Implement Math.tanh using fdlibm port.

Contributed by Raymond Toy: http://rtoy.github.io/fdlibm-js/

R=jkummerow@chromium.org
BUG=v8:3495
LOG=N

Review URL: https://codereview.chromium.org/1407213002

Cr-Commit-Position: refs/heads/master@{#31335}

src/js/math.js

@@ -182,18 +182,6 @@ function MathTrunc(x) {
   return x;
 }
 
-// ES6 draft 09-27-13, section 20.2.2.33.
-function MathTanh(x) {
-  x = TO_NUMBER(x);
-  // Idempotent for +/-0.
-  if (x === 0) return x;
-  // Returns +/-1 for +/-Infinity.
-  if (!NUMBER_IS_FINITE(x)) return MathSign(x);
-  var exp1 = MathExp(x);
-  var exp2 = MathExp(-x);
-  return (exp1 - exp2) / (exp1 + exp2);
-}
-
 // ES6 draft 09-27-13, section 20.2.2.5.
 function MathAsinh(x) {
   x = TO_NUMBER(x);
@@ -329,7 +317,6 @@ utils.InstallFunctions(GlobalMath, DONT_ENUM, [
   "imul", MathImul,
   "sign", MathSign,
   "trunc", MathTrunc,
-  "tanh", MathTanh,
   "asinh", MathAsinh,
   "acosh", MathAcosh,
   "atanh", MathAtanh,

src/third_party/fdlibm/fdlibm.js

@@ -843,6 +843,63 @@ function MathCosh(x) {
   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
+
+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
 //
@@ -1029,6 +1086,7 @@ utils.InstallFunctions(GlobalMath, DONT_ENUM, [
   "tan", MathTan,
   "sinh", MathSinh,
   "cosh", MathCosh,
+  "tanh", MathTanh,
   "log10", MathLog10,
   "log2", MathLog2,
   "log1p", MathLog1p,

test/mjsunit/es6/math-hyperbolic.js

@@ -186,3 +186,21 @@ assertEquals(1.7976931348621744e308, Math.cosh(-710.4758600739439));
 // Overflow.
 assertEquals(Infinity, Math.cosh(710.475860073944));
 assertEquals(Infinity, Math.cosh(-710.475860073944));
+
+// Implementation-specific tests for tanh.
+// Case |x| < 2^-55
+var two_56 = Math.pow(2, -56);
+assertEquals(two_56, Math.tanh(two_56));
+assertEquals(-two_56, Math.tanh(-two_56));
+// Case |x| < 1
+assertEquals(0.6, Math.tanh(Math.LN2));
+assertEquals(-0.6, Math.tanh(-Math.LN2));
+// Case  1 < |x| < 22
+assertEquals(15/17, Math.tanh(2 * Math.LN2));
+assertEquals(-15/17, Math.tanh(-2 * Math.LN2));
+// Case |x| > 22
+assertEquals(1, Math.tanh(100));
+assertEquals(-1, Math.tanh(-100));
+// Test against overflow
+assertEquals(1, Math.tanh(1e300));
+assertEquals(-1, Math.tanh(-1e300));