// Also define the initialization function that populates the lookup table
// and then wires up the function definitions.
function SetupTrigonometricFunctions() {
- // TODO(yangguo): The following table size has been chosen to satisfy
- // Sunspider's brittle result verification. Reconsider relevance.
- var samples = 4489;
- var pi = 3.1415926535897932;
- var pi_half = pi / 2;
- var inverse_pi_half = 2 / pi;
- var two_pi = 2 * pi;
- var four_pi = 4 * pi;
- var interval = pi_half / samples;
- var inverse_interval = samples / pi_half;
+ var samples = 1800; // Table size. Do not change arbitrarily.
+ var inverse_pi_half = 0.636619772367581343; // 2 / pi
+ var inverse_pi_half_s_26 = 9.48637384723993156e-9; // 2 / pi / (2^26)
+ var s_26 = 1 << 26;
+ var two_step_threshold = 1 << 27;
+ var index_convert = 1145.915590261646418; // samples / (pi / 2)
+ // pi / 2 rounded up
+ var pi_half = 1.570796326794896780; // 0x192d4454fb21f93f
+ // We use two parts for pi/2 to emulate a higher precision.
+ // pi_half_1 only has 26 significant bits for mantissa.
+ // Note that pi_half > pi_half_1 + pi_half_2
+ var pi_half_1 = 1.570796325802803040; // 0x00000054fb21f93f
+ var pi_half_2 = 9.920935796805404252e-10; // 0x3326a611460b113e
var table_sin;
var table_cos_interval;
// 1) Multiplication takes care of to-number conversion.
// 2) Reduce x to the first quadrant [0, pi/2].
// Conveniently enough, in case of +/-Infinity, we get NaN.
+ // Note that we try to use only 26 instead of 52 significant bits for
+ // mantissa to avoid rounding errors when multiplying. For very large
+ // input we therefore have additional steps.
// 3) Replace x by (pi/2-x) if x was in the 2nd or 4th quadrant.
// 4) Do a table lookup for the closest samples to the left and right of x.
// 5) Find the derivatives at those sampling points by table lookup:
// 6) Use cubic spline interpolation to approximate sin(x).
// 7) Negate the result if x was in the 3rd or 4th quadrant.
// 8) Get rid of -0 by adding 0.
- var Interpolation = function(x) {
- var double_index = x * inverse_interval;
+ var Interpolation = function(x, phase) {
+ if (x < 0 || x > pi_half) {
+ var multiple;
+ while (x < -two_step_threshold || x > two_step_threshold) {
+ // Let's assume this loop does not terminate.
+ // All numbers x in each loop forms a set S.
+ // (1) abs(x) > 2^27 for all x in S.
+ // (2) abs(multiple) != 0 since (2^27 * inverse_pi_half_s26) > 1
+ // (3) multiple is rounded down in 2^26 steps, so the rounding error is
+ // at most max(ulp, 2^26).
+ // (4) so for x > 2^27, we subtract at most (1+pi/4)x and at least
+ // (1-pi/4)x
+ // (5) The subtraction results in x' so that abs(x') <= abs(x)*pi/4.
+ // Note that this difference cannot be simply rounded off.
+ // Set S cannot exist since (5) violates (1). Loop must terminate.
+ multiple = MathFloor(x * inverse_pi_half_s_26) * s_26;
+ x = x - multiple * pi_half_1 - multiple * pi_half_2;
+ }
+ multiple = MathFloor(x * inverse_pi_half);
+ x = x - multiple * pi_half_1 - multiple * pi_half_2;
+ phase += multiple;
+ }
+ var double_index = x * index_convert;
+ if (phase & 1) double_index = samples - double_index;
var index = double_index | 0;
var t1 = double_index - index;
var t2 = 1 - t1;
var dy = y2 - y1;
return (t2 * y1 + t1 * y2 +
t1 * t2 * ((table_cos_interval[index] - dy) * t2 +
- (dy - table_cos_interval[index + 1]) * t1));
+ (dy - table_cos_interval[index + 1]) * t1))
+ * (1 - (phase & 2)) + 0;
}
var MathSinInterpolation = function(x) {
- // This is to make Sunspider's result verification happy.
- if (x > four_pi) x -= four_pi;
- var multiple = MathFloor(x * inverse_pi_half);
- if (%_IsMinusZero(multiple)) return multiple;
- x = (multiple & 1) * pi_half +
- (1 - ((multiple & 1) << 1)) * (x - multiple * pi_half);
- return Interpolation(x) * (1 - (multiple & 2)) + 0;
+ x = x * 1; // Convert to number and deal with -0.
+ if (%_IsMinusZero(x)) return x;
+ return Interpolation(x, 0);
}
- // Cosine is sine with a phase offset of pi/2.
+ // Cosine is sine with a phase offset.
var MathCosInterpolation = function(x) {
- var multiple = MathFloor(x * inverse_pi_half);
- var phase = multiple + 1;
- x = (phase & 1) * pi_half +
- (1 - ((phase & 1) << 1)) * (x - multiple * pi_half);
- return Interpolation(x) * (1 - (phase & 2)) + 0;
+ x = MathAbs(x); // Convert to number and get rid of -0.
+ return Interpolation(x, 1);
};
%SetInlineBuiltinFlag(Interpolation);
// Test Math.sin and Math.cos.
+// Flags: --allow-natives-syntax
+
function sinTest() {
assertEquals(0, Math.sin(0));
assertEquals(1, Math.sin(Math.PI / 2));
var test_inputs = [];
for (var i = -10000; i < 10000; i += 177) test_inputs.push(i/1257);
-var epsilon = 0.000001;
+var epsilon = 0.0000001;
test_inputs.push(0);
test_inputs.push(0 + epsilon);
var x = test_inputs[i];
var err_sin = abs_error(Math.sin, sin, x);
var err_cos = abs_error(Math.cos, cos, x)
- assertTrue(err_sin < 1E-13);
- assertTrue(err_cos < 1E-13);
+ assertEqualsDelta(0, err_sin, 1E-13);
+ assertEqualsDelta(0, err_cos, 1E-13);
squares.push(err_sin*err_sin + err_cos*err_cos);
}
}
var err_rms = Math.sqrt(squares[0] / test_inputs.length / 2);
-assertTrue(err_rms < 1E-14);
+assertEqualsDelta(0, err_rms, 1E-14);
assertEquals(-1, Math.cos({ valueOf: function() { return Math.PI; } }));
assertEquals(0, Math.sin("0x00000"));
assertTrue(isNaN(Math.cos("-Infinity")));
assertEquals("Infinity", String(Math.tan(Math.PI/2)));
assertEquals("-Infinity", String(Math.tan(-Math.PI/2)));
+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)));
+
+
+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);
projects / platform / upstream / v8.git / commitdiff