This documentation aims to use of the following naming and formatting conventions.
diff --git a/doc/html/math_toolkit/create.html b/doc/html/math_toolkit/create.html
index 0d6e93720..2dfb0c9a6 100644
--- a/doc/html/math_toolkit/create.html
+++ b/doc/html/math_toolkit/create.html
@@ -98,7 +98,7 @@
are not too complicated, but there is currently a lack of standard (de facto
or de jure) matrix library with which the conversions could work. This should
be remedied in a further revision. In the mean time, an example of how this
- could be done is presented here for R3, and here for R4 (example
+ could be done is presented here for R3, and here for R4 (example
test file).
Boost.Math documentation is provided in both HTML and PDF formats.
diff --git a/doc/html/math_toolkit/oct_overview.html b/doc/html/math_toolkit/oct_overview.html
index 5ff2831b3..1b1f7a505 100644
--- a/doc/html/math_toolkit/oct_overview.html
+++ b/doc/html/math_toolkit/oct_overview.html
@@ -56,7 +56,7 @@
- If you define the symbol TEST_VERBOSE, you will get additional output (verbose output); this will only
+ If you define the symbol TEST_VERBOSE, you will get additional output (verbose output); this will only
be helpfull if you enable message output at the same time, of course (by uncommenting
the relevant line in the test or by adding --log_level=messages
to your command line,...). In that case, and if you are running interactively,
diff --git a/doc/html/math_toolkit/quat_todo.html b/doc/html/math_toolkit/quat_todo.html
index f08d70e8f..c33d8d162 100644
--- a/doc/html/math_toolkit/quat_todo.html
+++ b/doc/html/math_toolkit/quat_todo.html
@@ -37,7 +37,7 @@
Put in place an Expression Template mechanism (perhaps borrowing from uBlas).
- Use uBlas for the link with rotations (and move from the example
+ Use uBlas for the link with rotations (and move from the example
implementation to an efficient one).
diff --git a/doc/math.pdf b/doc/math.pdf
new file mode 100644
index 000000000..5b1cc48b4
Binary files /dev/null and b/doc/math.pdf differ
diff --git a/doc/octonion/math-octonion.qbk b/doc/octonion/math-octonion.qbk
index 865899c7d..40a238b9c 100644
--- a/doc/octonion/math-octonion.qbk
+++ b/doc/octonion/math-octonion.qbk
@@ -33,8 +33,8 @@ A way of remembering things is by using the following multiplication table:
[$../octonion/graphics/octonion_blurb17.jpeg]
Octonions (and their kin) are described in far more details in this other
-[@../../quaternion/TQE.pdf document]
-(with [@../../quaternion/TQE_EA.pdf errata and addenda]).
+[@../quaternion/TQE.pdf document]
+(with [@../quaternion/TQE_EA.pdf errata and addenda]).
Some traditional constructs, such as the exponential, carry over without too
much change into the realms of octonions, but other, such as taking a square root,
diff --git a/quaternion/TQE.pdf b/doc/quaternion/TQE.pdf
similarity index 100%
rename from quaternion/TQE.pdf
rename to doc/quaternion/TQE.pdf
diff --git a/quaternion/TQE_EA.pdf b/doc/quaternion/TQE_EA.pdf
similarity index 100%
rename from quaternion/TQE_EA.pdf
rename to doc/quaternion/TQE_EA.pdf
diff --git a/quaternion/graphics/quaternion_blurb1.jpeg b/doc/quaternion/graphics/quaternion_blurb1.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb1.jpeg
rename to doc/quaternion/graphics/quaternion_blurb1.jpeg
diff --git a/quaternion/graphics/quaternion_blurb10.jpeg b/doc/quaternion/graphics/quaternion_blurb10.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb10.jpeg
rename to doc/quaternion/graphics/quaternion_blurb10.jpeg
diff --git a/quaternion/graphics/quaternion_blurb11.jpeg b/doc/quaternion/graphics/quaternion_blurb11.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb11.jpeg
rename to doc/quaternion/graphics/quaternion_blurb11.jpeg
diff --git a/quaternion/graphics/quaternion_blurb12.jpeg b/doc/quaternion/graphics/quaternion_blurb12.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb12.jpeg
rename to doc/quaternion/graphics/quaternion_blurb12.jpeg
diff --git a/quaternion/graphics/quaternion_blurb13.jpeg b/doc/quaternion/graphics/quaternion_blurb13.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb13.jpeg
rename to doc/quaternion/graphics/quaternion_blurb13.jpeg
diff --git a/quaternion/graphics/quaternion_blurb14.jpeg b/doc/quaternion/graphics/quaternion_blurb14.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb14.jpeg
rename to doc/quaternion/graphics/quaternion_blurb14.jpeg
diff --git a/quaternion/graphics/quaternion_blurb15.jpeg b/doc/quaternion/graphics/quaternion_blurb15.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb15.jpeg
rename to doc/quaternion/graphics/quaternion_blurb15.jpeg
diff --git a/quaternion/graphics/quaternion_blurb16.jpeg b/doc/quaternion/graphics/quaternion_blurb16.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb16.jpeg
rename to doc/quaternion/graphics/quaternion_blurb16.jpeg
diff --git a/quaternion/graphics/quaternion_blurb17.jpeg b/doc/quaternion/graphics/quaternion_blurb17.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb17.jpeg
