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+syntax: glob
+include *.rst
+include *.txt
+recursive-include src *.py *.c *.h
+global-exclude *.pyc *.so
+.PHONY: test
+	python test
+Quaternion arithmetics for Python.
+    >>> from quaternion import Quaternion as H
+    >>> q1 = H(2, 3, 2, 3)
+    >>> q2 = H(3, 2, 3, 2)
+    >>> q1 * q2
+    (-12 + 8i + 12j + 18k)
+    >>> q2 * q1)
+    (-12 + 18i + 12j + 8k))
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+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    GNU General Public License for more details.
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <>.
+Also add information on how to contact you by electronic and paper mail.
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+    <program>  Copyright (C) <year>  <name of author>
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+from setuptools import Extension
+from setuptools import find_packages
+from setuptools import setup
+    name='quaternion',
+    version='1.0',
+    license='GPL',
+    package_dir={'': 'src'},
+    packages=find_packages('src'),
+    ext_modules=[
+        Extension('quaternion._quaternion', ['src/quaternion/quaternion.c'])
+    ],
+    test_suite = "tests.suite",


+    from _quaternion import Quaternion
+except ImportError:
+    from quaternion import Quaternion


+#include <Python.h>
+#include <stdio.h>
+#include "math.h"
+#include "structmember.h"
+#include "quaternion.h"
+static void Quaternion_dealloc(Quaternion* self)
+    self->ob_type->tp_free((PyObject*)self);
+static PyObject *
+Quaternion_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
+    Quaternion *self;
+    self = (Quaternion *)type->tp_alloc(type, 0);
+    if (self != NULL) {
+        self->w = 0;
+        self->x = 0;
+        self->y = 0;
+        self->z = 0;
+    }
+    return (PyObject *)self;
+static int
+Quaternion_init(Quaternion *self, PyObject *args, PyObject *kwds)
+    static char *kwlist[] = {"w", "x", "y", "z", NULL};
+    if (! PyArg_ParseTupleAndKeywords(args, kwds, "|dddd", kwlist, 
+                                      &self->w, &self->x,
+                                      &self->y, &self->z))
+        return -1; 
+    return 0;
+static PyMemberDef Quaternion_members[] = {
+    {"w", T_DOUBLE, offsetof(Quaternion, w), 0, "w"},
+    {"x", T_DOUBLE, offsetof(Quaternion, x), 0, "x"},
+    {"y", T_DOUBLE, offsetof(Quaternion, y), 0, "y"},
+    {"z", T_DOUBLE, offsetof(Quaternion, z), 0, "z"},
+    {NULL}  /* Sentinel */
+void dbl2str(char *s, char *ss, double n)
+    long d = labs((long) n);
+    long f = (long) ((n - d) * 1000000);
+    if (f > 0)
+        sprintf(s, "%ld.%ld", d, f);
+    else
+        sprintf(s, "%ld", d);
+    if (n >= 0)
+        strcpy(ss, "+");
+    else
+        strcpy(ss, "-");
+static PyObject *
+Quaternion_str(Quaternion* self)
+    static PyObject *format = NULL;
+    PyObject *args, *result;
+    char w[50], ws[2];
+    char x[50], xs[2];
+    char y[50], ys[2];
+    char z[50], zs[2];
+    dbl2str(w, ws, self->w);
+    dbl2str(x, xs, self->x);
+    dbl2str(y, ys, self->y);
+    dbl2str(z, zs, self->z);
+    if (strcmp(ws, "+") == 0) strcpy(ws, "");
+    if (format == NULL) {
+        format = PyString_FromString("(%s%s %s %si %s %sj %s %sk)");
+        if (format == NULL) return NULL;
+    }
+    args = Py_BuildValue("ssssssss", ws, w, xs, x, ys, y, zs, z);
+    if (args == NULL) return NULL;
+    result = PyString_Format(format, args);
+    Py_DECREF(args);
+    return result;
+static PyObject *
+Quaternion_add(Quaternion *q1, Quaternion *q2)
+    Quaternion *result;
+    result = PyObject_New(Quaternion, &QuaternionType);
+    if (result != NULL) {
+        result->w = q1->w + q2->w;
+        result->x = q1->x + q2->x;
+        result->y = q1->y + q2->y;
+        result->z = q1->z + q2->z;
+    }
+    return (PyObject *)result;
+static PyObject *
+Quaternion_subtract(Quaternion *q1, Quaternion *q2)
+    Quaternion *result;
+    result = PyObject_New(Quaternion, &QuaternionType);
