caryclark@google.com | 9e49fb6 | 2012-08-27 14:11:33 +0000 | [diff] [blame] | 1 | /* |
| 2 | * Copyright 2012 Google Inc. |
| 3 | * |
| 4 | * Use of this source code is governed by a BSD-style license that can be |
| 5 | * found in the LICENSE file. |
| 6 | */ |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 7 | // http://metamerist.com/cbrt/CubeRoot.cpp |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 8 | // |
| 9 | |
| 10 | #include <math.h> |
caryclark@google.com | 27accef | 2012-01-25 18:57:23 +0000 | [diff] [blame] | 11 | #include "CubicUtilities.h" |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 12 | |
| 13 | #define TEST_ALTERNATIVES 0 |
| 14 | #if TEST_ALTERNATIVES |
| 15 | typedef float (*cuberootfnf) (float); |
| 16 | typedef double (*cuberootfnd) (double); |
| 17 | |
| 18 | // estimate bits of precision (32-bit float case) |
| 19 | inline int bits_of_precision(float a, float b) |
| 20 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 21 | const double kd = 1.0 / log(2.0); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 22 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 23 | if (a==b) |
| 24 | return 23; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 25 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 26 | const double kdmin = pow(2.0, -23.0); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 27 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 28 | double d = fabs(a-b); |
| 29 | if (d < kdmin) |
| 30 | return 23; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 31 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 32 | return int(-log(d)*kd); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 33 | } |
| 34 | |
| 35 | // estiamte bits of precision (64-bit double case) |
| 36 | inline int bits_of_precision(double a, double b) |
| 37 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 38 | const double kd = 1.0 / log(2.0); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 39 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 40 | if (a==b) |
| 41 | return 52; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 42 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 43 | const double kdmin = pow(2.0, -52.0); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 44 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 45 | double d = fabs(a-b); |
| 46 | if (d < kdmin) |
| 47 | return 52; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 48 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 49 | return int(-log(d)*kd); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 50 | } |
| 51 | |
| 52 | // cube root via x^(1/3) |
| 53 | static float pow_cbrtf(float x) |
| 54 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 55 | return (float) pow(x, 1.0f/3.0f); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 56 | } |
| 57 | |
| 58 | // cube root via x^(1/3) |
| 59 | static double pow_cbrtd(double x) |
| 60 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 61 | return pow(x, 1.0/3.0); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 62 | } |
| 63 | |
| 64 | // cube root approximation using bit hack for 32-bit float |
| 65 | static float cbrt_5f(float f) |
| 66 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 67 | unsigned int* p = (unsigned int *) &f; |
| 68 | *p = *p/3 + 709921077; |
| 69 | return f; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 70 | } |
| 71 | #endif |
| 72 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 73 | // cube root approximation using bit hack for 64-bit float |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 74 | // adapted from Kahan's cbrt |
| 75 | static double cbrt_5d(double d) |
| 76 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 77 | const unsigned int B1 = 715094163; |
| 78 | double t = 0.0; |
| 79 | unsigned int* pt = (unsigned int*) &t; |
| 80 | unsigned int* px = (unsigned int*) &d; |
| 81 | pt[1]=px[1]/3+B1; |
| 82 | return t; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 83 | } |
| 84 | |
| 85 | #if TEST_ALTERNATIVES |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 86 | // cube root approximation using bit hack for 64-bit float |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 87 | // adapted from Kahan's cbrt |
| 88 | #if 0 |
| 89 | static double quint_5d(double d) |
| 90 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 91 | return sqrt(sqrt(d)); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 92 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 93 | const unsigned int B1 = 71509416*5/3; |
| 94 | double t = 0.0; |
