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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.
*/
*** 31,80 ****
#include "libm.h" /* acosl/atanl/fabsl/isinfl/log1pl/logl/sqrtl */
#include "complex_wrapper.h"
#include "longdouble.h"
! /* INDENT OFF */
! static const long double
! zero = 0.0L,
! one = 1.0L,
! Acrossover = 1.5L,
! Bcrossover = 0.6417L,
! half = 0.5L,
! ln2 = 6.931471805599453094172321214581765680755e-0001L,
! Foursqrtu = 7.3344154702193886624856495681939326638255e-2466L, /* 2**-8189 */
#if defined(__x86)
! E = 5.4210108624275221700372640043497085571289e-20L, /* 2**-64 */
! pi = 3.141592653589793238295968524909085317631252110004425048828125L,
! pi_l = 1.666748583704175665659172893706807721468195923078e-19L,
! pi_2 = 1.5707963267948966191479842624545426588156260L,
! pi_2_l = 8.3337429185208783282958644685340386073409796e-20L,
! pi_4 = 0.78539816339744830957399213122727132940781302750110626220703125L,
! pi_4_l = 4.166871459260439164147932234267019303670489807695410e-20L,
! pi3_4 = 2.35619449019234492872197639368181398822343908250331878662109375L,
! pi3_4_l = 1.250061437778131749244379670280105791101146942308e-19L;
#else
! E = 9.6296497219361792652798897129246365926905e-35L, /* 2**-113 */
! pi = 3.1415926535897932384626433832795027974790680981372955730045043318L,
! pi_l = 8.6718101301237810247970440260433519687623233462565303417759356862e-35L,
! pi_2 = 1.5707963267948966192313216916397513987395340L,
! pi_2_l = 4.3359050650618905123985220130216759843811616e-35L,
! pi_4 = 0.785398163397448309615660845819875699369767024534323893251126L,
! pi_4_l = 2.167952532530945256199261006510837992190580836564132585443e-35L,
! pi3_4 = 2.35619449019234492884698253745962709810930107360297167975337824L,
! pi3_4_l = 6.503857597592835768597783019532513976571742509692397756331e-35L;
#endif
! /* INDENT ON */
#if defined(__x86)
static const int ip1 = 0x40400000; /* 2**65 */
#else
static const int ip1 = 0x40710000; /* 2**114 */
#endif
ldcomplex
! cacosl(ldcomplex z) {
long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
int ix, iy, hx, hy;
ldcomplex ans;
x = LD_RE(z);
--- 32,81 ----
#include "libm.h" /* acosl/atanl/fabsl/isinfl/log1pl/logl/sqrtl */
#include "complex_wrapper.h"
#include "longdouble.h"
! /* BEGIN CSTYLED */
! static const long double zero = 0.0L,
! one = 1.0L,
! Acrossover = 1.5L,
! Bcrossover = 0.6417L,
! half = 0.5L,
! ln2 = 6.931471805599453094172321214581765680755e-0001L,
! Foursqrtu = 7.3344154702193886624856495681939326638255e-2466L, /* 2**-8189 */
#if defined(__x86)
! E = 5.4210108624275221700372640043497085571289e-20L, /* 2**-64 */
! pi = 3.141592653589793238295968524909085317631252110004425048828125L,
! pi_l = 1.666748583704175665659172893706807721468195923078e-19L,
! pi_2 = 1.5707963267948966191479842624545426588156260L,
! pi_2_l = 8.3337429185208783282958644685340386073409796e-20L,
! pi_4 = 0.78539816339744830957399213122727132940781302750110626220703125L,
! pi_4_l = 4.166871459260439164147932234267019303670489807695410e-20L,
! pi3_4 = 2.35619449019234492872197639368181398822343908250331878662109375L,
! pi3_4_l = 1.250061437778131749244379670280105791101146942308e-19L;
#else
! E = 9.6296497219361792652798897129246365926905e-35L, /* 2**-113 */
! pi = 3.1415926535897932384626433832795027974790680981372955730045043318L,
! pi_l = 8.6718101301237810247970440260433519687623233462565303417759356862e-35L,
! pi_2 = 1.5707963267948966192313216916397513987395340L,
! pi_2_l = 4.3359050650618905123985220130216759843811616e-35L,
! pi_4 = 0.785398163397448309615660845819875699369767024534323893251126L,
