Implement Math.tanh using fdlibm port.

src/third_party/fdlibm/fdlibm.js

 // The following is adapted from fdlibm (http://www.netlib.org/fdlibm),
 //
 // ====================================================
 // Copyright (C) 1993-2004 by Sun Microsystems, Inc. All rights reserved.
 //
 // Developed at SunSoft, a Sun Microsystems, Inc. business.
 // Permission to use, copy, modify, and distribute this
 // software is freely granted, provided that this notice
 // is preserved.
 // ====================================================
@@ skipping 825 matching lines @@
   if (MathAbs(x) <= KCOSH_OVERFLOW) {
     var w = MathExp(0.5 * MathAbs(x));
     var t = 0.5 * w;
     return t * w;
   }
   if (NUMBER_IS_NAN(x)) return x;
   // |x| > overflowthreshold.
   return INFINITY;
 }
 
+// ES6 draft 09-27-13, section 20.2.2.33.
+// Math.tanh(x)
+// Method :
+//                                    x    -x
+//                                   e  - e
+//     0. tanh(x) is defined to be -----------
+//                                    x    -x
+//                                   e  + e
+//     1. reduce x to non-negative by tanh(-x) = -tanh(x).
+//     2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
+//                                             -t
+//         2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
+//                                            t + 2
+//                                                  2
+//         1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t = expm1(2x)
+//                                                t + 2
+//         22.0   <  x <= INF    : tanh(x) := 1.
+//
+// Special cases:
+//     tanh(NaN) is NaN;
+//     only tanh(0) = 0 is exact for finite argument.
+//
+
+define TWO_M55 = 2.77555756156289135105e-17;  // 2^-55, empty lower half

[Raymond Toy, 2015/10/16 17:07:25]

A bit late, but this comment is incorrect.  Since 2^-55 is a power of two, the
lower half is always empty.  The comment here implies to me that you've forcibly
made the lower half zero, but it was already zero anyway.

+
+function MathTanh(x) {
+  x = x * 1;  // Convert to number.
+  // x is Infinity or NaN
+  if (!NUMBER_IS_FINITE(x)) {
+    if (x > 0) return 1;
+    if (x < 0) return -1;
+    return x;
+  }
+
+  var ax = MathAbs(x);
+  var z;
+  // |x| < 22
+  if (ax < 22) {
+    if (ax < TWO_M55) {
+      // |x| < 2^-55, tanh(small) = small.
+      return x;
+    }
+    if (ax >= 1) {
+      // |x| >= 1
+      var t = MathExpm1(2 * ax);
+      z = 1 - 2 / (t + 2);
+    } else {
+      var t = MathExpm1(-2 * ax);
+      z = -t / (t + 2);
+    }
+  } else {
+    // |x| > 22, return +/- 1
+    z = 1;
+  }
+  return (x >= 0) ? z : -z;
+}
+
 // ES6 draft 09-27-13, section 20.2.2.21.
 // Return the base 10 logarithm of x
 //
 // Method :
 //      Let log10_2hi = leading 40 bits of log10(2) and
 //          log10_2lo = log10(2) - log10_2hi,
 //          ivln10   = 1/log(10) rounded.
 //      Then
 //              n = ilogb(x),
 //              if(n<0)  n = n+1;
@@ skipping 166 matching lines @@
 }
 
 //-------------------------------------------------------------------
 
 utils.InstallFunctions(GlobalMath, DONT_ENUM, [
   "cos", MathCos,
   "sin", MathSin,
   "tan", MathTan,
   "sinh", MathSinh,
   "cosh", MathCosh,
+  "tanh", MathTanh,
   "log10", MathLog10,
   "log2", MathLog2,
   "log1p", MathLog1p,
   "expm1", MathExpm1
 ]);
 
 %SetForceInlineFlag(MathSin);
 %SetForceInlineFlag(MathCos);
 
 })