1 /* 2 * Copyright (C) 2015 The Android Open Source Project 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 17 // THIS TYPICALLY TAKES > 4 MINUTES TO RUN! 18 // It should generate no output during that time. 19 20 package com.hp.creals; 21 22 import junit.framework.AssertionFailedError; 23 import junit.framework.TestCase; 24 25 import java.math.BigInteger; 26 import java.util.Random; 27 28 public class SlowCRTest extends TestCase { 29 private static void check(boolean x, String s) { 30 if (!x) throw new AssertionFailedError(s); 31 } 32 final static int TEST_PREC = -200; // 200 bits to the right of 33 // binary point. 34 final static int NRANDOM = 100; // Number of random values to 35 // test. Bigger ==> slower 36 private static void checkEq(CR x, CR y, String s) { 37 check(x.compareTo(y, TEST_PREC) == 0, s); 38 } 39 private static void checkApprEq(double x, double y, String s) { 40 check(Math.abs(x - y) <= 0.000001, s); 41 } 42 final static BigInteger MASK = 43 BigInteger.ONE.shiftLeft(-TEST_PREC).subtract(BigInteger.ONE); 44 private static boolean isApprInt(CR x) { 45 BigInteger appr = x.get_appr(TEST_PREC); 46 return appr.and(MASK).signum() == 0; 47 } 48 49 final static CR ZERO = CR.valueOf(0); 50 final static CR ONE = CR.valueOf(1); 51 final static CR TWO = CR.valueOf(2); 52 final static CR BIG = CR.valueOf(200).exp(); 53 final static CR SMALL = BIG.inverse(); 54 final static CR HALF_PI = CR.PI.divide(CR.valueOf(2)); 55 56 final static UnaryCRFunction ATAN = UnaryCRFunction.atanFunction; 57 final static UnaryCRFunction TAN = UnaryCRFunction.tanFunction; 58 final static UnaryCRFunction COSINE = UnaryCRFunction.sinFunction 59 .monotoneDerivative(ZERO, CR.PI); 60 final static UnaryCRFunction ARCSINE = 61 UnaryCRFunction.sinFunction.inverseMonotone(HALF_PI.negate(), 62 HALF_PI); 63 64 // Perform some consistency checks on trig functions at x 65 // We assume that x is within floating point range. 66 private static void checkTrig(CR x) { 67 double xAsDouble = x.doubleValue(); 68 if (Math.abs(xAsDouble) < 1000000.0) { 69 checkApprEq(x.sin().doubleValue(), Math.sin(xAsDouble), 70 "sin float compare:" + xAsDouble); 71 checkApprEq(x.cos().doubleValue(), Math.cos(xAsDouble), 72 "cos float compare:" + xAsDouble); 73 checkApprEq(TAN.execute(x).doubleValue(), Math.tan(xAsDouble), 74 "tan float compare:" + xAsDouble); 75 checkApprEq(ATAN.execute(x).doubleValue(), Math.atan(xAsDouble), 76 "atan float compare:" + xAsDouble); 77 } 78 if (Math.abs(xAsDouble) < 1.0) { 79 checkApprEq(x.asin().doubleValue(), Math.asin(xAsDouble), 80 "asin float compare:" + xAsDouble); 81 checkApprEq(x.acos().doubleValue(), Math.acos(xAsDouble), 82 "acos float compare:" + xAsDouble); 83 checkEq(ARCSINE.execute(x), x.asin(), 84 "inverse(sin) compare:" + xAsDouble); 85 } 86 if (xAsDouble < 3.1415926535 && xAsDouble > 0.0) { 87 checkApprEq(COSINE.execute(x).doubleValue(), Math.cos(xAsDouble), 88 "deriv(sin) float compare:" + xAsDouble); 89 checkEq(COSINE.execute(x), x.cos(), 90 "deriv(sin) float compare:" + xAsDouble); 91 } 92 // Check that sin(x+v) = sin(x)cos(v) + cos(x)sin(v) 93 // for a couple of different values of v. 94 for (int i = 1; i <= 5; ++i) { 95 CR v = CR.valueOf(i); 96 checkEq( 97 x.add(v).sin(), 98 x.sin().multiply(v.cos()).add(x.cos().multiply(v.sin())), 99 "Angle sum formula failed for " + xAsDouble + " + " + i); 100 } 101 checkEq(x.cos().multiply(x.cos()).add(x.sin().multiply(x.sin())), 102 CR.valueOf(1), 103 "sin(x)^2 + cos(x)^2 != 1:" + xAsDouble); 104 // Check that inverses are consistent 105 checkEq(x, TAN.execute(ATAN.execute(x)), 106 "tan(atan(" + xAsDouble + ")"); 107 CR xcos = x.cos(); 108 CR tmp = xcos.acos(); 109 // Result or its inverse should differ from x by an 110 // exact multiple of pi. 111 check(isApprInt(tmp.subtract(x).divide(CR.PI)) 112 || isApprInt(tmp.add(x).divide(CR.PI)), 113 "acos(cos):" + xAsDouble); 114 CR xsin = x.sin(); 115 tmp = ARCSINE.execute(xsin); 116 CR tmp2 = xsin.asin(); 117 checkEq(tmp, tmp2, "Asin(sin) computations differ:" + xAsDouble); 118 // Result or its inverse should differ from x by an 119 // exact multiple of pi. 120 