+    if (result != NULL) {
+        result->w = q1->w - q2->w;
+        result->x = q1->x - q2->x;
+        result->y = q1->y - q2->y;
+        result->z = q1->z - q2->z;
+    }
+    return (PyObject *)result;
+static PyObject *
+Quaternion_multiply(Quaternion *q1, Quaternion *q2)
+    Quaternion *result;
+    result = PyObject_New(Quaternion, &QuaternionType);
+    if (result != NULL) {
+        result->w = q1->w*q2->w - q1->x*q2->x - q1->y*q2->y - q1->z*q2->z;
+        result->x = q1->w*q2->x + q1->x*q2->w + q1->y*q2->z - q1->z*q2->y;
+        result->y = q1->w*q2->y - q1->x*q2->z + q1->y*q2->w + q1->z*q2->x;
+        result->z = q1->w*q2->z + q1->x*q2->y - q1->y*q2->x + q1->z*q2->w;
+    }
+    return (PyObject *)result;
+static PyObject *
+Quaternion_divide(Quaternion *q1, Quaternion *q2)
+    Quaternion *result;
+    double s = q2->w*q2->w + q2->x*q2->x + q2->y*q2->y + q2->z*q2->z;
+    result = PyObject_New(Quaternion, &QuaternionType);
+    if (result != NULL) {
+        result->w = (  q1->w*q2->w + q1->x*q2->x + q1->y*q2->y + q1->z*q2->z) / s;
+        result->x = (- q1->w*q2->x + q1->x*q2->w + q1->y*q2->z - q1->z*q2->y) / s;
+        result->y = (- q1->w*q2->y - q1->x*q2->z + q1->y*q2->w + q1->z*q2->x) / s;
+        result->z = (- q1->w*q2->z + q1->x*q2->y - q1->y*q2->x + q1->z*q2->w) / s;
+    }
+    return (PyObject *)result;
+static PyObject *
+Quaternion_absolute(Quaternion *q)
+    double result;
+    result = sqrt(q->w*q->w + q->x*q->x + q->y*q->y + q->z*q->z);
+    return Py_BuildValue("d", result);
+static PyMethodDef Quaternion_methods[] = {
+    {NULL}  /* Sentinel */
+static PyNumberMethods Quaternion_as_number = {
+    (binaryfunc)Quaternion_add,       /* nb_add */
+    (binaryfunc)Quaternion_subtract,  /* nb_subtract */
+    (binaryfunc)Quaternion_multiply,  /* nb_multiply */
+    (binaryfunc)Quaternion_divide,    /* nb_divide */
+    0,                                /* nb_remainder */
+    0,                                /* nb_divmod */
+    0,                                /* nb_power */
+    0,                                /* nb_negative */
+    0,                                /* nb_positive */
+    (unaryfunc)Quaternion_absolute,   /* nb_absolute */
+    0,                                /* nb_nonzero */
+    0,                                /* nb_invert */
+    0,                                /* nb_lshift */
+    0,                                /* nb_rshift */
+    0,                                /* nb_and */
+    0,                                /* nb_xor */
+    0,                                /* nb_or */
+    0,                                /* nb_coerce */
+    0,                                /* nb_int */
+    0,                                /* nb_long */
+    0,                                /* nb_float */
+    0,                                /* nb_oct */
+    0,                                /* nb_hex */
+    0,                                /* nb_inplace_add */
+    0,                                /* nb_inplace_subtract */
+    0,                                /* nb_inplace_multiply */
+    0,                                /* nb_inplace_divide */
+    0,                                /* nb_inplace_remainder */
+    0,                                /* nb_inplace_power */
+    0,                                /* nb_inplace_lshift */
+    0,                                /* nb_inplace_rshift */
+    0,                                /* nb_inplace_and */
+    0,                                /* nb_inplace_xor */
+    0,                                /* nb_inplace_or */
+    0,                                /* nb_floor_divide */
+    0,                                /* nb_true_divide */
+    0,                                /* nb_inplace_floor_divide */
+    0,                                /* nb_inplace_true_divide */
+    0,                                /* nb_index */
+static PyTypeObject QuaternionType = {
+    PyObject_HEAD_INIT(NULL)
+    0,                              /* ob_size */
