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11210 libm should be cstyle(1ONBLD) clean
*** 20,37 ****
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#pragma weak __casin = casin
! /* INDENT OFF */
/*
* dcomplex casin(dcomplex z);
*
* Alogrithm
* (based on T.E.Hull, Thomas F. Fairgrieve and Ping Tak Peter Tang's
--- 20,38 ----
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
+
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#pragma weak __casin = casin
!
/*
* dcomplex casin(dcomplex z);
*
* Alogrithm
* (based on T.E.Hull, Thomas F. Fairgrieve and Ping Tak Peter Tang's
*** 189,220 ****
* = 0.5*log(1+2y(y+sqrt(1+y^2)));
* = 0.5*log1p(2y(y+A));
*
* casin(z) = asin(B) + i sign(y) log (A + sqrt(A*A-1)),
*/
- /* INDENT ON */
#include "libm.h" /* asin/atan/fabs/log/log1p/sqrt */
#include "complex_wrapper.h"
! /* INDENT OFF */
! static const double
! zero = 0.0,
one = 1.0,
E = 1.11022302462515654042e-16, /* 2**-53 */
ln2 = 6.93147180559945286227e-01,
pi_2 = 1.570796326794896558e+00,
pi_2_l = 6.123233995736765886e-17,
pi_4 = 7.85398163397448278999e-01,
Foursqrtu = 5.96667258496016539463e-154, /* 2**(-509) */
Acrossover = 1.5,
Bcrossover = 0.6417,
half = 0.5;
! /* INDENT ON */
dcomplex
! casin(dcomplex z) {
double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
int ix, iy, hx, hy;
unsigned lx, ly;
dcomplex ans;
--- 190,219 ----
* = 0.5*log(1+2y(y+sqrt(1+y^2)));
* = 0.5*log1p(2y(y+A));
*
* casin(z) = asin(B) + i sign(y) log (A + sqrt(A*A-1)),
*/
#include "libm.h" /* asin/atan/fabs/log/log1p/sqrt */
#include "complex_wrapper.h"
! static const double zero = 0.0,
one = 1.0,
E = 1.11022302462515654042e-16, /* 2**-53 */
ln2 = 6.93147180559945286227e-01,
pi_2 = 1.570796326794896558e+00,
pi_2_l = 6.123233995736765886e-17,
pi_4 = 7.85398163397448278999e-01,
Foursqrtu = 5.96667258496016539463e-154, /* 2**(-509) */
Acrossover = 1.5,
Bcrossover = 0.6417,
half = 0.5;
!
dcomplex
! casin(dcomplex z)
! {
double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
int ix, iy, hx, hy;
unsigned lx, ly;
dcomplex ans;
*** 233,269 ****
/* x is inf or NaN */
if (ix >= 0x7ff00000) { /* x is inf or NaN */
if (ISINF(ix, lx)) { /* x is INF */
D_IM(ans) = x;
if (iy >= 0x7ff00000) {
if (ISINF(iy, ly))
/* casin(inf + i inf) = pi/4 + i inf */
D_RE(ans) = pi_4;
else /* casin(inf + i NaN) = NaN + i inf */
D_RE(ans) = y + y;
! } else /* casin(inf + iy) = pi/2 + i inf */
D_RE(ans) = pi_2;
} else { /* x is NaN */
if (iy >= 0x7ff00000) {
! /* INDENT OFF */
/*
* casin(NaN + i inf) = NaN + i inf
* casin(NaN + i NaN) = NaN + i NaN
*/
- /* INDENT ON */
D_IM(ans) = y + y;
D_RE(ans) = x + x;
} else {
/* casin(NaN + i y ) = NaN + i NaN */
D_IM(ans) = D_RE(ans) = x + y;
}
}
if (hx < 0)
D_RE(ans) = -D_RE(ans);
if (hy < 0)
D_IM(ans) = -D_IM(ans);
return (ans);
}
/* casin(+0 + i 0 ) = 0 + i 0. */
if ((ix | lx | iy | ly) == 0)
--- 232,272 ----
/* x is inf or NaN */
if (ix >= 0x7ff00000) { /* x is inf or NaN */
if (ISINF(ix, lx)) { /* x is INF */
D_IM(ans) = x;
+
if (iy >= 0x7ff00000) {
if (ISINF(iy, ly))
/* casin(inf + i inf) = pi/4 + i inf */
D_RE(ans) = pi_4;
else /* casin(inf + i NaN) = NaN + i inf */
D_RE(ans) = y + y;
! } else { /* casin(inf + iy) = pi/2 + i inf */
D_RE(ans) = pi_2;
+ }
} else { /* x is NaN */
if (iy >= 0x7ff00000) {
!
