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math: clean up inverse trigonometric functions

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modifications:
* avoid unsigned->signed conversions
* removed various volatile hacks
* use FORCE_EVAL when evaluating only for side-effects
* factor out R() rational approximation instead of manual inline
* __invtrigl.h now only provides __invtrigl_R, __pio2_hi and __pio2_lo
* use 2*pio2_hi, 2*pio2_lo instead of pi_hi, pi_lo

otherwise the logic is not changed, long double versions will
need a revisit when a genaral long double cleanup happens
This commit is contained in:
Szabolcs Nagy
2012-12-11 23:56:59 +01:00
parent 482ccd2f74
commit b12a73d5bf
12 changed files with 261 additions and 380 deletions
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61
src/math/acosl.c
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@ -23,55 +23,46 @@ long double acosl(long double x)
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
#define ACOS_CONST (BIAS - 65) /* 2**-65 */
long double acosl(long double x)
{
union IEEEl2bits u;
long double z, p, q, r, w, s, c, df;
long double z, w, s, c, df;
int16_t expsign, expt;
u.e = x;
expsign = u.xbits.expsign;
expt = expsign & 0x7fff;
if (expt >= BIAS) { /* |x| >= 1 */
if (expt == BIAS &&
/* |x| >= 1 or nan */
if (expt >= 0x3fff) {
if (expt == 0x3fff &&
((u.bits.manh & ~LDBL_NBIT) | u.bits.manl) == 0) {
if (expsign > 0)
return 0.0; /* acos(1) = 0 */
else
// FIXME
return pi_hi + 2.0 * pio2_lo; /* acos(-1)= pi */
return 0; /* acos(1) = 0 */
return 2*pio2_hi + 0x1p-1000; /* acos(-1)= pi */
}
return (x - x) / (x - x); /* acos(|x|>1) is NaN */
return 0/(x-x); /* acos(|x|>1) is NaN */
}
if (expt < BIAS - 1) { /* |x| < 0.5 */
if (expt < ACOS_CONST)
return pio2_hi + pio2_lo; /* x tiny: acosl=pi/2 */
z = x * x;
p = P(z);
q = Q(z);
r = p / q;
return pio2_hi - (x - (pio2_lo - x * r));
} else if (expsign < 0) { /* x < -0.5 */
/* |x| < 0.5 */
if (expt < 0x3fff - 1) {
if (expt < 0x3fff - 65)
return pio2_hi + 0x1p-1000; /* x < 0x1p-65: acosl(x)=pi/2 */
return pio2_hi - (x - (pio2_lo - x * __invtrigl_R(x*x)));
}
/* x < -0.5 */
if (expsign < 0) {
z = (1.0 + x) * 0.5;
p = P(z);
q = Q(z);
s = sqrtl(z);
r = p / q;
w = r * s - pio2_lo;
return pi_hi - 2.0 * (s + w);
} else { /* x > 0.5 */
z = (1.0 - x) * 0.5;
s = sqrtl(z);
u.e = s;
u.bits.manl = 0;
df = u.e;
c = (z - df * df) / (s + df);
p = P(z);
q = Q(z);
r = p / q;
w = r * s + c;
return 2.0 * (df + w);
w = __invtrigl_R(z) * s - pio2_lo;
return 2*(pio2_hi - (s + w));
}
/* x > 0.5 */
z = (1.0 - 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);
}
#endif