/*
* Copyright (C) 2015 The Android Open Source Project
*
* 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.
*/
// THIS TYPICALLY TAKES > 4 MINUTES TO RUN!
// It should generate no output during that time.
package com.hp.creals;
import junit.framework.AssertionFailedError;
import junit.framework.TestCase;
import java.math.BigInteger;
import java.util.Random;
public class SlowCRTest extends TestCase {
private static void check(boolean x, String s) {
if (!x) throw new AssertionFailedError(s);
}
final static int TEST_PREC = -200; // 200 bits to the right of
// binary point.
final static int NRANDOM = 100; // Number of random values to
// test. Bigger ==> slower
private static void checkEq(CR x, CR y, String s) {
check(x.compareTo(y, TEST_PREC) == 0, s);
}
private static void checkApprEq(double x, double y, String s) {
check(Math.abs(x - y) <= 0.000001, s);
}
final static BigInteger MASK =
BigInteger.ONE.shiftLeft(-TEST_PREC).subtract(BigInteger.ONE);
private static boolean isApprInt(CR x) {
BigInteger appr = x.get_appr(TEST_PREC);
return appr.and(MASK).signum() == 0;
}
final static CR ZERO = CR.valueOf(0);
final static CR ONE = CR.valueOf(1);
final static CR TWO = CR.valueOf(2);
final static CR BIG = CR.valueOf(200).exp();
final static CR SMALL = BIG.inverse();
final static CR HALF_PI = CR.PI.divide(CR.valueOf(2));
final static UnaryCRFunction ATAN = UnaryCRFunction.atanFunction;
final static UnaryCRFunction TAN = UnaryCRFunction.tanFunction;
final static UnaryCRFunction COSINE = UnaryCRFunction.sinFunction
.monotoneDerivative(ZERO, CR.PI);
final static UnaryCRFunction ARCSINE =
UnaryCRFunction.sinFunction.inverseMonotone(HALF_PI.negate(),
HALF_PI);
// Perform some consistency checks on trig functions at x
// We assume that x is within floating point range.
private static void checkTrig(CR x) {
double xAsDouble = x.doubleValue();
if (Math.abs(xAsDouble) < 1000000.0) {
checkApprEq(x.sin().doubleValue(), Math.sin(xAsDouble),
"sin float compare:" + xAsDouble);
checkApprEq(x.cos().doubleValue(), Math.cos(xAsDouble),
"cos float compare:" + xAsDouble);
checkApprEq(TAN.execute(x).doubleValue(), Math.tan(xAsDouble),
"tan float compare:" + xAsDouble);
checkApprEq(ATAN.execute(x).doubleValue(), Math.atan(xAsDouble),
"atan float compare:" + xAsDouble);
}
if (Math.abs(xAsDouble) < 1.0) {
checkApprEq(x.asin().doubleValue(), Math.asin(xAsDouble),
"asin float compare:" + xAsDouble);
checkApprEq(x.acos().doubleValue(), Math.acos(xAsDouble),
"acos float compare:" + xAsDouble);
checkEq(ARCSINE.execute(x), x.asin(),
"inverse(sin) compare:" + xAsDouble);
}
if (xAsDouble < 3.1415926535 && xAsDouble > 0.0) {
checkApprEq(COSINE.execute(x).doubleValue(), Math.cos(xAsDouble),
"deriv(sin) float compare:" + xAsDouble);
checkEq(COSINE.execute(x), x.cos(),
"deriv(sin) float compare:" + xAsDouble);
}
// Check that sin(x+v) = sin(x)cos(v) + cos(x)sin(v)
// for a couple of different values of v.
for (int i = 1; i <= 5; ++i) {
CR v = CR.valueOf(i);
checkEq(
x.add(v).sin(),
x.sin().multiply(v.cos()).add(x.cos().multiply(v.sin())),
"Angle sum formula failed for " + xAsDouble + " + " + i);
}
checkEq(x.cos().multiply(x.cos()).add(x.sin().multiply(x.sin())),
CR.valueOf(1),
"sin(x)^2 + cos(x)^2 != 1:" + xAsDouble);
// Check that inverses are consistent
checkEq(x, TAN.execute(ATAN.execute(x)),
"tan(atan(" + xAsDouble + ")");
CR xcos = x.cos();
CR tmp = xcos.acos();
// Result or its inverse should differ from x by an
// exact multiple of pi.
check(isApprInt(tmp.subtract(x).divide(CR.PI))
|| isApprInt(tmp.add(x).divide(CR.PI)),
"acos(cos):" + xAsDouble);
CR xsin = x.sin();
tmp = ARCSINE.execute(xsin);
CR tmp2 = xsin.asin();
checkEq(tmp, tmp2, "Asin(sin) computations differ:" + xAsDouble);
// Result or its inverse should differ from x by an
// exact multiple of pi.
