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Commit b12ba06e authored by Gus Caplan's avatar Gus Caplan Committed by Commit Bot
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[builtins] stop using imprecise fdlibm pow 

This CL reinstates the old pow implementation which calls out to the
system implementation of pow.

Bug: v8:9622
Change-Id: I3df997888ced3fb8b5bd4b810098e967649aaa55
Reviewed-on: https://chromium-review.googlesource.com/c/v8/v8/+/1774898Reviewed-by: 's avatarHannes Payer <hpayer@chromium.org>
Reviewed-by: 's avatarGeorg Neis <neis@chromium.org>
Commit-Queue: Georg Neis <neis@chromium.org>
Cr-Commit-Position: refs/heads/master@{#66303}
parent b0c4f2b0
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Showing with 53 additions and 304 deletions
src/base/ieee754.cc
View file @ b12ba06e
......@@ -2587,314 +2587,38 @@ double cosh(double x) {
}
/*
* ES2019 Draft 2019-01-02 12.6.4
* Math.pow & Exponentiation Operator
*
* Return X raised to the Yth power
*
* Method:
* Let x = 2 * (1+f)
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
* where w1 has 53-24 = 29 bit trailing zeros.
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
* arithmetic, where |y'|<=0.5.
* 3. Return x**y = 2**n*exp(y'*log2)
*
* Special cases:
* 1. (anything) ** 0 is 1
* 2. (anything) ** 1 is itself
* 3. (anything) ** NAN is NAN
* 4. NAN ** (anything except 0) is NAN
* 5. +-(|x| > 1) ** +INF is +INF
* 6. +-(|x| > 1) ** -INF is +0
* 7. +-(|x| < 1) ** +INF is +0
* 8. +-(|x| < 1) ** -INF is +INF
* 9. +-1 ** +-INF is NAN
* 10. +0 ** (+anything except 0, NAN) is +0
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
* 12. +0 ** (-anything except 0, NAN) is +INF
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
* 15. +INF ** (+anything except 0,NAN) is +INF
* 16. +INF ** (-anything except 0,NAN) is +0
* 17. -INF ** (anything) = -0 ** (-anything)
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
*
* Accuracy:
* pow(x,y) returns x**y nearly rounded. In particular,
* pow(integer, integer) always returns the correct integer provided it is
* representable.
*
* 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.
* ES2020 draft 08-18-2019, section 12.6.4
* Math.pow, **
*/
double pow(double x, double y) {
static const double
bp[] = {1.0, 1.5},
dp_h[] = {0.0, 5.84962487220764160156e-01}, // 0x3FE2B803, 0x40000000
dp_l[] = {0.0, 1.35003920212974897128e-08}, // 0x3E4CFDEB, 0x43CFD006
zero = 0.0, one = 1.0, two = 2.0,
two53 = 9007199254740992.0, // 0x43400000, 0x00000000
huge = 1.0e300, tiny = 1.0e-300,
// poly coefs for (3/2)*(log(x)-2s-2/3*s**3
L1 = 5.99999999999994648725e-01, // 0x3FE33333, 0x33333303
L2 = 4.28571428578550184252e-01, // 0x3FDB6DB6, 0xDB6FABFF
L3 = 3.33333329818377432918e-01, // 0x3FD55555, 0x518F264D
L4 = 2.72728123808534006489e-01, // 0x3FD17460, 0xA91D4101
L5 = 2.30660745775561754067e-01, // 0x3FCD864A, 0x93C9DB65
L6 = 2.06975017800338417784e-01, // 0x3FCA7E28, 0x4A454EEF
P1 = 1.66666666666666019037e-01, // 0x3FC55555, 0x5555553E
P2 = -2.77777777770155933842e-03, // 0xBF66C16C, 0x16BEBD93
P3 = 6.61375632143793436117e-05, // 0x3F11566A, 0xAF25DE2C
P4 = -1.65339022054652515390e-06, // 0xBEBBBD41, 0xC5D26BF1
P5 = 4.13813679705723846039e-08, // 0x3E663769, 0x72BEA4D0
lg2 = 6.93147180559945286227e-01, // 0x3FE62E42, 0xFEFA39EF
lg2_h = 6.93147182464599609375e-01, // 0x3FE62E43, 0x00000000
lg2_l = -1.90465429995776804525e-09, // 0xBE205C61, 0x0CA86C39
ovt = 8.0085662595372944372e-0017, // -(1024-log2(ovfl+.5ulp))
cp = 9.61796693925975554329e-01, // 0x3FEEC709, 0xDC3A03FD =2/(3ln2)
cp_h = 9.61796700954437255859e-01, // 0x3FEEC709, 0xE0000000 =(float)cp
