Revert "Implement trigonometric functions using a fdlibm port."

This reverts r22918 and r22920.

TBR=hpayer@chromium.org

Review URL: https://codereview.chromium.org/448633002

git-svn-id: https://v8.googlecode.com/svn/branches/bleeding_edge@22921 ce2b1a6d-e550-0410-aec6-3dcde31c8c00

.gitignore

@@ -63,7 +63,7 @@ shell_g
 /test/test262/tc39-test262-*
 /testing/gmock
 /testing/gtest
-/third_party/icu
+/third_party
 /tools/jsfunfuzz
 /tools/jsfunfuzz.zip
 /tools/oom_dump/oom_dump

BUILD.gn

@@ -194,7 +194,6 @@ action("js2c") {
     "src/string.js",
     "src/symbol.js",
     "src/uri.js",
-    "third_party/fdlibm/fdlibm.js",
     "src/math.js",
     "src/messages.js",
     "src/apinatives.js",
@@ -866,8 +865,6 @@ source_set("v8_base") {
     "src/zone-inl.h",
     "src/zone.cc",
     "src/zone.h",
-    "third_party/fdlibm/fdlibm.cc',
-    "third_party/fdlibm/fdlibm.h',
   ]
 
   if (v8_target_arch == "x86") {

DEPS

@@ -41,7 +41,6 @@ include_rules = [
   # Everybody can use some things.
   "+include",
   "+unicode",
-  "+third_party/fdlibm",
 ]
 
 # checkdeps.py shouldn't check for includes in these directories:

src/bootstrapper.cc

@@ -14,7 +14,7 @@
 #include "src/isolate-inl.h"
 #include "src/natives.h"
 #include "src/snapshot.h"
-#include "third_party/fdlibm/fdlibm.h"
+#include "src/trig-table.h"
 
 namespace v8 {
 namespace internal {
@@ -121,7 +121,7 @@ char* Bootstrapper::AllocateAutoDeletedArray(int bytes) {
 void Bootstrapper::TearDown() {
   if (delete_these_non_arrays_on_tear_down_ != NULL) {
     int len = delete_these_non_arrays_on_tear_down_->length();
-    DCHECK(len < 25);  // Don't use this mechanism for unbounded allocations.
+    DCHECK(len < 24);  // Don't use this mechanism for unbounded allocations.
     for (int i = 0; i < len; i++) {
       delete delete_these_non_arrays_on_tear_down_->at(i);
       delete_these_non_arrays_on_tear_down_->at(i) = NULL;
@@ -2651,19 +2651,43 @@ Genesis::Genesis(Isolate* isolate,
                                   NONE).Assert();
 
     // Initialize trigonometric lookup tables and constants.
-    const int constants_size = ARRAY_SIZE(TrigonometricConstants::constants);
-    const int table_num_bytes = constants_size * kDoubleSize;
-    v8::Local<v8::ArrayBuffer> trig_buffer = v8::ArrayBuffer::New(
+    const int table_num_bytes = TrigonometricLookupTable::table_num_bytes();
+    v8::Local<v8::ArrayBuffer> sin_buffer = v8::ArrayBuffer::New(
         reinterpret_cast<v8::Isolate*>(isolate),
-        const_cast<double*>(TrigonometricConstants::constants),
-        table_num_bytes);
-    v8::Local<v8::Float64Array> trig_table =
-        v8::Float64Array::New(trig_buffer, 0, constants_size);
+        TrigonometricLookupTable::sin_table(), table_num_bytes);
+    v8::Local<v8::ArrayBuffer> cos_buffer = v8::ArrayBuffer::New(
+        reinterpret_cast<v8::Isolate*>(isolate),
+        TrigonometricLookupTable::cos_x_interval_table(), table_num_bytes);
+    v8::Local<v8::Float64Array> sin_table = v8::Float64Array::New(
+        sin_buffer, 0, TrigonometricLookupTable::table_size());
+    v8::Local<v8::Float64Array> cos_table = v8::Float64Array::New(
+        cos_buffer, 0, TrigonometricLookupTable::table_size());
 
+    Runtime::DefineObjectProperty(builtins,
+                                  factory()->InternalizeOneByteString(
+                                      STATIC_ASCII_VECTOR("kSinTable")),
+                                  Utils::OpenHandle(*sin_table),
+                                  NONE).Assert();
+    Runtime::DefineObjectProperty(
+        builtins,
+        factory()->InternalizeOneByteString(
+            STATIC_ASCII_VECTOR("kCosXIntervalTable")),
+        Utils::OpenHandle(*cos_table),
+        NONE).Assert();
+    Runtime::DefineObjectProperty(
+        builtins,
+        factory()->InternalizeOneByteString(
+            STATIC_ASCII_VECTOR("kSamples")),
+        factory()->NewHeapNumber(
+            TrigonometricLookupTable::samples()),
+        NONE).Assert();
     Runtime::DefineObjectProperty(
         builtins,
-        factory()->InternalizeOneByteString(STATIC_ASCII_VECTOR("kTrig")),
-        Utils::OpenHandle(*trig_table), NONE).Assert();
+        factory()->InternalizeOneByteString(
+            STATIC_ASCII_VECTOR("kIndexConvert")),
+        factory()->NewHeapNumber(
+            TrigonometricLookupTable::samples_over_pi_half()),
+        NONE).Assert();
   }
 
   result_ = native_context();

src/math.js

@@ -56,6 +56,12 @@ function MathCeil(x) {
   return -MathFloor(-x);
 }
 
+// ECMA 262 - 15.8.2.7
+function MathCos(x) {
+  x = MathAbs(x);  // Convert to number and get rid of -0.
+  return TrigonometricInterpolation(x, 1);
+}
+
 // ECMA 262 - 15.8.2.8
 function MathExp(x) {
   return %MathExpRT(TO_NUMBER_INLINE(x));
@@ -158,16 +164,97 @@ function MathRound(x) {
   return %RoundNumber(TO_NUMBER_INLINE(x));
 }
 
