v8/test/mjsunit/sin-cos.js

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// Test Math.sin and Math.cos.

// Flags: --allow-natives-syntax

assertEquals("-Infinity", String(1/Math.sin(-0)));
assertEquals(1, Math.cos(-0));
assertEquals("-Infinity", String(1/Math.tan(-0)));

// Assert that minus zero does not cause deopt.
function no_deopt_on_minus_zero(x) {
  return Math.sin(x) + Math.cos(x) + Math.tan(x);
}

no_deopt_on_minus_zero(1);
no_deopt_on_minus_zero(1);
%OptimizeFunctionOnNextCall(no_deopt_on_minus_zero);
no_deopt_on_minus_zero(-0);
assertOptimized(no_deopt_on_minus_zero);


function sinTest() {
  assertEquals(0, Math.sin(0));
  assertEquals(1, Math.sin(Math.PI / 2));
}

function cosTest() {
  assertEquals(1, Math.cos(0));
  assertEquals(-1, Math.cos(Math.PI));
}

sinTest();
cosTest();

// By accident, the slow case for sine and cosine were both sine at
// some point.  This is a regression test for that issue.
var x = Math.pow(2, 30);
assertTrue(Math.sin(x) != Math.cos(x));

// Ensure that sine and log are not the same.
x = 0.5;
assertTrue(Math.sin(x) != Math.log(x));

// Test against approximation by series.
var factorial = [1];
var accuracy = 50;
for (var i = 1; i < accuracy; i++) {
  factorial[i] = factorial[i-1] * i;
}

// We sum up in the reverse order for higher precision, as we expect the terms
// to grow smaller for x reasonably close to 0.
function precision_sum(array) {
  var result = 0;
  while (array.length > 0) {
    result += array.pop();
  }
  return result;
}

function sin(x) {
  var sign = 1;
  var x2 = x*x;
  var terms = [];
  for (var i = 1; i < accuracy; i += 2) {
    terms.push(sign * x / factorial[i]);
    x *= x2;
    sign *= -1;
  }
  return precision_sum(terms);
}

function cos(x) {
  var sign = -1;
  var x2 = x*x;
  x = x2;
  var terms = [1];
  for (var i = 2; i < accuracy; i += 2) {
    terms.push(sign * x / factorial[i]);
    x *= x2;
    sign *= -1;
  }
  return precision_sum(terms);
}

function abs_error(fun, ref, x) {
  return Math.abs(ref(x) - fun(x));
}

var test_inputs = [];
for (var i = -10000; i < 10000; i += 177) test_inputs.push(i/1257);
var epsilon = 0.0000001;

test_inputs.push(0);
test_inputs.push(0 + epsilon);
test_inputs.push(0 - epsilon);
test_inputs.push(Math.PI/2);
test_inputs.push(Math.PI/2 + epsilon);
test_inputs.push(Math.PI/2 - epsilon);
test_inputs.push(Math.PI);
test_inputs.push(Math.PI + epsilon);
test_inputs.push(Math.PI - epsilon);
test_inputs.push(- 2*Math.PI);
test_inputs.push(- 2*Math.PI + epsilon);
test_inputs.push(- 2*Math.PI - epsilon);

var squares = [];
for (var i = 0; i < test_inputs.length; i++) {
  var x = test_inputs[i];
  var err_sin = abs_error(Math.sin, sin, x);
  var err_cos = abs_error(Math.cos, cos, x)
  assertEqualsDelta(0, err_sin, 1E-13);
  assertEqualsDelta(0, err_cos, 1E-13);
  squares.push(err_sin*err_sin + err_cos*err_cos);
}

