Ship ES6 Math functions.

src/math.js

Index: src/math.js
diff --git a/src/math.js b/src/math.js
index 6491399292b75233fdf4e54e4d447739fd1d8da0..9dc4b37d0ce2115ed9e9b5078f204fd060f926b9 100644
--- a/src/math.js
+++ b/src/math.js
@@ -254,6 +254,220 @@ function TrigonometricInterpolation(x, phase) {
          * (1 - (phase & 2)) + 0;
 }
 
+
+// ES6 draft 09-27-13, section 20.2.2.28.
+function MathSign(x) {
+  x = TO_NUMBER_INLINE(x);
+  if (x > 0) return 1;
+  if (x < 0) return -1;
+  if (x === 0) return x;
+  return NAN;
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.34.
+function MathTrunc(x) {
+  x = TO_NUMBER_INLINE(x);
+  if (x > 0) return MathFloor(x);
+  if (x < 0) return MathCeil(x);
+  if (x === 0) return x;
+  return NAN;
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.30.
+function MathSinh(x) {
+  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
+  // Idempotent for NaN, +/-0 and +/-Infinity.
+  if (x === 0 || !NUMBER_IS_FINITE(x)) return x;
+  return (MathExp(x) - MathExp(-x)) / 2;
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.12.
+function MathCosh(x) {
+  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
+  if (!NUMBER_IS_FINITE(x)) return MathAbs(x);
+  return (MathExp(x) + MathExp(-x)) / 2;
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.33.
+function MathTanh(x) {
+  if (!IS_NUMBER(x)) x = NonNumberToNumber(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) {
+  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
+  // Idempotent for NaN, +/-0 and +/-Infinity.
+  if (x === 0 || !NUMBER_IS_FINITE(x)) return x;
+  if (x > 0) return MathLog(x + MathSqrt(x * x + 1));
+  // This is to prevent numerical errors caused by large negative x.
+  return -MathLog(-x + MathSqrt(x * x + 1));
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.3.
+function MathAcosh(x) {
+  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
+  if (x < 1) return NAN;
+  // Idempotent for NaN and +Infinity.
+  if (!NUMBER_IS_FINITE(x)) return x;
+  return MathLog(x + MathSqrt(x + 1) * MathSqrt(x - 1));
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.7.
+function MathAtanh(x) {
+  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
+  // Idempotent for +/-0.
+  if (x === 0) return x;
+  // Returns NaN for NaN and +/- Infinity.
+  if (!NUMBER_IS_FINITE(x)) return NAN;
+  return 0.5 * MathLog((1 + x) / (1 - x));
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.21.
+function MathLog10(x) {
+  return MathLog(x) * 0.434294481903251828;  // log10(x) = log(x)/log(10).
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.22.
+function MathLog2(x) {
+  return MathLog(x) * 1.442695040888963407;  // log2(x) = log(x)/log(2).
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.17.
+function MathHypot(x, y) {  // Function length is 2.
+  // We may want to introduce fast paths for two arguments and when
+  // normalization to avoid overflow is not necessary.  For now, we
+  // simply assume the general case.
+  var length = %_ArgumentsLength();
+  var args = new InternalArray(length);
+  var max = 0;
+  for (var i = 0; i < length; i++) {
+    var n = %_Arguments(i);
+    if (!IS_NUMBER(n)) n = NonNumberToNumber(n);
+    if (n === INFINITY || n === -INFINITY) return INFINITY;
+    n = MathAbs(n);
+    if (n > max) max = n;
+    args[i] = n;
+  }
+
+  // Kahan summation to avoid rounding errors.
+  // Normalize the numbers to the largest one to avoid overflow.
+  if (max === 0) max = 1;
+  var sum = 0;
+  var compensation = 0;
+  for (var i = 0; i < length; i++) {
+    var n = args[i] / max;
+    var summand = n * n - compensation;
+    var preliminary = sum + summand;
