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11210 libm should be cstyle(1ONBLD) clean
*** 20,29 ****
--- 20,30 ----
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
+
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
*** 33,96 ****
/* atan2l/atan2pil/exp2l/expl/fabsl/hypotl/isinfl/logl/powl/sincosl/sincospil */
#include "complex_wrapper.h"
#include "longdouble.h"
#if defined(__sparc)
! #define HALF(x) ((int *) &x)[3] = 0; ((int *) &x)[2] &= 0xfe000000
! #define LAST(x) ((int *) &x)[3]
#elif defined(__x86)
! #define HALF(x) ((int *) &x)[0] = 0
! #define LAST(x) ((int *) &x)[0]
#endif
- /* INDENT OFF */
static const int hiinf = 0x7fff0000;
! static const long double
! tiny = 1.0e-4000L,
huge = 1.0e4000L,
#if defined(__x86)
! /* 43 significant bits, 21 trailing zeros */
ln2hil = 0.693147180559890330187045037746429443359375L,
ln2lol = 5.497923018708371174712471612513436025525412068e-14L,
#else /* sparc */
! /* 0x3FF962E4 2FEFA39E F35793C7 00000000 */
ln2hil = 0.693147180559945309417231592858066493070671489074L,
ln2lol = 5.28600110075004828645286235820646730106802446566153e-25L,
#endif
invln2 = 1.442695040888963407359924681001892137427e+0000L,
one = 1.0L,
zero = 0.0L;
- /* INDENT ON */
/*
* Assuming |t[0]| > |t[1]| and |t[2]| > |t[3]|, sum4fpl subroutine
* compute t[0] + t[1] + t[2] + t[3] into two long double fp numbers.
*/
! static long double sum4fpl(long double ta[], long double *w)
{
long double t1, t2, t3, t4, w1, w2, t;
! t1 = ta[0]; t2 = ta[1]; t3 = ta[2]; t4 = ta[3];
/*
* Rearrange ti so that |t1| >= |t2| >= |t3| >= |t4|
*/
if (fabsl(t4) > fabsl(t1)) {
! t = t1; t1 = t3; t3 = t;
! t = t2; t2 = t4; t4 = t;
} else if (fabsl(t3) > fabsl(t1)) {
! t = t1; t1 = t3;
if (fabsl(t4) > fabsl(t2)) {
! t3 = t4; t4 = t2; t2 = t;
} else {
! t3 = t2; t2 = t;
}
} else if (fabsl(t3) > fabsl(t2)) {
! t = t2; t2 = t3;
if (fabsl(t4) > fabsl(t2)) {
! t3 = t4; t4 = t;
! } else
t3 = t;
}
/* summing r = t1 + t2 + t3 + t4 to w1 + w2 */
w1 = t3 + t4;
w2 = t4 - (w1 - t3);
t = t2 + w1;
w2 += w1 - (t - t2);
--- 34,114 ----
/* atan2l/atan2pil/exp2l/expl/fabsl/hypotl/isinfl/logl/powl/sincosl/sincospil */
#include "complex_wrapper.h"
#include "longdouble.h"
#if defined(__sparc)
! #define HALF(x) ((int *)&x)[3] = 0; ((int *)&x)[2] &= 0xfe000000
! #define LAST(x) ((int *)&x)[3]
#elif defined(__x86)
! #define HALF(x) ((int *)&x)[0] = 0
! #define LAST(x) ((int *)&x)[0]
#endif
static const int hiinf = 0x7fff0000;
! static const long double tiny = 1.0e-4000L,
huge = 1.0e4000L,
#if defined(__x86)
! /* 43 significant bits, 21 trailing zeros */
ln2hil = 0.693147180559890330187045037746429443359375L,
ln2lol = 5.497923018708371174712471612513436025525412068e-14L,
#else /* sparc */
! /* 0x3FF962E4 2FEFA39E F35793C7 00000000 */
ln2hil = 0.693147180559945309417231592858066493070671489074L,
ln2lol = 5.28600110075004828645286235820646730106802446566153e-25L,
#endif
invln2 = 1.442695040888963407359924681001892137427e+0000L,
one = 1.0L,
zero = 0.0L;
/*
* Assuming |t[0]| > |t[1]| and |t[2]| > |t[3]|, sum4fpl subroutine
* compute t[0] + t[1] + t[2] + t[3] into two long double fp numbers.