+// ECMA 262 - 15.8.2.16
+function MathSin(x) {
+  x = x * 1;  // Convert to number and deal with -0.
+  if (%_IsMinusZero(x)) return x;
+  return TrigonometricInterpolation(x, 0);
+}
+
 // ECMA 262 - 15.8.2.17
 function MathSqrt(x) {
   return %_MathSqrtRT(TO_NUMBER_INLINE(x));
 }
 
+// ECMA 262 - 15.8.2.18
+function MathTan(x) {
+  return MathSin(x) / MathCos(x);
+}
+
 // Non-standard extension.
 function MathImul(x, y) {
   return %NumberImul(TO_NUMBER_INLINE(x), TO_NUMBER_INLINE(y));
 }
 
+
+var kInversePiHalf      = 0.636619772367581343;      // 2 / pi
+var kInversePiHalfS26   = 9.48637384723993156e-9;    // 2 / pi / (2^26)
+var kS26                = 1 << 26;
+var kTwoStepThreshold   = 1 << 27;
+// pi / 2 rounded up
+var kPiHalf             = 1.570796326794896780;      // 0x192d4454fb21f93f
+// We use two parts for pi/2 to emulate a higher precision.
+// pi_half_1 only has 26 significant bits for mantissa.
+// Note that pi_half > pi_half_1 + pi_half_2
+var kPiHalf1            = 1.570796325802803040;      // 0x00000054fb21f93f
+var kPiHalf2            = 9.920935796805404252e-10;  // 0x3326a611460b113e
+
+var kSamples;            // Initialized to a number during genesis.
+var kIndexConvert;       // Initialized to kSamples / (pi/2) during genesis.
+var kSinTable;           // Initialized to a Float64Array during genesis.
+var kCosXIntervalTable;  // Initialized to a Float64Array during genesis.
+
+// This implements sine using the following algorithm.
+// 1) Multiplication takes care of to-number conversion.
+// 2) Reduce x to the first quadrant [0, pi/2].
+//    Conveniently enough, in case of +/-Infinity, we get NaN.
+//    Note that we try to use only 26 instead of 52 significant bits for
+//    mantissa to avoid rounding errors when multiplying.  For very large
+//    input we therefore have additional steps.
+// 3) Replace x by (pi/2-x) if x was in the 2nd or 4th quadrant.
+// 4) Do a table lookup for the closest samples to the left and right of x.
+// 5) Find the derivatives at those sampling points by table lookup:
+//    dsin(x)/dx = cos(x) = sin(pi/2-x) for x in [0, pi/2].
+// 6) Use cubic spline interpolation to approximate sin(x).
+// 7) Negate the result if x was in the 3rd or 4th quadrant.
+// 8) Get rid of -0 by adding 0.
+function TrigonometricInterpolation(x, phase) {
+  if (x < 0 || x > kPiHalf) {
+    var multiple;
+    while (x < -kTwoStepThreshold || x > kTwoStepThreshold) {
+      // Let's assume this loop does not terminate.
+      // All numbers x in each loop forms a set S.
+      // (1) abs(x) > 2^27 for all x in S.
+      // (2) abs(multiple) != 0 since (2^27 * inverse_pi_half_s26) > 1
+      // (3) multiple is rounded down in 2^26 steps, so the rounding error is
+      //     at most max(ulp, 2^26).
+      // (4) so for x > 2^27, we subtract at most (1+pi/4)x and at least
+      //     (1-pi/4)x
+      // (5) The subtraction results in x' so that abs(x') <= abs(x)*pi/4.
+      //     Note that this difference cannot be simply rounded off.
+      // Set S cannot exist since (5) violates (1).  Loop must terminate.
+      multiple = MathFloor(x * kInversePiHalfS26) * kS26;
+      x = x - multiple * kPiHalf1 - multiple * kPiHalf2;
+    }
+    multiple = MathFloor(x * kInversePiHalf);
+    x = x - multiple * kPiHalf1 - multiple * kPiHalf2;
+    phase += multiple;
+  }
+  var double_index = x * kIndexConvert;
+  if (phase & 1) double_index = kSamples - double_index;
+  var index = double_index | 0;
+  var t1 = double_index - index;
+  var t2 = 1 - t1;
+  var y1 = kSinTable[index];
+  var y2 = kSinTable[index + 1];
+  var dy = y2 - y1;
+  return (t2 * y1 + t1 * y2 +
+              t1 * t2 * ((kCosXIntervalTable[index] - dy) * t2 +
+                         (dy - kCosXIntervalTable[index + 1]) * t1))
+         * (1 - (phase & 2)) + 0;
+}
+
+
 // ES6 draft 09-27-13, section 20.2.2.28.
 function MathSign(x) {
   x = TO_NUMBER_INLINE(x);
@@ -177,6 +264,7 @@ function MathSign(x) {
   return NAN;
 }
 
+
 // ES6 draft 09-27-13, section 20.2.2.34.
 function MathTrunc(x) {
   x = TO_NUMBER_INLINE(x);
@@ -186,6 +274,7 @@ function MathTrunc(x) {
   return NAN;
 }
 
+
 // ES6 draft 09-27-13, section 20.2.2.30.
 function MathSinh(x) {
   if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -194,6 +283,7 @@ function MathSinh(x) {
   return (MathExp(x) - MathExp(-x)) / 2;
 }
 
+
 // ES6 draft 09-27-13, section 20.2.2.12.
 function MathCosh(x) {
   if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -201,6 +291,7 @@ function MathCosh(x) {
   return (MathExp(x) + MathExp(-x)) / 2;
 }
 