+    "_quaternion.Quaternion",       /* tp_name */
+    sizeof(Quaternion),             /* tp_basicsize */
+    0,                              /* tp_itemsize */
+    (destructor)Quaternion_dealloc, /* tp_dealloc */
+    0,                              /* tp_print */
+    0,                              /* tp_getattr */
+    0,                              /* tp_setattr */
+    0,                              /* tp_compare */
+    0,                              /* tp_repr */
+    &Quaternion_as_number,           /* tp_as_number */
+    0,                              /* tp_as_sequence */
+    0,                              /* tp_as_mapping */
+    0,                              /* tp_hash */
+    0,                              /* tp_call */
+    (reprfunc)Quaternion_str,       /* tp_str */
+    0,                              /* tp_getattro */
+    0,                              /* tp_setattro */
+    0,                              /* tp_as_buffer */
+    "Quaternion object",            /* tp_doc */
+    0,		                    /* tp_traverse */
+    0,		                    /* tp_clear */
+    0,		                    /* tp_richcompare */
+    0,		                    /* tp_weaklistoffset */
+    0,		                    /* tp_iter */
+    0,		                    /* tp_iternext */
+    Quaternion_methods,             /* tp_methods */
+    Quaternion_members,             /* tp_members */
+    0,                              /* tp_getset */
+    0,                              /* tp_base */
+    0,                              /* tp_dict */
+    0,                              /* tp_descr_get */
+    0,                              /* tp_descr_set */
+    0,                              /* tp_dictoffset */
+    (initproc)Quaternion_init,      /* tp_init */
+    0,                              /* tp_alloc */
+    Quaternion_new,                 /* tp_new */
+static PyMethodDef quaternion_funcs[] = {
+    {NULL}
+    PyObject* m;
+    if (PyType_Ready(&QuaternionType) < 0) return;
+    m = Py_InitModule("_quaternion", quaternion_funcs);
+    if (m == NULL) return;
+    Py_INCREF(&QuaternionType);
+    PyModule_AddObject(m, "Quaternion", (PyObject *)&QuaternionType);


+#ifndef __QUATERNION_H__
+#define __QUATERNION_H__
+typedef struct {
+    PyObject_HEAD
+    double w;
+    double x;
+    double y;
+    double z;
+} Quaternion;
+static PyTypeObject QuaternionType;


+import math
+def dbl2str(n):
+    d = abs(int(n));
+    f = int((n - d) * 1000000);
+    s = '%d.%d' % (d, f) if f > 0 else '%d' % d
+    ss = '+' if n >= 0 else '-'
+    return ss, s
+class Quaternion(object):
+    def __init__(q, w=0, x=0, y=0, z=0):
+        q.w = w
+        q.x = x
+        q.y = y
+        q.z = z
+    def __add__(q1, q2):
+        return Quaternion(
+            q1.w + q2.w,
+            q1.x + q2.x,
+            q1.y + q2.y,
+            q1.z + q2.z,
+        )
+    def __sub__(q1, q2):
+        return Quaternion(
+            q1.w - q2.w,
+            q1.x - q2.x,
+            q1.y - q2.y,
+            q1.z - q2.z,
+        )
+    def __mul__(q1, q2):
+        return Quaternion(
+            q1.w*q2.w - q1.x*q2.x - q1.y*q2.y - q1.z*q2.z,
+            q1.w*q2.x + q1.x*q2.w + q1.y*q2.z - q1.z*q2.y,
+            q1.w*q2.y - q1.x*q2.z + q1.y*q2.w + q1.z*q2.x,
+            q1.w*q2.z + q1.x*q2.y - q1.y*q2.x + q1.z*q2.w,
+        )
+    def __div__(q1, q2):
+        s = float(q2.w*q2.w + q2.x*q2.x + q2.y*q2.y + q2.z*q2.z)
+        return Quaternion(
+            (  q1.w*q2.w + q1.x*q2.x + q1.y*q2.y + q1.z*q2.z) / s,
+            (- q1.w*q2.x + q1.x*q2.w + q1.y*q2.z - q1.z*q2.y) / s,
+            (- q1.w*q2.y - q1.x*q2.z + q1.y*q2.w + q1.z*q2.x) / s,
+            (- q1.w*q2.z + q1.x*q2.y - q1.y*q2.x + q1.z*q2.w) / s
+        )
+    def __abs__(q):
+        return math.sqrt(q.w*q.w + q.x*q.x + q.y*q.y + q.z*q.z);
+    def __neg__(q):
+        return Quaternion(-q.w, -q.x, -q.y, -q.z)
+    def __invert__(q):
+        """Conjugate of Quaternion.
