Numworks Epsilon  1.4.1
Graphing Calculator Operating System
trigo.cpp
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1 #include <quiz.h>
2 #include <poincare.h>
3 #include <ion.h>
4 #include <assert.h>
5 #include "helper.h"
6 
7 using namespace Poincare;
8 
9 QUIZ_CASE(poincare_parse_trigo) {
10  assert_parsed_expression_type("sin(0)", Expression::Type::Sine);
11  assert_parsed_expression_type("cos(0)", Expression::Type::Cosine);
12  assert_parsed_expression_type("tan(0)", Expression::Type::Tangent);
13  assert_parsed_expression_type("cosh(0)", Expression::Type::HyperbolicCosine);
14  assert_parsed_expression_type("sinh(0)", Expression::Type::HyperbolicSine);
15  assert_parsed_expression_type("tanh(0)", Expression::Type::HyperbolicTangent);
16  assert_parsed_expression_type("acos(0)", Expression::Type::ArcCosine);
17  assert_parsed_expression_type("asin(0)", Expression::Type::ArcSine);
18  assert_parsed_expression_type("atan(0)", Expression::Type::ArcTangent);
19  assert_parsed_expression_type("acosh(0)", Expression::Type::HyperbolicArcCosine);
20  assert_parsed_expression_type("asinh(0)", Expression::Type::HyperbolicArcSine);
21  assert_parsed_expression_type("atanh(0)", Expression::Type::HyperbolicArcTangent);
22 }
23 
24 QUIZ_CASE(poincare_trigo_evaluate) {
25  Complex<double> a[1] = {Complex<double>::Float(-0.4161468365)};
26  assert_parsed_expression_evaluates_to("cos(2)", a, Radian);
27  Complex<float> a1[1] = {Complex<float>::Cartesian(-1.0086248134f, -0.8893951958f)};
28  assert_parsed_expression_evaluates_to("cos(I-4)", a1, Radian);
29  Complex<double> b[1] = {Complex<double>::Float(0.9092974268)};
30  assert_parsed_expression_evaluates_to("sin(2)", b, Radian);
31  Complex<float> b1[1] = {Complex<float>::Cartesian( 1.16780727488f, -0.768162763456f)};
32  assert_parsed_expression_evaluates_to("sin(I-4)", b1, Radian);
33  Complex<double> c[1] = {Complex<double>::Float(-2.18503986326151899)};
34  assert_parsed_expression_evaluates_to("tan(2)", c, Radian);
35  Complex<float> c1[1] = {Complex<float>::Cartesian(-0.27355308280730f, 1.002810507583504f)};
36  assert_parsed_expression_evaluates_to("tan(I-4)", c1, Radian);
37  Complex<double> a2[1] = {Complex<double>::Float(3.762195691)};
38  assert_parsed_expression_evaluates_to("cosh(2)", a2, Radian);
39  Complex<float> a3[1] = {Complex<float>::Cartesian(14.754701170483756280f,-22.96367349919304059f)};
40  assert_parsed_expression_evaluates_to("cosh(I-4)", a3, Radian);
41  Complex<double> b2[1] = {Complex<double>::Float(3.62686040784701876)};
42  assert_parsed_expression_evaluates_to("sinh(2)", b2, Radian);
43  Complex<float> b3[1] = {Complex<float>::Cartesian(-14.744805188558725031023f, 22.979085577886129555168f)};
44  assert_parsed_expression_evaluates_to("sinh(I-4)", b3, Radian);
45  Complex<double> c2[1] = {Complex<double>::Float(0.9640275800758168839464)};
46  assert_parsed_expression_evaluates_to("tanh(2)", c2, Radian);
47  Complex<float> c3[1] = {Complex<float>::Cartesian(-1.00027905623446556836909f, 0.000610240921376259f)};
