Implement trigonometric functions using a fdlibm port.

test/mjsunit/sin-cos.js

 // Copyright 2011 the V8 project authors. All rights reserved.
 // Redistribution and use in source and binary forms, with or without
 // modification, are permitted provided that the following conditions are
 // met:
 //
 //     * Redistributions of source code must retain the above copyright
 //       notice, this list of conditions and the following disclaimer.
 //     * Redistributions in binary form must reproduce the above
 //       copyright notice, this list of conditions and the following
 //       disclaimer in the documentation and/or other materials provided
@@ skipping 139 matching lines @@
 }
 
 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")));
-assertEquals("Infinity", String(Math.tan(Math.PI/2)));
-assertEquals("-Infinity", String(Math.tan(-Math.PI/2)));
+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));
+// cos(pi/20) = sqrt(sqrt(2)*sqrt(sqrt(5)+5)+4)/2^(3/2)

[Raymond Toy, 2014/07/30 19:55:04]

This is tests the |x| < 0.3 branch in KERNELCOS.

[Yang, 2014/08/01 07:29:55]

Done.

+assertEquals(0.9876883405951378, Math.cos(Math.PI/20));
+assertEquals(0.7100335477927638, Math.cos(0.7812504768371582));
+assertEquals(0.7100338835660797, Math.cos(0.78125));

[Raymond Toy, 2014/07/30 19:55:04]

Lines 210-211 are testing the KERNELCOS test for x > 0.78125 and x <= 0.78125

[Yang, 2014/08/01 07:29:55]

Done.

+// cos(pi/8) = sqrt(sqrt(2)+1)/2^(3/4)

[Raymond Toy, 2014/07/30 19:55:05]

This tests the |x| > 0.3 branch in KERNELCOS

[Yang, 2014/08/01 07:29:56]

Done.

+assertEquals(0.9238795325112867, Math.cos(Math.PI/8));
+assertEquals(0.9238795325112867, Math.cos(-Math.PI/8));
+
+// Tests for Math.tan for |x| < pi/4
+assertEquals("Infinity", String(1/Math.tan(0.0)));

[Raymond Toy, 2014/07/30 19:55:05]

For the sin test, you used Infinity and +0.0. I think the tan test and the sin
test should be consistent here.

[Yang, 2014/08/01 07:29:56]

Done.

+assertEquals("-Infinity", String(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));
+assertEquals(0.8211418015898941, Math.tan(11/16));

[Raymond Toy, 2014/07/30 19:55:05]

Lines 222-223 tests the case |x| > 0.67434 in KERNELTAN.

[Yang, 2014/08/01 07:29:56]

Done.

+assertEquals(-0.8211418015898941, Math.tan(-11/16));
+assertEquals(0.41421356237309503, Math.tan(Math.PI / 8));

[Raymond Toy, 2014/07/30 19:55:04]

This tests the case in KERNELTAN for |x| < 0.67434.

[Yang, 2014/08/01 07:29:55]

Done.

+
+// 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));
+assertEquals(1.2246467991473532e-16, Math.sin(Math.PI));

[Raymond Toy, 2014/07/30 19:55:04]

Verifies Math.sin(Math.PI) is not zero because Math.PI is not pi so Math.sin
can't be zero.

[Yang, 2014/08/01 07:29:56]

Done.

+assertEquals(-7.047032979958965e-14, Math.sin(2200*Math.PI));
+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));

[Raymond Toy, 2014/07/30 19:55:05]

I think lines 233-236 are intended to test the 4 various cases in sin calling
kernelsin and kernelcos and some of the branches in the pi reduction code.

[Yang, 2014/08/01 07:29:56]

Done.

+assertEquals(-3.2103381051568376e-11, Math.sin(1048576/4 * Math.PI));
+
+// Tests for Math.cos.
+assertEquals(1, Math.cos(two_28));
+assertEquals(0.9689124217106447, Math.cos(0.25));
+assertEquals(0.8775825618903728, Math.cos(0.5));
+assertEquals(0.7073882691671998, Math.cos(0.785));

[Raymond Toy, 2014/07/30 19:55:04]

Lines 241-243 are more tests on the three possible branches in KERNELCOS.

[Yang, 2014/08/01 07:29:55]

Done.

+assertEquals(6.123233995736766e-17, Math.cos(Math.PI/2));

[Raymond Toy, 2014/07/30 19:55:05]

Verifies Math.cos(Math.PI/2) is not 0 because Math.PI/2 is not pi/2 so Math.cos
can't be zero.

[Yang, 2014/08/01 07:29:56]

Done.

+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));

[Raymond Toy, 2014/07/30 19:55:04]

Lines 245-248 tests the four possible cases in computing cos using KERNELCOS and
KERNELSIN.

[Yang, 2014/08/01 07:29:55]

Done.

+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));
+assertEquals(1.633123935319537e16, Math.tan(Math.PI/2));

[Raymond Toy, 2014/07/30 19:55:05]

Verifies Math.tan(Math.PI/2) is not an infinity because Math.PI/2 is not pi/2 so
Math.tan can't be an infinity.

[Yang, 2014/08/01 07:29:56]

Done.

+assertEquals(0.5463024898437905, Math.tan(0.5));
+assertEquals(0.8211418015898941, Math.tan(11/16));

[Raymond Toy, 2014/07/30 19:55:04]

255-256 tests (again) the various branches in KERNELTAN. Maybe line 256 should
be removed since we cover that in line 222.

[Yang, 2014/08/01 07:29:56]

Done.

+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));

[Raymond Toy, 2014/07/30 19:55:04]

Lines 258-259 verifies the two cases of tan calling KERNELTAN to compute the tan
or cot.

[Yang, 2014/08/01 07:29:56]

Done.

+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)));

[Raymond Toy, 2014/07/30 19:55:05]

I still think some test from special cases listed in the spec should be added
here.

[Yang, 2014/08/01 07:29:55]

Not sure what spec you are referring to here.