+
 // ES6 draft 09-27-13, section 20.2.2.33.
 function MathTanh(x) {
   if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -213,6 +304,7 @@ function MathTanh(x) {
   return (exp1 - exp2) / (exp1 + exp2);
 }
 
+
 // ES6 draft 09-27-13, section 20.2.2.5.
 function MathAsinh(x) {
   if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -223,6 +315,7 @@ function MathAsinh(x) {
   return -MathLog(-x + MathSqrt(x * x + 1));
 }
 
+
 // ES6 draft 09-27-13, section 20.2.2.3.
 function MathAcosh(x) {
   if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -232,6 +325,7 @@ function MathAcosh(x) {
   return MathLog(x + MathSqrt(x + 1) * MathSqrt(x - 1));
 }
 
+
 // ES6 draft 09-27-13, section 20.2.2.7.
 function MathAtanh(x) {
   if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -242,6 +336,7 @@ function MathAtanh(x) {
   return 0.5 * MathLog((1 + x) / (1 - x));
 }
 
+
 // ES6 draft 09-27-13, section 20.2.2.21.
 function MathLog10(x) {
   return MathLog(x) * 0.434294481903251828;  // log10(x) = log(x)/log(10).
@@ -253,6 +348,7 @@ function MathLog2(x) {
   return MathLog(x) * 1.442695040888963407;  // log2(x) = log(x)/log(2).
 }
 
+
 // ES6 draft 09-27-13, section 20.2.2.17.
 function MathHypot(x, y) {  // Function length is 2.
   // We may want to introduce fast paths for two arguments and when
@@ -285,12 +381,13 @@ function MathHypot(x, y) {  // Function length is 2.
   return MathSqrt(sum) * max;
 }
 
+
 // ES6 draft 09-27-13, section 20.2.2.16.
 function MathFroundJS(x) {
   return %MathFround(TO_NUMBER_INLINE(x));
 }
 
-// ES6 draft 07-18-14, section 20.2.2.11
+
 function MathClz32(x) {
   x = ToUint32(TO_NUMBER_INLINE(x));
   if (x == 0) return 32;
@@ -304,6 +401,7 @@ function MathClz32(x) {
   return result;
 }
 
+
 // 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
@@ -327,6 +425,8 @@ function CubeRoot(x) {
   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! + ...
@@ -347,6 +447,7 @@ function MathExpm1(x) {
   }
 }
 
+
 // 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! + ...
@@ -401,14 +502,14 @@ function SetUpMath() {
     "asin", MathAsinJS,
     "atan", MathAtanJS,
     "ceil", MathCeil,
-    "cos", MathCos,       // implemented by third_party/fdlibm
+    "cos", MathCos,
     "exp", MathExp,
     "floor", MathFloor,
     "log", MathLog,
     "round", MathRound,
-    "sin", MathSin,       // implemented by third_party/fdlibm
+    "sin", MathSin,
     "sqrt", MathSqrt,
-    "tan", MathTan,       // implemented by third_party/fdlibm
+    "tan", MathTan,
     "atan2", MathAtan2JS,
     "pow", MathPow,
     "max", MathMax,
@@ -436,6 +537,8 @@ function SetUpMath() {
   %SetInlineBuiltinFlag(MathRandom);
   %SetInlineBuiltinFlag(MathSin);
   %SetInlineBuiltinFlag(MathCos);
+  %SetInlineBuiltinFlag(MathTan);
+  %SetInlineBuiltinFlag(TrigonometricInterpolation);
 }
 
 SetUpMath();

src/runtime.cc

@@ -45,7 +45,6 @@
 #include "src/utils.h"
 #include "src/v8threads.h"
 #include "src/vm-state-inl.h"
-#include "third_party/fdlibm/fdlibm.h"
 
 #ifdef V8_I18N_SUPPORT
 #include "src/i18n.h"
@@ -7684,21 +7683,6 @@ RUNTIME_FUNCTION(Runtime_ConstructDouble) {
 }
 
 
-RUNTIME_FUNCTION(Runtime_RemPiO2) {
-  HandleScope handle_scope(isolate);
-  DCHECK(args.length() == 1);
-  CONVERT_DOUBLE_ARG_CHECKED(x, 0);
-  Factory* factory = isolate->factory();
-  double y[2];
-  int n = rempio2(x, y);
-  Handle<FixedArray> array = factory->NewFixedArray(3);
-  array->set(0, Smi::FromInt(n));
-  array->set(1, *factory->NewHeapNumber(y[0]));
-  array->set(2, *factory->NewHeapNumber(y[1]));
-  return *factory->NewJSArrayWithElements(array);
-}
-
-
 static const double kPiDividedBy4 = 0.78539816339744830962;
 
 

src/runtime.h

@@ -149,7 +149,6 @@ namespace internal {
   F(MathExpRT, 1, 1)                                        \
   F(RoundNumber, 1, 1)                                      \
   F(MathFround, 1, 1)                                       \
-  F(RemPiO2, 1, 1)                                          \
                                                             \
   /* Regular expressions */                                 \
   F(RegExpCompile, 3, 1)                                    \

src/trig-table.h

+// Copyright 2013 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.
+
+#ifndef V8_TRIG_TABLE_H_
+#define V8_TRIG_TABLE_H_
+
+
+namespace v8 {
+namespace internal {
+
+class TrigonometricLookupTable : public AllStatic {
+ public:
+  // Casting away const-ness to use as argument for typed array constructor.
+  static void* sin_table() {
+    return const_cast<double*>(&kSinTable[0]);
+  }
+
+  static void* cos_x_interval_table() {
+    return const_cast<double*>(&kCosXIntervalTable[0]);
+  }
+
+  static double samples_over_pi_half() { return kSamplesOverPiHalf; }
+  static int samples() { return kSamples; }
+  static int table_num_bytes() { return kTableSize * sizeof(*kSinTable); }
+  static int table_size() { return kTableSize; }
+
+ private:
+  static const double kSinTable[];
+  static const double kCosXIntervalTable[];
+  static const int kSamples;
+  static const int kTableSize;
+  static const double kSamplesOverPiHalf;
+};
+
+} }  // namespace v8::internal
+
+#endif  // V8_TRIG_TABLE_H_