48  assert_parsed_expression_evaluates_to("tanh(I-4)", c3, Radian);
49 }
50 
51 QUIZ_CASE(poincare_trigo_simplify) {
52  // -- sin/cos -> tan
53  assert_parsed_expression_simplify_to("sin(x)/cos(x)", "tan(x)");
54  assert_parsed_expression_simplify_to("cos(x)/sin(x)", "1/tan(x)");
55  assert_parsed_expression_simplify_to("sin(x)*P/cos(x)", "tan(x)*P");
56  assert_parsed_expression_simplify_to("sin(x)/(P*cos(x))", "tan(x)/P");
57  assert_parsed_expression_simplify_to("1*tan(2)*tan(5)", "tan(2)*tan(5)");
58  assert_parsed_expression_simplify_to("tan(62P/21)", "-tan(P/21)");
59  assert_parsed_expression_simplify_to("cos(26P/21)/sin(25P/17)", "cos((5*P)/21)/sin((8*P)/17)");
60  assert_parsed_expression_simplify_to("cos(62P/21)*P*3/sin(62P/21)", "-(3*P)/tan(P/21)");
61  assert_parsed_expression_simplify_to("cos(62P/21)/(P*3*sin(62P/21))", "-1/(3*tan(P/21)*P)");
62  assert_parsed_expression_simplify_to("sin(62P/21)*P*3/cos(62P/21)", "-3*tan(P/21)*P");
63  assert_parsed_expression_simplify_to("sin(62P/21)/(P*3cos(62P/21))", "-tan(P/21)/(3*P)");
64  assert_parsed_expression_simplify_to("-cos(P/62)ln(3)/(sin(P/62)P)", "-ln(3)/(tan(P/62)*P)");
65  assert_parsed_expression_simplify_to("-2cos(P/62)ln(3)/(sin(P/62)P)", "-(2*ln(3))/(tan(P/62)*P)");
66  // -- cos
67  assert_parsed_expression_simplify_to("cos(0)", "1");
68  assert_parsed_expression_simplify_to("cos(P)", "-1");
69  assert_parsed_expression_simplify_to("cos(P*4/7)", "-cos((3*P)/7)");
70  assert_parsed_expression_simplify_to("cos(P*35/29)", "-cos((6*P)/29)");
71  assert_parsed_expression_simplify_to("cos(-P*35/29)", "-cos((6*P)/29)");
72  assert_parsed_expression_simplify_to("cos(P*340000)", "1");
73  assert_parsed_expression_simplify_to("cos(-P*340001)", "-1");
74  assert_parsed_expression_simplify_to("cos(-P*R(2))", "cos(R(2)*P)");
75  assert_parsed_expression_simplify_to("cos(1311P/6)", "0");
76  assert_parsed_expression_simplify_to("cos(P/12)", "(R(2)+R(6))/4");
77  assert_parsed_expression_simplify_to("cos(-P/12)", "(R(2)+R(6))/4");
78  assert_parsed_expression_simplify_to("cos(-P17/8)", "R(2+R(2))/2");
79  assert_parsed_expression_simplify_to("cos(41P/6)", "-R(3)/2");
80  assert_parsed_expression_simplify_to("cos(P/4+1000P)", "R(2)/2");
81  assert_parsed_expression_simplify_to("cos(-P/3)", "1/2");
82  assert_parsed_expression_simplify_to("cos(41P/5)", "(1+R(5))/4");
83  assert_parsed_expression_simplify_to("cos(7P/10)", "-(R(2)*R(5-R(5)))/4");
84  assert_parsed_expression_simplify_to("cos(0)", "1", Expression::AngleUnit::Degree);
85  assert_parsed_expression_simplify_to("cos(180)", "-1", Expression::AngleUnit::Degree);
86  assert_parsed_expression_simplify_to("cos(720/7)", "-cos(540/7)", Expression::AngleUnit::Degree);
87  assert_parsed_expression_simplify_to("cos(6300/29)", "-cos(1080/29)", Expression::AngleUnit::Degree);
88  assert_parsed_expression_simplify_to("cos(-6300/29)", "-cos(1080/29)", Expression::AngleUnit::Degree);
89  assert_parsed_expression_simplify_to("cos(61200000)", "1", Expression::AngleUnit::Degree);