cp_l = -7.02846165095275826516e-09, // 0xBE3E2FE0, 0x145B01F5 =tail cp_h
ivln2 = 1.44269504088896338700e+00, // 0x3FF71547, 0x652B82FE =1/ln2
ivln2_h =
1.44269502162933349609e+00, // 0x3FF71547, 0x60000000 =24b 1/ln2
ivln2_l =
1.92596299112661746887e-08; // 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail
double z, ax, z_h, z_l, p_h, p_l;
double y1, t1, t2, r, s, t, u, v, w;
int i, j, k, yisint, n;
int hx, hy, ix, iy;
unsigned lx, ly;
EXTRACT_WORDS(hx, lx, x);
EXTRACT_WORDS(hy, ly, y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
/* y==zero: x**0 = 1 */
if ((iy | ly) == 0) return one;
/* +-NaN return x+y */
if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) || iy > 0x7ff00000 ||
((iy == 0x7ff00000) && (ly != 0))) {
return x + y;
}
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if (hx < 0) {
if (iy >= 0x43400000) {
yisint = 2; /* even integer y */
} else if (iy >= 0x3ff00000) {
k = (iy >> 20) - 0x3ff; /* exponent */
if (k > 20) {
j = ly >> (52 - k);
if ((j << (52 - k)) == static_cast<int>(ly)) yisint = 2 - (j & 1);
} else if (ly == 0) {
j = iy >> (20 - k);
if ((j << (20 - k)) == iy) yisint = 2 - (j & 1);
}
}
}
/* special value of y */
if (ly == 0) {
if (iy == 0x7ff00000) { /* y is +-inf */
if (((ix - 0x3ff00000) | lx) == 0) {
return y - y; /* inf**+-1 is NaN */
} else if (ix >= 0x3ff00000) { /* (|x|>1)**+-inf = inf,0 */
return (hy >= 0) ? y : zero;
} else { /* (|x|<1)**-,+inf = inf,0 */
return (hy < 0) ? -y : zero;
}
}
if (iy == 0x3ff00000) { /* y is +-1 */
if (hy < 0) {
return base::Divide(one, x);
} else {
return x;
}
}
if (hy == 0x40000000) return x * x; /* y is 2 */
if (hy == 0x3fe00000) { /* y is 0.5 */
if (hx >= 0) { /* x >= +0 */
return sqrt(x);
if (y == 0.0) {
return 1.0;
}
if (std::isnan(y) || ((x == 1 || x == -1) && std::isinf(y))) {
return std::numeric_limits<double>::quiet_NaN();
}
#if (defined(__MINGW64_VERSION_MAJOR) && \
(!defined(__MINGW64_VERSION_RC) || __MINGW64_VERSION_RC < 1)) || \
defined(V8_OS_AIX)
// MinGW64 and AIX have a custom implementation for pow. This handles certain
// special cases that are different.
if ((x == 0.0 || std::isinf(x)) && y != 0.0 && std::isfinite(y)) {
double f;
double result = ((x == 0.0) ^ (y > 0)) ? V8_INFINITY : 0;
// retain sign if odd integer exponent
return ((std::modf(y, &f) == 0.0) && (static_cast<int64_t>(y) & 1))
? copysign(result, x)
: result;
}
ax = fabs(x);
/* special value of x */
if (lx == 0) {
if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
z = ax; /*x is +-0,+-inf,+-1*/
if (hy < 0) z = base::Divide(one, z); /* z = (1/|x|) */
if (hx < 0) {
if (((ix - 0x3ff00000) | yisint) == 0) {
/* (-1)**non-int is NaN */
z = std::numeric_limits<double>::signaling_NaN();
} else if (yisint == 1) {
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
if (x == 2.0) {
int y_int = static_cast<int>(y);
if (y == y_int) {
return std::ldexp(1.0, y_int);
}
return z;
}
}
n = (hx >> 31) + 1;
/* (x<0)**(non-int) is NaN */
if ((n | yisint) == 0) {
return std::numeric_limits<double>::signaling_NaN();
}
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if ((n | (yisint - 1)) == 0) s = -one; /* (-ve)**(odd int) */
/* |y| is huge */
if (iy > 0x41e00000) { /* if |y| > 2**31 */
if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
if (ix <= 0x3fefffff) return (hy < 0) ? huge * huge : tiny * tiny;
if (ix >= 0x3ff00000) return (hy > 0) ? huge * huge : tiny * tiny;
}
/* over/underflow if x is not close to one */
if (ix < 0x3fefffff) return (hy < 0) ? s * huge * huge : s * tiny * tiny;
if (ix > 0x3ff00000) return (hy > 0) ? s * huge * huge : s * tiny * tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = ax - one; /* t has 20 trailing zeros */