test/mjsunit/debug-script.js

@@ -59,7 +59,7 @@ for (i = 0; i < scripts.length; i++) {
 }
 
 // This has to be updated if the number of native scripts change.
-assertTrue(named_native_count == 23 || named_native_count == 24);
+assertTrue(named_native_count == 22 || named_native_count == 23);
 // Only the 'gc' extension is loaded.
 assertEquals(1, extension_count);
 // This script and mjsunit.js has been loaded.  If using d8, d8 loads

test/mjsunit/mirror-script.js

@@ -84,7 +84,7 @@ function testScriptMirror(f, file_name, file_lines, type, compilation_type,
 
 // Test the script mirror for different functions.
 testScriptMirror(function(){}, 'mirror-script.js', 98, 2, 0);
-testScriptMirror(Math.round, 'native math.js', -1, 0, 0);
+testScriptMirror(Math.sin, 'native math.js', -1, 0, 0);
 testScriptMirror(eval('(function(){})'), null, 1, 2, 1, '(function(){})', 87);
 testScriptMirror(eval('(function(){\n  })'), null, 2, 2, 1, '(function(){\n  })', 88);
 

test/mjsunit/runtime-gen/rempio2.js

-// Copyright 2014 the V8 project authors. All rights reserved.
-// AUTO-GENERATED BY tools/generate-runtime-tests.py, DO NOT MODIFY
-// Flags: --allow-natives-syntax --harmony
-var _x = 1.5;
-%RemPiO2(_x);

test/mjsunit/sin-cos.js

@@ -157,8 +157,8 @@ assertEquals(0, Math.sin("0x00000"));
 assertEquals(1, Math.cos("0x00000"));
 assertTrue(isNaN(Math.sin(Infinity)));
 assertTrue(isNaN(Math.cos("-Infinity")));
-assertTrue(Math.tan(Math.PI/2) > 1e16);
-assertTrue(Math.tan(-Math.PI/2) < -1e16);
+assertEquals("Infinity", String(Math.tan(Math.PI/2)));
+assertEquals("-Infinity", String(Math.tan(-Math.PI/2)));
 assertEquals("-Infinity", String(1/Math.sin("-0")));
 