/*
* casin(NaN + i inf) = NaN + i inf
* casin(NaN + i NaN) = NaN + i NaN
*/
D_IM(ans) = y + y;
D_RE(ans) = x + x;
} else {
/* casin(NaN + i y ) = NaN + i NaN */
D_IM(ans) = D_RE(ans) = x + y;
}
}
+
if (hx < 0)
D_RE(ans) = -D_RE(ans);
+
if (hy < 0)
D_IM(ans) = -D_IM(ans);
+
return (ans);
}
/* casin(+0 + i 0 ) = 0 + i 0. */
if ((ix | lx | iy | ly) == 0)
*** 273,319 ****
if (ISINF(iy, ly)) { /* casin(x + i inf) = 0 + i inf */
D_IM(ans) = y;
D_RE(ans) = zero;
} else { /* casin(x + i NaN) = NaN + i NaN */
D_IM(ans) = x + y;
if ((ix | lx) == 0)
D_RE(ans) = x;
else
D_RE(ans) = y;
}
if (hx < 0)
D_RE(ans) = -D_RE(ans);
if (hy < 0)
D_IM(ans) = -D_IM(ans);
return (ans);
}
if ((iy | ly) == 0) { /* region 1: y=0 */
if (ix < 0x3ff00000) { /* |x| < 1 */
D_RE(ans) = asin(x);
D_IM(ans) = zero;
} else {
D_RE(ans) = pi_2;
! if (ix >= 0x43500000) /* |x| >= 2**54 */
D_IM(ans) = ln2 + log(x);
! else if (ix >= 0x3ff80000) /* x > Acrossover */
D_IM(ans) = log(x + sqrt((x - one) * (x +
one)));
! else {
xm1 = x - one;
D_IM(ans) = log1p(xm1 + sqrt(xm1 * (x + one)));
}
}
} else if (y <= E * fabs(x - one)) { /* region 2: y < tiny*|x-1| */
if (ix < 0x3ff00000) { /* x < 1 */
D_RE(ans) = asin(x);
D_IM(ans) = y / sqrt((one + x) * (one - x));
} else {
D_RE(ans) = pi_2;
! if (ix >= 0x43500000) { /* |x| >= 2**54 */
D_IM(ans) = ln2 + log(x);
! } else if (ix >= 0x3ff80000) /* x > Acrossover */
D_IM(ans) = log(x + sqrt((x - one) * (x +
one)));
else
D_IM(ans) = log1p((x - one) + sqrt((x - one) *
(x + one)));
--- 276,328 ----
if (ISINF(iy, ly)) { /* casin(x + i inf) = 0 + i inf */
D_IM(ans) = y;
D_RE(ans) = zero;
} else { /* casin(x + i NaN) = NaN + i NaN */
D_IM(ans) = x + y;
+
if ((ix | lx) == 0)
D_RE(ans) = x;
else
D_RE(ans) = y;
}
+
if (hx < 0)
D_RE(ans) = -D_RE(ans);
+
if (hy < 0)
D_IM(ans) = -D_IM(ans);
+
return (ans);
}
if ((iy | ly) == 0) { /* region 1: y=0 */
if (ix < 0x3ff00000) { /* |x| < 1 */
D_RE(ans) = asin(x);
D_IM(ans) = zero;
} else {
D_RE(ans) = pi_2;
!