rename to doc/quaternion/graphics/quaternion_blurb17.jpeg
diff --git a/quaternion/graphics/quaternion_blurb18.jpeg b/doc/quaternion/graphics/quaternion_blurb18.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb18.jpeg
rename to doc/quaternion/graphics/quaternion_blurb18.jpeg
diff --git a/quaternion/graphics/quaternion_blurb19.jpeg b/doc/quaternion/graphics/quaternion_blurb19.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb19.jpeg
rename to doc/quaternion/graphics/quaternion_blurb19.jpeg
diff --git a/quaternion/graphics/quaternion_blurb2.jpeg b/doc/quaternion/graphics/quaternion_blurb2.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb2.jpeg
rename to doc/quaternion/graphics/quaternion_blurb2.jpeg
diff --git a/quaternion/graphics/quaternion_blurb20.jpeg b/doc/quaternion/graphics/quaternion_blurb20.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb20.jpeg
rename to doc/quaternion/graphics/quaternion_blurb20.jpeg
diff --git a/quaternion/graphics/quaternion_blurb21.jpeg b/doc/quaternion/graphics/quaternion_blurb21.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb21.jpeg
rename to doc/quaternion/graphics/quaternion_blurb21.jpeg
diff --git a/quaternion/graphics/quaternion_blurb22.jpeg b/doc/quaternion/graphics/quaternion_blurb22.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb22.jpeg
rename to doc/quaternion/graphics/quaternion_blurb22.jpeg
diff --git a/quaternion/graphics/quaternion_blurb23.jpeg b/doc/quaternion/graphics/quaternion_blurb23.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb23.jpeg
rename to doc/quaternion/graphics/quaternion_blurb23.jpeg
diff --git a/quaternion/graphics/quaternion_blurb3.jpeg b/doc/quaternion/graphics/quaternion_blurb3.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb3.jpeg
rename to doc/quaternion/graphics/quaternion_blurb3.jpeg
diff --git a/quaternion/graphics/quaternion_blurb4.jpeg b/doc/quaternion/graphics/quaternion_blurb4.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb4.jpeg
rename to doc/quaternion/graphics/quaternion_blurb4.jpeg
diff --git a/quaternion/graphics/quaternion_blurb5.jpeg b/doc/quaternion/graphics/quaternion_blurb5.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb5.jpeg
rename to doc/quaternion/graphics/quaternion_blurb5.jpeg
diff --git a/quaternion/graphics/quaternion_blurb6.jpeg b/doc/quaternion/graphics/quaternion_blurb6.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb6.jpeg
rename to doc/quaternion/graphics/quaternion_blurb6.jpeg
diff --git a/quaternion/graphics/quaternion_blurb7.jpeg b/doc/quaternion/graphics/quaternion_blurb7.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb7.jpeg
rename to doc/quaternion/graphics/quaternion_blurb7.jpeg
diff --git a/quaternion/graphics/quaternion_blurb8.jpeg b/doc/quaternion/graphics/quaternion_blurb8.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb8.jpeg
rename to doc/quaternion/graphics/quaternion_blurb8.jpeg
diff --git a/quaternion/graphics/quaternion_blurb9.jpeg b/doc/quaternion/graphics/quaternion_blurb9.jpeg
similarity index 100%
rename from quaternion/graphics/quaternion_blurb9.jpeg
rename to doc/quaternion/graphics/quaternion_blurb9.jpeg
diff --git a/doc/quaternion/math-quaternion.qbk b/doc/quaternion/math-quaternion.qbk
index 7deec50e2..7ca042634 100644
--- a/doc/quaternion/math-quaternion.qbk
+++ b/doc/quaternion/math-quaternion.qbk
@@ -41,8 +41,8 @@ quaternions ['[^x]] and ['[^y]] such that __not_equal). A good mnemotechnical wa
things is by using the formula ['[^i*i = j*j = k*k = -1]].
Quaternions (and their kin) are described in far more details in this
-other [@../../quaternion/TQE.pdf document]
-(with [@../../quaternion/TQE_EA.pdf errata and addenda]).
+other [@../quaternion/TQE.pdf document]
+(with [@../quaternion/TQE_EA.pdf errata and addenda]).
Some traditional constructs, such as the exponential, carry over without
too much change into the realms of quaternions, but other, such as taking
@@ -753,9 +753,9 @@ but there is currently a lack of standard (de facto or de jure) matrix
library with which the conversions could work. This should be remedied in
a further revision. In the mean time, an example of how this could be
done is presented here for
-[@../../quaternion/HSO3.hpp __R3], and here for
-[@../../quaternion/HSO4.hpp __R4]
-([@../../quaternion/HSO3SO4.cpp example test file]).
+[@../../example/HSO3.hpp __R3], and here for
+[@../../example/HSO4.hpp __R4]
+([@../../example/HSO3SO4.cpp example test file]).
[endsect]
@@ -838,13 +838,13 @@ Computes the n-th power of the quaternion q.
[section:quat_tests Test Program]
-The [@../../quaternion/quaternion_test.cpp quaternion_test.cpp]
+The [@../../test/quaternion_test.cpp quaternion_test.cpp]
test program tests quaternions specializations for float, double and long double
-([@../../quaternion/output.txt sample output], with message output
+([@../quaternion/output.txt sample output], with message output
enabled).