 // Assert that the remainder after division by pi is reasonably precise.
@@ -185,96 +185,3 @@ for (var i = -1024; i < 1024; i++) {
 assertFalse(isNaN(Math.cos(1.57079632679489700)));
 assertFalse(isNaN(Math.cos(-1e-100)));
 assertFalse(isNaN(Math.cos(-1e-323)));
-
-// Tests for specific values expected from the fdlibm implementation.
-
-var two_32 = Math.pow(2, -32);
-var two_28 = Math.pow(2, -28);
-
-// Tests for Math.sin for |x| < pi/4
-assertEquals(Infinity, 1/Math.sin(+0.0));
-assertEquals(-Infinity, 1/Math.sin(-0.0));
-// sin(x) = x for x < 2^-27
-assertEquals(two_32, Math.sin(two_32));
-assertEquals(-two_32, Math.sin(-two_32));
-// sin(pi/8) = sqrt(sqrt(2)-1)/2^(3/4)
-assertEquals(0.3826834323650898, Math.sin(Math.PI/8));
-assertEquals(-0.3826834323650898, -Math.sin(Math.PI/8));
-
-// Tests for Math.cos for |x| < pi/4
-// cos(x) = 1 for |x| < 2^-27
-assertEquals(1, Math.cos(two_32));
-assertEquals(1, Math.cos(-two_32));
-// Test KERNELCOS for |x| < 0.3.
-// cos(pi/20) = sqrt(sqrt(2)*sqrt(sqrt(5)+5)+4)/2^(3/2)
-assertEquals(0.9876883405951378, Math.cos(Math.PI/20));
-// Test KERNELCOS for x ~= 0.78125
-assertEquals(0.7100335477927638, Math.cos(0.7812504768371582));
-assertEquals(0.7100338835660797, Math.cos(0.78125));
-// Test KERNELCOS for |x| > 0.3.
-// cos(pi/8) = sqrt(sqrt(2)+1)/2^(3/4)
-assertEquals(0.9238795325112867, Math.cos(Math.PI/8));
-// Test KERNELTAN for |x| < 0.67434.
-assertEquals(0.9238795325112867, Math.cos(-Math.PI/8));
-
-// Tests for Math.tan for |x| < pi/4
-assertEquals(Infinity, 1/Math.tan(0.0));
-assertEquals(-Infinity, 1/Math.tan(-0.0));
-// tan(x) = x for |x| < 2^-28
-assertEquals(two_32, Math.tan(two_32));
-assertEquals(-two_32, Math.tan(-two_32));
-// Test KERNELTAN for |x| > 0.67434.
-assertEquals(0.8211418015898941, Math.tan(11/16));
-assertEquals(-0.8211418015898941, Math.tan(-11/16));
-assertEquals(0.41421356237309503, Math.tan(Math.PI / 8));
-
-// Tests for Math.sin.
-assertEquals(0.479425538604203, Math.sin(0.5));
-assertEquals(-0.479425538604203, Math.sin(-0.5));
-assertEquals(1, Math.sin(Math.PI/2));
-assertEquals(-1, Math.sin(-Math.PI/2));
-// Test that Math.sin(Math.PI) != 0 since Math.PI is not exact.
-assertEquals(1.2246467991473532e-16, Math.sin(Math.PI));
-assertEquals(-7.047032979958965e-14, Math.sin(2200*Math.PI));
-// Test Math.sin for various phases.
-assertEquals(-0.7071067811865477, Math.sin(7/4 * Math.PI));
-assertEquals(0.7071067811865474, Math.sin(9/4 * Math.PI));
-assertEquals(0.7071067811865483, Math.sin(11/4 * Math.PI));
-assertEquals(-0.7071067811865479, Math.sin(13/4 * Math.PI));
-assertEquals(-3.2103381051568376e-11, Math.sin(1048576/4 * Math.PI));
-
-// Tests for Math.cos.
-assertEquals(1, Math.cos(two_28));
-// Cover different code paths in KERNELCOS.
-assertEquals(0.9689124217106447, Math.cos(0.25));
-assertEquals(0.8775825618903728, Math.cos(0.5));
-assertEquals(0.7073882691671998, Math.cos(0.785));
-// Test that Math.cos(Math.PI/2) != 0 since Math.PI is not exact.
-assertEquals(6.123233995736766e-17, Math.cos(Math.PI/2));
-// Test Math.cos for various phases.
-assertEquals(0.7071067811865474, Math.cos(7/4 * Math.PI));
-assertEquals(0.7071067811865477, Math.cos(9/4 * Math.PI));
-assertEquals(-0.7071067811865467, Math.cos(11/4 * Math.PI));
-assertEquals(-0.7071067811865471, Math.cos(13/4 * Math.PI));
-assertEquals(0.9367521275331447, Math.cos(1000000));
-assertEquals(-3.435757038074824e-12, Math.cos(1048575/2 * Math.PI));
-
-// Tests for Math.tan.
-assertEquals(two_28, Math.tan(two_28));
-// Test that  Math.tan(Math.PI/2) != Infinity since Math.PI is not exact.
-assertEquals(1.633123935319537e16, Math.tan(Math.PI/2));
-// Cover different code paths in KERNELTAN (tangent and cotangent)
-assertEquals(0.5463024898437905, Math.tan(0.5));
-assertEquals(2.0000000000000027, Math.tan(1.107148717794091));
-assertEquals(-1.0000000000000004, Math.tan(7/4*Math.PI));
-assertEquals(0.9999999999999994, Math.tan(9/4*Math.PI));
-assertEquals(-6.420676210313675e-11, Math.tan(1048576/2*Math.PI));
-assertEquals(2.910566692924059e11, Math.tan(1048575/2*Math.PI));
-
-// Test Hayne-Panek reduction.
-assertEquals(0.377820109360752e0, Math.sin(Math.pow(2, 120)));
-assertEquals(-0.9258790228548379e0, Math.cos(Math.pow(2, 120)));
-assertEquals(-0.40806638884180424e0, Math.tan(Math.pow(2, 120)));
-assertEquals(-0.377820109360752e0, Math.sin(-Math.pow(2, 120)));
-assertEquals(-0.9258790228548379e0, Math.cos(-Math.pow(2, 120)));
-assertEquals(0.40806638884180424e0, Math.tan(-Math.pow(2, 120)));

test/test262/test262.status

@@ -68,7 +68,14 @@
 
   ##################### DELIBERATE INCOMPATIBILITIES #####################
 
+  # This tests precision of Math functions.  The implementation for those
+  # trigonometric functions are platform/compiler dependent.  Furthermore, the
+  # expectation values by far deviates from the actual result given by an
+  # arbitrary-precision calculator, making those tests partly bogus.
+  'S15.8.2.7_A7': [PASS, FAIL_OK],  # Math.cos
   'S15.8.2.8_A6': [PASS, FAIL_OK],  # Math.exp (less precise with --fast-math)
+  'S15.8.2.16_A7': [PASS, FAIL_OK],  # Math.sin
+  'S15.8.2.18_A7': [PASS, FAIL_OK],  # Math.tan
 
   # Linux for ia32 (and therefore simulators) default to extended 80 bit
   # floating point formats, so these tests checking 64-bit FP precision fail.

third_party/fdlibm/LICENSE

-Copyright (C) 1993 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.

third_party/fdlibm/README.v8

-Name: Freely Distributable LIBM 
-Short Name: fdlibm
-URL: http://www.netlib.org/fdlibm/
-Version: 5.3 
-License: Freely Distributable.
-License File: LICENSE.
-Security Critical: yes.
-License Android Compatible: yes.
-
-Description:
-This is used to provide a accurate implementation for trigonometric functions
-used in V8.
-
-Local Modifications:
-For the use in V8, fdlibm has been reduced to include only sine, cosine and
-tangent.  To make inlining into generated code possible, a large portion of
-that has been translated to Javascript.  The rest remains in C, but has been
-refactored and reformatted to interoperate with the rest of V8.

