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11210 libm should be cstyle(1ONBLD) clean
@@ -16,22 +16,24 @@
* fields enclosed by brackets "[]" replaced with your own identifying
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
+
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
+
/*
* Copyright 2005 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#include "libm.h" /* __k_clog_r */
#include "complex_wrapper.h"
-/* INDENT OFF */
+
/*
* double __k_clog_r(double x, double y, double *e);
*
* Compute real part of complex natural logarithm of x+iy in extra precision
*
@@ -68,163 +70,161 @@
* r = 2/((zh+zt)+2(1+zk))
* s2 = r*(zh+zt)
* s2h = s2 rounded to float; v = 0.5*s2h;
* s2t = r*((((zh-s2h*(1+zk))-v*zh)+zt)-v*zt)
*/
-/* INDENT ON */
-static const double
-zero = 0.0,
-half = 0.5,
-two = 2.0,
-two120 = 1.32922799578491587290e+36, /* 2^120 */
-ln2_h = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
-ln2_t = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
-P1 = .083333333333333351554108717377986202224765262191125,
-P2 = .01249999999819227552330700574633767185896464873834375,
-P3 = .0022321938458645656605471559987512516234702284287265625;
-
-/*
-* T[2k, 2k+1] = log(1+k*2^-7) for k = 0, ..., 2^7 - 1,
-* with T[2k] * 2^40 is an int
-*/
+static const double zero = 0.0,
+ half = 0.5,
+ two = 2.0,
+ two120 = 1.32922799578491587290e+36, /* 2^120 */
+ ln2_h = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
+ ln2_t = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
+ P1 = .083333333333333351554108717377986202224765262191125,
+ P2 = .01249999999819227552330700574633767185896464873834375,
+ P3 = .0022321938458645656605471559987512516234702284287265625;
+/*
+ * T[2k, 2k+1] = log(1+k*2^-7) for k = 0, ..., 2^7 - 1,
+ * with T[2k] * 2^40 is an int
+ */
static const double TBL_log1k[] = {
-0.00000000000000000000e+00, 0.00000000000000000000e+00,
-7.78214044203195953742e-03, 2.29894100462035112076e-14,
-1.55041865355087793432e-02, 4.56474807636434698847e-13,
-2.31670592811497044750e-02, 3.84673753843363762372e-13,
-3.07716586667083902285e-02, 4.52981425779092882775e-14,
-3.83188643018002039753e-02, 3.36395218465265063278e-13,
-4.58095360309016541578e-02, 3.92549008891706208826e-13,
-5.32445145181554835290e-02, 6.56799336898521766515e-13,
-6.06246218158048577607e-02, 6.29984819938331143924e-13,
-6.79506619080711971037e-02, 4.36552290856295281946e-13,
-7.52234212368421140127e-02, 7.45411685916941618656e-13,
-8.24436692109884461388e-02, 8.61451293608781447223e-14,
-8.96121586893059429713e-02, 3.81189648692113819551e-13,
-9.67296264579999842681e-02, 5.51128027471986918274e-13,
-1.03796793680885457434e-01, 7.58107392301637643358e-13,
-1.10814366339582193177e-01, 7.07921017612766061755e-13,
-1.17783035655520507134e-01, 8.62947404296943765415e-13,
-1.24703478500123310369e-01, 8.33925494898414856118e-13,
-1.31576357788617315236e-01, 1.01957352237084734958e-13,