+        >>> q = Quaternion((2, 2, 2, 2))
+        >>> print(q)
+        (2 + 2i + 2j + 2k)
+        >>> print(~q)
+        (2 - 2i - 2j - 2k)
+        >>> print(~~q)
+        (2 + 2i + 2j + 2k)
+        """
+        return Quaternion((q.w, -q.x, -q.y, -q.z))
+    def as_tuple(self):
+        return (self.w, self.x, self.y, self.z)
+    def __str__(q):
+        args = list(
+            dbl2str(q.w) +
+            dbl2str(q.x) +
+            dbl2str(q.y) +
+            dbl2str(q.z)
+        )
+        if args[0] == '+':
+            args[0] = ''
+        return '(%s%s %s %si %s %sj %s %sk)' % tuple(args)
+    def normalize(q):
+        """Convert Quaternion to Unit Quaternion.
+        Unit Quaternion is Quaternion who's length is equal to 1.
+        >>> q = Quaternion((1, 3, 3, 3))
+        >>> q.normalize()
+        >>> print(q) # doctest: +ELLIPSIS
+        (0.1889822... + 0.5669467...i + 0.5669467...j + 0.5669467...k)
+        """
+        norm = abs(q)
+        q.w = q.w / norm,
+        q.x = q.x / norm,
+        q.y = q.y / norm,
+        q.z = q.z / norm,
+import unittest
+import quaternion.quaternion
+import quaternion._quaternion
+class QuaternionTestsMixin(object):
+    def test_add(self):
+        q1 = self.Q(5, 6, 7, 8)
+        q2 = self.Q(8, 7, 6, 5)
+        self.assertEqual(str(q1 + q2), '(13 + 13i + 13j + 13k)')
+    def test_sub(self):
+        q1 = self.Q(5, 6, 7, 8)
+        q2 = self.Q(8, 7, 6, 5)
+        self.assertEqual(str(q1 - q2), '(-3 - 1i + 1j + 3k)')
+    def test_mul(self):
+        q1 = self.Q(2, 3, 2, 3)
+        q2 = self.Q(3, 2, 3, 2)
+        self.assertEqual(str(q1 * q2), '(-12 + 8i + 12j + 18k)')
+        self.assertEqual(str(q2 * q1), '(-12 + 18i + 12j + 8k)')
+    def test_div(self):
+        q1 = self.Q(2, 3, 2, 3)
+        q2 = self.Q(3, 2, 3, 2)
+        self.assertEqual(str(q1 / q2), '(0.923076 + 0i + 0j + 0.384615k)')
+        self.assertEqual(str(q2 / q1), '(0.923076 + 0i + 0j - 0k)')
+class QuaternionPyTests(QuaternionTestsMixin, unittest.TestCase):
+    Q = quaternion.quaternion.Quaternion
+class QuaternionCTests(QuaternionTestsMixin, unittest.TestCase):
+    Q = quaternion._quaternion.Quaternion
+def suite():
+    suite = unittest.TestSuite()
+    loader = unittest.TestLoader()
+    suite.addTest(loader.loadTestsFromTestCase(QuaternionPyTests))
+    suite.addTest(loader.loadTestsFromTestCase(QuaternionCTests))
+    return suite
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