| 95 | unsigned int* pt = (unsigned int*) &t; |
| 96 | unsigned int* px = (unsigned int*) &d; |
| 97 | pt[1]=px[1]/5+B1; |
| 98 | return t; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 99 | } |
| 100 | #endif |
| 101 | |
| 102 | // iterative cube root approximation using Halley's method (float) |
| 103 | static float cbrta_halleyf(const float a, const float R) |
| 104 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 105 | const float a3 = a*a*a; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 106 | const float b= a * (a3 + R + R) / (a3 + a3 + R); |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 107 | return b; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 108 | } |
| 109 | #endif |
| 110 | |
| 111 | // iterative cube root approximation using Halley's method (double) |
| 112 | static double cbrta_halleyd(const double a, const double R) |
| 113 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 114 | const double a3 = a*a*a; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 115 | const double b= a * (a3 + R + R) / (a3 + a3 + R); |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 116 | return b; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 117 | } |
| 118 | |
| 119 | #if TEST_ALTERNATIVES |
| 120 | // iterative cube root approximation using Newton's method (float) |
| 121 | static float cbrta_newtonf(const float a, const float x) |
| 122 | { |
| 123 | // return (1.0 / 3.0) * ((a + a) + x / (a * a)); |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 124 | return a - (1.0f / 3.0f) * (a - x / (a*a)); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 125 | } |
| 126 | |
| 127 | // iterative cube root approximation using Newton's method (double) |
| 128 | static double cbrta_newtond(const double a, const double x) |
| 129 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 130 | return (1.0/3.0) * (x / (a*a) + 2*a); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 131 | } |
| 132 | |
| 133 | // cube root approximation using 1 iteration of Halley's method (double) |
| 134 | static double halley_cbrt1d(double d) |
| 135 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 136 | double a = cbrt_5d(d); |
| 137 | return cbrta_halleyd(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 138 | } |
| 139 | |
| 140 | // cube root approximation using 1 iteration of Halley's method (float) |
| 141 | static float halley_cbrt1f(float d) |
| 142 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 143 | float a = cbrt_5f(d); |
| 144 | return cbrta_halleyf(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 145 | } |
| 146 | |
| 147 | // cube root approximation using 2 iterations of Halley's method (double) |
| 148 | static double halley_cbrt2d(double d) |
| 149 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 150 | double a = cbrt_5d(d); |
| 151 | a = cbrta_halleyd(a, d); |
| 152 | return cbrta_halleyd(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 153 | } |
| 154 | #endif |
| 155 | |
| 156 | // cube root approximation using 3 iterations of Halley's method (double) |
| 157 | static double halley_cbrt3d(double d) |
| 158 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 159 | double a = cbrt_5d(d); |
| 160 | a = cbrta_halleyd(a, d); |
| 161 | a = cbrta_halleyd(a, d); |
| 162 | return cbrta_halleyd(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 163 | } |
| 164 | |
| 165 | #if TEST_ALTERNATIVES |
| 166 | // cube root approximation using 2 iterations of Halley's method (float) |
| 167 | static float halley_cbrt2f(float d) |
| 168 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 169 | float a = cbrt_5f(d); |
| 170 | a = cbrta_halleyf(a, d); |
| 171 | return cbrta_halleyf(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 172 | } |
| 173 | |
| 174 | // cube root approximation using 1 iteration of Newton's method (double) |
| 175 | static double newton_cbrt1d(double d) |
| 176 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 177 | double a = cbrt_5d(d); |
| 178 | return cbrta_newtond(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 179 | } |
| 180 | |
| 181 | // cube root approximation using 2 iterations of Newton's method (double) |
| 182 | static double newton_cbrt2d(double d) |
| 183 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 184 | double a = cbrt_5d(d); |
| 185 | a = cbrta_newtond(a, d); |
| 186 | return cbrta_newtond(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 187 | } |
| 188 | |
| 189 | // cube root approximation using 3 iterations of Newton's method (double) |
| 190 | static double newton_cbrt3d(double d) |
