Implement Math.log1p using port from fdlibm.

Port contributed by Raymond Toy <rtoy@google.com>.

R=rtoy@chromium.org
LOG=N
BUG=v8:3481

Review URL: https://codereview.chromium.org/457643002

git-svn-id: https://v8.googlecode.com/svn/branches/bleeding_edge@23082 ce2b1a6d-e550-0410-aec6-3dcde31c8c00
This commit is contained in:
yangguo@chromium.org 2014-08-12 13:36:33 +00:00
parent 44247036a7
commit 0f81d7698a
7 changed files with 234 additions and 52 deletions

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@ -2655,19 +2655,17 @@ Genesis::Genesis(Isolate* isolate,
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();
}

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@ -347,26 +347,6 @@ 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! + ...
// == 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() {
@ -428,7 +408,7 @@ function SetUpMath() {
"fround", MathFroundJS,
"clz32", MathClz32,
"cbrt", MathCbrt,
"log1p", MathLog1p,
"log1p", MathLog1p, // implemented by third_party/fdlibm
"expm1", MathExpm1
));

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@ -6,16 +6,16 @@ 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)));
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:
@ -35,5 +35,36 @@ function log1p(x) {
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));

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@ -26,7 +26,7 @@ namespace fdlibm {
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
@ -61,6 +61,17 @@ const double TrigonometricConstants::constants[] = {
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
};

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@ -22,8 +22,8 @@ namespace fdlibm {
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

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@ -13,21 +13,21 @@
// 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
@ -133,7 +133,7 @@ endmacro
// 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)
@ -177,7 +177,7 @@ endmacro
// thus, reducing the rounding error in the subtraction.
//
macro KCOS(x)
kTrig[13+x]
kMath[13+x]
endmacro
macro RETURN_KERNELCOS(X, Y, SIGN)
@ -199,6 +199,7 @@ 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.
@ -235,7 +236,7 @@ endmacro
// and will cause incorrect results.
//
macro KTAN(x)
kTrig[19+x]
kMath[19+x]
endmacro
function KernelTan(x, y, returnTan) {
@ -354,3 +355,164 @@ function MathTan(x) {
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);
}
}

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@ -51,7 +51,7 @@ EXPECTED_FUNCTION_COUNT = 428
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.