NONE).Assert();
// Initialize trigonometric lookup tables and constants.
- const int constants_size =
- ARRAY_SIZE(fdlibm::TrigonometricConstants::constants);
+ const int constants_size = ARRAY_SIZE(fdlibm::MathConstants::constants);
const int table_num_bytes = constants_size * kDoubleSize;
v8::Local<v8::ArrayBuffer> trig_buffer = v8::ArrayBuffer::New(
reinterpret_cast<v8::Isolate*>(isolate),
- const_cast<double*>(fdlibm::TrigonometricConstants::constants),
- table_num_bytes);
+ const_cast<double*>(fdlibm::MathConstants::constants), table_num_bytes);
v8::Local<v8::Float64Array> trig_table =
v8::Float64Array::New(trig_buffer, 0, constants_size);
Runtime::DefineObjectProperty(
builtins,
- factory()->InternalizeOneByteString(STATIC_ASCII_VECTOR("kTrig")),
+ factory()->InternalizeOneByteString(STATIC_ASCII_VECTOR("kMath")),
Utils::OpenHandle(*trig_table), NONE).Assert();
}
}
}
-// 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) {
- 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 SetUpMath() {
"fround", MathFroundJS,
"clz32", MathClz32,
"cbrt", MathCbrt,
- "log1p", MathLog1p,
+ "log1p", MathLog1p, // implemented by third_party/fdlibm
"expm1", MathExpm1
));
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)));
+assertEquals(Infinity, 1/Math.log1p(0));
+assertEquals(-Infinity, 1/Math.log1p(-0));
+assertEquals(Infinity, Math.log1p(Infinity));
+assertEquals(-Infinity, Math.log1p(-1));
assertTrue(isNaN(Math.log1p(-2)));
assertTrue(isNaN(Math.log1p(-Infinity)));
-for (var x = 1E300; x > 1E-1; x *= 0.8) {
+for (var x = 1E300; x > 1E16; x *= 0.8) {
var expected = Math.log(x + 1);
- assertEqualsDelta(expected, Math.log1p(x), expected * 1E-14);
+ assertEqualsDelta(expected, Math.log1p(x), expected * 1E-16);
}
// Values close to 0:
for (var x = 1E-1; x > 1E-300; x *= 0.8) {
var expected = log1p(x);
- assertEqualsDelta(expected, Math.log1p(x), expected * 1E-14);
+ assertEqualsDelta(expected, Math.log1p(x), expected * 1E-16);
}
+
+// Issue 3481.
+assertEquals(6.9756137364252422e-03,
+ Math.log1p(8070450532247929/Math.pow(2,60)));
+
+// Tests related to the fdlibm implementation.
+// Test largest double value.
+assertEquals(709.782712893384, Math.log1p(1.7976931348623157e308));
+// Test small values.
+assertEquals(Math.pow(2, -55), Math.log1p(Math.pow(2, -55)));
+assertEquals(9.313225741817976e-10, Math.log1p(Math.pow(2, -30)));
+// Cover various code paths.
+// -.2929 < x < .41422, k = 0
+assertEquals(-0.2876820724517809, Math.log1p(-0.25));
+assertEquals(0.22314355131420976, Math.log1p(0.25));
+// 0.41422 < x < 9.007e15
+assertEquals(2.3978952727983707, Math.log1p(10));
+// x > 9.007e15
+assertEquals(36.841361487904734, Math.log1p(10e15));
+// Normalize u.
+assertEquals(37.08337388996168, Math.log1p(12738099905822720));
+// Normalize u/2.
+assertEquals(37.08336444902049, Math.log1p(12737979646738432));
+// |f| = 0, k != 0
+assertEquals(1.3862943611198906, Math.log1p(3));
+// |f| != 0, k != 0
+assertEquals(1.3862945995384413, Math.log1p(3 + Math.pow(2,-20)));
+// final if-clause: k = 0
+assertEquals(0.5596157879354227, Math.log1p(0.75));
+// final if-clause: k != 0
+assertEquals(0.8109302162163288, Math.log1p(1.25));
inline double scalbn(double x, int y) { return _scalb(x, y); }
#endif // _MSC_VER
-const double TrigonometricConstants::constants[] = {
+const double MathConstants::constants[] = {
6.36619772367581382433e-01, // invpio2 0
1.57079632673412561417e+00, // pio2_1 1
6.07710050650619224932e-11, // pio2_1t 2
2.59073051863633712884e-05, // T12 31
7.85398163397448278999e-01, // pio4 32
3.06161699786838301793e-17, // pio4lo 33
+ 6.93147180369123816490e-01, // ln2_hi 34
+ 1.90821492927058770002e-10, // ln2_lo 35
+ 1.80143985094819840000e+16, // 2^54 36
+ 6.666666666666666666e-01, // 2/3 37
+ 6.666666666666735130e-01, // LP1 38
+ 3.999999999940941908e-01, // 39
+ 2.857142874366239149e-01, // 40
+ 2.222219843214978396e-01, // 41
+ 1.818357216161805012e-01, // 42
+ 1.531383769920937332e-01, // 43
+ 1.479819860511658591e-01, // LP7 44
};
int rempio2(double x, double* y);
// Constants to be exposed to builtins via Float64Array.
