Harmony: implement Math.cbrt, Math.expm1 and Math.log1p.

BUG=v8:2938
LOG=N
R=jarin@chromium.org

Review URL: https://codereview.chromium.org/163563003

git-svn-id: http://v8.googlecode.com/svn/branches/bleeding_edge@19486 ce2b1a6d-e550-0410-aec6-3dcde31c8c00

src/harmony-math.js

@@ -174,6 +174,24 @@ function MathClz32(x) {
 }
 
 
+//ES6 draft 09-27-13, section 20.2.2.9.
+function MathCbrt(x) {
+  return %Math_cbrt(TO_NUMBER_INLINE(x));
+}
+
+
+//ES6 draft 09-27-13, section 20.2.2.14.
+function MathExpm1(x) {
+  return %Math_expm1(TO_NUMBER_INLINE(x));
+}
+
+
+//ES6 draft 09-27-13, section 20.2.2.20.
+function MathLog1p(x) {
+  return %Math_log1p(TO_NUMBER_INLINE(x));
+}
+
+
 function ExtendMath() {
   %CheckIsBootstrapping();
 
@@ -191,7 +209,10 @@ function ExtendMath() {
     "log2", MathLog2,
     "hypot", MathHypot,
     "fround", MathFround,
-    "clz32", MathClz32
+    "clz32", MathClz32,
+    "cbrt", MathCbrt,
+    "log1p", MathLog1p,
+    "expm1", MathExpm1
   ));
 }
 

src/runtime.cc

@@ -7647,33 +7647,110 @@ RUNTIME_FUNCTION(MaybeObject*, Runtime_StringCompare) {
 }
 
 
-RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_acos) {
+#define RUNTIME_UNARY_MATH(NAME)                                               \
+RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_##NAME) {                          \
+  SealHandleScope shs(isolate);                                                \
+  ASSERT(args.length() == 1);                                                  \
+  isolate->counters()->math_##NAME()->Increment();                             \
+  CONVERT_DOUBLE_ARG_CHECKED(x, 0);                                            \
+  return isolate->heap()->AllocateHeapNumber(std::NAME(x));                    \
+}
+
+RUNTIME_UNARY_MATH(acos)
+RUNTIME_UNARY_MATH(asin)
+RUNTIME_UNARY_MATH(atan)
+RUNTIME_UNARY_MATH(log)
+#undef RUNTIME_UNARY_MATH
+
+
+// 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);
-  isolate->counters()->math_acos()->Increment();
-
   CONVERT_DOUBLE_ARG_CHECKED(x, 0);
-  return isolate->heap()->AllocateHeapNumber(std::acos(x));
+  if (x == 0 || std::isinf(x)) return args[0];
+  double result = (x > 0) ? CubeRoot(x) : -CubeRoot(-x);
+  return isolate->heap()->AllocateHeapNumber(result);
 }
 
 
-RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_asin) {
+RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_log1p) {
   SealHandleScope shs(isolate);
   ASSERT(args.length() == 1);
-  isolate->counters()->math_asin()->Increment();
-
   CONVERT_DOUBLE_ARG_CHECKED(x, 0);
-  return isolate->heap()->AllocateHeapNumber(std::asin(x));
+
+  double x_abs = std::fabs(x);
+  // 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.
+  static const double threshold_2 = 1.0 / 0x00800000;
+  static const double threshold_3 = 1.0 / 0x00008000;
+  static const double threshold_7 = 1.0 / 0x00000080;
+
+  double result;
+  if (x_abs < threshold_2) {
+    result = x * (1.0/1.0 - x * 1.0/2.0);
+  } else if (x_abs < threshold_3) {
+    result = x * (1.0/1.0 - x * (1.0/2.0 - x * (1.0/3.0)));
+  } else if (x_abs < threshold_7) {
+    result = x * (1.0/1.0 - x * (1.0/2.0 - x * (
+                  1.0/3.0 - x * (1.0/4.0 - x * (
+                  1.0/5.0 - x * (1.0/6.0 - x * (
+                  1.0/7.0)))))));
+  } else {  // Use regular log if not close enough to 0.
+    result = std::log(1.0 + x);
+  }
+  return isolate->heap()->AllocateHeapNumber(result);
 }
 
