Implement Math.log2 via ported extract from fdlibm.

test/mjsunit/es6/math-log2-log10.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
 //       with the distribution.
 //     * Neither the name of Google Inc. nor the names of its
 //       contributors may be used to endorse or promote products derived
 //       from this software without specific prior written permission.
 //
 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
+// Flags: --allow-natives-syntax
+
 [Math.log10, Math.log2].forEach( function(fun) {
   assertTrue(isNaN(fun(NaN)));
   assertTrue(isNaN(fun(fun)));
   assertTrue(isNaN(fun({ toString: function() { return NaN; } })));
   assertTrue(isNaN(fun({ valueOf: function() { return -1; } })));
   assertTrue(isNaN(fun({ valueOf: function() { return "abc"; } })));
   assertTrue(isNaN(fun(-0.1)));
   assertTrue(isNaN(fun(-1)));
   assertEquals("-Infinity", String(fun(0)));
   assertEquals("-Infinity", String(fun(-0)));
   assertEquals(0, fun(1));
   assertEquals("Infinity", String(fun(Infinity)));
 });
 
 for (var i = -310; i <= 308; i += 0.5) {
   assertEquals(i, Math.log10(Math.pow(10, i)));
-  assertEqualsDelta(i, Math.log2(Math.pow(2, i)), 1E-13);
+  // Square roots are tested below.
+  if (i != -0.5 && i != 0.5) assertEquals(i, Math.log2(Math.pow(2, i)));
 }
 
 // Test denormals.
 assertEquals(-307.77759430519706, Math.log10(1.5 * Math.pow(2, -1023)));
+
+// Test Math.log2(2^k) for -1074 <= k <= 1023.
+var n = -1074;
+// This loop covers n from -1074 to -1043
+for (var lowbits = 1; lowbits <= 0x80000000; lowbits *= 2) {
+  var x = %_ConstructDouble(0, lowbits);
+  assertEquals(n, Math.log2(x));
+  n++;
+}
+// This loop covers n from -1042 to -1023
+for (var hibits = 1; hibits <= 0x80000; hibits *= 2) {
+  var x = %_ConstructDouble(hibits, 0);
+  assertEquals(n, Math.log2(x));
+  n++;
+}
+// The rest of the normal values of 2^n
+var x = 1;
+for (var n = -1022; n <= 1023; ++n) {
+  var x = Math.pow(2, n);
+  assertEquals(n, Math.log2(x));
+}
+
+// Test special values.
+// Expectation isn't exactly 1/2 because Math.SQRT2 isn't exactly sqrt(2).
+assertEquals(0.5000000000000001, Math.log2(Math.SQRT2));
+
+// Expectation isn't exactly -1/2 because Math.SQRT1_2 isn't exactly sqrt(1/2).
+assertEquals(-0.4999999999999999, Math.log2(Math.SQRT1_2));
+
+assertEquals(3.321928094887362, Math.log2(10));
+assertEquals(6.643856189774724, Math.log2(100));
+
+// Test relationships
+x = 1;
+for (var k = 0; k < 1000; ++k) {
+  var y = Math.abs(Math.log2(x) + Math.log2(1/x));
+  assertEqualsDelta(0, y, 1.5e-14);
+  x *= 1.1;
+}
+
+x = Math.pow(2, -100);
+for (var k = 0; k < 1000; ++k) {
+  var y = Math.log2(x);
+  var expected = Math.log(x) / Math.LN2;
+  var err = Math.abs(y - expected) / expected;
+  assertEqualsDelta(0, err, 1e-15);
+  x *= 1.1;
+}