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/* origin: FreeBSD /usr/src/lib/msun/src/e_asinl.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* See comments in asin.c.
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
*/
#include "libm.h" // for ldshape, ldshape::(anonymous), FORCE_EVAL
#include <float.h> // for LDBL_MANT_DIG, LDBL_MAX_EXP
#include <math.h> // for asinl, fabsl, sqrtl
#include <stdint.h> // for uint16_t
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double asinl(long double x)
{
return asin(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h" // for __invtrigl_R, pio2_hi, pio2_lo
#if LDBL_MANT_DIG == 64
#define CLOSETO1(u) ((u).i.m >> 56 >= 0xf7)
#define CLEARBOTTOM(u) ((u).i.m &= -1ULL << 32)
#elif LDBL_MANT_DIG == 113
#define CLOSETO1(u) (u.i.top >= 0xee00)
#define CLEARBOTTOM(u) (u.i.lo = 0)
#endif
long double asinl(long double x)
{
union ldshape u = { x };
long double z, r, s;
uint16_t e = u.i.se & 0x7fff;
int sign = u.i.se >> 15;
if (e >= 0x3fff) { /* |x| >= 1 or nan */
/* asin(+-1)=+-pi/2 with inexact */
if (x == 1 || x == -1)
return x * pio2_hi + 0x1p-120f;
return 0 / (x - x);
}
if (e < 0x3fff - 1) { /* |x| < 0.5 */
if (e < 0x3fff - (LDBL_MANT_DIG + 1) / 2) {
/* return x with inexact if x!=0 */
FORCE_EVAL(x + 0x1p120f);
return x;
}
return x + x * __invtrigl_R(x * x);
}
/* 1 > |x| >= 0.5 */
z = (1.0 - fabsl(x)) * 0.5;
s = sqrtl(z);
r = __invtrigl_R(z);
if (CLOSETO1(u)) {
x = pio2_hi - (2 * (s + s * r) - pio2_lo);
} else {
long double f, c;
u.f = s;
CLEARBOTTOM(u);
f = u.f;
c = (z - f * f) / (s + f);
x = 0.5 * pio2_hi -
(2 * s * r - (pio2_lo - 2 * c) - (0.5 * pio2_hi - 2 * f));
}
return sign ? -x : x;
}
#endif
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