If you define the symbol TEST_VERBOSE, you will get
-additional output ([@../../quaternion/output_more.txt verbose output]);
+additional output ([@../quaternion/output_more.txt verbose output]);
this will only be helpfull if you enable message output at the same time,
of course (by uncommenting the relevant line in the test or by adding
[^--log_level=messages] to your command line,...). In that case, and if you
@@ -859,8 +859,8 @@ operator with input of your choice from the standard input
Please refer to the following PDF's:
-*[@../../quaternion/TQE.pdf The Quaternionic Exponential (and beyond)]
-*[@../../quaternion/TQE_EA.pdf The Quaternionic Exponential (and beyond) ERRATA & ADDENDA]
+*[@../quaternion/TQE.pdf The Quaternionic Exponential (and beyond)]
+*[@../quaternion/TQE_EA.pdf The Quaternionic Exponential (and beyond) ERRATA & ADDENDA]
[endsect]
@@ -900,7 +900,7 @@ Thank you to all who contributed to the discution about this library.
* Rewrite input operatore using Spirit (creates a dependency).
* Put in place an Expression Template mechanism (perhaps borrowing from uBlas).
* Use uBlas for the link with rotations (and move from the
-[@../../quaternion/HSO3SO4.cpp example]
+[@../../example/HSO3SO4.cpp example]
implementation to an efficient one).
[endsect]
diff --git a/quaternion/output.txt b/doc/quaternion/output.txt
similarity index 100%
rename from quaternion/output.txt
rename to doc/quaternion/output.txt
diff --git a/quaternion/output_more.txt b/doc/quaternion/output_more.txt
similarity index 100%
rename from quaternion/output_more.txt
rename to doc/quaternion/output_more.txt
diff --git a/quaternion/HSO3.hpp b/example/HSO3.hpp
similarity index 100%
rename from quaternion/HSO3.hpp
rename to example/HSO3.hpp
diff --git a/quaternion/HSO3SO4.cpp b/example/HSO3SO4.cpp
similarity index 100%
rename from quaternion/HSO3SO4.cpp
rename to example/HSO3SO4.cpp
diff --git a/quaternion/HSO4.hpp b/example/HSO4.hpp
similarity index 100%
rename from quaternion/HSO4.hpp
rename to example/HSO4.hpp
diff --git a/example/Jamfile.v2 b/example/Jamfile.v2
index 81c22b061..4db544243 100644
--- a/example/Jamfile.v2
+++ b/example/Jamfile.v2
@@ -114,6 +114,7 @@ run students_t_example2.cpp ;
run students_t_example3.cpp ;
run students_t_single_sample.cpp ;
run students_t_two_samples.cpp ;
+run HSO3SO4.cpp ;
run root_elliptic_finding.cpp /boost/timer : : : release static ;
run root_finding_algorithms.cpp /boost/timer : : : release static ;
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 2a28539ca..864ed8161 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -886,12 +886,12 @@ run ../test/common_factor_test.cpp
run octonion_test.cpp
../../test/build//boost_unit_test_framework ;
-run ../quaternion/quaternion_test.cpp
+run quaternion_test.cpp
../../test/build//boost_unit_test_framework ;
-run ../quaternion/quaternion_mult_incl_test.cpp
- ../quaternion/quaternion_mi1.cpp
- ../quaternion/quaternion_mi2.cpp
+run quaternion_mult_incl_test.cpp
+ quaternion_mi1.cpp
+ quaternion_mi2.cpp
../../test/build//boost_unit_test_framework ;
diff --git a/test/octonion_test.cpp b/test/octonion_test.cpp
new file mode 100644
index 000000000..03c494843
--- /dev/null
+++ b/test/octonion_test.cpp
@@ -0,0 +1,775 @@
+// test file for octonion.hpp
+
+// (C) Copyright Hubert Holin 2001.
+// Distributed under the Boost Software License, Version 1.0. (See
+// accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+
+#include
+
+
+#include
+
+#include
+#include
+
+#include
+
+
+template
+struct string_type_name;
+
+#define DEFINE_TYPE_NAME(Type) \
+template<> struct string_type_name \
+{ \
+ static char const * _() \
+ { \
+ return #Type; \
+ } \
+}
+
+DEFINE_TYPE_NAME(float);
+DEFINE_TYPE_NAME(double);
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+DEFINE_TYPE_NAME(long double);
+#endif
+
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+typedef boost::mpl::list test_types;
+#else
+typedef boost::mpl::list test_types;
+#endif
+
+// Apple GCC 4.0 uses the "double double" format for its long double,
+// which means that epsilon is VERY small but useless for
+// comparisons. So, don't do those comparisons.