! if (ix >= 0x43500000) { /* |x| >= 2**54 */
D_IM(ans) = ln2 + log(x);
! } else if (ix >= 0x3ff80000) { /* x > Acrossover */
D_IM(ans) = log(x + sqrt((x - one) * (x +
one)));
! } else {
xm1 = x - one;
D_IM(ans) = log1p(xm1 + sqrt(xm1 * (x + one)));
}
}
} else if (y <= E * fabs(x - one)) { /* region 2: y < tiny*|x-1| */
if (ix < 0x3ff00000) { /* x < 1 */
D_RE(ans) = asin(x);
D_IM(ans) = y / sqrt((one + x) * (one - x));
} else {
D_RE(ans) = pi_2;
!
! if (ix >= 0x43500000) /* |x| >= 2**54 */
D_IM(ans) = ln2 + log(x);
! else if (ix >= 0x3ff80000) /* x > Acrossover */
D_IM(ans) = log(x + sqrt((x - one) * (x +
one)));
else
D_IM(ans) = log1p((x - one) + sqrt((x - one) *
(x + one)));
*** 332,341 ****
--- 341,351 ----
D_IM(ans) = ln2 + log(y) + half * log1p(t * t);
} else if (x < Foursqrtu) {
/* region 6: x is very small, < 4sqrt(min) */
A = sqrt(one + y * y);
D_RE(ans) = x / A; /* may underflow */
+
if (iy >= 0x3ff80000) /* if y > Acrossover */
D_IM(ans) = log(y + A);
else
D_IM(ans) = half * log1p((y + y) * (y + A));
} else { /* safe region */
*** 345,379 ****
R = sqrt(xp1 * xp1 + y2);
S = sqrt(xm1 * xm1 + y2);
A = half * (R + S);
B = x / A;
! if (B <= Bcrossover)
D_RE(ans) = asin(B);
! else { /* use atan and an accurate approx to a-x */
Apx = A + x;
if (x <= one)
D_RE(ans) = atan(x / sqrt(half * Apx * (y2 /
(R + xp1) + (S - xm1))));
else
D_RE(ans) = atan(x / (y * sqrt(half * (Apx /
(R + xp1) + Apx / (S + xm1)))));
}
if (A <= Acrossover) {
/* use log1p and an accurate approx to A-1 */
if (x < one)
Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
else
Am1 = half * (y2 / (R + xp1) + (S + xm1));
D_IM(ans) = log1p(Am1 + sqrt(Am1 * (A + one)));
} else {
D_IM(ans) = log(A + sqrt(A * A - one));
}
}
if (hx < 0)
D_RE(ans) = -D_RE(ans);
if (hy < 0)
D_IM(ans) = -D_IM(ans);
return (ans);
}
--- 355,393 ----
R = sqrt(xp1 * xp1 + y2);
S = sqrt(xm1 * xm1 + y2);
A = half * (R + S);
B = x / A;
! if (B <= Bcrossover) {
D_RE(ans) = asin(B);
! } else { /* use atan and an accurate approx to a-x */
Apx = A + x;
+
if (x <= one)
D_RE(ans) = atan(x / sqrt(half * Apx * (y2 /
(R + xp1) + (S - xm1))));
else
D_RE(ans) = atan(x / (y * sqrt(half * (Apx /
(R + xp1) + Apx / (S + xm1)))));
}
+
if (A <= Acrossover) {
/* use log1p and an accurate approx to A-1 */
if (x < one)
Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
else
Am1 = half * (y2 / (R + xp1) + (S + xm1));
+
D_IM(ans) = log1p(Am1 + sqrt(Am1 * (A + one)));
} else {
D_IM(ans) = log(A + sqrt(A * A - one));
}
}
if (hx < 0)
D_RE(ans) = -D_RE(ans);
+
if (hy < 0)
D_IM(ans) = -D_IM(ans);
return (ans);
}