Experimental parser: merge r19949

src/harmony-math.js

 // Copyright 2013 the V8 project authors. All rights reserved.
 // Redistribution and use in source and binary forms, with or without
 // modification, are permitted provided that the following conditions are
 // met:
 //
 //     * Redistributions of source code must retain the above copyright
 //       notice, this list of conditions and the following disclaimer.
 //     * 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 156 matching lines @@
   // 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.
+// 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.
+
+// 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) {
-  return %Math_expm1(TO_NUMBER_INLINE(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.
+// 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) {
-  return %Math_log1p(TO_NUMBER_INLINE(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 ExtendMath() {
   %CheckIsBootstrapping();
 
   // Set up the non-enumerable functions on the Math object.
   InstallFunctions($Math, DONT_ENUM, $Array(
     "sign", MathSign,
     "trunc", MathTrunc,
     "sinh", MathSinh,
     "cosh", MathCosh,
     "tanh", MathTanh,
     "asinh", MathAsinh,
     "acosh", MathAcosh,
     "atanh", MathAtanh,
     "log10", MathLog10,
     "log2", MathLog2,
     "hypot", MathHypot,
     "fround", MathFround,
     "clz32", MathClz32,
     "cbrt", MathCbrt,
     "log1p", MathLog1p,
     "expm1", MathExpm1
   ));
 }
 
 
 ExtendMath();