+    compensation = (preliminary - sum) - summand;
+    sum = preliminary;
+  }
+  return MathSqrt(sum) * max;
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.16.
+function MathFroundJS(x) {
+  return %MathFround(TO_NUMBER_INLINE(x));
+}
+
+
+function MathClz32(x) {
+  x = ToUint32(TO_NUMBER_INLINE(x));
+  if (x == 0) return 32;
+  var result = 0;
+  // Binary search.
+  if ((x & 0xFFFF0000) === 0) { x <<= 16; result += 16; };
+  if ((x & 0xFF000000) === 0) { x <<=  8; result +=  8; };
+  if ((x & 0xF0000000) === 0) { x <<=  4; result +=  4; };
+  if ((x & 0xC0000000) === 0) { x <<=  2; result +=  2; };
+  if ((x & 0x80000000) === 0) { x <<=  1; result +=  1; };
+  return result;
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.9.
+// Cube root approximation, refer to: http://metamerist.com/cbrt/cbrt.htm
+// Using initial approximation adapted from Kahan's cbrt and 4 iterations
+// of Newton's method.
+function MathCbrt(x) {
+  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
+  if (x == 0 || !NUMBER_IS_FINITE(x)) return x;
+  return x >= 0 ? CubeRoot(x) : -CubeRoot(-x);
+}
+
+macro NEWTON_ITERATION_CBRT(x, approx)
+  (1.0 / 3.0) * (x / (approx * approx) + 2 * approx);
+endmacro
+
+function CubeRoot(x) {
+  var approx_hi = MathFloor(%_DoubleHi(x) / 3) + 0x2A9F7893;
+  var approx = %_ConstructDouble(approx_hi, 0);
+  approx = NEWTON_ITERATION_CBRT(x, approx);
+  approx = NEWTON_ITERATION_CBRT(x, approx);
+  approx = NEWTON_ITERATION_CBRT(x, approx);
+  return NEWTON_ITERATION_CBRT(x, approx);
+}
+
+
+
+// ES6 draft 09-27-13, section 20.2.2.14.
+// Use Taylor series to approximate.
+// exp(x) - 1 at 0 == -1 + exp(0) + exp'(0)*x/1! + exp''(0)*x^2/2! + ...
+//                 == x/1! + x^2/2! + x^3/3! + ...
+// The closer x is to 0, the fewer terms are required.
+function MathExpm1(x) {
+  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
+  var xabs = MathAbs(x);
+  if (xabs < 2E-7) {
+    return x * (1 + x * (1/2));
+  } else if (xabs < 6E-5) {
+    return x * (1 + x * (1/2 + x * (1/6)));
+  } else if (xabs < 2E-2) {
+    return x * (1 + x * (1/2 + x * (1/6 +
+           x * (1/24 + x * (1/120 + x * (1/720))))));
+  } else {  // Use regular exp if not close enough to 0.
+    return MathExp(x) - 1;
+  }
+}
+
+
+// ES6 draft 09-27-13, section 20.2.2.20.
+// Use Taylor series to approximate. With y = x + 1;
+// log(y) at 1 == log(1) + log'(1)(y-1)/1! + log''(1)(y-1)^2/2! + ...
+//             == 0 + x - x^2/2 + x^3/3 ...
+// The closer x is to 0, the fewer terms are required.
+function MathLog1p(x) {
+  if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
+  var xabs = MathAbs(x);
+  if (xabs < 1E-7) {
+    return x * (1 - x * (1/2));
+  } else if (xabs < 3E-5) {
+    return x * (1 - x * (1/2 - x * (1/3)));
+  } else if (xabs < 7E-3) {
+    return x * (1 - x * (1/2 - x * (1/3 - x * (1/4 -
+           x * (1/5 - x * (1/6 - x * (1/7)))))));
+  } else {  // Use regular log if not close enough to 0.
+    return MathLog(1 + x);
+  }
+}
+
 // -------------------------------------------------------------------
 
 function SetUpMath() {
@@ -300,7 +514,23 @@ function SetUpMath() {
     "pow", MathPow,
     "max", MathMax,
     "min", MathMin,
-    "imul", MathImul
+    "imul", MathImul,
+    "sign", MathSign,
+    "trunc", MathTrunc,
+    "sinh", MathSinh,
+    "cosh", MathCosh,
+    "tanh", MathTanh,
+    "asinh", MathAsinh,
+    "acosh", MathAcosh,
+    "atanh", MathAtanh,
+    "log10", MathLog10,
+    "log2", MathLog2,
+    "hypot", MathHypot,
+    "fround", MathFroundJS,
+    "clz32", MathClz32,
+    "cbrt", MathCbrt,
+    "log1p", MathLog1p,
+    "expm1", MathExpm1
   ));
 
   %SetInlineBuiltinFlag(MathCeil);