-1.38402322858382831328e-01, 7.36304357708705134617e-13,
-1.45182009843665582594e-01, 8.32314688404647202319e-13,
-1.51916042025732167531e-01, 1.09807540998552379211e-13,
-1.58605030175749561749e-01, 8.89022343972466269900e-13,
-1.65249572894936136436e-01, 3.71026439894104998399e-13,
-1.71850256926518341061e-01, 1.40881279371111350341e-13,
-1.78407657472234859597e-01, 5.83437522462346671423e-13,
-1.84922338493379356805e-01, 6.32635858668445232946e-13,
-1.91394852999110298697e-01, 5.19155912393432989209e-13,
-1.97825743329303804785e-01, 6.16075577558872326221e-13,
-2.04215541428311553318e-01, 3.79338185766902218086e-13,
-2.10564769106895255391e-01, 4.54382278998146218219e-13,
-2.16873938300523150247e-01, 9.12093724991498410553e-14,
-2.23143551314024080057e-01, 1.85675709597960106615e-13,
-2.29374101064422575291e-01, 4.23254700234549300166e-13,
-2.35566071311950508971e-01, 8.16400106820959292914e-13,
-2.41719936886511277407e-01, 6.33890736899755317832e-13,
-2.47836163904139539227e-01, 4.41717553713155466566e-13,
-2.53915209980732470285e-01, 2.30973852175869394892e-13,
-2.59957524436686071567e-01, 2.39995404842117353465e-13,
-2.65963548496984003577e-01, 1.53937761744554075681e-13,
-2.71933715483100968413e-01, 5.40790418614551497411e-13,
-2.77868451003087102436e-01, 3.69203750820800887027e-13,
-2.83768173129828937817e-01, 8.15660529536291275782e-13,
-2.89633292582948342897e-01, 9.43339818951269030846e-14,
-2.95464212893421063200e-01, 4.14813187042585679830e-13,
-3.01261330577290209476e-01, 8.71571536970835103739e-13,
-3.07025035294827830512e-01, 8.40315630479242455758e-14,
-3.12755710003330023028e-01, 5.66865358290073900922e-13,
-3.18453731118097493891e-01, 4.37121919574291444278e-13,
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-3.51976423156884266064e-01, 2.93918591876480007730e-13,
-3.57455888921322184615e-01, 4.81589611172320539489e-13,
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+ 0.00000000000000000000e+00, 0.00000000000000000000e+00,
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+ 5.64070138284478161950e-01, 3.24804121719935740729e-13,
+ 5.68504735351780254859e-01, 8.88457219261483317716e-13,
+ 5.72919753561109246220e-01, 6.76262872317054154667e-13,
+ 5.77315365034337446559e-01, 4.86157758891509033842e-13,
+ 5.81691739634152327199e-01, 4.70155322075549811780e-13,
+ 5.86049045003164792433e-01, 4.13416470738355643357e-13,
+ 5.90387446602107957006e-01, 6.84176364159146659095e-14,
+ 5.94707107746216934174e-01, 4.75855340044306376333e-13,
+ 5.99008189645246602595e-01, 8.36796786747576938145e-13,
+ 6.03290851438032404985e-01, 5.18573553063418286042e-14,
+ 6.07555250224322662689e-01, 2.19132812293400917731e-13,
+ 6.11801541105705837253e-01, 2.87066276408616768331e-13,
+ 6.16029877214714360889e-01, 7.99658758518543977451e-13,
+ 6.20240409751204424538e-01, 6.53104313776336534177e-13,
+ 6.24433288011459808331e-01, 4.33692711555820529733e-13,