90  assert_parsed_expression_simplify_to("cos(-61200180)", "-1", Expression::AngleUnit::Degree);
91  assert_parsed_expression_simplify_to("cos(-180*R(2))", "cos(180*R(2))", Expression::AngleUnit::Degree);
92  assert_parsed_expression_simplify_to("cos(39330)", "0", Expression::AngleUnit::Degree);
93  assert_parsed_expression_simplify_to("cos(15)", "(R(2)+R(6))/4", Expression::AngleUnit::Degree);
94  assert_parsed_expression_simplify_to("cos(-15)", "(R(2)+R(6))/4", Expression::AngleUnit::Degree);
95  assert_parsed_expression_simplify_to("cos(-765/2)", "R(2+R(2))/2", Expression::AngleUnit::Degree);
96  assert_parsed_expression_simplify_to("cos(7380/6)", "-R(3)/2", Expression::AngleUnit::Degree);
97  assert_parsed_expression_simplify_to("cos(180045)", "R(2)/2", Expression::AngleUnit::Degree);
98  assert_parsed_expression_simplify_to("cos(-60)", "1/2", Expression::AngleUnit::Degree);
99  assert_parsed_expression_simplify_to("cos(7380/5)", "(1+R(5))/4", Expression::AngleUnit::Degree);
100  assert_parsed_expression_simplify_to("cos(112.5)", "-R(2-R(2))/2", Expression::AngleUnit::Degree);
101  // -- sin
102  assert_parsed_expression_simplify_to("sin(0)", "0");
103  assert_parsed_expression_simplify_to("sin(P)", "0");
104  assert_parsed_expression_simplify_to("sin(P*35/29)", "-sin((6*P)/29)");
105  assert_parsed_expression_simplify_to("sin(-P*35/29)", "sin((6*P)/29)");
106  assert_parsed_expression_simplify_to("sin(P*340000)", "0");
107  assert_parsed_expression_simplify_to("sin(P*340001)", "0");
108  assert_parsed_expression_simplify_to("sin(-P*340001)", "0");
109  assert_parsed_expression_simplify_to("sin(P/12)", "((-R(2))+R(6))/4");
110  assert_parsed_expression_simplify_to("sin(-P/12)", "(R(2)-R(6))/4");
111  assert_parsed_expression_simplify_to("sin(-P*R(2))", "-sin(R(2)*P)");
112  assert_parsed_expression_simplify_to("sin(1311P/6)", "1");
113  assert_parsed_expression_simplify_to("sin(-P17/8)", "-R(2-R(2))/2");
114  assert_parsed_expression_simplify_to("sin(41P/6)", "1/2");
115  assert_parsed_expression_simplify_to("sin(-3P/10)", "((-1)-R(5))/4");
116  assert_parsed_expression_simplify_to("sin(P/4+1000P)", "R(2)/2");
117  assert_parsed_expression_simplify_to("sin(-P/3)", "-R(3)/2");
118  assert_parsed_expression_simplify_to("sin(17P/5)", "-(R(2)*R(5+R(5)))/4");
119  assert_parsed_expression_simplify_to("sin(P/5)", "(R(2)*R(5-R(5)))/4");
120  assert_parsed_expression_simplify_to("sin(0)", "0", Expression::AngleUnit::Degree);
121  assert_parsed_expression_simplify_to("sin(180)", "0", Expression::AngleUnit::Degree);
122  assert_parsed_expression_simplify_to("sin(6300/29)", "-sin(1080/29)", Expression::AngleUnit::Degree);
123  assert_parsed_expression_simplify_to("sin(-6300/29)", "sin(1080/29)", Expression::AngleUnit::Degree);
124  assert_parsed_expression_simplify_to("sin(61200000)", "0", Expression::AngleUnit::Degree);
125  assert_parsed_expression_simplify_to("sin(61200180)", "0", Expression::AngleUnit::Degree);
126  assert_parsed_expression_simplify_to("sin(-61200180)", "0", Expression::AngleUnit::Degree);
