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math: long double inverse trigonometric cleanup (acosl, asinl, atanl, atan2l)

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* added ld128 support from freebsd fdlibm (untested)
* using new ldshape union instead of IEEEl2bits
* inexact status flag is not supported
This commit is contained in:
Szabolcs Nagy
2013-09-03 15:02:10 +00:00
parent c2a0dfea62
commit bcd797a5ba
6 changed files with 180 additions and 103 deletions
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57
src/math/acosl.c
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@ -23,46 +23,45 @@ long double acosl(long double x)
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
#if LDBL_MANT_DIG == 64
#define CLEARBOTTOM(u) (u.i.m &= -1ULL << 32)
#elif LDBL_MANT_DIG == 113
#define CLEARBOTTOM(u) (u.i.lo = 0)
#endif
long double acosl(long double x)
{
union IEEEl2bits u;
long double z, w, s, c, df;
int16_t expsign, expt;
u.e = x;
expsign = u.xbits.expsign;
expt = expsign & 0x7fff;
union ldshape u = {x};
long double z, s, c, f;
uint16_t e = u.i.se & 0x7fff;
/* |x| >= 1 or nan */
if (expt >= 0x3fff) {
if (expt == 0x3fff &&
((u.bits.manh & ~LDBL_NBIT) | u.bits.manl) == 0) {
if (expsign > 0)
return 0; /* acos(1) = 0 */
return 2*pio2_hi + 0x1p-120f; /* acos(-1)= pi */
}
return 0/(x-x); /* acos(|x|>1) is NaN */
if (e >= 0x3fff) {
if (x == 1)
return 0;
if (x == -1)
return 2*pio2_hi + 0x1p-120f;
return 0/(x-x);
}
/* |x| < 0.5 */
if (expt < 0x3fff - 1) {
if (expt < 0x3fff - 65)
return pio2_hi + 0x1p-120f; /* x < 0x1p-65: acosl(x)=pi/2 */
return pio2_hi - (x - (pio2_lo - x * __invtrigl_R(x*x)));
if (e < 0x3fff - 1) {
if (e < 0x3fff - LDBL_MANT_DIG - 1)
return pio2_hi + 0x1p-120f;
return pio2_hi - (__invtrigl_R(x*x)*x - pio2_lo + x);
}
/* x < -0.5 */
if (expsign < 0) {
z = (1.0 + x) * 0.5;
if (u.i.se >> 15) {
z = (1 + x)*0.5;
s = sqrtl(z);
w = __invtrigl_R(z) * s - pio2_lo;
return 2*(pio2_hi - (s + w));
return 2*(pio2_hi - (__invtrigl_R(z)*s - pio2_lo + s));
}
/* x > 0.5 */
z = (1.0 - x) * 0.5;
z = (1 - x)*0.5;
s = sqrtl(z);
u.e = s;
u.bits.manl = 0;
df = u.e;
c = (z - df * df) / (s + df);
w = __invtrigl_R(z) * s + c;
return 2*(df + w);
u.f = s;
CLEARBOTTOM(u);
f = u.f;
c = (z - f*f)/(s + f);
return 2*(__invtrigl_R(z)*s + c + f);
}
#endif