| 191 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 192 | double a = cbrt_5d(d); |
| 193 | a = cbrta_newtond(a, d); |
| 194 | a = cbrta_newtond(a, d); |
| 195 | return cbrta_newtond(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 196 | } |
| 197 | |
| 198 | // cube root approximation using 4 iterations of Newton's method (double) |
| 199 | static double newton_cbrt4d(double d) |
| 200 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 201 | double a = cbrt_5d(d); |
| 202 | a = cbrta_newtond(a, d); |
| 203 | a = cbrta_newtond(a, d); |
| 204 | a = cbrta_newtond(a, d); |
| 205 | return cbrta_newtond(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 206 | } |
| 207 | |
| 208 | // cube root approximation using 2 iterations of Newton's method (float) |
| 209 | static float newton_cbrt1f(float d) |
| 210 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 211 | float a = cbrt_5f(d); |
| 212 | return cbrta_newtonf(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 213 | } |
| 214 | |
| 215 | // cube root approximation using 2 iterations of Newton's method (float) |
| 216 | static float newton_cbrt2f(float d) |
| 217 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 218 | float a = cbrt_5f(d); |
| 219 | a = cbrta_newtonf(a, d); |
| 220 | return cbrta_newtonf(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 221 | } |
| 222 | |
| 223 | // cube root approximation using 3 iterations of Newton's method (float) |
| 224 | static float newton_cbrt3f(float d) |
| 225 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 226 | float a = cbrt_5f(d); |
| 227 | a = cbrta_newtonf(a, d); |
| 228 | a = cbrta_newtonf(a, d); |
| 229 | return cbrta_newtonf(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 230 | } |
| 231 | |
| 232 | // cube root approximation using 4 iterations of Newton's method (float) |
| 233 | static float newton_cbrt4f(float d) |
| 234 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 235 | float a = cbrt_5f(d); |
| 236 | a = cbrta_newtonf(a, d); |
| 237 | a = cbrta_newtonf(a, d); |
| 238 | a = cbrta_newtonf(a, d); |
| 239 | return cbrta_newtonf(a, d); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 240 | } |
| 241 | |
| 242 | static double TestCubeRootf(const char* szName, cuberootfnf cbrt, double rA, double rB, int rN) |
| 243 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 244 | const int N = rN; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 245 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 246 | float dd = float((rB-rA) / N); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 247 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 248 | // calculate 1M numbers |
| 249 | int i=0; |
| 250 | float d = (float) rA; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 251 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 252 | double s = 0.0; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 253 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 254 | for(d=(float) rA, i=0; i<N; i++, d += dd) |
| 255 | { |
| 256 | s += cbrt(d); |
| 257 | } |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 258 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 259 | double bits = 0.0; |
| 260 | double worstx=0.0; |
| 261 | double worsty=0.0; |
| 262 | int minbits=64; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 263 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 264 | for(d=(float) rA, i=0; i<N; i++, d += dd) |
| 265 | { |
| 266 | float a = cbrt((float) d); |
| 267 | float b = (float) pow((double) d, 1.0/3.0); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 268 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 269 | int bc = bits_of_precision(a, b); |
| 270 | bits += bc; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 271 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 272 | if (b > 1.0e-6) |
| 273 | { |
| 274 | if (bc < minbits) |
| 275 | { |
| 276 | minbits = bc; |
| 277 | worstx = d; |
| 278 | worsty = a; |
| 279 | } |
| 280 | } |
| 281 | } |
| 282 | |
| 283 | bits /= N; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 284 | |
| 285 | printf(" %3d mbp %6.3f abp\n", minbits, bits); |
| 286 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 287 | return s; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 288 | } |
| 289 | |
| 290 | |
| 291 | static double TestCubeRootd(const char* szName, cuberootfnd cbrt, double rA, double rB, int rN) |
| 292 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 293 | const int N = rN; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 294 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 295 | double dd = (rB-rA) / N; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 296 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 297 | int i=0; |