127  assert_parsed_expression_simplify_to("sin(15)", "((-R(2))+R(6))/4", Expression::AngleUnit::Degree);
128  assert_parsed_expression_simplify_to("sin(-15)", "(R(2)-R(6))/4", Expression::AngleUnit::Degree);
129  assert_parsed_expression_simplify_to("sin(-180*R(2))", "-sin(180*R(2))", Expression::AngleUnit::Degree);
130  assert_parsed_expression_simplify_to("sin(39330)", "1", Expression::AngleUnit::Degree);
131  assert_parsed_expression_simplify_to("sin(-765/2)", "-R(2-R(2))/2", Expression::AngleUnit::Degree);
132  assert_parsed_expression_simplify_to("sin(1230)", "1/2", Expression::AngleUnit::Degree);
133  assert_parsed_expression_simplify_to("sin(180045)", "R(2)/2", Expression::AngleUnit::Degree);
134  assert_parsed_expression_simplify_to("sin(-60)", "-R(3)/2", Expression::AngleUnit::Degree);
135  assert_parsed_expression_simplify_to("sin(612)", "-(R(2)*R(5+R(5)))/4", Expression::AngleUnit::Degree);
136  assert_parsed_expression_simplify_to("sin(36)", "(R(2)*R(5-R(5)))/4", Expression::AngleUnit::Degree);
137  // -- tan
138  assert_parsed_expression_simplify_to("tan(0)", "0");
139  assert_parsed_expression_simplify_to("tan(P)", "0");
140  assert_parsed_expression_simplify_to("tan(P*35/29)", "tan((6*P)/29)");
141  assert_parsed_expression_simplify_to("tan(-P*35/29)", "-tan((6*P)/29)");
142  assert_parsed_expression_simplify_to("tan(P*340000)", "0");
143  assert_parsed_expression_simplify_to("tan(P*340001)", "0");
144  assert_parsed_expression_simplify_to("tan(-P*340001)", "0");
145  assert_parsed_expression_simplify_to("tan(P/12)", "2-R(3)");
146  assert_parsed_expression_simplify_to("tan(-P/12)", "(-2)+R(3)");
147  assert_parsed_expression_simplify_to("tan(-P*R(2))", "-tan(R(2)*P)");
148  assert_parsed_expression_simplify_to("tan(1311P/6)", "undef");
149  assert_parsed_expression_simplify_to("tan(-P17/8)", "1-R(2)");
150  assert_parsed_expression_simplify_to("tan(41P/6)", "-R(3)/3");
151  assert_parsed_expression_simplify_to("tan(P/4+1000P)", "1");
152  assert_parsed_expression_simplify_to("tan(-P/3)", "-R(3)");
153  assert_parsed_expression_simplify_to("tan(-P/10)", "-(R(5)*R(5-2*R(5)))/5");
154  assert_parsed_expression_simplify_to("tan(0)", "0", Expression::AngleUnit::Degree);
155  assert_parsed_expression_simplify_to("tan(180)", "0", Expression::AngleUnit::Degree);
156  assert_parsed_expression_simplify_to("tan(6300/29)", "tan(1080/29)", Expression::AngleUnit::Degree);
157  assert_parsed_expression_simplify_to("tan(-6300/29)", "-tan(1080/29)", Expression::AngleUnit::Degree);
158  assert_parsed_expression_simplify_to("tan(61200000)", "0", Expression::AngleUnit::Degree);
159  assert_parsed_expression_simplify_to("tan(61200180)", "0", Expression::AngleUnit::Degree);
160  assert_parsed_expression_simplify_to("tan(-61200180)", "0", Expression::AngleUnit::Degree);
161  assert_parsed_expression_simplify_to("tan(15)", "2-R(3)", Expression::AngleUnit::Degree);
162  assert_parsed_expression_simplify_to("tan(-15)", "(-2)+R(3)", Expression::AngleUnit::Degree);
163  assert_parsed_expression_simplify_to("tan(-180*R(2))", "-tan(180*R(2))", Expression::AngleUnit::Degree);