+ 6.28608659421843185555e-01, 5.30952189118357790115e-13,
+ 6.32766669570628437214e-01, 4.09392332186786656392e-13,
+ 6.36907462236194987781e-01, 8.74243839148582888557e-13,
+ 6.41031179420679109171e-01, 2.52181884568428814231e-13,
+ 6.45137961372711288277e-01, 8.73413388168702670246e-13,
+ 6.49227946624705509748e-01, 4.04309142530119209805e-13,
+ 6.53301272011958644725e-01, 7.86994033233553225797e-13,
+ 6.57358072708120744210e-01, 2.39285932153437645135e-13,
+ 6.61398482245203922503e-01, 1.61085757539324585156e-13,
+ 6.65422632544505177066e-01, 5.85271884362515112697e-13,
+ 6.69430653942072240170e-01, 5.57027128793880294600e-13,
+ 6.73422675211440946441e-01, 7.25773856816637653180e-13,
+ 6.77398823590920073912e-01, 8.86066898134949155668e-13,
+ 6.81359224807238206267e-01, 6.64862680714687006264e-13,
+ 6.85304003098281100392e-01, 6.38316151706465171657e-13,
+ 6.89233281238557538018e-01, 2.51442307283760746611e-13,
};
/*
* Compute N*log2 + log(1+zk+zh+zt) in extra precision
*/
-static double k_log_NKz(int N, int K, double zh, double *zt)
+static double
+k_log_NKz(int N, int K, double zh, double *zt)
{
double y, r, w, s2, s2h, s2t, t, zk, v, P;
((int *)&zk)[HIWORD] = 0x3ff00000 + (K << 13);
((int *)&zk)[LOWORD] = 0;
@@ -235,11 +235,11 @@
v = half * s2h;
w = s2 * s2;
s2t = r * ((((zh - s2h * zk) - v * zh) + (*zt)) - v * (*zt));
P = s2t + (w * s2) * ((P1 + w * P2) + (w * w) * P3);
P += N * ln2_t + TBL_log1k[K + K + 1];
- t = N*ln2_h + TBL_log1k[K+K];
+ t = N * ln2_h + TBL_log1k[K + K];
y = t + (P + s2h);
P -= ((y - t) - s2h);
*zt = P;
return (y);
}
@@ -253,65 +253,81 @@
ix = (((int *)&x)[HIWORD]) & ~0x80000000;
lx = ((unsigned *)&x)[LOWORD];
iy = (((int *)&y)[HIWORD]) & ~0x80000000;
ly = ((unsigned *)&y)[LOWORD];
- y = fabs(y); x = fabs(x);
+ y = fabs(y);
+ x = fabs(x);
+
if (ix < iy || (ix == iy && lx < ly)) { /* force x >= y */
- tk = x; x = y; y = tk;
- n = ix, ix = iy; iy = n;
- n = lx, lx = ly; ly = n;
+ tk = x;
+ x = y;
+ y = tk;
+ n = ix, ix = iy;
+ iy = n;
+ n = lx, lx = ly;
+ ly = n;
}
+
*er = zero;
- nx = ix >> 20; ny = iy >> 20;
+ nx = ix >> 20;
+ ny = iy >> 20;
+
if (nx >= 0x7ff) { /* x or y is Inf or NaN */
if (ISINF(ix, lx))
return (x);
else if (ISINF(iy, ly))
return (y);
else
- return (x+y);
+ return (x + y);
}
+
/*
* for tiny y (double y < 2^-35, extended y < 2^-46, quad y < 2^-70):
* log(sqrt(1+y^2)) = (y^2)/2 - (y^4)/8 + ... ~= (y^2)/2
*/
if ((((ix - 0x3ff00000) | lx) == 0) && ny < (0x3ff - 35)) {
t2 = y * y;
+
if (ny >= 565) { /* compute er = tail of t2 */
((int *)&wh)[HIWORD] = iy;
((unsigned *)&wh)[LOWORD] = ly & 0xf8000000;
*er = half * ((y - wh) * (y + wh) - (t2 - wh * wh));
}
+
return (half * t2);
}
+
/*
* x or y is subnormal or zero
*/
if (nx == 0) {
- if ((ix | lx) == 0)
+ if ((ix | lx) == 0) {
return (-1.0 / x);
- else {
+ } else {
x *= two120;
y *= two120;
ix = ((int *)&x)[HIWORD];
lx = ((unsigned *)&x)[LOWORD];
iy = ((int *)&y)[HIWORD];
