1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
|
/*****
* runpair.in
*
* Runtime functions for pair operations.
*
*****/
pair => primPair()
#include "pair.h"
using namespace camp;
namespace run {
extern pair zero;
}
pair sin(pair z)
{
return pair(sin(z.getx())*cosh(z.gety()),cos(z.getx())*sinh(z.gety()));
}
pair exp(pair z)
{
return exp(z.getx())*expi(z.gety());
}
pair gamma(pair z)
{
static double p[]={0.99999999999980993,676.5203681218851,-1259.1392167224028,
771.32342877765313,-176.61502916214059,12.507343278686905,
-0.13857109526572012,9.9843695780195716e-6,
1.5056327351493116e-7};
static int n=sizeof(p)/sizeof(double);
static double root2pi=sqrt(2*PI);
if(z.getx() < 0.5)
return PI/(sin(PI*z)*gamma(1.0-z));
z -= 1.0;
pair x=p[0];
for(int i=1; i < n; ++i)
x += p[i]/(z+i);
pair t=n-1.5+z;
return root2pi*pow(t,z+0.5)*exp(-t)*x;
}
// Autogenerated routines:
pair :pairZero()
{
return zero;
}
pair :realRealToPair(real x, real y)
{
return pair(x,y);
}
pair :pairNegate(pair z)
{
return -z;
}
real xpart:pairXPart(pair z)
{
return z.getx();
}
real ypart:pairYPart(pair z)
{
return z.gety();
}
real length(pair z)
{
return z.length();
}
real abs(pair z)
{
return z.length();
}
pair sqrt(explicit pair z)
{
return Sqrt(z);
}
// Return the angle of z in radians.
real angle(pair z, bool warn=true)
{
if(!warn && z.getx() == 0.0 && z.gety() == 0.0) return 0.0;
return z.angle();
}
// Return the angle of z in degrees in the interval [0,360).
real degrees(pair z, bool warn=true)
{
if(!warn && z.getx() == 0.0 && z.gety() == 0.0) return 0.0;
return principalBranch(degrees(z.angle()));
}
// Convert degrees to radians.
real radians(real degrees)
{
return radians(degrees);
}
// Convert radians to degrees.
real degrees(real radians)
{
return degrees(radians);
}
// Convert radians to degrees in [0,360).
real Degrees(real radians)
{
return principalBranch(degrees(radians));
}
real Sin(real deg)
{
return sin(radians(deg));
}
real Cos(real deg)
{
return cos(radians(deg));
}
real Tan(real deg)
{
return tan(radians(deg));
}
real aSin(real x)
{
return degrees(asin(x));
}
real aCos(real x)
{
return degrees(acos(x));
}
real aTan(real x)
{
return degrees(atan(x));
}
pair unit(pair z)
{
return unit(z);
}
pair dir(real degrees)
{
return expi(radians(degrees));
}
pair dir(explicit pair z)
{
return unit(z);
}
pair expi(real angle)
{
return expi(angle);
}
pair exp(explicit pair z)
{
return exp(z);
}
pair log(explicit pair z)
{
return pair(log(z.length()),z.angle());
}
pair sin(explicit pair z)
{
return sin(z);
}
pair cos(explicit pair z)
{
return pair(cos(z.getx())*cosh(z.gety()),-sin(z.getx())*sinh(z.gety()));
}
// Complex Gamma function
pair gamma(explicit pair z)
{
return gamma(z);
}
pair conj(pair z)
{
return conj(z);
}
pair realmult(pair z, pair w)
{
return pair(z.getx()*w.getx(),z.gety()*w.gety());
}
// To avoid confusion, a dot product requires explicit pair arguments.
real dot(explicit pair z, explicit pair w)
{
return dot(z,w);
}
pair bezier(pair a, pair b, pair c, pair d, real t)
{
real onemt=1-t;
real onemt2=onemt*onemt;
return onemt2*onemt*a+t*(3.0*(onemt2*b+t*onemt*c)+t*t*d);
}
pair bezierP(pair a, pair b, pair c, pair d, real t)
{
return 3.0*(t*t*(d-a+3.0*(b-c))+t*(2.0*(a+c)-4.0*b)+b-a);
}
pair bezierPP(pair a, pair b, pair c, pair d, real t)
{
return 6.0*(t*(d-a+3.0*(b-c))+a+c-2.0*b);
}
pair bezierPPP(pair a, pair b, pair c, pair d)
{
return 6.0*(d-a+3.0*(b-c));
}
|