164  assert_parsed_expression_simplify_to("tan(39330)", "undef", Expression::AngleUnit::Degree);
165  assert_parsed_expression_simplify_to("tan(-382.5)", "1-R(2)", Expression::AngleUnit::Degree);
166  assert_parsed_expression_simplify_to("tan(1230)", "-R(3)/3", Expression::AngleUnit::Degree);
167  assert_parsed_expression_simplify_to("tan(180045)", "1", Expression::AngleUnit::Degree);
168  assert_parsed_expression_simplify_to("tan(-60)", "-R(3)", Expression::AngleUnit::Degree);
169  assert_parsed_expression_simplify_to("tan(tan(tan(tan(9))))", "tan(tan(tan(tan(9))))");
170  // -- acos
171  assert_parsed_expression_simplify_to("acos(-1/2)", "(2*P)/3");
172  assert_parsed_expression_simplify_to("acos(-1.2)", "undef");
173  assert_parsed_expression_simplify_to("acos(cos(2/3))", "2/3");
174  assert_parsed_expression_simplify_to("acos(cos(3/2))", "3/2");
175  assert_parsed_expression_simplify_to("cos(acos(3/2))", "undef");
176  assert_parsed_expression_simplify_to("cos(acos(2/3))", "2/3");
177  assert_parsed_expression_simplify_to("acos(cos(12))", "acos(cos(12))");
178  assert_parsed_expression_simplify_to("acos(cos(4P/7))", "(4*P)/7");
179  assert_parsed_expression_simplify_to("acos(-cos(2))", "(-2)+P");
180  assert_parsed_expression_simplify_to("acos(-1/2)", "120", Expression::AngleUnit::Degree);
181  assert_parsed_expression_simplify_to("acos(-1.2)", "undef", Expression::AngleUnit::Degree);
182  assert_parsed_expression_simplify_to("acos(cos(2/3))", "2/3", Expression::AngleUnit::Degree);
183  assert_parsed_expression_simplify_to("acos(cos(190))", "170", Expression::AngleUnit::Degree);
184  assert_parsed_expression_simplify_to("acos(cos(75))", "75", Expression::AngleUnit::Degree);
185  assert_parsed_expression_simplify_to("cos(acos(190))", "undef", Expression::AngleUnit::Degree);
186  assert_parsed_expression_simplify_to("cos(acos(75))", "undef", Expression::AngleUnit::Degree);
187  assert_parsed_expression_simplify_to("acos(cos(12))", "12", Expression::AngleUnit::Degree);
188  assert_parsed_expression_simplify_to("acos(cos(720/7))", "720/7", Expression::AngleUnit::Degree);
189  // -- asin
190  assert_parsed_expression_simplify_to("asin(-1/2)", "-P/6");
191  assert_parsed_expression_simplify_to("asin(-1.2)", "undef");
192  assert_parsed_expression_simplify_to("asin(sin(2/3))", "2/3");
193  assert_parsed_expression_simplify_to("sin(asin(2/3))", "2/3");
194  assert_parsed_expression_simplify_to("sin(asin(3/2))", "undef");
195  assert_parsed_expression_simplify_to("asin(sin(3/2))", "3/2");
196  assert_parsed_expression_simplify_to("asin(sin(12))", "asin(sin(12))");
197  assert_parsed_expression_simplify_to("asin(sin(-P/7))", "-P/7");
198  assert_parsed_expression_simplify_to("asin(sin(-R(2)))", "-R(2)");
199  assert_parsed_expression_simplify_to("asin(-1/2)", "-30", Expression::AngleUnit::Degree);
200  assert_parsed_expression_simplify_to("asin(-1.2)", "undef", Expression::AngleUnit::Degree);
201  assert_parsed_expression_simplify_to("asin(sin(75))", "75", Expression::AngleUnit::Degree);