*/
! static long double
! sum4fpl(long double ta[], long double *w)
{
long double t1, t2, t3, t4, w1, w2, t;
!
! t1 = ta[0];
! t2 = ta[1];
! t3 = ta[2];
! t4 = ta[3];
!
/*
* Rearrange ti so that |t1| >= |t2| >= |t3| >= |t4|
*/
if (fabsl(t4) > fabsl(t1)) {
! t = t1;
! t1 = t3;
! t3 = t;
! t = t2;
! t2 = t4;
! t4 = t;
} else if (fabsl(t3) > fabsl(t1)) {
! t = t1;
! t1 = t3;
!
if (fabsl(t4) > fabsl(t2)) {
! t3 = t4;
! t4 = t2;
! t2 = t;
} else {
! t3 = t2;
! t2 = t;
}
} else if (fabsl(t3) > fabsl(t2)) {
! t = t2;
! t2 = t3;
!
if (fabsl(t4) > fabsl(t2)) {
! t3 = t4;
! t4 = t;
! } else {
t3 = t;
}
+ }
+
/* summing r = t1 + t2 + t3 + t4 to w1 + w2 */
w1 = t3 + t4;
w2 = t4 - (w1 - t3);
t = t2 + w1;
w2 += w1 - (t - t2);
*** 102,112 ****
*w = w2 - (w1 - t);
return (w1);
}
ldcomplex
! cpowl(ldcomplex z, ldcomplex w) {
ldcomplex ans;
long double x, y, u, v, t, c, s, r;
long double t1, t2, t3, t4, x1, x2, y1, y2, u1, v1, b[4], w1, w2;
int ix, iy, hx, hy, hv, hu, iu, iv, i, j, k;
--- 120,131 ----
*w = w2 - (w1 - t);
return (w1);
}
ldcomplex
! cpowl(ldcomplex z, ldcomplex w)
! {
ldcomplex ans;
long double x, y, u, v, t, c, s, r;
long double t1, t2, t3, t4, x1, x2, y1, y2, u1, v1, b[4], w1, w2;
int ix, iy, hx, hy, hv, hu, iu, iv, i, j, k;
*** 122,280 ****
iy = hy & 0x7fffffff;
iu = hu & 0x7fffffff;
iv = hv & 0x7fffffff;
j = 0;
if (v == zero) { /* z**(real) */
if (u == one) { /* (anything) ** 1 is itself */
LD_RE(ans) = x;
LD_IM(ans) = y;
} else if (u == zero) { /* (anything) ** 0 is 1 */
LD_RE(ans) = one;
LD_IM(ans) = zero;
} else if (y == zero) { /* real ** real */
LD_IM(ans) = zero;
if (hx < 0 && ix < hiinf && iu < hiinf) {
/* -x ** u is exp(i*pi*u)*pow(x,u) */
r = powl(-x, u);
sincospil(u, &s, &c);
! LD_RE(ans) = (c == zero)? c: c * r;
! LD_IM(ans) = (s == zero)? s: s * r;
! } else
LD_RE(ans) = powl(x, u);
} else if (x == zero || ix >= hiinf || iy >= hiinf) {
! if (isnanl(x) || isnanl(y) || isnanl(u))
LD_RE(ans) = LD_IM(ans) = x + y + u;
! else {
if (x == zero)
r = fabsl(y);
else
r = fabsl(x) + fabsl(y);
t = atan2pil(y, x);
sincospil(t * u, &s, &c);
! LD_RE(ans) = (c == zero)? c: c * r;
! LD_IM(ans) = (s == zero)? s: s * r;
}
} else if (fabsl(x) == fabsl(y)) { /* |x| = |y| */
if (hx >= 0) {
! t = (hy >= 0)? 0.25L : -0.25L;
sincospil(t * u, &s, &c);