 
-RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_atan) {
+RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_expm1) {
   SealHandleScope shs(isolate);
   ASSERT(args.length() == 1);
-  isolate->counters()->math_atan()->Increment();
-
   CONVERT_DOUBLE_ARG_CHECKED(x, 0);
-  return isolate->heap()->AllocateHeapNumber(std::atan(x));
+
+  double x_abs = std::fabs(x);
+  // 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.
+  static const double threshold_2 = 1.0 / 0x00400000;
+  static const double threshold_3 = 1.0 / 0x00004000;
+  static const double threshold_6 = 1.0 / 0x00000040;
+
+  double result;
+  if (x_abs < threshold_2) {
+    result = x * (1.0/1.0 + x * (1.0/2.0));
+  } else if (x_abs < threshold_3) {
+    result = x * (1.0/1.0 + x * (1.0/2.0 + x * (1.0/6.0)));
+  } else if (x_abs < threshold_6) {
+    result = x * (1.0/1.0 + x * (1.0/2.0 + x * (
+                  1.0/6.0 + x * (1.0/24.0 + x * (
+                  1.0/120.0 + x * (1.0/720.0))))));
+  } else {  // Use regular exp if not close enough to 0.
+    result = std::exp(x) - 1.0;
+  }
+  return isolate->heap()->AllocateHeapNumber(result);
 }
 
 
@@ -7724,16 +7801,6 @@ RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_floor) {
 }
 
 
-RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_log) {
-  SealHandleScope shs(isolate);
-  ASSERT(args.length() == 1);
-  isolate->counters()->math_log()->Increment();
-
-  CONVERT_DOUBLE_ARG_CHECKED(x, 0);
-  return isolate->heap()->AllocateHeapNumber(std::log(x));
-}
-
-
 // Slow version of Math.pow.  We check for fast paths for special cases.
 // Used if SSE2/VFP3 is not available.
 RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_pow) {

src/runtime.h

@@ -177,14 +177,17 @@ namespace internal {
   F(Math_acos, 1, 1) \
   F(Math_asin, 1, 1) \
   F(Math_atan, 1, 1) \
-  F(Math_atan2, 2, 1) \
+  F(Math_log, 1, 1) \
+  F(Math_cbrt, 1, 1) \
+  F(Math_log1p, 1, 1) \
+  F(Math_expm1, 1, 1) \
+  F(Math_sqrt, 1, 1) \
   F(Math_exp, 1, 1) \
   F(Math_floor, 1, 1) \
-  F(Math_log, 1, 1) \
   F(Math_pow, 2, 1) \
   F(Math_pow_cfunction, 2, 1) \
+  F(Math_atan2, 2, 1) \
   F(RoundNumber, 1, 1) \
-  F(Math_sqrt, 1, 1) \
   F(Math_fround, 1, 1) \
   \
   /* Regular expressions */ \

test/mjsunit/harmony/math-cbrt.js

+// Copyright 2014 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// Flags: --harmony-maths
+
+assertTrue(isNaN(Math.cbrt(NaN)));
+assertTrue(isNaN(Math.cbrt(function() {})));
+assertTrue(isNaN(Math.cbrt({ toString: function() { return NaN; } })));
+assertTrue(isNaN(Math.cbrt({ valueOf: function() { return "abc"; } })));
+assertEquals("Infinity", String(1/Math.cbrt(0)));
+assertEquals("-Infinity", String(1/Math.cbrt(-0)));
+assertEquals("Infinity", String(Math.cbrt(Infinity)));
+assertEquals("-Infinity", String(Math.cbrt(-Infinity)));
+
+for (var i = 1E-100; i < 1E100; i *= Math.PI) {
+  assertEqualsDelta(i, Math.cbrt(i*i*i), i * 1E-15);
+}
+
+for (var i = -1E-100; i > -1E100; i *= Math.E) {
+  assertEqualsDelta(i, Math.cbrt(i*i*i), -i * 1E-15);
+}
+
+// Let's be exact at least for small integers.
+for (var i = 2; i < 10000; i++) {
+  assertEquals(i, Math.cbrt(i*i*i));
+}

