// 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) {
- return %Math_cbrt(TO_NUMBER_INLINE(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! + ...
}
-// 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.
-inline double CubeRootNewtonIteration(double approx, double x) {
- return (1.0 / 3.0) * (x / (approx * approx) + 2 * approx);
-}
-
-
-inline double CubeRoot(double x) {
- static const uint64_t magic = V8_2PART_UINT64_C(0x2A9F7893, 00000000);
- uint64_t xhigh = double_to_uint64(x);
- double approx = uint64_to_double(xhigh / 3 + magic);
-
- approx = CubeRootNewtonIteration(approx, x);
- approx = CubeRootNewtonIteration(approx, x);
- approx = CubeRootNewtonIteration(approx, x);
- return CubeRootNewtonIteration(approx, x);
-}
-
-
-RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_cbrt) {
- SealHandleScope shs(isolate);
- ASSERT(args.length() == 1);
- CONVERT_DOUBLE_ARG_CHECKED(x, 0);
- if (x == 0 || std::isinf(x)) return args[0];
- double result = (x > 0) ? CubeRoot(x) : -CubeRoot(-x);
- return isolate->heap()->AllocateHeapNumber(result);
-}
-
-
static const double kPiDividedBy4 = 0.78539816339744830962;