} else if ((LAST(u) & 3) == 0) {
! t = (hy >= 0)? 0.75L : -0.75L;
sincospil(t * u, &s, &c);
} else {
! r = (hy >= 0)? u : -u;
t = -0.25L * r;
w1 = r + t;
w2 = t - (w1 - r);
sincospil(w1, &t1, &t2);
sincospil(w2, &t3, &t4);
s = t1 * t4 + t3 * t2;
c = t2 * t4 - t1 * t3;
}
if (ix < 0x3ffe0000) /* |x| < 1/2 */
r = powl(fabsl(x + x), u) * exp2l(-0.5L * u);
else if (ix >= 0x3fff0000 || iu < 0x400cfff8)
/* |x| >= 1 or |u| < 16383 */
r = powl(fabsl(x), u) * exp2l(0.5L * u);
else /* special treatment */
j = 2;
if (j == 0) {
! LD_RE(ans) = (c == zero)? c: c * r;
! LD_IM(ans) = (s == zero)? s: s * r;
}
! } else
j = 1;
if (j == 0)
return (ans);
}
if (iu >= hiinf || iv >= hiinf || ix >= hiinf || iy >= hiinf) {
/*
* non-zero imag part(s) with inf component(s) yields NaN
*/
t = fabsl(x) + fabsl(y) + fabsl(u) + fabsl(v);
LD_RE(ans) = LD_IM(ans) = t - t;
} else {
k = 0; /* no scaling */
if (iu > 0x7ffe0000 || iv > 0x7ffe0000) {
u *= 1.52587890625000000000e-05L;
v *= 1.52587890625000000000e-05L;
k = 1; /* scale u and v by 2**-16 */
}
/*
* Use similated higher precision arithmetic to compute:
* r = u * log(hypot(x, y)) - v * atan2(y, x)
* q = u * atan2(y, x) + v * log(hypot(x, y))
*/
t1 = __k_clog_rl(x, y, &t2);
t3 = __k_atan2l(y, x, &t4);
! x1 = t1; HALF(x1);
! y1 = t3; HALF(y1);
! u1 = u; HALF(u1);
! v1 = v; HALF(v1);
x2 = t2 - (x1 - t1); /* log(hypot(x,y)) = x1 + x2 */
y2 = t4 - (y1 - t3); /* atan2(y,x) = y1 + y2 */
/* compute q = u * atan2(y, x) + v * log(hypot(x, y)) */
if (j != 2) {
b[0] = u1 * y1;
b[1] = (u - u1) * y1 + u * y2;
if (j == 1) { /* v = 0 */
w1 = b[0] + b[1];
w2 = b[1] - (w1 - b[0]);
} else {
b[2] = v1 * x1;
b[3] = (v - v1) * x1 + v * x2;
w1 = sum4fpl(b, &w2);
}
sincosl(w1, &t1, &t2);
sincosl(w2, &t3, &t4);
s = t1 * t4 + t3 * t2;
c = t2 * t4 - t1 * t3;
! if (k == 1) /* square j times */
for (i = 0; i < 10; i++) {
t1 = s * c;
c = (c + s) * (c - s);
s = t1 + t1;
}
}
/* compute r = u * (t1, t2) - v * (t3, t4) */
b[0] = u1 * x1;
b[1] = (u - u1) * x1 + u * x2;
if (j == 1) { /* v = 0 */
w1 = b[0] + b[1];
w2 = b[1] - (w1 - b[0]);
} else {
b[2] = -v1 * y1;
b[3] = (v1 - v) * y1 - v * y2;
w1 = sum4fpl(b, &w2);
}
/* scale back unless w1 is large enough to cause exception */
if (k != 0 && fabsl(w1) < 20000.0L) {
! w1 *= 65536.0L; w2 *= 65536.0L;