ly = ((unsigned *)&y)[LOWORD];
nx = (ix >> 20) - 120;
ny = (iy >> 20) - 120;
+
/* guard subnormal flush to 0 */
if ((ix | lx) == 0)
return (-1.0 / x);
}
} else if (ny == 0) { /* y subnormal, scale it */
y *= two120;
iy = ((int *)&y)[HIWORD];
ly = ((unsigned *)&y)[LOWORD];
ny = (iy >> 20) - 120;
}
+
n = nx - ny;
+
/*
* return log(x) when y is zero or x >> y so that
* log(x) ~ log(sqrt(x*x+y*y)) to 27 extra bits
* (n > 62 for double, 78 for i386 extended, 122 for quad)
*/
@@ -325,88 +341,119 @@
zh = (double)((float)z);
i >>= 13;
k = i & 0x7f; /* index of zk */
n = nx - 0x3ff;
*er = z - zh;
+
if (i >> 17) { /* if zk = 2.0, adjust scaling */
n += 1;
- zh *= 0.5; *er *= 0.5;
+ zh *= 0.5;
+ *er *= 0.5;
}
+
w = k_log_NKz(n, k, zh, er);
} else {
/*
* compute z = x*x + y*y
*/
ix = (ix & 0xfffff) | 0x3ff00000;
iy = (iy & 0xfffff) | (0x3ff00000 - (n << 20));
- ((int *)&x)[HIWORD] = ix; ((int *)&y)[HIWORD] = iy;
- t1 = x * x; t2 = y * y;
+ ((int *)&x)[HIWORD] = ix;
+ ((int *)&y)[HIWORD] = iy;
+ t1 = x * x;
+ t2 = y * y;
j = ((lx >> 26) + 1) >> 1;
((int *)&wh)[HIWORD] = ix + (j >> 5);
((unsigned *)&wh)[LOWORD] = (j << 27);
- z = t1+t2;
+ z = t1 + t2;
+
/*
* higher precision simulation x*x = t1 + t3, y*y = t2 + t4
*/
tk = wh - x;
t3 = tk * tk - (two * wh * tk - (wh * wh - t1));
j = ((ly >> 26) + 1) >> 1;
((int *)&wh)[HIWORD] = iy + (j >> 5);
((unsigned *)&wh)[LOWORD] = (j << 27);
tk = wh - y;
t4 = tk * tk - (two * wh * tk - (wh * wh - t2));
+
/*
* find zk matches z to 7.5 bits
*/
nx -= 0x3ff;
iz = ((int *)&z)[HIWORD] + 0x1000;
k = (iz >> 13) & 0x7f;
nz = (iz >> 20) - 0x3ff;
((int *)&zk)[HIWORD] = iz & 0xffffe000;
((int *)&zk)[LOWORD] = 0;
+
/*
* order t1,t2,t3,t4 according to their size
*/
if (t2 >= fabs(t3)) {
if (fabs(t3) < fabs(t4)) {
- wh = t3; t3 = t4; t4 = wh;
+ wh = t3;
+ t3 = t4;
+ t4 = wh;
}
} else {
- wh = t2; t2 = t3; t3 = wh;
+ wh = t2;
+ t2 = t3;
+ t3 = wh;
}
+
/*
* higher precision simulation: x * x + y * y = t1 + t2 + t3 + t4
* = zk (7 bits) + zh (24 bits) + *er (tail) and call k_log_NKz
*/
tk = t1 - zk;
zh = ((tk + t2) + t3) + t4;
((int *)&zh)[LOWORD] &= 0xe0000000;
w = fabs(zh);
- if (w >= fabs(t2))
+
+ if (w >= fabs(t2)) {
*er = (((tk - zh) + t2) + t3) + t4;
- else {
+ } else {
if (n == 0) {
wh = half * zk;
wh = (t1 - wh) - (wh - t2);
- } else
+ } else {
wh = tk + t2;
- if (w >= fabs(t3))
+ }
+
+ if (w >= fabs(t3)) {
*er = ((wh - zh) + t3) + t4;
- else {
+ } else {
z = t3;
t3 += t4;
t4 -= t3 - z;
+
if (w >= fabs(t3))
*er = ((wh - zh) + t3) + t4;
else
*er = ((wh + t3) - zh) + t4;
}
}
- if (nz == 3) {zh *= 0.125; *er *= 0.125; }
- if (nz == 2) {zh *= 0.25; *er *= 0.25; }
- if (nz == 1) {zh *= half; *er *= half; }
+
+ if (nz == 3) {
+ zh *= 0.125;
+ *er *= 0.125;
+ }
+
+ if (nz == 2) {
+ zh *= 0.25;
+ *er *= 0.25;
+ }
+
+ if (nz == 1) {
+ zh *= half;
+ *er *= half;
+ }
+
nz += nx + nx;
w = half * k_log_NKz(nz, k, zh, er);
*er *= half;
}
+
return (w);
}