``) and ``atan2(1, 1)`` are both ``pi/4``, but ``atan2(-1, |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
220 |
-1)`` is ``-3*pi/4``. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
221 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
222 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
223 |
.. function:: cos(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
224 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
225 |
Return the cosine of *x* radians. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
226 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
227 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
228 |
.. function:: hypot(x, y) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
229 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
230 |
Return the Euclidean norm, ``sqrt(x*x + y*y)``. This is the length of the vector |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
231 |
from the origin to point ``(x, y)``. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
232 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
233 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
234 |
.. function:: sin(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
235 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
236 |
Return the sine of *x* radians. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
237 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
238 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
239 |
.. function:: tan(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
240 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
241 |
Return the tangent of *x* radians. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
242 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
243 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
244 |
Angular conversion: |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
245 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
246 |
.. function:: degrees(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
247 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
248 |
Converts angle *x* from radians to degrees. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
249 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
250 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
251 |
.. function:: radians(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
252 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
253 |
Converts angle *x* from degrees to radians. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
254 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
255 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
256 |
Hyperbolic functions: |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
257 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
258 |
.. function:: acosh(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
259 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
260 |
Return the inverse hyperbolic cosine of *x*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
261 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
262 |
.. versionadded:: 2.6 |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
263 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
264 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
265 |
.. function:: asinh(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
266 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
267 |
Return the inverse hyperbolic sine of *x*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
268 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
269 |
.. versionadded:: 2.6 |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
270 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
271 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
272 |
.. function:: atanh(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
273 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
274 |
Return the inverse hyperbolic tangent of *x*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
275 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
276 |
.. versionadded:: 2.6 |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
277 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
278 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
279 |
.. function:: cosh(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
280 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
281 |
Return the hyperbolic cosine of *x*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
282 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
283 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
284 |
.. function:: sinh(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
285 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
286 |
Return the hyperbolic sine of *x*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
287 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
288 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
289 |
.. function:: tanh(x) |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
290 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
291 |
Return the hyperbolic tangent of *x*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
292 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
293 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
294 |
The module also defines two mathematical constants: |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
295 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
296 |
.. data:: pi |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
297 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
298 |
The mathematical constant *pi*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
299 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
300 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
301 |
.. data:: e |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
302 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
303 |
The mathematical constant *e*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
304 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
305 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
306 |
.. note:: |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
307 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
308 |
The :mod:`math` module consists mostly of thin wrappers around the platform C |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
309 |
math library functions. Behavior in exceptional cases is loosely specified |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
310 |
by the C standards, and Python inherits much of its math-function |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
311 |
error-reporting behavior from the platform C implementation. As a result, |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
312 |
the specific exceptions raised in error cases (and even whether some |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
313 |
arguments are considered to be exceptional at all) are not defined in any |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
314 |
useful cross-platform or cross-release way. For example, whether |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
315 |
``math.log(0)`` returns ``-Inf`` or raises :exc:`ValueError` or |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
316 |
:exc:`OverflowError` isn't defined, and in cases where ``math.log(0)`` raises |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
317 |
:exc:`OverflowError`, ``math.log(0L)`` may raise :exc:`ValueError` instead. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
318 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
319 |
All functions return a quiet *NaN* if at least one of the args is *NaN*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
320 |
Signaling *NaN*\s raise an exception. The exception type still depends on the |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
321 |
platform and libm implementation. It's usually :exc:`ValueError` for *EDOM* |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
322 |
and :exc:`OverflowError` for errno *ERANGE*. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
323 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
324 |
.. versionchanged:: 2.6 |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
325 |
In earlier versions of Python the outcome of an operation with NaN as |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
326 |
input depended on platform and libm implementation. |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
327 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
328 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
329 |
.. seealso:: |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
330 |
|
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
331 |
Module :mod:`cmath` |
2fb8b9db1c86
Initial QEMU (symbian-qemu-0.9.1-12) import
martin.trojer@nokia.com
parents:
diff
changeset
|
332 |
Complex number versions of many of these functions. |