| 298 | |
| 299 | double s = 0.0; |
| 300 | double d = 0.0; |
| 301 | |
| 302 | for(d=rA, i=0; i<N; i++, d += dd) |
| 303 | { |
| 304 | s += cbrt(d); |
| 305 | } |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 306 | |
| 307 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 308 | double bits = 0.0; |
| 309 | double worstx = 0.0; |
| 310 | double worsty = 0.0; |
| 311 | int minbits = 64; |
| 312 | for(d=rA, i=0; i<N; i++, d += dd) |
| 313 | { |
| 314 | double a = cbrt(d); |
| 315 | double b = pow(d, 1.0/3.0); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 316 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 317 | int bc = bits_of_precision(a, b); // min(53, count_matching_bitsd(a, b) - 12); |
| 318 | bits += bc; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 319 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 320 | if (b > 1.0e-6) |
| 321 | { |
| 322 | if (bc < minbits) |
| 323 | { |
| 324 | bits_of_precision(a, b); |
| 325 | minbits = bc; |
| 326 | worstx = d; |
| 327 | worsty = a; |
| 328 | } |
| 329 | } |
| 330 | } |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 331 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 332 | bits /= N; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 333 | |
| 334 | printf(" %3d mbp %6.3f abp\n", minbits, bits); |
| 335 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 336 | return s; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 337 | } |
| 338 | |
| 339 | static int _tmain() |
| 340 | { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 341 | // a million uniform steps through the range from 0.0 to 1.0 |
| 342 | // (doing uniform steps in the log scale would be better) |
| 343 | double a = 0.0; |
| 344 | double b = 1.0; |
| 345 | int n = 1000000; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 346 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 347 | printf("32-bit float tests\n"); |
| 348 | printf("----------------------------------------\n"); |
| 349 | TestCubeRootf("cbrt_5f", cbrt_5f, a, b, n); |
| 350 | TestCubeRootf("pow", pow_cbrtf, a, b, n); |
| 351 | TestCubeRootf("halley x 1", halley_cbrt1f, a, b, n); |
| 352 | TestCubeRootf("halley x 2", halley_cbrt2f, a, b, n); |
| 353 | TestCubeRootf("newton x 1", newton_cbrt1f, a, b, n); |
| 354 | TestCubeRootf("newton x 2", newton_cbrt2f, a, b, n); |
| 355 | TestCubeRootf("newton x 3", newton_cbrt3f, a, b, n); |
| 356 | TestCubeRootf("newton x 4", newton_cbrt4f, a, b, n); |
| 357 | printf("\n\n"); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 358 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 359 | printf("64-bit double tests\n"); |
| 360 | printf("----------------------------------------\n"); |
| 361 | TestCubeRootd("cbrt_5d", cbrt_5d, a, b, n); |
| 362 | TestCubeRootd("pow", pow_cbrtd, a, b, n); |
| 363 | TestCubeRootd("halley x 1", halley_cbrt1d, a, b, n); |
| 364 | TestCubeRootd("halley x 2", halley_cbrt2d, a, b, n); |
| 365 | TestCubeRootd("halley x 3", halley_cbrt3d, a, b, n); |
| 366 | TestCubeRootd("newton x 1", newton_cbrt1d, a, b, n); |
| 367 | TestCubeRootd("newton x 2", newton_cbrt2d, a, b, n); |
| 368 | TestCubeRootd("newton x 3", newton_cbrt3d, a, b, n); |
| 369 | TestCubeRootd("newton x 4", newton_cbrt4d, a, b, n); |
| 370 | printf("\n\n"); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 371 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 372 | return 0; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 373 | } |
| 374 | #endif |
| 375 | |
| 376 | double cube_root(double x) { |
caryclark@google.com | 9f60291 | 2013-01-24 21:47:16 +0000 | [diff] [blame^] | 377 | if (approximately_zero_cubed(x)) { |
caryclark@google.com | 235f56a | 2012-09-14 14:19:30 +0000 | [diff] [blame] | 378 | return 0; |
| 379 | } |
| 380 | double result = halley_cbrt3d(fabs(x)); |
| 381 | if (x < 0) { |
| 382 | result = -result; |
| 383 | } |
| 384 | return result; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 385 | } |
| 386 | |
| 387 | #if TEST_ALTERNATIVES |
| 388 | // http://bytes.com/topic/c/answers/754588-tips-find-cube-root-program-using-c |
| 389 | /* cube root */ |
| 390 | int icbrt(int n) { |
| 391 | int t=0, x=(n+2)/3; /* works for n=0 and n>=1 */ |
| 392 | for(; t!=x;) { |
| 393 | int x3=x*x*x; |
| 394 | t=x; |
| 395 | x*=(2*n + x3); |
| 396 | x/=(2*x3 + n); |
| 397 | } |
| 398 | return x ; /* always(?) equal to floor(n^(1/3)) */ |
| 399 | } |
| 400 | #endif |