202  assert_parsed_expression_simplify_to("sin(asin(75))", "undef", Expression::AngleUnit::Degree);
203  assert_parsed_expression_simplify_to("sin(asin(190))", "undef", Expression::AngleUnit::Degree);
204  assert_parsed_expression_simplify_to("asin(sin(32))", "32", Expression::AngleUnit::Degree);
205  assert_parsed_expression_simplify_to("asin(sin(400))", "40", Expression::AngleUnit::Degree);
206  assert_parsed_expression_simplify_to("asin(sin(-180/7))", "-180/7", Expression::AngleUnit::Degree);
207  // -- atan
208  assert_parsed_expression_simplify_to("atan(-1)", "-P/4");
209  assert_parsed_expression_simplify_to("atan(-1.2)", "-atan(6/5)");
210  assert_parsed_expression_simplify_to("atan(tan(2/3))", "2/3");
211  assert_parsed_expression_simplify_to("tan(atan(2/3))", "2/3");
212  assert_parsed_expression_simplify_to("tan(atan(5/2))", "5/2");
213  assert_parsed_expression_simplify_to("atan(tan(5/2))", "atan(tan(5/2))");
214  assert_parsed_expression_simplify_to("atan(tan(5/2))", "atan(tan(5/2))");
215  assert_parsed_expression_simplify_to("atan(tan(-P/7))", "-P/7");
216  assert_parsed_expression_simplify_to("atan(R(3))", "P/3");
217  assert_parsed_expression_simplify_to("atan(tan(-R(2)))", "-R(2)");
218  assert_parsed_expression_simplify_to("atan(-1)", "-45", Expression::AngleUnit::Degree);
219  assert_parsed_expression_simplify_to("atan(-1.2)", "-atan(6/5)", Expression::AngleUnit::Degree);
220  assert_parsed_expression_simplify_to("atan(tan(-45))", "-45", Expression::AngleUnit::Degree);
221  assert_parsed_expression_simplify_to("tan(atan(120))", "120", Expression::AngleUnit::Degree);
222  assert_parsed_expression_simplify_to("tan(atan(2293))", "2293", Expression::AngleUnit::Degree);
223  assert_parsed_expression_simplify_to("atan(tan(2293))", "-47", Expression::AngleUnit::Degree);
224  assert_parsed_expression_simplify_to("atan(tan(1808))", "8", Expression::AngleUnit::Degree);
225  assert_parsed_expression_simplify_to("atan(tan(-180/7))", "-180/7", Expression::AngleUnit::Degree);
226  assert_parsed_expression_simplify_to("atan(R(3))", "60", Expression::AngleUnit::Degree);
227 }
Poincare::Complex::Cartesian
static Complex< T > Cartesian(T a, T b)
Definition: complex.cpp:28
assert_parsed_expression_type
void assert_parsed_expression_type(const char *expression, Poincare::Expression::Type type)
Definition: helper.cpp:54
c
c(generic_all_nodes)
assert_parsed_expression_simplify_to
void assert_parsed_expression_simplify_to(const char *expression, const char *simplifiedExpression, Expression::AngleUnit angleUnit)
Definition: helper.cpp:90
Radian
constexpr Poincare::Expression::AngleUnit Radian
Definition: helper.h:4
assert_parsed_expression_evaluates_to
void assert_parsed_expression_evaluates_to(const char *expression, Complex< T > *results, int numberOfRows, int numberOfColumns, Expression::AngleUnit angleUnit)
Definition: helper.cpp:69
Poincare::Complex::Float
static Complex< T > Float(T x)
Definition: complex.cpp:23
QUIZ_CASE
QUIZ_CASE(poincare_parse_trigo)
Definition: trigo.cpp:9