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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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28
src/math/atanf.c
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@ -38,28 +38,26 @@ static const float aT[] = {
6.1687607318e-02,
};
static const float huge = 1.0e30;
float atanf(float x)
{
float w,s1,s2,z;
int32_t ix,hx,id;
uint32_t ix,sign;
int id;
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
GET_FLOAT_WORD(ix, x);
sign = ix>>31;
ix &= 0x7fffffff;
if (ix >= 0x4c800000) { /* if |x| >= 2**26 */
if (ix > 0x7f800000) /* NaN */
return x+x;
if (hx > 0)
return atanhi[3] + *(volatile float *)&atanlo[3];
else
return -atanhi[3] - *(volatile float *)&atanlo[3];
if (isnan(x))
return x;
z = atanhi[3] + 0x1p-120f;
return sign ? -z : z;
}
if (ix < 0x3ee00000) { /* |x| < 0.4375 */
if (ix < 0x39800000) { /* |x| < 2**-12 */
/* raise inexact */
if(huge+x>1.0f)
return x;
/* raise inexact if x!=0 */
FORCE_EVAL(x + 0x1p120f);
return x;
}
id = -1;
} else {
@ -91,5 +89,5 @@ float atanf(float x)
if (id < 0)
return x - x*(s1+s2);
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return hx < 0 ? -z : z;
return sign ? -z : z;
}