third_party/fdlibm/fdlibm.cc

-// The following is adapted from fdlibm (http://www.netlib.org/fdlibm).
-//
-// ====================================================
-// Copyright (C) 1993 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.
-// ====================================================
-//
-// The original source code covered by the above license above has been
-// modified significantly by Google Inc.
-// Copyright 2014 the V8 project authors. All rights reserved.
-
-#include <cmath>
-
-#include "src/v8.h"
-
-#include "src/double.h"
-#include "third_party/fdlibm/fdlibm.h"
-
-
-namespace v8 {
-namespace internal {
-
-const double TrigonometricConstants::constants[] = {
-    6.36619772367581382433e-01,   // invpio2   0
-    1.57079632673412561417e+00,   // pio2_1    1
-    6.07710050650619224932e-11,   // pio2_1t   2
-    6.07710050630396597660e-11,   // pio2_2    3
-    2.02226624879595063154e-21,   // pio2_2t   4
-    2.02226624871116645580e-21,   // pio2_3    5
-    8.47842766036889956997e-32,   // pio2_3t   6
-    -1.66666666666666324348e-01,  // S1        7
-    8.33333333332248946124e-03,   //           8
-    -1.98412698298579493134e-04,  //           9
-    2.75573137070700676789e-06,   //          10
-    -2.50507602534068634195e-08,  //          11
-    1.58969099521155010221e-10,   // S6       12
-    4.16666666666666019037e-02,   // C1       13
-    -1.38888888888741095749e-03,  //          14
-    2.48015872894767294178e-05,   //          15
-    -2.75573143513906633035e-07,  //          16
-    2.08757232129817482790e-09,   //          17
-    -1.13596475577881948265e-11,  // C6       18
-    3.33333333333334091986e-01,   // T0       19
-    1.33333333333201242699e-01,   //          20
-    5.39682539762260521377e-02,   //          21
-    2.18694882948595424599e-02,   //          22
-    8.86323982359930005737e-03,   //          23
-    3.59207910759131235356e-03,   //          24
-    1.45620945432529025516e-03,   //          25
-    5.88041240820264096874e-04,   //          26
-    2.46463134818469906812e-04,   //          27
-    7.81794442939557092300e-05,   //          28
-    7.14072491382608190305e-05,   //          29
-    -1.85586374855275456654e-05,  //          30
-    2.59073051863633712884e-05,   // T12      31
-    7.85398163397448278999e-01,   // pio4     32
-    3.06161699786838301793e-17,   // pio4lo   33
-};
-
-
-// Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
-static const int two_over_pi[] = {
-    0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C,
-    0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649,
-    0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 0xA73EE8, 0x8235F5, 0x2EBB44,
-    0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C, 0x845F8B,
-    0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D,
-    0x367ECF, 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
-    0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330,
-    0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 0x91615E, 0xE61B08,
-    0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA,
-    0x73A8C9, 0x60E27B, 0xC08C6B};
-
-static const double zero = 0.0;
-static const double two24 = 1.6777216e+07;
-static const double one = 1.0;
-static const double twon24 = 5.9604644775390625e-08;
-
-static const double PIo2[] = {
-    1.57079625129699707031e+00,  // 0x3FF921FB, 0x40000000
-    7.54978941586159635335e-08,  // 0x3E74442D, 0x00000000
-    5.39030252995776476554e-15,  // 0x3CF84698, 0x80000000
-    3.28200341580791294123e-22,  // 0x3B78CC51, 0x60000000
-    1.27065575308067607349e-29,  // 0x39F01B83, 0x80000000
-    1.22933308981111328932e-36,  // 0x387A2520, 0x40000000
-    2.73370053816464559624e-44,  // 0x36E38222, 0x80000000
-    2.16741683877804819444e-51   // 0x3569F31D, 0x00000000
-};
-
-
-int __kernel_rem_pio2(double* x, double* y, int e0, int nx) {
-  static const int32_t jk = 3;
-  double fw;
-  int32_t jx = nx - 1;
-  int32_t jv = (e0 - 3) / 24;
-  if (jv < 0) jv = 0;
-  int32_t q0 = e0 - 24 * (jv + 1);
-  int32_t m = jx + jk;
-
-  double f[10];
-  for (int i = 0, j = jv - jx; i <= m; i++, j++) {
-    f[i] = (j < 0) ? zero : static_cast<double>(two_over_pi[j]);
-  }
-
-  double q[10];
-  for (int i = 0; i <= jk; i++) {
-    fw = 0.0;
-    for (int j = 0; j <= jx; j++) fw += x[j] * f[jx + i - j];
-    q[i] = fw;
-  }
-
-  int32_t jz = jk;
-
-recompute:
-
-  int32_t iq[10];
-  double z = q[jz];
-  for (int i = 0, j = jz; j > 0; i++, j--) {
-    fw = static_cast<double>(static_cast<int32_t>(twon24 * z));
-    iq[i] = static_cast<int32_t>(z - two24 * fw);
-    z = q[j - 1] + fw;
-  }
-
-  z = scalbn(z, q0);
-  z -= 8.0 * std::floor(z * 0.125);
-  int32_t n = static_cast<int32_t>(z);
-  z -= static_cast<double>(n);
-  int32_t ih = 0;
-  if (q0 > 0) {
-    int32_t i = (iq[jz - 1] >> (24 - q0));
-    n += i;
-    iq[jz - 1] -= i << (24 - q0);
-    ih = iq[jz - 1] >> (23 - q0);
-  } else if (q0 == 0) {
-    ih = iq[jz - 1] >> 23;
-  } else if (z >= 0.5) {
-    ih = 2;
-  }
-
-  if (ih > 0) {
-    n += 1;
-    int32_t carry = 0;
-    for (int i = 0; i < jz; i++) {
-      int32_t j = iq[i];
-      if (carry == 0) {
-        if (j != 0) {
-          carry = 1;
-          iq[i] = 0x1000000 - j;
-        }
-      } else {
-        iq[i] = 0xffffff - j;
-      }
-    }
-    if (q0 == 1) {
-      iq[jz - 1] &= 0x7fffff;
-    } else if (q0 == 2) {
-      iq[jz - 1] &= 0x3fffff;
-    }
-    if (ih == 2) {
-      z = one - z;
-      if (carry != 0) z -= scalbn(one, q0);
-    }
-  }
-
-  if (z == zero) {
-    int32_t j = 0;
-    for (int i = jz - 1; i >= jk; i--) j |= iq[i];
-    if (j == 0) {
-      int32_t k = 1;
-      while (iq[jk - k] == 0) k++;
-      for (int i = jz + 1; i <= jz + k; i++) {
-        f[jx + i] = static_cast<double>(two_over_pi[jv + i]);
-        for (j = 0, fw = 0.0; j <= jx; j++) fw += x[j] * f[jx + i - j];
-        q[i] = fw;
-      }
-      jz += k;
-      goto recompute;
-    }
-  }
-
-  if (z == 0.0) {
-    jz -= 1;
-    q0 -= 24;
-    while (iq[jz] == 0) {
-      jz--;
-      q0 -= 24;
-    }
-  } else {
-    z = scalbn(z, -q0);
-    if (z >= two24) {
-      fw = static_cast<double>(static_cast<int32_t>(twon24 * z));
-      iq[jz] = static_cast<int32_t>(z - two24 * fw);
-      jz += 1;
-      q0 += 24;
-      iq[jz] = static_cast<int32_t>(fw);
-    } else {
-      iq[jz] = static_cast<int32_t>(z);
-    }
-  }
-
-  fw = scalbn(one, q0);
-  for (int i = jz; i >= 0; i--) {
-    q[i] = fw * static_cast<double>(iq[i]);
-    fw *= twon24;
-  }
-
-  double fq[10];
-  for (int i = jz; i >= 0; i--) {
-    fw = 0.0;
-    for (int k = 0; k <= jk && k <= jz - i; k++) fw += PIo2[k] * q[i + k];
-    fq[jz - i] = fw;
-  }
-
-  fw = 0.0;
-  for (int i = jz; i >= 0; i--) fw += fq[i];
-  y[0] = (ih == 0) ? fw : -fw;
-  fw = fq[0] - fw;
-  for (int i = 1; i <= jz; i++) fw += fq[i];
-  y[1] = (ih == 0) ? fw : -fw;
-  return n & 7;
-}
-
-
-int rempio2(double x, double* y) {
-  int32_t hx = static_cast<int32_t>(double_to_uint64(x) >> 32);
-  int32_t ix = hx & 0x7fffffff;
-
-  if (ix >= 0x7ff00000) {
-    *y = base::OS::nan_value();
-    return 0;
-  }
-
-  int32_t e0 = (ix >> 20) - 1046;
-  uint64_t zi = double_to_uint64(x) & 0xFFFFFFFFu;
-  zi |= static_cast<uint64_t>(ix - (e0 << 20)) << 32;
-  double z = uint64_to_double(zi);
-
-  double tx[3];
-  for (int i = 0; i < 2; i++) {
-    tx[i] = static_cast<double>(static_cast<int32_t>(z));
-    z = (z - tx[i]) * two24;
-  }
-  tx[2] = z;
-
-  int nx = 3;
-  while (tx[nx - 1] == zero) nx--;
-  int n = __kernel_rem_pio2(tx, y, e0, nx);
-  if (hx < 0) {
-    y[0] = -y[0];
-    y[1] = -y[1];
-    return -n;
-  }
-  return n;
-}
-}
-}  // namespace v8::internal