+#if (defined(__APPLE_CC__) && defined(__GNUC__) && __GNUC__ == 4) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
+typedef boost::mpl::list near_eps_test_types;
+#else
+typedef boost::mpl::list near_eps_test_types;
+#endif
+
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+ // gcc 2.x ignores function scope using declarations,
+ // put them in the scope of the enclosing namespace instead:
+using ::std::sqrt;
+using ::std::atan;
+using ::std::log;
+using ::std::exp;
+using ::std::cos;
+using ::std::sin;
+using ::std::tan;
+using ::std::cosh;
+using ::std::sinh;
+using ::std::tanh;
+
+using ::std::numeric_limits;
+
+using ::boost::math::abs;
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+
+
+#ifdef BOOST_NO_STDC_NAMESPACE
+using ::sqrt;
+using ::atan;
+using ::log;
+using ::exp;
+using ::cos;
+using ::sin;
+using ::tan;
+using ::cosh;
+using ::sinh;
+using ::tanh;
+#endif /* BOOST_NO_STDC_NAMESPACE */
+
+#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
+using ::boost::math::real;
+using ::boost::math::unreal;
+using ::boost::math::sup;
+using ::boost::math::l1;
+using ::boost::math::abs;
+using ::boost::math::norm;
+using ::boost::math::conj;
+using ::boost::math::exp;
+using ::boost::math::pow;
+using ::boost::math::cos;
+using ::boost::math::sin;
+using ::boost::math::tan;
+using ::boost::math::cosh;
+using ::boost::math::sinh;
+using ::boost::math::tanh;
+using ::boost::math::sinc_pi;
+using ::boost::math::sinhc_pi;
+#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
+
+// Provide standard floating point abs() overloads if older Microsoft
+// library is used with _MSC_EXTENSIONS defined. This code also works
+// for the Intel compiler using the Microsoft library.
+#if defined(_MSC_EXTENSIONS) && defined(_MSC_VER) && _MSC_VER < 1310
+inline float abs(float v)
+{
+ return(fabs(v));
+}
+
+inline double abs(double v)
+{
+ return(fabs(v));
+}
+
+inline long double abs(long double v)
+{
+ return(fabs(v));
+}
+#endif /* BOOST_WORKAROUND(BOOST_MSVC) */
+
+
+// explicit (if ludicrous) instanciation
+#if !BOOST_WORKAROUND(__GNUC__, < 3)
+template class ::boost::math::octonion;
+#else
+// gcc doesn't like the absolutely-qualified namespace
+template class boost::math::octonion;
+#endif /* !BOOST_WORKAROUND(__GNUC__) */
+
+
+namespace
+{
+ template
+ ::boost::math::octonion index_i_element(int idx)
+ {
+ return(
+ ::boost::math::octonion(
+ (idx == 0) ?
+ static_cast(1) :
+ static_cast(0),
+ (idx == 1) ?
+ static_cast(1) :
+ static_cast(0),
+ (idx == 2) ?
+ static_cast(1) :
+ static_cast(0),
+ (idx == 3) ?
+ static_cast(1) :
+ static_cast(0),
+ (idx == 4) ?
+ static_cast(1) :
+ static_cast(0),
+ (idx == 5) ?
+ static_cast(1) :
+ static_cast(0),
+ (idx == 6) ?
+ static_cast(1) :
+ static_cast(0),
+ (idx == 7) ?
+ static_cast(1) :
+ static_cast(0)
+ ));
+ }
+}
+
+
+
+void octonion_manual_test()
+{
+ // tests for evaluation by humans
+
+
+ // using default constructor
+ ::boost::math::octonion o0;
+
+ ::boost::math::octonion oa[2];
+
+ // using constructor "O seen as R^8"
+ ::boost::math::octonion o1(1,2,3,4,5,6,7,8);
+
+ ::std::complex c0(9,10);
+
+ // using constructor "O seen as C^4"
+ ::boost::math::octonion o2(c0);
+
+ ::boost::math::quaternion q0(11,12,13,14);
+
+ // using constructor "O seen as H^2"
+ ::boost::math::octonion o3(q0);
+
+ // using UNtemplated copy constructor
+ ::boost::math::octonion o4(o1);
+
+ // using templated copy constructor
+ ::boost::math::octonion o5(o2);
+
+ // using UNtemplated assignment operator
+ o5 = o3;
+ oa[0] = o0;
+
+ // using templated assignment operator
+ o5 = o2;
+ oa[1] = o5;
+
+ float f0(15);
+
+ // using converting assignment operator
+ o0 = f0;
+
+ // using converting assignment operator
+ o2 = c0;
+
+ // using converting assignment operator
+ o5 = q0;
+
+ // using += (const T &)
+ o4 += f0;
+
+ // using += (const ::std::complex &)
+ o2 += c0;
+
+ // using += (const ::boost::math::quaternion &)
+ o3 += q0;
+
+ // using += (const quaternion &)
+ o5 += o4;
+
+ // using -= (const T &)
+ o1 -= f0;
+
+ // using -= (const ::std::complex &)
+ o2 -= c0;