// Sum squares up by adding them pairwise, to avoid losing precision.
while (squares.length > 1) {
  var reduced = [];
  if (squares.length % 2 == 1) reduced.push(squares.pop());
  // Remaining number of elements is even.
  while(squares.length > 1) reduced.push(squares.pop() + squares.pop());
  squares = reduced;
}

var err_rms = Math.sqrt(squares[0] / test_inputs.length / 2);
assertEqualsDelta(0, err_rms, 1E-14);

assertEquals(-1, Math.cos({ valueOf: function() { return Math.PI; } }));
assertEquals(0, Math.sin("0x00000"));
assertEquals(1, Math.cos("0x00000"));
assertTrue(isNaN(Math.sin(Infinity)));
assertTrue(isNaN(Math.cos("-Infinity")));
assertTrue(Math.tan(Math.PI/2) > 1e16);
assertTrue(Math.tan(-Math.PI/2) < -1e16);
assertEquals("-Infinity", String(1/Math.sin("-0")));

// Assert that the remainder after division by pi is reasonably precise.
function assertError(expected, x, epsilon) {
  assertTrue(Math.abs(x - expected) < epsilon);
}

assertEqualsDelta(0.9367521275331447,  Math.cos(1e06),  1e-15);
assertEqualsDelta(0.8731196226768560,  Math.cos(1e10),  1e-08);
assertEqualsDelta(0.9367521275331447,  Math.cos(-1e06), 1e-15);
assertEqualsDelta(0.8731196226768560,  Math.cos(-1e10), 1e-08);
assertEqualsDelta(-0.3499935021712929, Math.sin(1e06),  1e-15);
assertEqualsDelta(-0.4875060250875106, Math.sin(1e10),  1e-08);
assertEqualsDelta(0.3499935021712929,  Math.sin(-1e06), 1e-15);
assertEqualsDelta(0.4875060250875106,  Math.sin(-1e10), 1e-08);
assertEqualsDelta(0.7796880066069787,  Math.sin(1e16),  1e-05);
assertEqualsDelta(-0.6261681981330861, Math.cos(1e16),  1e-05);

// Assert that remainder calculation terminates.
for (var i = -1024; i < 1024; i++) {
  assertFalse(isNaN(Math.sin(Math.pow(2, i))));
}

assertFalse(isNaN(Math.cos(1.57079632679489700)));
assertFalse(isNaN(Math.cos(-1e-100)));
assertFalse(isNaN(Math.cos(-1e-323)));

// Tests for specific values expected from the fdlibm implementation.

var two_32 = Math.pow(2, -32);
var two_28 = Math.pow(2, -28);

// Tests for Math.sin for |x| < pi/4
assertEquals(Infinity, 1/Math.sin(+0.0));
assertEquals(-Infinity, 1/Math.sin(-0.0));
// sin(x) = x for x < 2^-27
assertEquals(two_32, Math.sin(two_32));
assertEquals(-two_32, Math.sin(-two_32));
// sin(pi/8) = sqrt(sqrt(2)-1)/2^(3/4)
assertEquals(0.3826834323650898, Math.sin(Math.PI/8));
assertEquals(-0.3826834323650898, -Math.sin(Math.PI/8));

// Tests for Math.cos for |x| < pi/4
// cos(x) = 1 for |x| < 2^-27
assertEquals(1, Math.cos(two_32));
assertEquals(1, Math.cos(-two_32));
// Test KERNELCOS for |x| < 0.3.
// cos(pi/20) = sqrt(sqrt(2)*sqrt(sqrt(5)+5)+4)/2^(3/2)
assertEquals(0.9876883405951378, Math.cos(Math.PI/20));
// Test KERNELCOS for x ~= 0.78125
assertEquals(0.7100335477927638, Math.cos(0.7812504768371582));
assertEquals(0.7100338835660797, Math.cos(0.78125));
// Test KERNELCOS for |x| > 0.3.
// cos(pi/8) = sqrt(sqrt(2)+1)/2^(3/4)
assertEquals(0.9238795325112867, Math.cos(Math.PI/8));
// Test KERNELTAN for |x| < 0.67434.
assertEquals(0.9238795325112867, Math.cos(-Math.PI/8));