test/mjsunit/harmony/math-expm1.js

+// Copyright 2014 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// Flags: --harmony-maths --no-fast-math
+
+assertTrue(isNaN(Math.expm1(NaN)));
+assertTrue(isNaN(Math.expm1(function() {})));
+assertTrue(isNaN(Math.expm1({ toString: function() { return NaN; } })));
+assertTrue(isNaN(Math.expm1({ valueOf: function() { return "abc"; } })));
+assertEquals("Infinity", String(1/Math.expm1(0)));
+assertEquals("-Infinity", String(1/Math.expm1(-0)));
+assertEquals("Infinity", String(Math.expm1(Infinity)));
+assertEquals(-1, Math.expm1(-Infinity));
+
+for (var x = 0.1; x < 700; x += 0.1) {
+  var expected = Math.exp(x) - 1;
+  assertEqualsDelta(expected, Math.expm1(x), expected * 1E-14);
+  expected = Math.exp(-x) - 1;
+  assertEqualsDelta(expected, Math.expm1(-x), -expected * 1E-14);
+}
+
+// Values close to 0:
+// Use six terms of Taylor expansion at 0 for exp(x) as test expectation:
+// exp(x) - 1 == exp(0) + exp(0) * x + x * x / 2 + ... - 1
+//            == x + x * x / 2 + x * x * x / 6 + ...
+function expm1(x) {
+  return x * (1 + x * (1/2 + x * (
+              1/6 + x * (1/24 + x * (
+              1/120 + x * (1/720 + x * (
+              1/5040 + x * (1/40320 + x*(
+              1/362880 + x * (1/3628800))))))))));
+}
+
+for (var x = 1E-1; x > 1E-300; x *= 0.8) {
+  var expected = expm1(x);
+  assertEqualsDelta(expected, Math.expm1(x), expected * 1E-14);
+}

test/mjsunit/harmony/math-log1p.js

+// Copyright 2014 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// Flags: --harmony-maths
+
+assertTrue(isNaN(Math.log1p(NaN)));
+assertTrue(isNaN(Math.log1p(function() {})));
+assertTrue(isNaN(Math.log1p({ toString: function() { return NaN; } })));
+assertTrue(isNaN(Math.log1p({ valueOf: function() { return "abc"; } })));
+assertEquals("Infinity", String(1/Math.log1p(0)));
+assertEquals("-Infinity", String(1/Math.log1p(-0)));
+assertEquals("Infinity", String(Math.log1p(Infinity)));
+assertEquals("-Infinity", String(Math.log1p(-1)));
+assertTrue(isNaN(Math.log1p(-2)));
+assertTrue(isNaN(Math.log1p(-Infinity)));
+
+for (var x = 1E300; x > 1E-1; x *= 0.8) {
+  var expected = Math.log(x + 1);
+  assertEqualsDelta(expected, Math.log1p(x), expected * 1E-14);
+}
+
+// Values close to 0:
+// Use Taylor expansion at 1 for log(x) as test expectation:
+// log1p(x) == log(x + 1) == 0 + x / 1 - x^2 / 2 + x^3 / 3 - ...
+function log1p(x) {
+  var terms = [];
+  var prod = x;
+  for (var i = 1; i <= 20; i++) {
+    terms.push(prod / i);
+    prod *= -x;
+  }
+  var sum = 0;
+  while (terms.length > 0) sum += terms.pop();
+  return sum;
+}
+
+for (var x = 1E-1; x > 1E-300; x *= 0.8) {
+  var expected = log1p(x);
+  assertEqualsDelta(expected, Math.log1p(x), expected * 1E-14);
+}