+
+ // using -= (const ::boost::math::quaternion &)
+ o5 -= q0;
+
+ // using -= (const octonion &)
+ o3 -= o4;
+
+ double d0(16);
+ ::std::complex c1(17,18);
+ ::boost::math::quaternion q1(19,20,21,22);
+
+ // using *= (const T &)
+ o2 *= d0;
+
+ // using *= (const ::std::complex &)
+ o2 *= c1;
+
+ // using *= (const ::boost::math::quaternion &)
+ o2 *= q1;
+
+ // using *= (const octonion &)
+ o2 *= o4;
+
+ long double l0(23);
+ ::std::complex c2(24,25);
+
+ // using /= (const T &)
+ o5 /= l0;
+
+ // using /= (const ::std::complex &)
+ o5 /= c2;
+
+ // using /= (const quaternion &)
+ o5 /= q0;
+
+ // using /= (const octonion &)
+ o5 /= o5;
+
+ // using + (const T &, const octonion &)
+ ::boost::math::octonion o6 = f0+o0;
+
+ // using + (const octonion &, const T &)
+ ::boost::math::octonion o7 = o0+f0;
+
+ // using + (const ::std::complex &, const quaternion &)
+ ::boost::math::octonion o8 = c0+o2;
+
+ // using + (const octonion &, const ::std::complex &)
+ ::boost::math::octonion o9 = o2+c0;
+
+ // using + (const ::boost::math::quaternion, const octonion &)
+ ::boost::math::octonion o10 = q0+o3;
+
+ // using + (const octonion &, const ::boost::math::quaternion &)
+ ::boost::math::octonion o11 = o3+q0;
+
+ // using + (const quaternion &,const quaternion &)
+ ::boost::math::octonion o12 = o0+o4;
+
+ // using - (const T &, const octonion &)
+ o6 = f0-o0;
+
+ // using - (const octonion &, const T &)
+ o7 = o0-f0;
+
+ // using - (const ::std::complex &, const octonion &)
+ o8 = c0-o2;
+
+ // using - (const octonion &, const ::std::complex &)
+ o9 = o2-c0;
+
+ // using - (const quaternion &,const octonion &)
+ o10 = q0-o3;
+
+ // using - (const octonion &,const quaternion &)
+ o11 = o3-q0;
+
+ // using - (const octonion &,const octonion &)
+ o12 = o0-o4;
+
+ // using * (const T &, const octonion &)
+ o6 = f0*o0;
+
+ // using * (const octonion &, const T &)
+ o7 = o0*f0;
+
+ // using * (const ::std::complex &, const octonion &)
+ o8 = c0*o2;
+
+ // using * (const octonion &, const ::std::complex &)
+ o9 = o2*c0;
+
+ // using * (const quaternion &,const octonion &)
+ o10 = q0*o3;
+
+ // using * (const octonion &,const quaternion &)
+ o11 = o3*q0;
+
+ // using * (const octonion &,const octonion &)
+ o12 = o0*o4;
+
+ // using / (const T &, const octonion &)
+ o6 = f0/o0;
+
+ // using / (const octonion &, const T &)
+ o7 = o0/f0;
+
+ // using / (const ::std::complex &, const octonion &)
+ o8 = c0/o2;
+
+ // using / (const octonion &, const ::std::complex &)
+ o9 = o2/c0;
+
+ // using / (const ::boost::math::quaternion &, const octonion &)
+ o10 = q0/o3;
+
+ // using / (const octonion &, const ::boost::math::quaternion &)
+ o11 = o3/q0;
+
+ // using / (const octonion &,const octonion &)
+ o12 = o0/o4;
+
+ // using + (const octonion &)
+ o4 = +o0;
+
+ // using - (const octonion &)
+ o0 = -o4;
+
+ // using == (const T &, const octonion &)
+ f0 == o0;
+
+ // using == (const octonion &, const T &)
+ o0 == f0;
+
+ // using == (const ::std::complex &, const octonion &)
+ c0 == o2;
+
+ // using == (const octonion &, const ::std::complex &)
+ o2 == c0;
+
+ // using == (const ::boost::math::quaternion &, const octonion &)
+ q0 == o3;
+
+ // using == (const octonion &, const ::boost::math::quaternion &)
+ o3 == q0;
+
+ // using == (const octonion &,const octonion &)
+ o0 == o4;
+
+ // using != (const T &, const octonion &)
+ f0 != o0;
+
+ // using != (const octonion &, const T &)
+ o0 != f0;
+
+ // using != (const ::std::complex &, const octonion &)
+ c0 != o2;
+
+ // using != (const octonion &, const ::std::complex &)
+ o2 != c0;
+
+ // using != (const ::boost::math::quaternion &, const octonion &)
+ q0 != o3;
+
+ // using != (const octonion &, const ::boost::math::quaternion &)
+ o3 != q0;
+
+ // using != (const octonion &,const octonion &)
+ o0 != o4;
+
+ BOOST_TEST_MESSAGE("Please input an octonion...");
+
+#ifdef BOOST_INTERACTIVE_TEST_INPUT_ITERATOR
+ ::std::cin >> o0;
+
+ if (::std::cin.fail())
+ {
+ BOOST_TEST_MESSAGE("You have entered nonsense!");
+ }
+ else
+ {
+ BOOST_TEST_MESSAGE("You have entered the octonion " << o0 << " .");