third_party/fdlibm/fdlibm.h

-// The following is adapted from fdlibm (http://www.netlib.org/fdlibm).
-//
-// ====================================================
-// Copyright (C) 1993 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.
-// ====================================================
-//
-// The original source code covered by the above license above has been
-// modified significantly by Google Inc.
-// Copyright 2014 the V8 project authors. All rights reserved.
-
-#ifndef V8_FDLIBM_H_
-#define V8_FDLIBM_H_
-
-namespace v8 {
-namespace internal {
-
-int rempio2(double x, double* y);
-
-// Constants to be exposed to builtins via Float64Array.
-struct TrigonometricConstants {
-  static const double constants[34];
-};
-}
-}  // namespace v8::internal
-
-#endif  // V8_FDLIBM_H_

tools/generate-runtime-tests.py

@@ -47,11 +47,11 @@ EXPAND_MACROS = [
 # that the parser doesn't bit-rot. Change the values as needed when you add,
 # remove or change runtime functions, but make sure we don't lose our ability
 # to parse them!
-EXPECTED_FUNCTION_COUNT = 427
-EXPECTED_FUZZABLE_COUNT = 330
+EXPECTED_FUNCTION_COUNT = 426
+EXPECTED_FUZZABLE_COUNT = 329
 EXPECTED_CCTEST_COUNT = 7
 EXPECTED_UNKNOWN_COUNT = 16
-EXPECTED_BUILTINS_COUNT = 809
+EXPECTED_BUILTINS_COUNT = 813
 
 
 # Don't call these at all.

tools/generate-trig-table.py

+#!/usr/bin/env python
+#
+# 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.
+
+# This is a utility for populating the lookup table for the
+# approximation of trigonometric functions.
+
+import sys, math
+
+SAMPLES = 1800
+
+TEMPLATE = """\
+// Copyright 2013 Google Inc. All Rights Reserved.
+
+// This file was generated from a python script.
+
+#include "src/v8.h"
+#include "src/trig-table.h"
+
+namespace v8 {
+namespace internal {
+
+  const double TrigonometricLookupTable::kSinTable[] =
+      { %(sine_table)s };
+  const double TrigonometricLookupTable::kCosXIntervalTable[] =
+      { %(cosine_table)s };
+  const int TrigonometricLookupTable::kSamples = %(samples)i;
+  const int TrigonometricLookupTable::kTableSize = %(table_size)i;
+  const double TrigonometricLookupTable::kSamplesOverPiHalf =
+      %(samples_over_pi_half)s;
+
+} }  // v8::internal
+"""
+
+def main():
+  pi_half = math.pi / 2
+  interval = pi_half / SAMPLES
+  sin = []
+  cos_times_interval = []
+  table_size = SAMPLES + 2
+
+  for i in range(0, table_size):
+    sample = i * interval
+    sin.append(repr(math.sin(sample)))
+    cos_times_interval.append(repr(math.cos(sample) * interval))
+
+  output_file = sys.argv[1]
+  output = open(str(output_file), "w")
+  output.write(TEMPLATE % {
+    'sine_table': ','.join(sin),
+    'cosine_table': ','.join(cos_times_interval),
+    'samples': SAMPLES,
+    'table_size': table_size,
+    'samples_over_pi_half': repr(SAMPLES / pi_half)
+  })
+
+if __name__ == "__main__":
+  main()