check(isApprInt(tmp.subtract(x).divide(CR.PI)) 121 || isApprInt(tmp.add(x).divide(CR.PI)), 122 "acos(cos):" + xAsDouble); 123 } 124 125 private static void checkExpLn(CR x) { 126 double xAsDouble = x.doubleValue(); 127 if (Math.abs(xAsDouble) < 10.0) { 128 checkApprEq(x.exp().doubleValue(), Math.exp(xAsDouble), 129 "exp float compare:" + xAsDouble); 130 } 131 if (Math.abs(xAsDouble) <= 1000.0) { 132 checkEq(x, x.exp().ln(), "ln(exp) failed:" + xAsDouble); 133 checkEq(x.multiply(CR.valueOf(2)).exp(), 134 135 x.exp().multiply(x.exp()), 136 "exp^2 failed:" + xAsDouble); 137 } 138 if (xAsDouble > 0.000000001) { 139 checkApprEq(x.ln().doubleValue(), Math.log(xAsDouble), 140 "exp float compare:" + xAsDouble); 141 checkEq(x, x.ln().exp(), "exp(ln) failed:" + xAsDouble); 142 checkEq(x.ln().divide(CR.valueOf(2)), x.sqrt().ln(), 143 "ln(sqrt) failed:" + xAsDouble); 144 // Check that ln(xv) = ln(x) + ln(v) for various v 145 for (int i = 1; i <= 5; ++i) { 146 CR v = CR.valueOf(i); 147 checkEq( 148 x.ln().add(v.ln()), 149 x.multiply(v).ln(), 150 "ln(product) formula failed for:" + xAsDouble + "," + i); 151 } 152 } 153 } 154 155 private static void checkBasic(CR x) { 156 checkEq(x.abs().sqrt().multiply(x.abs().sqrt()), x.abs(), 157 "sqrt*sqrt:" + x.doubleValue()); 158 if (!x.get_appr(TEST_PREC).equals(BigInteger.ZERO)) { 159 checkEq(x.inverse().inverse(), x, 160 "inverse(inverse):" + x.doubleValue()); 161 } 162 } 163 164 public void testSlowTrig() { 165 checkEq(ZERO.acos(), CR.PI.divide(TWO), "acos(0)"); 166 checkEq(ONE.acos(), ZERO, "acos(1)"); 167 checkEq(ONE.negate().acos(), CR.PI, "acos(-1)"); 168 checkEq(ZERO.asin(), ZERO, "asin(0)"); 169 checkEq(ONE.asin(), CR.PI.divide(TWO), "asin(1)"); 170 checkEq(ONE.negate().asin(), CR.PI.divide(TWO).negate(), "asin(-1)"); 171 checkTrig(ZERO); 172 CR BIG = CR.valueOf(200).exp(); 173 checkTrig(BIG); 174 checkTrig(BIG.negate()); 175 checkTrig(SMALL); 176 checkTrig(SMALL.negate()); 177 checkTrig(CR.PI); 178 checkTrig(CR.PI.subtract(SMALL)); 179 checkTrig(CR.PI.add(SMALL)); 180 checkTrig(CR.PI.negate()); 181 checkTrig(CR.PI.negate().subtract(SMALL)); 182 checkTrig(CR.PI.negate().add(SMALL)); 183 Random r = new Random(); // Random seed! 184 for (int i = 0; i < NRANDOM; ++i) { 185 double d = Math.exp(2.0 * r.nextDouble() - 1.0); 186 if (r.nextBoolean()) d = -d; 187 final CR x = CR.valueOf(d); 188 checkTrig(x); 189 } 190 // And a few big ones 191 for (int i = 0; i < 10; ++i) { 192 double d = Math.exp(200.0 * r.nextDouble()); 193 if (r.nextBoolean()) d = -d; 194 final CR x = CR.valueOf(d); 195 checkTrig(x); 196 } 197 } 198 199 public void testSlowExpLn() { 200 checkEq(CR.valueOf(1).ln(), CR.valueOf(0), "ln(1) != 0"); 201 checkExpLn(CR.valueOf(0)); 202 CR BIG = CR.valueOf(200).exp(); 203 checkExpLn(BIG); 204 checkExpLn(BIG.negate()); 205 checkExpLn(SMALL); 206 checkExpLn(SMALL.negate()); 207 checkExpLn(CR.PI); 208 checkExpLn(ONE); 209 checkExpLn(ONE.subtract(SMALL)); 210 checkExpLn(ONE.negate().subtract(SMALL)); 211 Random r = new Random(); // Random seed! 212 for (int i = 0; i < NRANDOM; ++i) { 213 double d = Math.exp(10.0 * r.nextDouble() - 1.0); 214 if (r.nextBoolean()) d = -d; 215 final CR x = CR.valueOf(d); 216 checkExpLn(x); 217 } 218 // And a few big ones 219 for (int i = 0; i < 10; ++i) { 220 double d = Math.exp(200.0 * r.nextDouble()); 221 if (r.nextBoolean()) d = -d; 222 final CR x = CR.valueOf(d); 223 checkExpLn(x); 224 } 225 } 226 227 public void testSlowBasic() { 228 checkEq(ZERO.sqrt(), ZERO, "sqrt(0)"); 229 checkEq(ZERO.abs(), ZERO, "abs(0)"); 230 for (int i = 100; i >= -2900; --i) { 231 check(CR.PI.compareTo(CR.atan_PI, i) == 0, "pi(" + i + ")"); 232 } 233 Random r = new Random(); // Random seed! 234 for (int i = 0; i < NRANDOM; ++i) { 235 double d = Math.exp(10.0 * r.nextDouble() - 1.0); 236 if (r.nextBoolean()) d = -d; 237 final CR x = CR.valueOf(d); 238 checkBasic(x); 239 } 240 // And a few very big ones, but within IEEE double range 241 for (int i = 0; i < 10; ++i) { 242 double d = Math.exp(600.0 * r.nextDouble()); 243 if (r.nextBoolean()) d = -d; 244 final CR x = CR.valueOf(d); 245 checkBasic(x); 246 } 247 } 248 } 249
