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1 | # |
2 | # Trigonometric functions, mostly inherited from Math::Complex. |
3 | # -- Jarkko Hietaniemi, April 1997 |
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4 | # -- Raphael Manfredi, September 1996 (indirectly: because of Math::Complex) |
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5 | # |
6 | |
7 | require Exporter; |
8 | package Math::Trig; |
9 | |
10 | use strict; |
11 | |
12 | use Math::Complex qw(:trig); |
13 | |
14 | use vars qw($VERSION $PACKAGE |
15 | @ISA |
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16 | @EXPORT); |
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17 | |
18 | @ISA = qw(Exporter); |
19 | |
20 | $VERSION = 1.00; |
21 | |
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22 | my @angcnv = qw(rad2deg rad2grad |
23 | deg2rad deg2grad |
24 | grad2rad grad2deg); |
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25 | |
26 | @EXPORT = (@{$Math::Complex::EXPORT_TAGS{'trig'}}, |
27 | @angcnv); |
28 | |
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29 | use constant pi2 => 2 * pi; |
30 | use constant DR => pi2/360; |
31 | use constant RD => 360/pi2; |
32 | use constant DG => 400/360; |
33 | use constant GD => 360/400; |
34 | use constant RG => 400/pi2; |
35 | use constant GR => pi2/400; |
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36 | |
37 | # |
38 | # Truncating remainder. |
39 | # |
40 | |
41 | sub remt ($$) { |
42 | # Oh yes, POSIX::fmod() would be faster. Possibly. If it is available. |
43 | $_[0] - $_[1] * int($_[0] / $_[1]); |
44 | } |
45 | |
46 | # |
47 | # Angle conversions. |
48 | # |
49 | |
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50 | sub rad2deg ($) { remt(RD * $_[0], 360) } |
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51 | |
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52 | sub deg2rad ($) { remt(DR * $_[0], pi2) } |
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53 | |
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54 | sub grad2deg ($) { remt(GD * $_[0], 360) } |
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55 | |
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56 | sub deg2grad ($) { remt(DG * $_[0], 400) } |
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57 | |
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58 | sub rad2grad ($) { remt(RG * $_[0], 400) } |
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59 | |
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60 | sub grad2rad ($) { remt(GR * $_[0], pi2) } |
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61 | |
62 | =head1 NAME |
63 | |
64 | Math::Trig - trigonometric functions |
65 | |
66 | =head1 SYNOPSIS |
67 | |
68 | use Math::Trig; |
69 | |
70 | $x = tan(0.9); |
71 | $y = acos(3.7); |
72 | $z = asin(2.4); |
73 | |
74 | $halfpi = pi/2; |
75 | |
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76 | $rad = deg2rad(120); |
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77 | |
78 | =head1 DESCRIPTION |
79 | |
80 | C<Math::Trig> defines many trigonometric functions not defined by the |
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81 | core Perl which defines only the C<sin()> and C<cos()>. The constant |
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82 | B<pi> is also defined as are a few convenience functions for angle |
83 | conversions. |
84 | |
85 | =head1 TRIGONOMETRIC FUNCTIONS |
86 | |
87 | The tangent |
88 | |
89 | tan |
90 | |
91 | The cofunctions of the sine, cosine, and tangent (cosec/csc and cotan/cot |
92 | are aliases) |
93 | |
94 | csc cosec sec cot cotan |
95 | |
96 | The arcus (also known as the inverse) functions of the sine, cosine, |
97 | and tangent |
98 | |
99 | asin acos atan |
100 | |
101 | The principal value of the arc tangent of y/x |
102 | |
103 | atan2(y, x) |
104 | |
105 | The arcus cofunctions of the sine, cosine, and tangent (acosec/acsc |
106 | and acotan/acot are aliases) |
107 | |
108 | acsc acosec asec acot acotan |
109 | |
110 | The hyperbolic sine, cosine, and tangent |
111 | |
112 | sinh cosh tanh |
113 | |
114 | The cofunctions of the hyperbolic sine, cosine, and tangent (cosech/csch |
115 | and cotanh/coth are aliases) |
116 | |
117 | csch cosech sech coth cotanh |
118 | |
119 | The arcus (also known as the inverse) functions of the hyperbolic |
120 | sine, cosine, and tangent |
121 | |
122 | asinh acosh atanh |
123 | |
124 | The arcus cofunctions of the hyperbolic sine, cosine, and tangent |
125 | (acsch/acosech and acoth/acotanh are aliases) |
126 | |
127 | acsch acosech asech acoth acotanh |
128 | |
129 | The trigonometric constant B<pi> is also defined. |
130 | |
131 | $pi2 = 2 * pi; |
