[builtins] Introduce proper Float64Log2 and Float64Log10 operators.

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 739 matching lines @@
       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;
-//              x = scalbn(x,-n);
-//              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
-//
-// Note 1:
-//      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
-//      mode must set to Round-to-Nearest.
-// Note 2:
-//      [1/log(10)] rounded to 53 bits has error .198 ulps;
-//      log10 is monotonic at all binary break points.
-//
-// Special cases:
-//      log10(x) is NaN if x < 0;
-//      log10(+INF) is +INF; log10(0) is -INF;
-//      log10(NaN) is that NaN;
-//      log10(10**N) = N  for N=0,1,...,22.
-//
-
-define IVLN10 = 4.34294481903251816668e-01;
-define LOG10_2HI = 3.01029995663611771306e-01;
-define LOG10_2LO = 3.69423907715893078616e-13;
-
-function MathLog10(x) {
-  x = x * 1;  // Convert to number.
-  var hx = %_DoubleHi(x);
-  var lx = %_DoubleLo(x);
-  var k = 0;
-
-  if (hx < 0x00100000) {
-    // x < 2^-1022
-    // log10(+/- 0) = -Infinity.
-    if (((hx & 0x7fffffff) | lx) === 0) return -INFINITY;
-    // log10 of negative number is NaN.
-    if (hx < 0) return NaN;
-    // Subnormal number. Scale up x.
-    k -= 54;
-    x *= TWO54;
-    hx = %_DoubleHi(x);
-    lx = %_DoubleLo(x);
-  }
-
-  // Infinity or NaN.
-  if (hx >= 0x7ff00000) return x;
-
-  k += (hx >> 20) - 1023;
-  var i = (k & 0x80000000) >>> 31;
-  hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
-  var y = k + i;
-  x = %_ConstructDouble(hx, lx);
-
-  var z = y * LOG10_2LO + IVLN10 * %math_log(x);
-  return z + y * LOG10_2HI;
-}
-
-
-// ES6 draft 09-27-13, section 20.2.2.22.
-// Return the base 2 logarithm of x
-//
-// fdlibm does not have an explicit log2 function, but fdlibm's pow
-// function does implement an accurate log2 function as part of the
-// pow implementation.  This extracts the core parts of that as a
-// separate log2 function.
-
-// Method:
-// Compute log2(x) in two pieces:
-// log2(x) = w1 + w2
-// where w1 has 53-24 = 29 bits of trailing zeroes.
-
-define DP_H = 5.84962487220764160156e-01;
-define DP_L = 1.35003920212974897128e-08;
-
-// Polynomial coefficients for (3/2)*(log2(x) - 2*s - 2/3*s^3)
-define LOG2_1 = 5.99999999999994648725e-01;
-define LOG2_2 = 4.28571428578550184252e-01;
-define LOG2_3 = 3.33333329818377432918e-01;
-define LOG2_4 = 2.72728123808534006489e-01;
-define LOG2_5 = 2.30660745775561754067e-01;
-define LOG2_6 = 2.06975017800338417784e-01;
-
-// cp = 2/(3*ln(2)). Note that cp_h + cp_l is cp, but with more accuracy.
-define CP = 9.61796693925975554329e-01;
-define CP_H = 9.61796700954437255859e-01;
-define CP_L = -7.02846165095275826516e-09;
-// 2^53
-define TWO53 = 9007199254740992; 
-
-function MathLog2(x) {
-  x = x * 1;  // Convert to number.
-  var ax = MathAbs(x);
-  var hx = %_DoubleHi(x);
-  var lx = %_DoubleLo(x);
-  var ix = hx & 0x7fffffff;
-
-  // Handle special cases.
-  // log2(+/- 0) = -Infinity
-  if ((ix | lx) == 0) return -INFINITY;
-
-  // log(x) = NaN, if x < 0
-  if (hx < 0) return NaN;
-
-  // log2(Infinity) = Infinity, log2(NaN) = NaN
-  if (ix >= 0x7ff00000) return x;
-
-  var n = 0;
-
-  // Take care of subnormal number.
-  if (ix < 0x00100000) {
-    ax *= TWO53;
-    n -= 53;
-    ix = %_DoubleHi(ax);
-  }
-
-  n += (ix >> 20) - 0x3ff;
-  var j = ix & 0x000fffff;
-
-  // Determine interval.
-  ix = j | 0x3ff00000;  // normalize ix.
-
-  var bp = 1;
-  var dp_h = 0;
-  var dp_l = 0;
-  if (j > 0x3988e) {  // |x| > sqrt(3/2)
-    if (j < 0xbb67a) {  // |x| < sqrt(3)
-      bp = 1.5;
-      dp_h = DP_H;
-      dp_l = DP_L;
-    } else {
-      n += 1;
-      ix -= 0x00100000;
-    }
-  }
- 
-  ax = %_ConstructDouble(ix, %_DoubleLo(ax));
-
-  // Compute ss = s_h + s_l = (x - 1)/(x+1) or (x - 1.5)/(x + 1.5)
-  var u = ax - bp;
-  var v = 1 / (ax + bp);
-  var ss = u * v;
-  var s_h = %_ConstructDouble(%_DoubleHi(ss), 0);
-
-  // t_h = ax + bp[k] High
-  var t_h = %_ConstructDouble(%_DoubleHi(ax + bp), 0)
-  var t_l = ax - (t_h - bp);
-  var s_l = v * ((u - s_h * t_h) - s_h * t_l);
-
-  // Compute log2(ax)
-  var s2 = ss * ss;
-  var r = s2 * s2 * (LOG2_1 + s2 * (LOG2_2 + s2 * (LOG2_3 + s2 * (
-                     LOG2_4 + s2 * (LOG2_5 + s2 * LOG2_6)))));
-  r += s_l * (s_h + ss);
-  s2  = s_h * s_h;
-  t_h = %_ConstructDouble(%_DoubleHi(3.0 + s2 + r), 0);
-  t_l = r - ((t_h - 3.0) - s2);
-  // u + v = ss * (1 + ...)
-  u = s_h * t_h;
-  v = s_l * t_h + t_l * ss;
-
-  // 2 / (3 * log(2)) * (ss + ...)
-  var p_h = %_ConstructDouble(%_DoubleHi(u + v), 0);
-  var p_l = v - (p_h - u);
-  var z_h = CP_H * p_h;
-  var z_l = CP_L * p_h + p_l * CP + dp_l;
-
-  // log2(ax) = (ss + ...) * 2 / (3 * log(2)) = n + dp_h + z_h + z_l
-  var t = n;
-  var t1 = %_ConstructDouble(%_DoubleHi(((z_h + z_l) + dp_h) + t), 0);
-  var t2 = z_l - (((t1 - t) - dp_h) - z_h);
-
-  // t1 + t2 = log2(ax), sum up because we do not care about extra precision.
-  return t1 + t2;
-}
-
 //-------------------------------------------------------------------
 
 utils.InstallFunctions(GlobalMath, DONT_ENUM, [
   "cos", MathCos,
   "sin", MathSin,
   "tan", MathTan,
   "sinh", MathSinh,
   "cosh", MathCosh,
   "tanh", MathTanh,
-  "log10", MathLog10,
-  "log2", MathLog2,
   "expm1", MathExpm1
 ]);
 
 %SetForceInlineFlag(MathSin);
 %SetForceInlineFlag(MathCos);
 
 })