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math: clean up atan2.c

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* remove volatile hacks
* don't care about inexact flag for now (removed all the +-tiny)
* fix atanl to raise underflow properly
* remove signed int arithmetics
* use pi/2 instead of pi_o_2 (gcc generates the same code, which is not
correct, but it does not matter: we mainly care about nearest rounding)
This commit is contained in:
Szabolcs Nagy
2013-08-15 14:05:19 +00:00
parent 31c5fb80b9
commit 6d85096f49
4 changed files with 73 additions and 103 deletions
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src/math/atan2l.c
+13 -23
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@@ -29,26 +29,22 @@ long double atan2l(long double y, long double x)
{
union IEEEl2bits ux, uy;
long double z;
int32_t k,m;
int16_t exptx, expsignx, expty, expsigny;
int m;
uint16_t exptx, expsignx, expty, expsigny;
if (isnan(x) || isnan(y))
return x+y;
if (x == 1)
return atanl(y);
uy.e = y;
expsigny = uy.xbits.expsign;
expty = expsigny & 0x7fff;
ux.e = x;
expsignx = ux.xbits.expsign;
exptx = expsignx & 0x7fff;
if ((exptx==0x7fff &&
((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
(expty==0x7fff &&
((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */
return x+y;
if (expsignx==0x3fff && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
return atanl(y);
m = ((expsigny>>15)&1) | ((expsignx>>14)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if (expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
if (y == 0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
@@ -56,9 +52,8 @@ long double atan2l(long double y, long double x)
case 3: return -2*pio2_hi-0x1p-120f; /* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if (exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
return expsigny < 0 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
if (x == 0)
return m&1 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
/* when x is INF */
if (exptx == 0x7fff) {
if (expty == 0x7fff) {
@@ -78,17 +73,12 @@ long double atan2l(long double y, long double x)
}
}
/* when y is INF */
if (expty == 0x7fff)
return expsigny < 0 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
if (exptx+120 < expty || expty == 0x7fff)
return m&1 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
/* compute y/x */
k = expty-exptx;
if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
z = pio2_hi+0x1p-120f;
m &= 1;
} else if (expsignx < 0 && k < -LDBL_MANT_DIG-2) /* |y/x| tiny, x<0 */
if ((m&2) && expty+120 < exptx) /* |y/x| tiny, x<0 */
z = 0.0;
else /* safe to do y/x */
else
z = atanl(fabsl(y/x));
switch (m) {
case 0: return z; /* atan(+,+) */