Port fdlibm implementation for Math.cosh.

test/mjsunit/es6/math-hyperbolic.js

 // Copyright 2013 the V8 project authors. All rights reserved.
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 // modification, are permitted provided that the following conditions are
 // met:
 //
 //     * Redistributions of source code must retain the above copyright
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 //     * 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 90 matching lines @@
 });
 
 
 // Some random samples.
 assertEqualsDelta(74.203210577788, Math.sinh(5), 1E-12);
 assertEqualsDelta(-74.203210577788, Math.sinh(-5), 1E-12);
 
 assertEqualsDelta(1.1276259652063, Math.cosh(0.5), 1E-12);
 assertEqualsDelta(74.209948524787, Math.cosh(5), 1E-12);
 assertEqualsDelta(1.1276259652063, Math.cosh(-0.5), 1E-12);
 assertEqualsDelta(74.209948524787, Math.cosh(-5), 1E-12);

[Raymond Toy, 2014/08/29 16:23:31]

Is there any reason to keep the tests in 108-111? If yes, then you should
probably use the correct values and test for equality: cosh(0.5) =
1.1276259652063807d0, and cosh(5) = 74.20994852478785d0

The same goes for the sinh tests in lines 105-106: sinh(5) = 74.20321057778875d0

If you want some further tests, you could use the properties cosh(x) + sinh(x) =
exp(x) and cosh(x)^2-sinh(x)^2 = 1.

[Yang, 2014/09/01 09:35:42]

I corrected those test expectations. I think we are fine regarding tests so far.
Actually I was hoping that we would eventually get some coverage in Test262 once
we have formal specification on accuracy.

[Raymond Toy, 2014/09/02 22:33:27]

I was assuming you'd change the assertEqualsDelta to assertEquals, since there's
no delta required now. Oh well.

 
 assertEqualsDelta(0.4621171572600, Math.tanh(0.5), 1E-12);
 assertEqualsDelta(0.9999092042625, Math.tanh(5), 1E-12);
 assertEqualsDelta(-0.4621171572600, Math.tanh(-0.5), 1E-12);
 assertEqualsDelta(-0.9999092042625, Math.tanh(-5), 1E-12);
 
 assertEqualsDelta(0.4812118250596, Math.asinh(0.5), 1E-12);
 assertEqualsDelta(2.3124383412727, Math.asinh(5), 1E-12);
 assertEqualsDelta(-0.4812118250596, Math.asinh(-0.5), 1E-12);
 assertEqualsDelta(-2.3124383412727, Math.asinh(-5), 1E-12);
@@ skipping 37 matching lines @@
 assertEquals(1.3440585709080678e43, Math.sinh(100));
 assertEquals(-1.3440585709080678e43, Math.sinh(-100));
 // No overflow, case |x| in [log(maxdouble), threshold]
 assertEquals(1.7976931348621744e308, Math.sinh(710.4758600739439));
 assertEquals(-1.7976931348621744e308, Math.sinh(-710.4758600739439));
 // Overflow, case |x| > threshold
 assertEquals(Infinity, Math.sinh(710.475860073944));
 assertEquals(-Infinity, Math.sinh(-710.475860073944));
 assertEquals(Infinity, Math.sinh(1000));
 assertEquals(-Infinity, Math.sinh(-1000));
+
+// Implementation-specific tests for cosh.
+// Case |x| < 2^-55
+assertEquals(1, Math.cosh(Math.pow(2, -55)));
+assertEquals(1, Math.cosh(-Math.pow(2, -55)));

[Raymond Toy, 2014/08/29 16:23:31]

Oops. This is a mistake in original test. If we want to test |x| < 2^-55, we
can't use 2^-55.  Replace with 2^-56.

[Yang, 2014/09/01 09:35:42]

Done.

+// Case |x| < 1/2*log(2). cosh(Math.LN2/4) = (sqrt(2)+1)/2^(5/4)
+assertEquals(1.0150517651282178, Math.cosh(Math.LN2/4));
+assertEquals(1.0150517651282178, Math.cosh(-Math.LN2/4));
+// Case 1/2*log(2) < |x| < 22. cosh(10*Math.LN2) = 1048577/2048
+assertEquals(512.00048828125, Math.cosh(10*Math.LN2));
+assertEquals(512.00048828125, Math.cosh(-10*Math.LN2));
+// Case 22 <= |x| < log(maxdouble)
+assertEquals(2.1474836479999983e9, Math.cosh(32*Math.LN2));
+assertEquals(2.1474836479999983e9, Math.cosh(-32*Math.LN2));
+// Case log(maxdouble) <= |x| <= overflowthreshold
+assertEquals(1.7976931348621744e308, Math.cosh(710.4758600739439));
+assertEquals(1.7976931348621744e308, Math.cosh(-710.4758600739439));
+// Overflow.
+assertEquals(Infinity, Math.cosh(710.475860073944));
+assertEquals(Infinity, Math.cosh(-710.475860073944));