}
hx = HI_XWORD(w1);
ix = hx & 0x7fffffff;
/* compute exp(w1 + w2) */
k = 0;
! if (ix < 0x3f8c0000) /* exp(tiny < 2**-115) = 1 */
r = one;
! else if (ix >= 0x400c6760) /* overflow/underflow */
! r = (hx < 0)? tiny * tiny : huge * huge;
! else { /* compute exp(w1 + w2) */
! k = (int) (invln2 * w1 + ((hx >= 0)? 0.5L : -0.5L));
! t1 = (long double) k;
t2 = w1 - t1 * ln2hil;
t3 = w2 - t1 * ln2lol;
r = expl(t2 + t3);
}
! if (c != zero) c *= r;
! if (s != zero) s *= r;
if (k != 0) {
c = scalbnl(c, k);
s = scalbnl(s, k);
}
LD_RE(ans) = c;
LD_IM(ans) = s;
}
return (ans);
}
--- 141,332 ----
iy = hy & 0x7fffffff;
iu = hu & 0x7fffffff;
iv = hv & 0x7fffffff;
j = 0;
+
if (v == zero) { /* z**(real) */
if (u == one) { /* (anything) ** 1 is itself */
LD_RE(ans) = x;
LD_IM(ans) = y;
} else if (u == zero) { /* (anything) ** 0 is 1 */
LD_RE(ans) = one;
LD_IM(ans) = zero;
} else if (y == zero) { /* real ** real */
LD_IM(ans) = zero;
+
if (hx < 0 && ix < hiinf && iu < hiinf) {
/* -x ** u is exp(i*pi*u)*pow(x,u) */
r = powl(-x, u);
sincospil(u, &s, &c);
! LD_RE(ans) = (c == zero) ? c : c *r;
! LD_IM(ans) = (s == zero) ? s : s *r;
! } else {
LD_RE(ans) = powl(x, u);
+ }
} else if (x == zero || ix >= hiinf || iy >= hiinf) {
! if (isnanl(x) || isnanl(y) || isnanl(u)) {
LD_RE(ans) = LD_IM(ans) = x + y + u;
! } else {
if (x == zero)
r = fabsl(y);
else
r = fabsl(x) + fabsl(y);
+
t = atan2pil(y, x);
sincospil(t * u, &s, &c);
! LD_RE(ans) = (c == zero) ? c : c *r;
! LD_IM(ans) = (s == zero) ? s : s *r;
}
} else if (fabsl(x) == fabsl(y)) { /* |x| = |y| */
if (hx >= 0) {
! t = (hy >= 0) ? 0.25L : -0.25L;
sincospil(t * u, &s, &c);
} else if ((LAST(u) & 3) == 0) {
! t = (hy >= 0) ? 0.75L : -0.75L;
sincospil(t * u, &s, &c);
} else {
! r = (hy >= 0) ? u : -u;
t = -0.25L * r;
w1 = r + t;
w2 = t - (w1 - r);
sincospil(w1, &t1, &t2);
sincospil(w2, &t3, &t4);
s = t1 * t4 + t3 * t2;
c = t2 * t4 - t1 * t3;
}
+
if (ix < 0x3ffe0000) /* |x| < 1/2 */
r = powl(fabsl(x + x), u) * exp2l(-0.5L * u);
else if (ix >= 0x3fff0000 || iu < 0x400cfff8)
/* |x| >= 1 or |u| < 16383 */
r = powl(fabsl(x), u) * exp2l(0.5L * u);
else /* special treatment */
j = 2;
+
if (j == 0) {
! LD_RE(ans) = (c == zero) ? c : c *r;
! LD_IM(ans) = (s == zero) ? s : s *r;
}
! } else {
j = 1;
+ }
+
if (j == 0)