! pi_4_l = 2.167952532530945256199261006510837992190580836564132585443e-35L,
! pi3_4 = 2.35619449019234492884698253745962709810930107360297167975337824L,
! pi3_4_l = 6.503857597592835768597783019532513976571742509692397756331e-35L;
#endif
! /* END CSTYLED */
#if defined(__x86)
static const int ip1 = 0x40400000; /* 2**65 */
#else
static const int ip1 = 0x40710000; /* 2**114 */
#endif
ldcomplex
! cacosl(ldcomplex z)
! {
long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
int ix, iy, hx, hy;
ldcomplex ans;
x = LD_RE(z);
*** 95,104 ****
--- 96,106 ----
/* |y| is inf or NaN */
if (iy >= 0x7fff0000) {
if (isinfl(y)) { /* cacos(x + i inf) = pi/2 - i inf */
LD_IM(ans) = -y;
+
if (ix < 0x7fff0000) {
LD_RE(ans) = pi_2 + pi_2_l;
} else if (isinfl(x)) {
if (hx >= 0)
LD_RE(ans) = pi_4 + pi_4_l;
*** 107,187 ****
} else {
LD_RE(ans) = x;
}
} else { /* cacos(x + i NaN) = NaN + i NaN */
LD_RE(ans) = y + x;
if (isinfl(x))
LD_IM(ans) = -fabsl(x);
else
LD_IM(ans) = y;
}
return (ans);
}
y = fabsl(y);
if (ix >= 0x7fff0000) { /* x is inf or NaN */
if (isinfl(x)) { /* x is INF */
LD_IM(ans) = -fabsl(x);
if (iy >= 0x7fff0000) {
if (isinfl(y)) {
! /* INDENT OFF */
! /* cacos(inf + i inf) = pi/4 - i inf */
! /* cacos(-inf+ i inf) =3pi/4 - i inf */
! /* INDENT ON */
if (hx >= 0)
LD_RE(ans) = pi_4 + pi_4_l;
else
LD_RE(ans) = pi3_4 + pi3_4_l;
! } else
! /* INDENT OFF */
! /* cacos(inf + i NaN) = NaN - i inf */
! /* INDENT ON */
LD_RE(ans) = y + y;
} else {
! /* INDENT OFF */
! /* cacos(inf + iy ) = 0 - i inf */
! /* cacos(-inf+ iy ) = pi - i inf */
! /* INDENT ON */
if (hx >= 0)
LD_RE(ans) = zero;
else
LD_RE(ans) = pi + pi_l;
}
} else { /* x is NaN */
! /* INDENT OFF */
/*
* cacos(NaN + i inf) = NaN - i inf
* cacos(NaN + i y ) = NaN + i NaN
* cacos(NaN + i NaN) = NaN + i NaN
*/
- /* INDENT ON */
LD_RE(ans) = x + y;
! if (iy >= 0x7fff0000) {
LD_IM(ans) = -y;
! } else {
LD_IM(ans) = x;
}
! }
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
if (y == zero) { /* region 1: y=0 */
if (ix < 0x3fff0000) { /* |x| < 1 */
LD_RE(ans) = acosl(x);
LD_IM(ans) = zero;
} else {
LD_RE(ans) = zero;
x = fabsl(x);
! if (ix >= ip1) /* i386 ? 2**65 : 2**114 */
LD_IM(ans) = ln2 + logl(x);
! else if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
one)));
! else {
xm1 = x - one;
LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
one)));
}
}
--- 109,195 ----
} else {
LD_RE(ans) = x;
}
} else { /* cacos(x + i NaN) = NaN + i NaN */
LD_RE(ans) = y + x;
+
if (isinfl(x))
LD_IM(ans) = -fabsl(x);
else
LD_IM(ans) = y;
}
+
return (ans);
}
y = fabsl(y);
if (ix >= 0x7fff0000) { /* x is inf or NaN */
if (isinfl(x)) { /* x is INF */
LD_IM(ans) = -fabsl(x);
+
if (iy >= 0x7fff0000) {
if (isinfl(y)) {
! /*
! * cacos(inf + i inf) = pi/4 - i inf
! * cacos(-inf+ i inf) =3pi/4 - i inf
! */
if (hx >= 0)
LD_RE(ans) = pi_4 + pi_4_l;
else
LD_RE(ans) = pi3_4 + pi3_4_l;
! } else {
! /*
! * cacos(inf + i NaN) = NaN - i inf
! */
LD_RE(ans) = y + y;
+ }
} else {
! /*
! * cacos(inf + iy ) = 0 - i inf
! * cacos(-inf+ iy ) = pi - i inf
! */
if (hx >= 0)
LD_RE(ans) = zero;
else
LD_RE(ans) = pi + pi_l;
}
} else { /* x is NaN */
!
/*
* cacos(NaN + i inf) = NaN - i inf
* cacos(NaN + i y ) = NaN + i NaN
* cacos(NaN + i NaN) = NaN + i NaN
*/
LD_RE(ans) = x + y;
!
! if (iy >= 0x7fff0000)
LD_IM(ans) = -y;
! else
LD_IM(ans) = x;
}
!
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
+
return (ans);
}
if (y == zero) { /* region 1: y=0 */
if (ix < 0x3fff0000) { /* |x| < 1 */
LD_RE(ans) = acosl(x);
LD_IM(ans) = zero;
} else {
LD_RE(ans) = zero;
x = fabsl(x);
!