-struct TrigonometricConstants {
- static const double constants[34];
+struct MathConstants {
+ static const double constants[45];
};
}
} // namespace v8::internal
// modified significantly by Google Inc.
// Copyright 2014 the V8 project authors. All rights reserved.
//
-// The following is a straightforward translation of fdlibm routines for
-// sin, cos, and tan, by Raymond Toy (rtoy@google.com).
+// The following is a straightforward translation of fdlibm routines
+// by Raymond Toy (rtoy@google.com).
-var kTrig; // Initialized to a Float64Array during genesis and is not writable.
+var kMath; // Initialized to a Float64Array during genesis and is not writable.
-const INVPIO2 = kTrig[0];
-const PIO2_1 = kTrig[1];
-const PIO2_1T = kTrig[2];
-const PIO2_2 = kTrig[3];
-const PIO2_2T = kTrig[4];
-const PIO2_3 = kTrig[5];
-const PIO2_3T = kTrig[6];
-const PIO4 = kTrig[32];
-const PIO4LO = kTrig[33];
+const INVPIO2 = kMath[0];
+const PIO2_1 = kMath[1];
+const PIO2_1T = kMath[2];
+const PIO2_2 = kMath[3];
+const PIO2_2T = kMath[4];
+const PIO2_3 = kMath[5];
+const PIO2_3T = kMath[6];
+const PIO4 = kMath[32];
+const PIO4LO = kMath[33];
// Compute k and r such that x - k*pi/2 = r where |r| < pi/4. For
// precision, r is returned as two values y0 and y1 such that r = y0 + y1
// sin(x) = X + (S1*X + (X *(r-Y/2)+Y))
//
macro KSIN(x)
-kTrig[7+x]
+kMath[7+x]
endmacro
macro RETURN_KERNELSIN(X, Y, SIGN)
// thus, reducing the rounding error in the subtraction.
//
macro KCOS(x)
-kTrig[13+x]
+kMath[13+x]
endmacro
macro RETURN_KERNELCOS(X, Y, SIGN)
}
endmacro
+
// kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
// Input x is assumed to be bounded by ~pi/4 in magnitude.
// Input y is the tail of x.
// and will cause incorrect results.
//
macro KTAN(x)
-kTrig[19+x]
+kMath[19+x]
endmacro
function KernelTan(x, y, returnTan) {
REMPIO2(x);
return KernelTan(y0, y1, (n & 1) ? -1 : 1);
}
+
+// ES6 draft 09-27-13, section 20.2.2.20.
+// Math.log1p
+//
+// Method :
+// 1. Argument Reduction: find k and f such that
+// 1+x = 2^k * (1+f),
+// where sqrt(2)/2 < 1+f < sqrt(2) .
+//
+// Note. If k=0, then f=x is exact. However, if k!=0, then f
+// may not be representable exactly. In that case, a correction
+// term is need. Let u=1+x rounded. Let c = (1+x)-u, then
+// log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
+// and add back the correction term c/u.
+// (Note: when x > 2**53, one can simply return log(x))
+//
+// 2. Approximation of log1p(f).
+// Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+// = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+// = 2s + s*R
+// We use a special Reme algorithm on [0,0.1716] to generate
+// a polynomial of degree 14 to approximate R The maximum error
+// of this polynomial approximation is bounded by 2**-58.45. In
+// other words,
+// 2 4 6 8 10 12 14
+// R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s
+// (the values of Lp1 to Lp7 are listed in the program)
+// and
+// | 2 14 | -58.45
+// | Lp1*s +...+Lp7*s - R(z) | <= 2
+// | |
+// Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+// In order to guarantee error in log below 1ulp, we compute log
+// by
+// log1p(f) = f - (hfsq - s*(hfsq+R)).
+//
+// 3. Finally, log1p(x) = k*ln2 + log1p(f).
+// = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
+// Here ln2 is split into two floating point number:
+// ln2_hi + ln2_lo,
+// where n*ln2_hi is always exact for |n| < 2000.
