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

/*
 * Copyright (C) 2006-2009 Mihai Preda.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 */

package org.javia.arity;

class MoreMath {
    private static final double LOG2E  = 1.4426950408889634074;

    public static final double asinh(double x) {
        return (x < 0) ? -asinh(-x) : Math.log(x + x + 1/(Math.sqrt(x*x + 1) + x));
    }
    
    public static final double acosh(double x) {
        return Math.log(x + x - 1/(Math.sqrt(x*x - 1) + x));
    }

    public static final double atanh(double x) {
        return (x < 0) ? -atanh(-x) : 0.5 * Math.log(1. + (x + x)/(1 - x));
    }

    public static final double trunc(double x) {
        return x >= 0 ? Math.floor(x) : Math.ceil(x);
    }

    public static final double gcd(double x, double y) {
        if (Double.isNaN(x) || Double.isNaN(y) ||
            Double.isInfinite(x) || Double.isInfinite(y)) {
            return Double.NaN;
        }
        x = Math.abs(x);
        y = Math.abs(y);
        while (x < y * 1e15) {
            final double save = y;
            y = x % y;
            x = save;
        } 
        return x;
    }

    static final double GAMMA[] = {
        57.156235665862923517,
        -59.597960355475491248,
        14.136097974741747174,
        -0.49191381609762019978,
        .33994649984811888699e-4,
        .46523628927048575665e-4,
        -.98374475304879564677e-4,
        .15808870322491248884e-3,
        -.21026444172410488319e-3,
        .21743961811521264320e-3,
        -.16431810653676389022e-3,
        .84418223983852743293e-4,
        -.26190838401581408670e-4,
        .36899182659531622704e-5
    };
 
    public static final double lgamma(double x) {
        double tmp = x + 5.2421875; //== 607/128. + .5;
        double sum = 0.99999999999999709182;
        for (int i = 0; i < GAMMA.length; ++i) {
            sum += GAMMA[i] / ++x;
        }

        return 0.9189385332046727418 //LN_SQRT2PI, ln(sqrt(2*pi))
            + Math.log(sum)
            + (tmp-4.7421875)*Math.log(tmp) - tmp
            ;
    }

    static final double FACT[] = {
        1.0,
        40320.0,
        2.0922789888E13,
        6.204484017332394E23,
        2.631308369336935E35,
        8.159152832478977E47,
        1.2413915592536073E61,
        7.109985878048635E74,
        1.2688693218588417E89,
        6.1234458376886085E103,
        7.156945704626381E118,
        1.8548264225739844E134,
        9.916779348709496E149,
        1.0299016745145628E166,
        1.974506857221074E182,
        6.689502913449127E198,
        3.856204823625804E215,
        3.659042881952549E232,
        5.5502938327393044E249,
        1.3113358856834524E267,
        4.7147236359920616E284,
        2.5260757449731984E302,
    };

    public static final double factorial(double x) {
        if (x < 0) { // x <= -1 ?
            return Double.NaN;
        }
        if (x <= 170) {
            if (Math.floor(x) == x) {
                int n = (int)x;
                double extra = x;
                switch (n & 7) {
                case 7: extra *= --x;
                case 6: extra *= --x;
                case 5: extra *= --x;
                case 4: extra *= --x;
                case 3: extra *= --x;
                case 2: extra *= --x;
                case 1: return FACT[n >> 3] * extra;
                case 0: return FACT[n >> 3];
                }
            }
        }
        return Math.exp(lgamma(x));
    }

    public static final double combinations(double n, double k) {
        if (n < 0 || k < 0) { return Double.NaN; }
        if (n < k) { return 0; }
        if (Math.floor(n) == n && Math.floor(k) == k) {
            k = Math.min(k, n-k);
            if (n <= 170 && 12 < k && k <= 170) {
                return factorial(n)/factorial(k)/factorial(n-k);
            } else {
                double r = 1, diff = n-k;
                for (double i = k; i > .5 && r < Double.POSITIVE_INFINITY; --i) {
                    r *= (diff+i)/i;
                }
                return r;
            }
        } else {
            return Math.exp(lgamma(n) - lgamma(k) - lgamma(n-k));
        }
    }

    public static final double permutations(double n, double k) {
        if (n < 0 || k < 0) { return Double.NaN; }
        if (n < k) { return 0; }
        if (Math.floor(n) == n && Math.floor(k) == k) {
            if (n <= 170 && 10 < k && k <= 170) {
                return factorial(n)/factorial(n-k);
            } else {
                double r = 1, limit = n-k+.5;
                for (double i = n; i > limit && r < Double.POSITIVE_INFINITY; --i) {
                    r *= i;
                }
                return r;
            }
        } else {
            return Math.exp(lgamma(n) - lgamma(n-k));
        }
    }

    public static final double log2(double x) {
        return Math.log(x) * LOG2E;
    }

    private static final boolean isPiMultiple(double x) {
        // x % y == 0
        final double d = x / Math.PI;
        return d == Math.floor(d);
    }

    public static final double sin(double x) {
        return isPiMultiple(x) ? 0 : Math.sin(x);
    }

    public static final double cos(double x) {
        return isPiMultiple(x-Math.PI/2) ? 0 : Math.cos(x);
    }

    public static final double tan(double x) {
        return isPiMultiple(x) ? 0 : Math.tan(x);
    }

    public static final int intLog10(double x) {
        //an alternative implem is using a for loop.
        return (int)Math.floor(Math.log10(x));
        //return (int)log10(x);
    }

    public static final double intExp10(int exp) {
        return Double.parseDouble("1E" + exp);
    }
}