! if (ix >= ip1) { /* i386 ? 2**65 : 2**114 */
LD_IM(ans) = ln2 + logl(x);
! } else if (ix >= 0x3fff8000) { /* x > Acrossover */
LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
one)));
! } else {
xm1 = x - one;
LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
one)));
}
}
*** 190,222 ****
if (ix < 0x3fff0000) { /* x < 1 */
LD_RE(ans) = acosl(x);
x = fabsl(x);
LD_IM(ans) = y / sqrtl((one + x) * (one - x));
} else if (ix >= ip1) { /* i386 ? 2**65 : 2**114 */
! if (hx >= 0)
LD_RE(ans) = y / x;
! else {
! if (ix >= ip1 + 0x00040000)
LD_RE(ans) = pi + pi_l;
! else {
t = pi_l + y / x;
LD_RE(ans) = pi + t;
}
}
LD_IM(ans) = ln2 + logl(fabsl(x));
} else {
x = fabsl(x);
t = sqrtl((x - one) * (x + one));
! LD_RE(ans) = (hx >= 0)? y / t : pi - (y / t - pi_l);
if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + t);
else
LD_IM(ans) = log1pl(t - (one - x));
}
} else if (y < Foursqrtu) { /* region 3 */
t = sqrtl(y);
! LD_RE(ans) = (hx >= 0)? t : pi + pi_l;
LD_IM(ans) = t;
} else if (E * y - one >= fabsl(x)) { /* region 4 */
LD_RE(ans) = pi_2 + pi_2_l;
LD_IM(ans) = ln2 + logl(y);
} else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
--- 198,232 ----
if (ix < 0x3fff0000) { /* x < 1 */
LD_RE(ans) = acosl(x);
x = fabsl(x);
LD_IM(ans) = y / sqrtl((one + x) * (one - x));
} else if (ix >= ip1) { /* i386 ? 2**65 : 2**114 */
! if (hx >= 0) {
LD_RE(ans) = y / x;
! } else {
! if (ix >= ip1 + 0x00040000) {
LD_RE(ans) = pi + pi_l;
! } else {
t = pi_l + y / x;
LD_RE(ans) = pi + t;
}
}
+
LD_IM(ans) = ln2 + logl(fabsl(x));
} else {
x = fabsl(x);
t = sqrtl((x - one) * (x + one));
! LD_RE(ans) = (hx >= 0) ? y / t : pi - (y / t - pi_l);
!
if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + t);
else
LD_IM(ans) = log1pl(t - (one - x));
}
} else if (y < Foursqrtu) { /* region 3 */
t = sqrtl(y);
! LD_RE(ans) = (hx >= 0) ? t : pi + pi_l;
LD_IM(ans) = t;
} else if (E * y - one >= fabsl(x)) { /* region 4 */
LD_RE(ans) = pi_2 + pi_2_l;
LD_IM(ans) = ln2 + logl(y);
} else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
*** 226,235 ****
--- 236,246 ----
LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
} else if (fabsl(x) < Foursqrtu) {
/* region 6: x is very small, < 4sqrt(min) */
LD_RE(ans) = pi_2 + pi_2_l;
A = sqrtl(one + y * y);
+
if (iy >= 0x3fff8000) /* if y > Acrossover */
LD_IM(ans) = logl(y + A);
else
LD_IM(ans) = half * log1pl((y + y) * (y + A));
} else { /* safe region */
*** 240,266 ****
R = sqrtl(xp1 * xp1 + y2);
S = sqrtl(xm1 * xm1 + y2);
A = half * (R + S);
B = t / A;
! if (B <= Bcrossover)
! LD_RE(ans) = (hx >= 0)? acosl(B) : acosl(-B);
! else { /* use atan and an accurate approx to a-x */
Apx = A + t;
if (t <= one)
LD_RE(ans) = atan2l(sqrtl(half * Apx * (y2 /
(R + xp1) + (S - xm1))), x);
else
LD_RE(ans) = atan2l((y * sqrtl(half * (Apx /
(R + xp1) + Apx / (S + xm1)))), x);
}
if (A <= Acrossover) {
/* use log1p and an accurate approx to A-1 */
if (ix < 0x3fff0000)
Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
else
Am1 = half * (y2 / (R + xp1) + (S + xm1));
LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
} else {
LD_IM(ans) = logl(A + sqrtl(A * A - one));
}
}
--- 251,280 ----
R = sqrtl(xp1 * xp1 + y2);
S = sqrtl(xm1 * xm1 + y2);
A = half * (R + S);
B = t / A;
! if (B <= Bcrossover) {
! LD_RE(ans) = (hx >= 0) ? acosl(B) : acosl(-B);
! } else { /* use atan and an accurate approx to a-x */
Apx = A + t;
+
if (t <= one)
LD_RE(ans) = atan2l(sqrtl(half * Apx * (y2 /
(R + xp1) + (S - xm1))), x);
else
LD_RE(ans) = atan2l((y * sqrtl(half * (Apx /
(R + xp1) + Apx / (S + xm1)))), x);
}
+
if (A <= Acrossover) {
/* use log1p and an accurate approx to A-1 */
if (ix < 0x3fff0000)
Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
else
Am1 = half * (y2 / (R + xp1) + (S + xm1));
+
LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
} else {
LD_IM(ans) = logl(A + sqrtl(A * A - one));
}
}