+//
+// Special cases:
+// log1p(x) is NaN with signal if x < -1 (including -INF) ;
+// log1p(+INF) is +INF; log1p(-1) is -INF with signal;
+// log1p(NaN) is that NaN with no signal.
+//
+// Accuracy:
+// according to an error analysis, the error is always less than
+// 1 ulp (unit in the last place).
+//
+// Constants:
+// The hexadecimal values are the intended ones for the following
+// constants. The decimal values may be used, provided that the
+// compiler will convert from decimal to binary accurately enough
+// to produce the hexadecimal values shown.
+//
+// Note: Assuming log() return accurate answer, the following
+// algorithm can be used to compute log1p(x) to within a few ULP:
+//
+// u = 1+x;
+// if (u==1.0) return x ; else
+// return log(u)*(x/(u-1.0));
+//
+// See HP-15C Advanced Functions Handbook, p.193.
+//
+const LN2_HI = kMath[34];
+const LN2_LO = kMath[35];
+const TWO54 = kMath[36];
+const TWO_THIRD = kMath[37];
+macro KLOGP1(x)
+(kMath[38+x])
+endmacro
+
+function MathLog1p(x) {
+ x = x * 1; // Convert to number.
+ var hx = %_DoubleHi(x);
+ var ax = hx & 0x7fffffff;
+ var k = 1;
+ var f = x;
+ var hu = 1;
+ var c = 0;
+ var u = x;
+
+ if (hx < 0x3fda827a) {
+ // x < 0.41422
+ if (ax >= 0x3ff00000) { // |x| >= 1
+ if (x === -1) {
+ return -INFINITY; // log1p(-1) = -inf
+ } else {
+ return NAN; // log1p(x<-1) = NaN
+ }
+ } else if (ax < 0x3c900000) {
+ // For |x| < 2^-54 we can return x.
+ return x;
+ } else if (ax < 0x3e200000) {
+ // For |x| < 2^-29 we can use a simple two-term Taylor series.
+ return x - x * x * 0.5;
+ }
+
+ if ((hx > 0) || (hx <= -0x402D413D)) { // (int) 0xbfd2bec3 = -0x402d413d
+ // -.2929 < x < 0.41422
+ k = 0;
+ }
+ }
+
+ // Handle Infinity and NAN
+ if (hx >= 0x7ff00000) return x;
+
+ if (k !== 0) {
+ if (hx < 0x43400000) {
+ // x < 2^53
+ u = 1 + x;
+ hu = %_DoubleHi(u);
+ k = (hu >> 20) - 1023;
+ c = (k > 0) ? 1 - (u - x) : x - (u - 1);
+ c = c / u;
+ } else {
+ hu = %_DoubleHi(u);
+ k = (hu >> 20) - 1023;
+ }
+ hu = hu & 0xfffff;
+ if (hu < 0x6a09e) {
+ u = %_ConstructDouble(hu | 0x3ff00000, %_DoubleLo(u)); // Normalize u.
+ } else {
+ ++k;
+ u = %_ConstructDouble(hu | 0x3fe00000, %_DoubleLo(u)); // Normalize u/2.
+ hu = (0x00100000 - hu) >> 2;
+ }
+ f = u - 1;
+ }
+
+ var hfsq = 0.5 * f * f;
+ if (hu === 0) {
+ // |f| < 2^-20;
+ if (f === 0) {
+ if (k === 0) {
+ return 0.0;
+ } else {
+ return k * LN2_HI + (c + k * LN2_LO);
+ }
+ }
+ var R = hfsq * (1 - TWO_THIRD * f);
+ if (k === 0) {
+ return f - R;
+ } else {
+ return k * LN2_HI - ((R - (k * LN2_LO + c)) - f);
+ }
+ }
+
+ var s = f / (2 + f);
+ var z = s * s;
+ var R = z * (KLOGP1(0) + z * (KLOGP1(1) + z *
+ (KLOGP1(2) + z * (KLOGP1(3) + z *
+ (KLOGP1(4) + z * (KLOGP1(5) + z * KLOGP1(6)))))));
+ if (k === 0) {
+ return f - (hfsq - s * (hfsq + R));
+ } else {
+ return k * LN2_HI - ((hfsq - (s * (hfsq + R) + (k * LN2_LO + c))) - f);
+ }
+}
EXPECTED_FUZZABLE_COUNT = 331
EXPECTED_CCTEST_COUNT = 7
EXPECTED_UNKNOWN_COUNT = 16
-EXPECTED_BUILTINS_COUNT = 809
+EXPECTED_BUILTINS_COUNT = 808
# Don't call these at all.
projects / platform / upstream / v8.git / commitdiff