return (ans);
}
+
if (iu >= hiinf || iv >= hiinf || ix >= hiinf || iy >= hiinf) {
/*
* non-zero imag part(s) with inf component(s) yields NaN
*/
t = fabsl(x) + fabsl(y) + fabsl(u) + fabsl(v);
LD_RE(ans) = LD_IM(ans) = t - t;
} else {
k = 0; /* no scaling */
+
if (iu > 0x7ffe0000 || iv > 0x7ffe0000) {
u *= 1.52587890625000000000e-05L;
v *= 1.52587890625000000000e-05L;
k = 1; /* scale u and v by 2**-16 */
}
+
/*
* Use similated higher precision arithmetic to compute:
* r = u * log(hypot(x, y)) - v * atan2(y, x)
* q = u * atan2(y, x) + v * log(hypot(x, y))
*/
t1 = __k_clog_rl(x, y, &t2);
t3 = __k_atan2l(y, x, &t4);
! x1 = t1;
! HALF(x1);
! y1 = t3;
! HALF(y1);
! u1 = u;
! HALF(u1);
! v1 = v;
! HALF(v1);
x2 = t2 - (x1 - t1); /* log(hypot(x,y)) = x1 + x2 */
y2 = t4 - (y1 - t3); /* atan2(y,x) = y1 + y2 */
+
/* compute q = u * atan2(y, x) + v * log(hypot(x, y)) */
if (j != 2) {
b[0] = u1 * y1;
b[1] = (u - u1) * y1 + u * y2;
+
if (j == 1) { /* v = 0 */
w1 = b[0] + b[1];
w2 = b[1] - (w1 - b[0]);
} else {
b[2] = v1 * x1;
b[3] = (v - v1) * x1 + v * x2;
w1 = sum4fpl(b, &w2);
}
+
sincosl(w1, &t1, &t2);
sincosl(w2, &t3, &t4);
s = t1 * t4 + t3 * t2;
c = t2 * t4 - t1 * t3;
!
! if (k == 1) { /* square j times */
for (i = 0; i < 10; i++) {
t1 = s * c;
c = (c + s) * (c - s);
s = t1 + t1;
}
}
+ }
+
/* compute r = u * (t1, t2) - v * (t3, t4) */
b[0] = u1 * x1;
b[1] = (u - u1) * x1 + u * x2;
+
if (j == 1) { /* v = 0 */
w1 = b[0] + b[1];
w2 = b[1] - (w1 - b[0]);
} else {
b[2] = -v1 * y1;
b[3] = (v1 - v) * y1 - v * y2;
w1 = sum4fpl(b, &w2);
}
+
/* scale back unless w1 is large enough to cause exception */
if (k != 0 && fabsl(w1) < 20000.0L) {
! w1 *= 65536.0L;
! w2 *= 65536.0L;
}
+
hx = HI_XWORD(w1);
ix = hx & 0x7fffffff;
/* compute exp(w1 + w2) */
k = 0;
!
! if (ix < 0x3f8c0000) { /* exp(tiny < 2**-115) = 1 */
r = one;
! } else if (ix >= 0x400c6760) { /* overflow/underflow */
! r = (hx < 0) ? tiny * tiny : huge * huge;
! } else { /* compute exp(w1 + w2) */
! k = (int)(invln2 * w1 + ((hx >= 0) ? 0.5L : -0.5L));
! t1 = (long double)k;
t2 = w1 - t1 * ln2hil;
t3 = w2 - t1 * ln2lol;
r = expl(t2 + t3);
}
!
! if (c != zero)
! c *= r;
!
! if (s != zero)
! s *= r;
!
if (k != 0) {
c = scalbnl(c, k);
s = scalbnl(s, k);
}
+
LD_RE(ans) = c;
LD_IM(ans) = s;
}
+
return (ans);
}