[170] | 1 | /****************************************************************************/ |
---|
| 2 | /* MATHFNS.C: utility routines for various sorts of math operations. Most */ |
---|
| 3 | /* these functions work with real values, meaning that they can handle */ |
---|
| 4 | /* either floats or doubles, depending on compiler switches. */ |
---|
| 5 | /* Copyright (c) 2001 by Joshua E. Barnes, Honolulu, Hawai`i. */ |
---|
| 6 | /****************************************************************************/ |
---|
| 7 | |
---|
| 8 | #include "stdinc.h" |
---|
| 9 | #include "mathfns.h" |
---|
| 10 | |
---|
| 11 | #if !defined(LINUX) |
---|
| 12 | long random(void); |
---|
| 13 | #endif |
---|
| 14 | |
---|
| 15 | /* |
---|
| 16 | * RSQR, RQBE: compute x*x and x*x*x. |
---|
| 17 | */ |
---|
| 18 | |
---|
| 19 | real rsqr(real x) |
---|
| 20 | { |
---|
| 21 | return (x * x); |
---|
| 22 | } |
---|
| 23 | |
---|
| 24 | real rqbe(real x) |
---|
| 25 | { |
---|
| 26 | return (x * x * x); |
---|
| 27 | } |
---|
| 28 | |
---|
| 29 | /* |
---|
| 30 | * RLOG2, REXP2: log, inverse log to base two. |
---|
| 31 | */ |
---|
| 32 | |
---|
| 33 | real rlog2(real x) |
---|
| 34 | { |
---|
| 35 | return (rlog(x) / M_LN2); |
---|
| 36 | } |
---|
| 37 | |
---|
| 38 | real rexp2(real x) |
---|
| 39 | { |
---|
| 40 | return (rexp(M_LN2 * x)); |
---|
| 41 | } |
---|
| 42 | |
---|
| 43 | /* |
---|
| 44 | * RDEX: inverse log base ten. |
---|
| 45 | */ |
---|
| 46 | |
---|
| 47 | real rdex(real x) |
---|
| 48 | { |
---|
| 49 | return (rexp(M_LN10 * x)); |
---|
| 50 | } |
---|
| 51 | |
---|
| 52 | #if defined(SINGLEPREC) |
---|
| 53 | |
---|
| 54 | /* |
---|
| 55 | * FCBRT: floating cube root. |
---|
| 56 | */ |
---|
| 57 | |
---|
| 58 | float fcbrt(float x) |
---|
| 59 | { |
---|
| 60 | return ((float) cbrt((double) x)); |
---|
| 61 | } |
---|
| 62 | |
---|
| 63 | #endif |
---|
| 64 | |
---|
| 65 | /* |
---|
| 66 | * XRANDOM: floating-point random number routine. |
---|
| 67 | */ |
---|
| 68 | |
---|
| 69 | double xrandom(double xl, double xh) |
---|
| 70 | { |
---|
| 71 | |
---|
| 72 | return (xl + (xh - xl) * ((double) random()) / 2147483647.0); |
---|
| 73 | } |
---|
| 74 | |
---|
| 75 | /* |
---|
| 76 | * GRANDOM: normally distributed random number (polar method). |
---|
| 77 | * Reference: Knuth, vol. 2, p. 104. |
---|
| 78 | */ |
---|
| 79 | |
---|
| 80 | double grandom(double mean, double sdev) |
---|
| 81 | { |
---|
| 82 | double v1, v2, s; |
---|
| 83 | |
---|
| 84 | do { |
---|
| 85 | v1 = xrandom(-1.0, 1.0); |
---|
| 86 | v2 = xrandom(-1.0, 1.0); |
---|
| 87 | s = v1*v1 + v2*v2; |
---|
| 88 | } while (s >= 1.0); |
---|
| 89 | return (mean + sdev * v1 * sqrt(-2.0 * log(s) / s)); |
---|
| 90 | } |
---|
| 91 | |
---|
| 92 | /* |
---|
| 93 | * PICKSHELL: pick point on shell. |
---|
| 94 | */ |
---|
| 95 | |
---|
| 96 | void pickshell(real vec[], int ndim, real rad) |
---|
| 97 | { |
---|
| 98 | real rsq, rscale; |
---|
| 99 | int i; |
---|
| 100 | |
---|
| 101 | do { |
---|
| 102 | rsq = 0.0; |
---|
| 103 | for (i = 0; i < ndim; i++) { |
---|
| 104 | vec[i] = xrandom(-1.0, 1.0); |
---|
| 105 | rsq = rsq + vec[i] * vec[i]; |
---|
| 106 | } |
---|
| 107 | } while (rsq > 1.0); |
---|
| 108 | rscale = rad / rsqrt(rsq); |
---|
| 109 | for (i = 0; i < ndim; i++) |
---|
| 110 | vec[i] = vec[i] * rscale; |
---|
| 111 | } |
---|
| 112 | |
---|
| 113 | /* |
---|
| 114 | * PICKBALL: pick point within ball. |
---|
| 115 | */ |
---|
| 116 | |
---|
| 117 | void pickball(real vec[], int ndim, real rad) |
---|
| 118 | { |
---|
| 119 | real rsq; |
---|
| 120 | int i; |
---|
| 121 | |
---|
| 122 | do { |
---|
| 123 | rsq = 0.0; |
---|
| 124 | for (i = 0; i < ndim; i++) { |
---|
| 125 | vec[i] = xrandom(-1.0, 1.0); |
---|
| 126 | rsq = rsq + vec[i] * vec[i]; |
---|
| 127 | } |
---|
| 128 | } while (rsq > 1.0); |
---|
| 129 | for (i = 0; i < ndim; i++) |
---|
| 130 | vec[i] = vec[i] * rad; |
---|
| 131 | } |
---|
| 132 | |
---|
| 133 | /* |
---|
| 134 | * PICKBOX: pick point within box. |
---|
| 135 | */ |
---|
| 136 | |
---|
| 137 | void pickbox(real vec[], int ndim, real size) |
---|
| 138 | { |
---|
| 139 | int i; |
---|
| 140 | |
---|
| 141 | for (i = 0; i < ndim; i++) |
---|
| 142 | vec[i] = xrandom(- size, size); |
---|
| 143 | } |
---|