w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
v = t * ivln2_l - w * ivln2;
t1 = u + v;
SET_LOW_WORD(t1, 0);
t2 = v - (t1 - u);
} else {
double ss, s2, s_h, s_l, t_h, t_l;
n = 0;
/* take care subnormal number */
if (ix < 0x00100000) {
ax *= two53;
n -= 53;
GET_HIGH_WORD(ix, ax);
}
n += ((ix) >> 20) - 0x3ff;
j = ix & 0x000fffff;
/* determine interval */
ix = j | 0x3ff00000; /* normalize ix */
if (j <= 0x3988E) {
k = 0; /* |x|<sqrt(3/2) */
} else if (j < 0xBB67A) {
k = 1; /* |x|<sqrt(3) */
} else {
k = 0;
n += 1;
ix -= 0x00100000;
}
SET_HIGH_WORD(ax, ix);
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = base::Divide(one, ax + bp[k]);
ss = u * v;
s_h = ss;
SET_LOW_WORD(s_h, 0);
/* t_h=ax+bp[k] High */
t_h = zero;
SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
t_l = ax - (t_h - bp[k]);
s_l = v * ((u - s_h * t_h) - s_h * t_l);
/* compute log(ax) */
s2 = ss * ss;
r = s2 * s2 *
(L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
r += s_l * (s_h + ss);
s2 = s_h * s_h;
t_h = 3.0 + s2 + r;
SET_LOW_WORD(t_h, 0);
t_l = r - ((t_h - 3.0) - s2);
/* u+v = ss*(1+...) */
u = s_h * t_h;
v = s_l * t_h + t_l * ss;
/* 2/(3log2)*(ss+...) */
p_h = u + v;
SET_LOW_WORD(p_h, 0);
p_l = v - (p_h - u);
z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = cp_l * p_h + p_l * cp + dp_l[k];
/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = static_cast<double>(n);
t1 = (((z_h + z_l) + dp_h[k]) + t);
SET_LOW_WORD(t1, 0);
t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
}
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
y1 = y;
SET_LOW_WORD(y1, 0);
p_l = (y - y1) * t1 + y * t2;
p_h = y1 * t1;
z = p_l + p_h;
EXTRACT_WORDS(j, i, z);
if (j >= 0x40900000) { /* z >= 1024 */
if (((j - 0x40900000) | i) != 0) { /* if z > 1024 */
return s * huge * huge; /* overflow */
} else {
if (p_l + ovt > z - p_h) return s * huge * huge; /* overflow */
}
} else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
if (((j - 0xc090cc00) | i) != 0) { /* z < -1075 */
return s * tiny * tiny; /* underflow */
} else {
if (p_l <= z - p_h) return s * tiny * tiny; /* underflow */
}
}
/*
* compute 2**(p_h+p_l)
*/
i = j & 0x7fffffff;
k = (i >> 20) - 0x3ff;
n = 0;
if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j + (0x00100000 >> (k + 1));
k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
t = zero;
SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
if (j < 0) n = -n;
p_h -= t;
}
t = p_l + p_h;
SET_LOW_WORD(t, 0);
u = t * lg2_h;
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
z = u + v;
w = v - (z - u);
t = z * z;
t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
r = base::Divide(z * t1, (t1 - two) - (w + z * w));
z = one - (r - z);
GET_HIGH_WORD(j, z);
j += static_cast<int>(static_cast<uint32_t>(n) << 20);
if ((j >> 20) <= 0) {
z = scalbn(z, n); /* subnormal output */
} else {
int tmp;
GET_HIGH_WORD(tmp, z);
SET_HIGH_WORD(z, tmp + static_cast<int>(static_cast<uint32_t>(n) << 20));
}
return s * z;
#endif
return std::pow(x, y);
}
/*
......
test/mjsunit/regress/regress-9622.js 0 → 100644
View file @ b12ba06e
// Copyright 2019 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.
'use strict';
assertEquals(0.6840442338072671 ** 2.4, 0.4019777798321958);
const constants = {
'0': 1,
'-1': 0.1,
'-2': 0.01,
'-3': 0.001,
'-4': 0.0001,
'-5': 0.00001,
'-6': 0.000001,
'-7': 0.0000001,
'-8': 0.00000001,
'-9': 0.000000001,
};
for (let i = 0; i > -10; i -= 1) {
assertEquals(10 ** i, constants[i]);
assertEquals(10 ** i, 1 / (10 ** -i));
}
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