+ }
+#else
+ ::std::istringstream bogus("(1,2,3,4,5,6,7,8)");
+
+ bogus >> o0;
+
+ BOOST_TEST_MESSAGE("You have entered the octonion " << o0 << " .");
+#endif
+
+ BOOST_TEST_MESSAGE("For this octonion:");
+
+ BOOST_TEST_MESSAGE( "the value of the real part is "
+ << real(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the unreal part is "
+ << unreal(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the sup norm is "
+ << sup(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the l1 norm is "
+ << l1(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the magnitude (euclidian norm) is "
+ << abs(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the (Cayley) norm is "
+ << norm(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the conjugate is "
+ << conj(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the exponential is "
+ << exp(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the cube is "
+ << pow(o0,3));
+
+ BOOST_TEST_MESSAGE( "the value of the cosinus is "
+ << cos(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the sinus is "
+ << sin(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the tangent is "
+ << tan(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the hyperbolic cosinus is "
+ << cosh(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the hyperbolic sinus is "
+ << sinh(o0));
+
+ BOOST_TEST_MESSAGE( "the value of the hyperbolic tangent is "
+ << tanh(o0));
+
+#ifdef BOOST_NO_TEMPLATE_TEMPLATES
+ BOOST_TEST_MESSAGE( "no template templates, can't compute cardinal functions");
+#else /* BOOST_NO_TEMPLATE_TEMPLATES */
+ BOOST_TEST_MESSAGE( "the value of the Sinus Cardinal (of index pi) is "
+ << sinc_pi(o0));
+
+ BOOST_TEST_MESSAGE( "the value of "
+ << "the Hyperbolic Sinus Cardinal (of index pi) is "
+ << sinhc_pi(o0));
+#endif /* BOOST_NO_TEMPLATE_TEMPLATES */
+
+ BOOST_TEST_MESSAGE(" ");
+
+ float rho = ::std::sqrt(4096.0f);
+ float theta = ::std::atan(1.0f);
+ float phi1 = ::std::atan(1.0f);
+ float phi2 = ::std::atan(1.0f);
+ float phi3 = ::std::atan(1.0f);
+ float phi4 = ::std::atan(1.0f);
+ float phi5 = ::std::atan(1.0f);
+ float phi6 = ::std::atan(1.0f);
+
+ BOOST_TEST_MESSAGE( "The value of the octonion represented "
+ << "in spherical form by "
+ << "rho = " << rho << " , theta = " << theta
+ << " , phi1 = " << phi1 << " , phi2 = " << phi2
+ << " , phi3 = " << phi3 << " , phi4 = " << phi4
+ << " , phi5 = " << phi5 << " , phi6 = " << phi6
+ << " is "
+ << ::boost::math::spherical(rho, theta,
+ phi1, phi2, phi3, phi4, phi5, phi6));
+
+ float rho1 = 1;
+ float rho2 = 2;
+ float rho3 = ::std::sqrt(2.0f);
+ float rho4 = ::std::sqrt(8.0f);
+ float theta1 = 0;
+ float theta2 = ::std::atan(1.0f)*2;
+ float theta3 = ::std::atan(1.0f);
+ float theta4 = ::std::atan(::std::sqrt(3.0f));
+
+ BOOST_TEST_MESSAGE( "The value of the octonion represented "
+ << "in multipolar form by "
+ << "rho1 = " << rho1 << " , theta1 = " << theta1
+ << " , rho2 = " << rho2 << " , theta2 = " << theta2
+ << "rho3 = " << rho3 << " , theta3 = " << theta3
+ << " , rho4 = " << rho4 << " , theta4 = " << theta4
+ << " is "
+ << ::boost::math::multipolar(rho1, theta1, rho2, theta2,
+ rho3, theta3, rho4, theta4));
+
+ float r = ::std::sqrt(2.0f);
+ float angle = ::std::atan(1.0f);
+ float h1 = 3;
+ float h2 = 4;
+ float h3 = 5;
+ float h4 = 6;
+ float h5 = 7;
+ float h6 = 8;
+
+ BOOST_TEST_MESSAGE( "The value of the octonion represented "
+ << "in cylindrical form by "
+ << "r = " << r << " , angle = " << angle
+ << " , h1 = " << h1 << " , h2 = " << h2
+ << " , h3 = " << h3 << " , h4 = " << h4
+ << " , h5 = " << h5 << " , h6 = " << h6
+ << " is " << ::boost::math::cylindrical(r, angle,
+ h1, h2, h3, h4, h5, h6));
+
+ double real_1(1);
+ ::std::complex complex_1(1);
+ ::std::complex complex_i(0,1);
+ ::boost::math::quaternion quaternion_1(1);
+ ::boost::math::quaternion quaternion_i(0,1);
+ ::boost::math::quaternion quaternion_j(0,0,1);
+ ::boost::math::quaternion quaternion_k(0,0,0,1);
+ ::boost::math::octonion octonion_1(1);
+ ::boost::math::octonion octonion_i(0,1);