tools/gyp/v8.gyp

@@ -121,12 +121,14 @@
           'dependencies': [
             'mksnapshot#host',
             'js2c#host',
+            'generate_trig_table#host',
           ],
         }, {
           'toolsets': ['target'],
           'dependencies': [
             'mksnapshot',
             'js2c',
+            'generate_trig_table',
           ],
         }],
         ['component=="shared_library"', {
@@ -151,6 +153,7 @@
       'sources': [
         '<(SHARED_INTERMEDIATE_DIR)/libraries.cc',
         '<(SHARED_INTERMEDIATE_DIR)/experimental-libraries.cc',
+        '<(SHARED_INTERMEDIATE_DIR)/trig-table.cc',
         '<(INTERMEDIATE_DIR)/snapshot.cc',
         '../../src/snapshot-common.cc',
       ],
@@ -194,16 +197,17 @@
       'sources': [
         '<(SHARED_INTERMEDIATE_DIR)/libraries.cc',
         '<(SHARED_INTERMEDIATE_DIR)/experimental-libraries.cc',
+        '<(SHARED_INTERMEDIATE_DIR)/trig-table.cc',
         '../../src/snapshot-common.cc',
         '../../src/snapshot-empty.cc',
       ],
       'conditions': [
         ['want_separate_host_toolset==1', {
           'toolsets': ['host', 'target'],
-          'dependencies': ['js2c#host'],
+          'dependencies': ['js2c#host', 'generate_trig_table#host'],
         }, {
           'toolsets': ['target'],
-          'dependencies': ['js2c'],
+          'dependencies': ['js2c', 'generate_trig_table'],
         }],
         ['component=="shared_library"', {
           'defines': [
@@ -222,12 +226,14 @@
           'dependencies': [
             'mksnapshot#host',
             'js2c#host',
+            'generate_trig_table#host',
             'natives_blob#host',
         ]}, {
           'toolsets': ['target'],
           'dependencies': [
             'mksnapshot',
             'js2c',
+            'generate_trig_table',
             'natives_blob',
           ],
         }],
@@ -251,6 +257,7 @@
         '../..',
       ],
       'sources': [
+        '<(SHARED_INTERMEDIATE_DIR)/trig-table.cc',
         '../../src/natives-external.cc',
         '../../src/snapshot-external.cc',
       ],
@@ -284,6 +291,32 @@
         },
       ],
     },
+    { 'target_name': 'generate_trig_table',
+      'type': 'none',
+      'conditions': [
+        ['want_separate_host_toolset==1', {
+          'toolsets': ['host'],
+        }, {
+          'toolsets': ['target'],
+        }],
+      ],
+      'actions': [
+        {
+          'action_name': 'generate',
+          'inputs': [
+            '../../tools/generate-trig-table.py',
+          ],
+          'outputs': [
+            '<(SHARED_INTERMEDIATE_DIR)/trig-table.cc',
+          ],
+          'action': [
+            'python',
+            '../../tools/generate-trig-table.py',
+            '<@(_outputs)',
+          ],
+        },
+      ]
+    },
     {
       'target_name': 'v8_base',
       'type': 'static_library',
@@ -735,8 +768,6 @@
         '../../src/zone-inl.h',
         '../../src/zone.cc',
         '../../src/zone.h',
-        '../../third_party/fdlibm/fdlibm.cc',
-        '../../third_party/fdlibm/fdlibm.h',
       ],
       'conditions': [
         ['want_separate_host_toolset==1', {
@@ -1389,7 +1420,6 @@
           '../../src/array.js',
           '../../src/string.js',
           '../../src/uri.js',
-          '../../third_party/fdlibm/fdlibm.js',
           '../../src/math.js',
           '../../src/messages.js',
           '../../src/apinatives.js',

tools/js2c.py

@@ -218,27 +218,6 @@ def ExpandInlineMacros(lines):
     lines = ExpandMacroDefinition(lines, pos, name_pattern, macro, non_expander)
 
 
-INLINE_CONSTANT_PATTERN = re.compile(r'const\s+([a-zA-Z0-9_]+)\s*=\s*([^;\n]+)[;\n]')
-
-def ExpandInlineConstants(lines):
-  pos = 0
-  while True:
-    const_match = INLINE_CONSTANT_PATTERN.search(lines, pos)
-    if const_match is None:
-      # no more constants
-      return lines
-    name = const_match.group(1)
-    replacement = const_match.group(2)
-    name_pattern = re.compile("\\b%s\\b" % name)
-
-    # remove constant definition and replace
-    lines = (lines[:const_match.start()] +
-             re.sub(name_pattern, replacement, lines[const_match.end():]))
-
-    # advance position to where the constant defintion was
-    pos = const_match.start()
-
-
 HEADER_TEMPLATE = """\
 // Copyright 2011 Google Inc. All Rights Reserved.
 
@@ -354,7 +333,6 @@ def BuildFilterChain(macro_filename):
   filter_chain.extend([
     RemoveCommentsAndTrailingWhitespace,
     ExpandInlineMacros,
-    ExpandInlineConstants,
     Validate,
     jsmin.JavaScriptMinifier().JSMinify
   ])