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Diffstat (limited to 'deps/v8/src/base/ieee754.cc')
-rw-r--r--deps/v8/src/base/ieee754.cc335
1 files changed, 331 insertions, 4 deletions
diff --git a/deps/v8/src/base/ieee754.cc b/deps/v8/src/base/ieee754.cc
index d9846b7254..4fcb4df001 100644
--- a/deps/v8/src/base/ieee754.cc
+++ b/deps/v8/src/base/ieee754.cc
@@ -309,7 +309,7 @@ int32_t __ieee754_rem_pio2(double x, double *y) {
GET_LOW_WORD(low, x);
SET_LOW_WORD(z, low);
e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */
- SET_HIGH_WORD(z, ix - static_cast<int32_t>(e0 << 20));
+ SET_HIGH_WORD(z, ix - static_cast<int32_t>(static_cast<uint32_t>(e0) << 20));
for (i = 0; i < 2; i++) {
tx[i] = static_cast<double>(static_cast<int32_t>(z));
z = (z - tx[i]) * two24;
@@ -1569,9 +1569,12 @@ double exp(double x) {
/* x is now in primary range */
t = x * x;
if (k >= -1021) {
- INSERT_WORDS(twopk, 0x3FF00000 + (k << 20), 0);
+ INSERT_WORDS(
+ twopk,
+ 0x3FF00000 + static_cast<int32_t>(static_cast<uint32_t>(k) << 20), 0);
} else {
- INSERT_WORDS(twopk, 0x3FF00000 + ((k + 1000) << 20), 0);
+ INSERT_WORDS(twopk, 0x3FF00000 + (static_cast<uint32_t>(k + 1000) << 20),
+ 0);
}
c = x - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
if (k == 0) {
@@ -2341,7 +2344,10 @@ double expm1(double x) {
if (k == 0) {
return x - (x * e - hxs); /* c is 0 */
} else {
- INSERT_WORDS(twopk, 0x3FF00000 + (k << 20), 0); /* 2^k */
+ INSERT_WORDS(
+ twopk,
+ 0x3FF00000 + static_cast<int32_t>(static_cast<uint32_t>(k) << 20),
+ 0); /* 2^k */
e = (x * (e - c) - c);
e -= hxs;
if (k == -1) return 0.5 * (x - e) - 0.5;
@@ -2642,6 +2648,317 @@ 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.
+ */
+
+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);
+ }
+ }
+ }
+
+ 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) */
+ }
+ }
+ 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;
+}
+
+/*
* ES6 draft 09-27-13, section 20.2.2.30.
* Math.sinh
* Method :
@@ -2752,6 +3069,16 @@ double tanh(double x) {
return (jx >= 0) ? z : -z;
}
+#undef EXTRACT_WORDS
+#undef EXTRACT_WORD64
+#undef GET_HIGH_WORD
+#undef GET_LOW_WORD
+#undef INSERT_WORDS
+#undef INSERT_WORD64
+#undef SET_HIGH_WORD
+#undef SET_LOW_WORD
+#undef STRICT_ASSIGN
+
} // namespace ieee754
} // namespace base
} // namespace v8
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