+ ::boost::math::octonion octonion_j(0,0,1);
+ ::boost::math::octonion octonion_k(0,0,0,1);
+ ::boost::math::octonion octonion_e_prime(0,0,0,0,1);
+ ::boost::math::octonion octonion_i_prime(0,0,0,0,0,1);
+ ::boost::math::octonion octonion_j_prime(0,0,0,0,0,0,1);
+ ::boost::math::octonion octonion_k_prime(0,0,0,0,0,0,0,1);
+
+
+ BOOST_TEST_MESSAGE(" ");
+
+ BOOST_TEST_MESSAGE( "Real 1: " << real_1
+ << " ; Complex 1: " << complex_1
+ << " ; Quaternion 1: " << quaternion_1
+ << " ; Octonion 1: " << octonion_1 << " .");
+
+ BOOST_TEST_MESSAGE( "Complex i: " << complex_i
+ << " ; Quaternion i: " << quaternion_i
+ << " ; Octonion i : " << octonion_i << " .");
+
+ BOOST_TEST_MESSAGE( "Quaternion j: " << quaternion_j
+ << " ; Octonion j: " << octonion_j << " .");
+
+ BOOST_TEST_MESSAGE( "Quaternion k: " << quaternion_k
+ << " ; Octonion k: " << octonion_k << " .");
+
+ BOOST_TEST_MESSAGE( "Quaternion e\': " << octonion_e_prime << " .");
+
+ BOOST_TEST_MESSAGE( "Quaternion i\': " << octonion_i_prime << " .");
+
+ BOOST_TEST_MESSAGE( "Quaternion j\': " << octonion_j_prime << " .");
+
+ BOOST_TEST_MESSAGE( "Quaternion k\': " << octonion_k_prime << " .");
+
+ BOOST_TEST_MESSAGE(" ");
+
+ BOOST_TEST_MESSAGE( octonion_1*octonion_1 << " ; "
+ << octonion_1*octonion_i << " ; "
+ << octonion_1*octonion_j << " ; "
+ << octonion_1*octonion_k << " ; "
+ << octonion_1*octonion_e_prime << " ; "
+ << octonion_1*octonion_i_prime << " ; "
+ << octonion_1*octonion_j_prime << " ; "
+ << octonion_1*octonion_k_prime << " ; ");
+
+ BOOST_TEST_MESSAGE( octonion_i*octonion_1 << " ; "
+ << octonion_i*octonion_i << " ; "
+ << octonion_i*octonion_j << " ; "
+ << octonion_i*octonion_k << " ; "
+ << octonion_i*octonion_e_prime << " ; "
+ << octonion_i*octonion_i_prime << " ; "
+ << octonion_i*octonion_j_prime << " ; "
+ << octonion_i*octonion_k_prime << " ; ");
+
+ BOOST_TEST_MESSAGE( octonion_j*octonion_1 << " ; "
+ << octonion_j*octonion_i << " ; "
+ << octonion_j*octonion_j << " ; "
+ << octonion_j*octonion_k << " ; "
+ << octonion_j*octonion_e_prime << " ; "
+ << octonion_j*octonion_i_prime << " ; "
+ << octonion_j*octonion_j_prime << " ; "
+ << octonion_j*octonion_k_prime << " ; ");
+
+ BOOST_TEST_MESSAGE( octonion_k*octonion_1 << " ; "
+ << octonion_k*octonion_i << " ; "
+ << octonion_k*octonion_j << " ; "
+ << octonion_k*octonion_k << " ; "
+ << octonion_k*octonion_e_prime << " ; "
+ << octonion_k*octonion_i_prime << " ; "
+ << octonion_k*octonion_j_prime << " ; "
+ << octonion_k*octonion_k_prime << " ; ");
+
+ BOOST_TEST_MESSAGE( octonion_e_prime*octonion_1 << " ; "
+ << octonion_e_prime*octonion_i << " ; "
+ << octonion_e_prime*octonion_j << " ; "
+ << octonion_e_prime*octonion_k << " ; "
+ << octonion_e_prime*octonion_e_prime << " ; "
+ << octonion_e_prime*octonion_i_prime << " ; "
+ << octonion_e_prime*octonion_j_prime << " ; "
+ << octonion_e_prime*octonion_k_prime << " ; ");
+
+ BOOST_TEST_MESSAGE( octonion_i_prime*octonion_1 << " ; "
+ << octonion_i_prime*octonion_i << " ; "
+ << octonion_i_prime*octonion_j << " ; "
+ << octonion_i_prime*octonion_k << " ; "
+ << octonion_i_prime*octonion_e_prime << " ; "
+ << octonion_i_prime*octonion_i_prime << " ; "
+ << octonion_i_prime*octonion_j_prime << " ; "
+ << octonion_i_prime*octonion_k_prime << " ; ");
+
+ BOOST_TEST_MESSAGE( octonion_j_prime*octonion_1 << " ; "
+ << octonion_j_prime*octonion_i << " ; "
+ << octonion_j_prime*octonion_j << " ; "
+ << octonion_j_prime*octonion_k << " ; "
+ << octonion_j_prime*octonion_e_prime << " ; "
+ << octonion_j_prime*octonion_i_prime << " ; "
+ << octonion_j_prime*octonion_j_prime << " ; "
+ << octonion_j_prime*octonion_k_prime << " ; ");
+
+ BOOST_TEST_MESSAGE( octonion_k_prime*octonion_1 << " ; "
+ << octonion_k_prime*octonion_i << " ; "
+ << octonion_k_prime*octonion_j << " ; "
+ << octonion_k_prime*octonion_k << " ; "
+ << octonion_k_prime*octonion_e_prime << " ; "
+ << octonion_k_prime*octonion_i_prime << " ; "
+ << octonion_k_prime*octonion_j_prime << " ; "
+ << octonion_k_prime*octonion_k_prime << " ; ");
+
+ BOOST_TEST_MESSAGE(" ");
