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11210 libm should be cstyle(1ONBLD) clean
@@ -16,23 +16,25 @@
* 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_rl */
#include "complex_wrapper.h"
#include "longdouble.h"
-/* INDENT OFF */
+
/*
* long double __k_clog_rl(long double x, long double y, long double *e);
*
* Compute real part of complex natural logarithm of x+iy in extra precision
*
@@ -72,297 +74,296 @@
* r = 2/((zh+zt)+2(1+zk))
* s2 = r*(zh+zt)
* s2h = s2 rounded to double; v = 0.5*s2h;
* s2t = r*((((zh-s2h*(1+zk))-v*zh)+zt)-v*zt)
*/
-/* INDENT ON */
-static const long double
-zero = 0.0L,
-half = 0.5L,
-two = 2.0L,
-two240 = 1.7668470647783843295832975007429185158274839e+72L, /* 2^240 */
+static const long double zero = 0.0L,
+ half = 0.5L,
+ two = 2.0L,
+ two240 = 1.7668470647783843295832975007429185158274839e+72L; /* 2^240 */
/* first 48 bits of ln2 */
-ln2_h = 0.693147180559943620892227045260369777679443359375L,
-ln2_t = 1.68852500507619780679039605677498525525412068e-15L,
-P1 = .083333333333333333333333333333333333341023785768375L,
-P2 = .01249999999999999999999999999999679085402075766159375L,
-P3 = .002232142857142857142857143310092047621284490564671875L,
-P4 = .00043402777777777777774746781319264872413156956512109375L,
-P5 = .0000887784090909101756336594019277185263940665468935546875L,
-P6 = .000018780048055589639895360927834628371268354778446533203125L,
-P7 = .000004069227854328982921366736003458838031087153635406494140625L;
+static const long double
+ ln2_h = 0.693147180559943620892227045260369777679443359375L,
+ ln2_t = 1.68852500507619780679039605677498525525412068e-15L,
+ P1 = .083333333333333333333333333333333333341023785768375L,
+ P2 = .01249999999999999999999999999999679085402075766159375L,
+ P3 = .002232142857142857142857143310092047621284490564671875L,
+ P4 = .00043402777777777777774746781319264872413156956512109375L,
+ P5 = .0000887784090909101756336594019277185263940665468935546875L,
+ P6 = .000018780048055589639895360927834628371268354778446533203125L,
+ P7 = .000004069227854328982921366736003458838031087153635406494140625L;
/*
* T[2k, 2k+1] = log(1+k*2**-7) for k = 0, ..., 2**7 - 1,
* with T[2k] * 2^48 is an int
*/
-
static const long double TBL_log1k[] = {
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-1.7505042236510958082472042641283104263139e-15L,
-5.3244514518809182845870964229106903076172e-02L,
-3.1000199992295574218738634002122149891138e-15L,
-6.0624621816433688081815489567816257476807e-02L,
-1.1544987906424726040058093958345197512800e-15L,
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};
/*
* Compute N*log2 + log(1+zk+zh+zt) in extra precision
*/
-static long double k_log_NKzl(int N, int K, long double zh, long double *zt)
+static long double
+k_log_NKzl(int N, int K, long double zh, long double *zt)
{
long double y, r, w, s2, s2h, s2t, t, zk, v, P;
double dzk;
#if !defined(__x86)
@@ -371,19 +372,18 @@
#endif
((int *)&dzk)[HIWORD] = 0x3ff00000 + (K << 13);
((int *)&dzk)[LOWORD] = 0;
t = zh + (*zt);
- zk = (long double) dzk;
+ zk = (long double)dzk;
r = two / (t + two * zk);
s2h = s2 = r * t;
/* split s2 into correctly rounded half */
#if defined(__x86)
((unsigned *)&s2h)[0] = 0; /* 32 bits chopped */
#else
-
lx = ((unsigned *)&s2h)[2]; /* 56 bits rounded */
j = ((lx >> 24) + 1) >> 1;
((unsigned *)&s2h)[2] = (j << 25);
lx = ((unsigned *)&s2h)[1];
ly = lx + (j >> 7);
@@ -393,14 +393,14 @@
#endif
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 + w * P4)
- + (w * w) * (P5 + w * P6 + (w * w) * P7)));
+ P = s2t + (w * s2) * ((P1 + w * P2) + (w * w) * ((P3 + w * P4) + (w *
+ w) * (P5 + w * P6 + (w * w) * P7)));
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);
}
@@ -417,26 +417,35 @@
unsigned lx, ly;
#endif
ix = HI_XWORD(x) & ~0x80000000;
iy = HI_XWORD(y) & ~0x80000000;
- y = fabsl(y); x = fabsl(x);
+ y = fabsl(y);
+ x = fabsl(x);
+
if (ix < iy || (ix < 0x7fff0000 && ix == iy && x < y)) {
/* force x >= y */
- tk = x; x = y; y = tk;
- n = ix, ix = iy; iy = n;
+ tk = x;
+ x = y;
+ y = tk;
+ n = ix, ix = iy;
+ iy = n;
}
+
*er = zero;
- nx = ix >> 16; ny = iy >> 16;
+ nx = ix >> 16;
+ ny = iy >> 16;
+
if (nx >= 0x7fff) { /* x or y is Inf or NaN */
if (isinfl(x))
return (x);
else if (isinfl(y))
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
*/
@@ -445,45 +454,51 @@
#else
if (x == 1.0L && ny < (0x3fff - 70)) {
#endif
t2 = y * y;
+
if (ny >= 8305) { /* compute er = tail of t2 */
- dk = (double) y;
+ dk = (double)y;
#if defined(__x86)
((unsigned *)&dk)[LOWORD] &= 0xfffe0000;
#endif
- wh = (long double) dk;
+ wh = (long double)dk;
*er = half * ((y - wh) * (y + wh) - (t2 - wh * wh));
}
+
return (half * t2);
}
+
/*
* x or y is subnormal or zero
*/
if (nx == 0) {
- if (x == 0.0L)
+ if (x == 0.0L) {
return (-1.0L / x);
- else {
+ } else {
x *= two240;
y *= two240;
ix = HI_XWORD(x);
iy = HI_XWORD(y);
nx = (ix >> 16) - 240;
ny = (iy >> 16) - 240;
+
/* guard subnormal flush to 0 */
if (x == 0.0L)
return (-1.0L / x);
}
} else if (ny == 0) { /* y subnormal, scale it */
y *= two240;
iy = HI_XWORD(y);
ny = (iy >> 16) - 240;
}
+
n = nx - ny;
+
/*
* When y is zero or when x >> y, i.e., n > 62, 78, 122 for DBLE,
* EXTENDED, QUAD respectively,
* log(x) = log(sqrt(x * x + y * y)) to 27 extra bits.
