GRASS GIS 8 Programmer's Manual 8.2.1RC1(2022)-exported
as241.c
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1#include <math.h>
2
3
4/*-
5 * algorithm as241 appl. statist. (1988) 37(3):477-484.
6 * produces the normal deviate z corresponding to a given lower tail
7 * area of p; z is accurate to about 1 part in 10**7.
8 *
9 * the hash sums below are the sums of the mantissas of the coefficients.
10 * they are included for use in checking transcription.
11 */
12double Cdhc_ppnd7(double p)
13{
14 static double zero = 0.0, one = 1.0, half = 0.5;
15 static double split1 = 0.425, split2 = 5.0;
16 static double const1 = 0.180625, const2 = 1.6;
17
18 /* coefficients for p close to 0.5 */
19 static double a[4] = { 3.3871327179, 5.0434271938e+01,
20 1.5929113202e+02, 5.9109374720e+01
21 };
22 static double b[4] = { 0.0, 1.7895169469e+01, 7.8757757664e+01,
23 6.7187563600e+01
24 };
25
26 /* hash sum ab 32.3184577772 */
27 /* coefficients for p not close to 0, 0.5 or 1. */
28 static double c[4] = { 1.4234372777e+00, 2.7568153900e+00,
29 1.3067284816e+00, 1.7023821103e-01
30 };
31 static double d[3] = { 0.0, 7.3700164250e-01, 1.2021132975e-01 };
32
33 /* hash sum cd 15.7614929821 */
34 /* coefficients for p near 0 or 1. */
35 static double e[4] = { 6.6579051150e+00, 3.0812263860e+00,
36 4.2868294337e-01, 1.7337203997e-02
37 };
38 static double f[3] = { 0.0, 2.4197894225e-01, 1.2258202635e-02 };
39
40 /* hash sum ef 19.4052910204 */
41 double q, r, ret;
42
43 q = p - half;
44 if (fabs(q) <= split1) {
45 r = const1 - q * q;
46 ret = q * (((a[3] * r + a[2]) * r + a[1]) * r + a[0]) /
47 (((b[3] * r + b[2]) * r + b[1]) * r + one);
48
49 return ret;;
50 }
51 /* else */
52
53 if (q < zero)
54 r = p;
55 else
56 r = one - p;
57
58 if (r <= zero)
59 return zero;
60
61 r = sqrt(-log(r));
62 if (r <= split2) {
63 r = r - const2;
64 ret = (((c[3] * r + c[2]) * r + c[1]) * r + c[0]) /
65 ((d[2] * r + d[1]) * r + one);
66 }
67 else {
68 r = r - split2;
69 ret = (((e[3] * r + e[2]) * r + e[1]) * r + e[0]) /
70 ((f[2] * r + f[1]) * r + one);
71 }
72
73 if (q < zero)
74 ret = -ret;
75
76 return ret;;
77}
78
79
80/*-
81 * algorithm as241 appl. statist. (1988) 37(3):
82 *
83 * produces the normal deviate z corresponding to a given lower
84 * tail area of p; z is accurate to about 1 part in 10**16.
85 *
86 * the hash sums below are the sums of the mantissas of the
87 * coefficients. they are included for use in checking
88 * transcription.
89 */
90double ppnd16(double p)
91{
92 static double zero = 0.0, one = 1.0, half = 0.5;
93 static double split1 = 0.425, split2 = 5.0;
94 static double const1 = 0.180625, const2 = 1.6;
95
96 /* coefficients for p close to 0.5 */
97 static double a[8] = {
98 3.3871328727963666080e0,
99 1.3314166789178437745e+2,
100 1.9715909503065514427e+3,
101 1.3731693765509461125e+4,
102 4.5921953931549871457e+4,
103 6.7265770927008700853e+4,
104 3.3430575583588128105e+4,
105 2.5090809287301226727e+3
106 };
107 static double b[8] = { 0.0,
108 4.2313330701600911252e+1,
109 6.8718700749205790830e+2,
110 5.3941960214247511077e+3,
111 2.1213794301586595867e+4,
112 3.9307895800092710610e+4,
113 2.8729085735721942674e+4,
114 5.2264952788528545610e+3
115 };
116
117 /* hash sum ab 55.8831928806149014439 */
118 /* coefficients for p not close to 0, 0.5 or 1. */
119 static double c[8] = {
120 1.42343711074968357734e0,
121 4.63033784615654529590e0,
122 5.76949722146069140550e0,
123 3.64784832476320460504e0,
124 1.27045825245236838258e0,
125 2.41780725177450611770e-1,
126 2.27238449892691845833e-2,
127 7.74545014278341407640e-4
128 };
129 static double d[8] = { 0.0,
130 2.05319162663775882187e0,
131 1.67638483018380384940e0,
132 6.89767334985100004550e-1,
133 1.48103976427480074590e-1,
134 1.51986665636164571966e-2,
135 5.47593808499534494600e-4,
136 1.05075007164441684324e-9
137 };
138
139 /* hash sum cd 49.33206503301610289036 */
140 /* coefficients for p near 0 or 1. */
141 static double e[8] = {
142 6.65790464350110377720e0,
143 5.46378491116411436990e0,
144 1.78482653991729133580e0,
145 2.96560571828504891230e-1,
146 2.65321895265761230930e-2,
147 1.24266094738807843860e-3,
148 2.71155556874348757815e-5,
149 2.01033439929228813265e-7
150 };
151 static double f[8] = { 0.0,
152 5.99832206555887937690e-1,
153 1.36929880922735805310e-1,
154 1.48753612908506148525e-2,
155 7.86869131145613259100e-4,
156 1.84631831751005468180e-5,
157 1.42151175831644588870e-7,
158 2.04426310338993978564e-15
159 };
160
161 /* hash sum ef 47.52583317549289671629 */
162 double q, r, ret;
163
164 q = p - half;
165 if (fabs(q) <= split1) {
166 r = const1 - q * q;
167 ret = q * (((((((a[7] * r + a[6]) * r + a[5]) * r + a[4]) * r + a[3])
168 * r + a[2]) * r + a[1]) * r + a[0]) /
169 (((((((b[7] * r + b[6]) * r + b[5]) * r + b[4]) * r + b[3])
170 * r + b[2]) * r + b[1]) * r + one);
171
172 return ret;
173 }
174 /* else */
175
176 if (q < zero)
177 r = p;
178 else
179 r = one - p;
180
181 if (r <= zero)
182 return zero;
183
184 r = sqrt(-log(r));
185 if (r <= split2) {
186 r -= const2;
187 ret = (((((((c[7] * r + c[6]) * r + c[5]) * r + c[4]) * r + c[3])
188 * r + c[2]) * r + c[1]) * r + c[0]) /
189 (((((((d[7] * r + d[6]) * r + d[5]) * r + d[4]) * r + d[3])
190 * r + d[2]) * r + d[1]) * r + one);
191 }
192 else {
193 r -= split2;
194 ret = (((((((e[7] * r + e[6]) * r + e[5]) * r + e[4]) * r + e[3])
195 * r + e[2]) * r + e[1]) * r + e[0]) /
196 (((((((f[7] * r + f[6]) * r + f[5]) * r + f[4]) * r + f[3])
197 * r + f[2]) * r + f[1]) * r + one);
198 }
199
200 if (q < zero)
201 ret = -ret;
202
203 return ret;
204}
double ppnd16(double p)
Definition: as241.c:90
double Cdhc_ppnd7(double p)
Definition: as241.c:12
double b
double r