// Tests for Math.tan for |x| < pi/4
assertEquals(Infinity, 1/Math.tan(0.0));
assertEquals(-Infinity, 1/Math.tan(-0.0));
// tan(x) = x for |x| < 2^-28
assertEquals(two_32, Math.tan(two_32));
assertEquals(-two_32, Math.tan(-two_32));
// Test KERNELTAN for |x| > 0.67434.
assertEquals(0.8211418015898941, Math.tan(11/16));
assertEquals(-0.8211418015898941, Math.tan(-11/16));
assertEquals(0.41421356237309503, Math.tan(Math.PI / 8));

// Tests for Math.sin.
assertEquals(0.479425538604203, Math.sin(0.5));
assertEquals(-0.479425538604203, Math.sin(-0.5));
assertEquals(1, Math.sin(Math.PI/2));
assertEquals(-1, Math.sin(-Math.PI/2));
// Test that Math.sin(Math.PI) != 0 since Math.PI is not exact.
assertEquals(1.2246467991473532e-16, Math.sin(Math.PI));
assertEquals(-7.047032979958965e-14, Math.sin(2200*Math.PI));
// Test Math.sin for various phases.
assertEquals(-0.7071067811865477, Math.sin(7/4 * Math.PI));
assertEquals(0.7071067811865474, Math.sin(9/4 * Math.PI));
assertEquals(0.7071067811865483, Math.sin(11/4 * Math.PI));
assertEquals(-0.7071067811865479, Math.sin(13/4 * Math.PI));
assertEquals(-3.2103381051568376e-11, Math.sin(1048576/4 * Math.PI));

// Tests for Math.cos.
assertEquals(1, Math.cos(two_28));
// Cover different code paths in KERNELCOS.
assertEquals(0.9689124217106447, Math.cos(0.25));
assertEquals(0.8775825618903728, Math.cos(0.5));
assertEquals(0.7073882691671998, Math.cos(0.785));
// Test that Math.cos(Math.PI/2) != 0 since Math.PI is not exact.
assertEquals(6.123233995736766e-17, Math.cos(Math.PI/2));
// Test Math.cos for various phases.
assertEquals(0.7071067811865474, Math.cos(7/4 * Math.PI));
assertEquals(0.7071067811865477, Math.cos(9/4 * Math.PI));
assertEquals(-0.7071067811865467, Math.cos(11/4 * Math.PI));
assertEquals(-0.7071067811865471, Math.cos(13/4 * Math.PI));
assertEquals(0.9367521275331447, Math.cos(1000000));
assertEquals(-3.435757038074824e-12, Math.cos(1048575/2 * Math.PI));

// Tests for Math.tan.
assertEquals(two_28, Math.tan(two_28));
// Test that  Math.tan(Math.PI/2) != Infinity since Math.PI is not exact.
assertEquals(1.633123935319537e16, Math.tan(Math.PI/2));
// Cover different code paths in KERNELTAN (tangent and cotangent)
assertEquals(0.5463024898437905, Math.tan(0.5));
assertEquals(2.0000000000000027, Math.tan(1.107148717794091));
assertEquals(-1.0000000000000004, Math.tan(7/4*Math.PI));
assertEquals(0.9999999999999994, Math.tan(9/4*Math.PI));
assertEquals(-6.420676210313675e-11, Math.tan(1048576/2*Math.PI));
assertEquals(2.910566692924059e11, Math.tan(1048575/2*Math.PI));

// Test Hayne-Panek reduction.
assertEquals(0.377820109360752e0, Math.sin(Math.pow(2, 120)));
assertEquals(-0.9258790228548379e0, Math.cos(Math.pow(2, 120)));
assertEquals(-0.40806638884180424e0, Math.tan(Math.pow(2, 120)));
assertEquals(-0.377820109360752e0, Math.sin(-Math.pow(2, 120)));
assertEquals(-0.9258790228548379e0, Math.cos(-Math.pow(2, 120)));
assertEquals(0.40806638884180424e0, Math.tan(-Math.pow(2, 120)));