merge libmaple docs ("leaflabs-docs") into ./docs

In the past, libample documentation was forked out of this repository
because the documentation had increased in scope. For the librambutan,
and the rambutan project in general, we will try to keep documentation
closer to the source code, so the librambutan-specific documentation
should live here. Other sections of leaflabs-docs will be culled in a
following commit.

This merge attempts to maintain history by using a subtree strategy.
Followed directions at:

    http://nuclearsquid.com/writings/subtree-merging-and-you/

Full history for files should be accessible using the "--follow" flag to
git log, eg:

    git log --follow docs/source/adc.rst

It should be possible to pull patches from leaflabs-docs with:

    git pull -s subtree leaflabs-docs master

... at least until the docs in this repository diverge significantly.

1 files changed, 185 insertions, 0 deletions

diff --git a/docs/source/lang/cpp/bitwisemath.rst b/docs/source/lang/cpp/bitwisemath.rst
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+.. highlight:: cpp
+
+.. _lang-bitwisemath:
+
+Bitwise Operators (``&``, ``|``, ``^``, ``~``)
+==============================================
+
+The bitwise operators perform their calculations at the bit level of
+variables. They help solve a wide range of common programming
+problems.
+
+Much of the material here is adapted for Maple from an (Arduino)
+`tutorial on bitwise math
+<http://www.arduino.cc/playground/Code/BitMath>`_\ .  Another great
+resource is the Wikipedia article on `bitwise operations
+<http://en.wikipedia.org/wiki/Bitwise_operation>`_\ .
+
+Below are descriptions and syntax for all of the operators.
+
+.. contents:: Contents
+   :local:
+
+.. _lang-bitwisemath-and:
+
+Bitwise AND (``&``)
+-------------------
+
+The bitwise AND operator in C++ is a single ampersand, ``&``, used
+between two other integer expressions. Bitwise AND operates on each
+bit position of the surrounding expressions independently, according
+to this rule: if both input bits are 1, the resulting output is 1,
+otherwise the output is 0. Another way of expressing this is::
+
+        0  0  1  1    operand1
+        0  1  0  1    operand2
+        ----------
+        0  0  0  1    (operand1 & operand2) = result
+
+
+On the Maple, the type ``int`` is a 32-bit value, so using ``&``
+between two ``int`` expressions causes 32 simultaneous AND operations
+to occur. In a code fragment like::
+
+        int a =  92;    // in binary: 00000000000000000000000001011100
+        int b = 101;    // in binary: 00000000000000000000000001100101
+        int c = a & b;  // result:    00000000000000000000000001000100,
+                        //    (or 68 in decimal).
+
+
+Each of the 32 bits in ``a`` and ``b`` are processed using bitwise
+AND, and all 32 resulting bits are stored in ``c``, resulting in the
+value 1000100 in binary, which is 68 in decimal.
+
+
+.. _lang-bitwisemath-or:
+
+Bitwise OR (``|``)
+------------------
+
+The bitwise OR operator in C++ is the vertical bar symbol, ``|``. Like
+the ``&`` operator, ``|`` operates independently on each bit in its
+two surrounding integer expressions, but what it does is
+different. The bitwise OR of two bits is 1 if either or both of the
+input bits is 1, otherwise it is 0.  For example::
+
+        0  0  1  1    operand1
+        0  1  0  1    operand2
+        ----------
+        0  1  1  1    (operand1 | operand2) = result
+
+Here is an example of bitwise OR used in a snippet of C++ code (using
+``char``, which takes up 8 bits of memory, instead of ``int``, which
+uses 32)::
+
+        char a =  92;    // in binary: 01011100
+        char b = 101;    // in binary: 01100101
+        char c = a | b;  // result:    01111101, or 125 in decimal.
+
+.. _lang-bitwisemath-xor:
+
+Bitwise XOR (``^``)
+-------------------
+
+There is a somewhat unusual operator in C++ called bitwise EXCLUSIVE
+OR, also known as bitwise XOR. (In English, this is usually pronounced
+"zor" or "ex-or"). The bitwise XOR operator is written using the caret
+symbol, ``^``. This operator is very similar to the bitwise OR
+operator ``|``, except it evaluates to 0 for a given bit position when
+both of the input bits for that position are 1::
+
+        0  0  1  1    operand1
+        0  1  0  1    operand2
+        ----------
+        0  1  1  0    (operand1 ^ operand2) = result
+
+
+Another way to look at bitwise XOR is that each bit in the result
+is a 1 if the input bits are different, or 0 if they are the same.
+
+Here is a simple example::
+
+        int x = 12;     // binary (ignoring extra bits): 1100
+        int y = 10;     // binary:                       1010
+        int z = x ^ y;  // binary:                       0110, or decimal 6
+
+
+
+The ^ operator is often used to toggle (i.e. change from 0 to 1, or 1
+to 0) some of the bits in an integer expression. In a bitwise OR
+operation if there is a 1 in the mask bit, that bit is inverted; if
+there is a 0, the bit is not inverted and stays the same. Below is a
+program to toggle the built-in LED pin (you can also accomplish this
+with :ref:`lang-toggleled`)::
+
+    // Toggle built-in LED pin
+
+    int toggle = 0;
+
+    // demo for Exclusive OR
+    void setup(){
+        pinMode(BOARD_LED_PIN, OUTPUT);
+    }
+
+    void loop(){
+        toggle = toggle ^ 1;
+        digitalWrite(BOARD_LED_PIN, toggle);
+        delay(100);
+    }
+
+.. _lang-bitwisemath-not:
+
+Bitwise NOT (``~``)
+-------------------
+
+The bitwise NOT operator in C++ is the tilde character ``~``. Unlike
+``&`` and ``|``, the bitwise NOT operator is applied to a single
+operand to its right. Bitwise NOT changes each bit to its opposite: 0
+becomes 1, and 1 becomes 0. For example::
+
+        0  1    operand1
+        ----
+        1  0   ~operand1 = result
+
+Another example::
+
+        char a = 103;    // binary:  01100111
+        char b = ~a;     // binary:  10011000 = -104
+
+You might be surprised to see a negative number like -104 as the
+result of this operation. This is because the highest bit in an int
+variable is the so-called "sign bit". If the highest bit is 1, the
+number is interpreted as negative. This encoding of positive and
+negative numbers is referred to as *two's complement*. For more
+information, see the Wikipedia article on `two's
+complement. <http://en.wikipedia.org/wiki/Twos_complement>`_
+
+As an aside, it is interesting to note that (under two's complement
+arithmetic) for any integer ``x``, ``~x`` is the same as ``-x-1``.
+
+At times, the sign bit in a signed integer expression can cause
+some unwanted surprises.
+
+
+Uses
+----
+
+One of the most common uses of bitwise operations is to select or
+manipulate a particular bit (or bits) from an integer value, often
+called `bit masking
+<http://en.wikipedia.org/wiki/Mask_%28computing%29>`_\ . See the
+linked Wikipedia article for more information and examples.
+
+If you really want to see bit-twiddling techniques in their full
+glory, you could do much worse than to get yourself a copy of
+`Hacker's Delight <http://www.hackersdelight.org/>`_\ .
+
+
+See Also
+--------
+
+- :ref:`Boolean operations <lang-boolean>` (``&&``, ``||``)
+- :ref:`Compound bitwise operations <lang-compoundbitwise>` (``&=``,
+   ``|=``, ``^=``).
+
+.. include:: /arduino-cc-attribution.txt