check(isApprInt(tmp.subtract(x).divide(CR.PI))
|| isApprInt(tmp.add(x).divide(CR.PI)),
"acos(cos):" + xAsDouble);
}
private static void checkExpLn(CR x) {
double xAsDouble = x.doubleValue();
if (Math.abs(xAsDouble) < 10.0) {
checkApprEq(x.exp().doubleValue(), Math.exp(xAsDouble),
"exp float compare:" + xAsDouble);
}
if (Math.abs(xAsDouble) <= 1000.0) {
checkEq(x, x.exp().ln(), "ln(exp) failed:" + xAsDouble);
checkEq(x.multiply(CR.valueOf(2)).exp(),
x.exp().multiply(x.exp()),
"exp^2 failed:" + xAsDouble);
}
if (xAsDouble > 0.000000001) {
checkApprEq(x.ln().doubleValue(), Math.log(xAsDouble),
"exp float compare:" + xAsDouble);
checkEq(x, x.ln().exp(), "exp(ln) failed:" + xAsDouble);
checkEq(x.ln().divide(CR.valueOf(2)), x.sqrt().ln(),
"ln(sqrt) failed:" + xAsDouble);
// Check that ln(xv) = ln(x) + ln(v) for various v
for (int i = 1; i <= 5; ++i) {
CR v = CR.valueOf(i);
checkEq(
x.ln().add(v.ln()),
x.multiply(v).ln(),
"ln(product) formula failed for:" + xAsDouble + "," + i);
}
}
}
private static void checkBasic(CR x) {
checkEq(x.abs().sqrt().multiply(x.abs().sqrt()), x.abs(),
"sqrt*sqrt:" + x.doubleValue());
if (!x.get_appr(TEST_PREC).equals(BigInteger.ZERO)) {
checkEq(x.inverse().inverse(), x,
"inverse(inverse):" + x.doubleValue());
}
}
public void testSlowTrig() {
checkEq(ZERO.acos(), CR.PI.divide(TWO), "acos(0)");
checkEq(ONE.acos(), ZERO, "acos(1)");
checkEq(ONE.negate().acos(), CR.PI, "acos(-1)");
checkEq(ZERO.asin(), ZERO, "asin(0)");
checkEq(ONE.asin(), CR.PI.divide(TWO), "asin(1)");
checkEq(ONE.negate().asin(), CR.PI.divide(TWO).negate(), "asin(-1)");
checkTrig(ZERO);
CR BIG = CR.valueOf(200).exp();
checkTrig(BIG);
checkTrig(BIG.negate());
checkTrig(SMALL);
checkTrig(SMALL.negate());
checkTrig(CR.PI);
checkTrig(CR.PI.subtract(SMALL));
checkTrig(CR.PI.add(SMALL));
checkTrig(CR.PI.negate());
checkTrig(CR.PI.negate().subtract(SMALL));
checkTrig(CR.PI.negate().add(SMALL));
Random r = new Random(); // Random seed!
for (int i = 0; i < NRANDOM; ++i) {
double d = Math.exp(2.0 * r.nextDouble() - 1.0);
if (r.nextBoolean()) d = -d;
final CR x = CR.valueOf(d);
checkTrig(x);
}
// And a few big ones
for (int i = 0; i < 10; ++i) {
double d = Math.exp(200.0 * r.nextDouble());
if (r.nextBoolean()) d = -d;
final CR x = CR.valueOf(d);
checkTrig(x);
}
}
public void testSlowExpLn() {
checkEq(CR.valueOf(1).ln(), CR.valueOf(0), "ln(1) != 0");
checkExpLn(CR.valueOf(0));
CR BIG = CR.valueOf(200).exp();
checkExpLn(BIG);
checkExpLn(BIG.negate());
checkExpLn(SMALL);
checkExpLn(SMALL.negate());
checkExpLn(CR.PI);
checkExpLn(ONE);
checkExpLn(ONE.subtract(SMALL));
checkExpLn(ONE.negate().subtract(SMALL));
Random r = new Random(); // Random seed!
for (int i = 0; i < NRANDOM; ++i) {
double d = Math.exp(10.0 * r.nextDouble() - 1.0);
if (r.nextBoolean()) d = -d;
final CR x = CR.valueOf(d);
checkExpLn(x);
}
// And a few big ones
for (int i = 0; i < 10; ++i) {
double d = Math.exp(200.0 * r.nextDouble());
if (r.nextBoolean()) d = -d;
final CR x = CR.valueOf(d);
checkExpLn(x);
}
}
public void testSlowBasic() {
checkEq(ZERO.sqrt(), ZERO, "sqrt(0)");
checkEq(ZERO.abs(), ZERO, "abs(0)");
Random r = new Random(); // Random seed!
for (int i = 0; i < NRANDOM; ++i) {
double d = Math.exp(10.0 * r.nextDouble() - 1.0);
if (r.nextBoolean()) d = -d;
final CR x = CR.valueOf(d);
checkBasic(x);
}
// And a few very big ones, but within IEEE double range
for (int i = 0; i < 10; ++i) {
double d = Math.exp(600.0 * r.nextDouble());
if (r.nextBoolean()) d = -d;
final CR x = CR.valueOf(d);
checkBasic(x);
}
}
}