+
+ BOOST_TEST_MESSAGE("i\'*(e\'*j) : "
+ << octonion_i_prime*(octonion_e_prime*octonion_j) << " ;");
+
+ BOOST_TEST_MESSAGE("(i\'*e\')*j : "
+ << (octonion_i_prime*octonion_e_prime)*octonion_j << " ;");
+
+ BOOST_TEST_MESSAGE(" ");
+}
+
+
+BOOST_TEST_CASE_TEMPLATE_FUNCTION(multiplication_test, T)
+{
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+#else /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ using ::std::numeric_limits;
+
+ using ::boost::math::abs;
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+
+
+ BOOST_TEST_MESSAGE("Testing multiplication for "
+ << string_type_name::_() << ".");
+
+ BOOST_REQUIRE_PREDICATE(::std::less_equal(),
+ (abs(::boost::math::octonion(1,0,0,0,0,0,0,0)*
+ ::boost::math::octonion(1,0,0,0,0,0,0,0)-
+ static_cast(1)))
+ (numeric_limits::epsilon()));
+
+ for (int idx = 1; idx < 8; ++idx)
+ {
+ ::boost::math::octonion toto = index_i_element(idx);
+
+ BOOST_REQUIRE_PREDICATE(::std::less_equal(),
+ (abs(toto*toto+static_cast(1)))
+ (numeric_limits::epsilon()));
+ }
+}
+
+
+BOOST_TEST_CASE_TEMPLATE_FUNCTION(exp_test, T)
+{
+#if BOOST_WORKAROUND(__GNUC__, < 3)
+#else /* BOOST_WORKAROUND(__GNUC__, < 3) */
+ using ::std::numeric_limits;
+
+ using ::std::atan;
+
+ using ::boost::math::abs;
+#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
+
+
+ BOOST_TEST_MESSAGE("Testing exp for "
+ << string_type_name::_() << ".");
+
+ for (int idx = 1; idx < 8; ++idx)
+ {
+ ::boost::math::octonion toto =
+ static_cast(4)*atan(static_cast(1))*index_i_element(idx);
+
+ BOOST_CHECK_PREDICATE(::std::less_equal(),
+ (abs(exp(toto)+static_cast(1)))
+ (2*numeric_limits::epsilon()));
+ }
+}
+
+
+boost::unit_test::test_suite * init_unit_test_suite(int, char *[])
+{
+ ::boost::unit_test::unit_test_log.
+ set_threshold_level(::boost::unit_test::log_messages);
+
+ boost::unit_test::test_suite * test =
+ BOOST_TEST_SUITE("octonion_test");
+
+ BOOST_TEST_MESSAGE("Results of octonion test.");
+ BOOST_TEST_MESSAGE(" ");
+ BOOST_TEST_MESSAGE("(C) Copyright Hubert Holin 2003-2005.");
+ BOOST_TEST_MESSAGE("Distributed under the Boost Software License, Version 1.0.");
+ BOOST_TEST_MESSAGE("(See accompanying file LICENSE_1_0.txt or copy at");
+ BOOST_TEST_MESSAGE("http://www.boost.org/LICENSE_1_0.txt)");
+ BOOST_TEST_MESSAGE(" ");
+
+#define BOOST_OCTONION_COMMON_GENERATOR(fct) \
+ test->add(BOOST_TEST_CASE_TEMPLATE(fct##_test, test_types));
+
+#define BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS(fct) \
+ test->add(BOOST_TEST_CASE_TEMPLATE(fct##_test, near_eps_test_types));
+
+
+#define BOOST_OCTONION_TEST \
+ BOOST_OCTONION_COMMON_GENERATOR(multiplication) \
+ BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS(exp)
+
+
+ BOOST_OCTONION_TEST
+
+
+#undef BOOST_OCTONION_TEST
+
+#undef BOOST_OCTONION_COMMON_GENERATOR
+#undef BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS
+
+#ifdef BOOST_OCTONION_TEST_VERBOSE
+
+ test->add(BOOST_TEST_CASE(octonion_manual_test));
+
+#endif /* BOOST_OCTONION_TEST_VERBOSE */
+
+ return test;
+}
+
+#undef DEFINE_TYPE_NAME
diff --git a/quaternion/quaternion_mi1.cpp b/test/quaternion_mi1.cpp
similarity index 100%
rename from quaternion/quaternion_mi1.cpp
rename to test/quaternion_mi1.cpp
diff --git a/quaternion/quaternion_mi1.h b/test/quaternion_mi1.h
similarity index 100%
rename from quaternion/quaternion_mi1.h
rename to test/quaternion_mi1.h
diff --git a/quaternion/quaternion_mi2.cpp b/test/quaternion_mi2.cpp
similarity index 100%
rename from quaternion/quaternion_mi2.cpp
rename to test/quaternion_mi2.cpp
diff --git a/quaternion/quaternion_mi2.h b/test/quaternion_mi2.h
similarity index 100%
rename from quaternion/quaternion_mi2.h
rename to test/quaternion_mi2.h
diff --git a/quaternion/quaternion_mult_incl_test.cpp b/test/quaternion_mult_incl_test.cpp
similarity index 100%
rename from quaternion/quaternion_mult_incl_test.cpp
rename to test/quaternion_mult_incl_test.cpp
diff --git a/quaternion/quaternion_test.cpp b/test/quaternion_test.cpp
similarity index 100%
rename from quaternion/quaternion_test.cpp
rename to test/quaternion_test.cpp