*/
@@ -494,11 +509,11 @@
if (n > 122 || y == 0.0L) {
#endif
XFSCALE(x, (0x3fff - (ix >> 16)));
i = ((ix & 0xffff) + 0x100) >> 9; /* 7.5 bits of x */
- zk = 1.0L + ((long double) i) * 0.0078125L;
+ zk = 1.0L + ((long double)i) * 0.0078125L;
z = x - zk;
dk = (double)z;
#if defined(__x86)
((unsigned *)&dk)[LOWORD] &= 0xfffe0000;
@@ -506,25 +521,29 @@
zh = (long double)dk;
k = i & 0x7f; /* index of zk */
n = nx - 0x3fff;
*er = z - zh;
+
if (i == 0x80) { /* if zk = 2.0, adjust scaling */
n += 1;
- zh *= 0.5L; *er *= 0.5L;
+ zh *= 0.5L;
+ *er *= 0.5L;
}
+
w = k_log_NKzl(n, k, zh, er);
} else {
/*
* compute z = x*x + y*y
*/
XFSCALE(x, (0x3fff - (ix >> 16)));
XFSCALE(y, (0x3fff - n - (iy >> 16)));
ix = (ix & 0xffff) | 0x3fff0000;
iy = (iy & 0xffff) | (0x3fff0000 - (n << 16));
nx -= 0x3fff;
- t1 = x * x; t2 = y * y;
+ t1 = x * x;
+ t2 = y * y;
wh = x;
/* split x into correctly rounded half */
#if defined(__x86)
((unsigned *)&wh)[0] = 0; /* 32 bits chopped */
@@ -537,11 +556,12 @@
((unsigned *)&wh)[1] = ly;
((unsigned *)&wh)[0] += (ly == 0 && lx != 0);
((unsigned *)&wh)[3] = 0;
#endif
- 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));
@@ -561,31 +581,42 @@
((unsigned *)&wh)[3] = 0;
#endif
tk = wh - y;
t4 = tk * tk - (two * wh * tk - (wh * wh - t2));
+
/*
* find zk matches z to 7.5 bits
*/
iz = HI_XWORD(z);
k = ((iz & 0xffff) + 0x100) >> 9; /* 7.5 bits of x */
nz = (iz >> 16) - 0x3fff + (k >> 7);
k &= 0x7f;
- zk = 1.0L + ((long double) k) * 0.0078125L;
- if (nz == 1) zk += zk;
- else if (nz == 2) zk *= 4.0L;
- else if (nz == 3) zk *= 8.0L;
+ zk = 1.0L + ((long double)k) * 0.0078125L;
+
+ if (nz == 1)
+ zk += zk;
+ else if (nz == 2)
+ zk *= 4.0L;
+ else if (nz == 3)
+ zk *= 8.0L;
+
/*
* order t1, t2, t3, t4 according to their size
*/
if (t2 >= fabsl(t3)) {
if (fabsl(t3) < fabsl(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;
@@ -604,42 +635,48 @@
((unsigned *)&zh)[0] += (ly == 0 && lx != 0);
((unsigned *)&zh)[3] = 0;
#endif
w = fabsl(zh);
- if (w >= fabsl(t2))
-{
- *er = (((tk - zh) + t2) + t3) + t4;
-}
-
- else {
+ if (w >= fabsl(t2)) {
+ *er = (((tk - zh) + t2) + t3) + t4;
+ } else {
if (n == 0) {
wh = half * zk;
wh = (t1 - wh) - (wh - t2);
- } else
+ } else {
wh = tk + t2;
- if (w >= fabsl(t3))
+ }
+
+ if (w >= fabsl(t3)) {
*er = ((wh - zh) + t3) + t4;
- else {
+ } else {
z = t3;
t3 += t4;
t4 -= t3 - z;
+
if (w >= fabsl(t3))
*er = ((wh - zh) + t3) + t4;
else
*er = ((wh + t3) - zh) + t4;
}
}
+
if (nz == 3) {
- zh *= 0.125L; *er *= 0.125L;
+ zh *= 0.125L;
+ *er *= 0.125L;
} else if (nz == 2) {
- zh *= 0.25L; *er *= 0.25L;
+ zh *= 0.25L;
+ *er *= 0.25L;
} else if (nz == 1) {
- zh *= half; *er *= half;
+ zh *= half;
+ *er *= half;
}
+
nz += nx + nx;
w = half * k_log_NKzl(nz, k, zh, er);
*er *= half;
}
+
return (w);
}