132 | |
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133 | =head2 ERRORS DUE TO DIVISION BY ZERO |
134 | |
135 | The following functions |
136 | |
137 | tan |
138 | sec |
139 | csc |
140 | cot |
141 | asec |
142 | acsc |
143 | tanh |
144 | sech |
145 | csch |
146 | coth |
147 | atanh |
148 | asech |
149 | acsch |
150 | acoth |
151 | |
152 | cannot be computed for all arguments because that would mean dividing |
153 | by zero. These situations cause fatal runtime errors looking like this |
154 | |
155 | cot(0): Division by zero. |
156 | (Because in the definition of cot(0), the divisor sin(0) is 0) |
157 | Died at ... |
158 | |
159 | For the C<csc>, C<cot>, C<asec>, C<acsc>, C<csch>, C<coth>, C<asech>, |
160 | C<acsch>, the argument cannot be C<0> (zero). For the C<atanh>, |
161 | C<acoth>, the argument cannot be C<1> (one). For the C<tan>, C<sec>, |
162 | C<tanh>, C<sech>, the argument cannot be I<pi/2 + k * pi>, where I<k> is |
163 | any integer. |
164 | |
165 | =head2 SIMPLE (REAL) ARGUMENTS, COMPLEX RESULTS |
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166 | |
167 | Please note that some of the trigonometric functions can break out |
168 | from the B<real axis> into the B<complex plane>. For example |
169 | C<asin(2)> has no definition for plain real numbers but it has |
170 | definition for complex numbers. |
171 | |
172 | In Perl terms this means that supplying the usual Perl numbers (also |
173 | known as scalars, please see L<perldata>) as input for the |
174 | trigonometric functions might produce as output results that no more |
175 | are simple real numbers: instead they are complex numbers. |
176 | |
177 | The C<Math::Trig> handles this by using the C<Math::Complex> package |
178 | which knows how to handle complex numbers, please see L<Math::Complex> |
179 | for more information. In practice you need not to worry about getting |
180 | complex numbers as results because the C<Math::Complex> takes care of |
181 | details like for example how to display complex numbers. For example: |
182 | |
183 | print asin(2), "\n"; |
184 | |
185 | should produce something like this (take or leave few last decimals): |
186 | |
187 | 1.5707963267949-1.31695789692482i |
188 | |
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189 | That is, a complex number with the real part of approximately C<1.571> |
190 | and the imaginary part of approximately C<-1.317>. |
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191 | |
192 | =head1 ANGLE CONVERSIONS |
193 | |
194 | (Plane, 2-dimensional) angles may be converted with the following functions. |
195 | |
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196 | $radians = deg2rad($degrees); |
197 | $radians = grad2rad($gradians); |
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198 | |
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199 | $degrees = rad2deg($radians); |
200 | $degrees = grad2deg($gradians); |
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201 | |
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202 | $gradians = deg2grad($degrees); |
203 | $gradians = rad2grad($radians); |
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204 | |
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205 | The full circle is 2 I<pi> radians or I<360> degrees or I<400> gradians. |
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206 | |
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207 | =head1 BUGS |
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208 | |
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209 | Saying C<use Math::Trig;> exports many mathematical routines in the |
210 | caller environment and even overrides some (C<sin>, C<cos>). This is |
211 | construed as a feature by the Authors, actually... ;-) |
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212 | |
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213 | The code is not optimized for speed, especially because we use |
214 | C<Math::Complex> and thus go quite near complex numbers while doing |
215 | the computations even when the arguments are not. This, however, |
216 | cannot be completely avoided if we want things like C<asin(2)> to give |
217 | an answer instead of giving a fatal runtime error. |
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218 | |
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219 | =head1 AUTHORS |
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220 | |
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221 | Jarkko Hietaniemi <F<jhi@iki.fi>> and |
222 | Raphael Manfredi <F<Raphael_Manfredi@grenoble.hp.com>>. |
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223 | |
224 | =cut |
225 | |
226 | # eof |