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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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59
src/math/atan2f.c
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@ -15,72 +15,63 @@
#include "libm.h"
static const volatile float
tiny = 1.0e-30;
static const float
pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
pi = 3.1415927410e+00; /* 0x40490fdb */
static const volatile float
pi = 3.1415927410e+00, /* 0x40490fdb */
pi_lo = -8.7422776573e-08; /* 0xb3bbbd2e */
float atan2f(float y, float x)
{
float z;
int32_t k,m,hx,hy,ix,iy;
uint32_t m,ix,iy;
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
GET_FLOAT_WORD(hy, y);
iy = hy & 0x7fffffff;
if (ix > 0x7f800000 || iy > 0x7f800000) /* x or y is NaN */
if (isnan(x) || isnan(y))
return x+y;
if (hx == 0x3f800000) /* x=1.0 */
GET_FLOAT_WORD(ix, x);
GET_FLOAT_WORD(iy, y);
if (ix == 0x3f800000) /* x=1.0 */
return atanf(y);
m = ((hy>>31)&1) | ((hx>>30)&2); /* 2*sign(x)+sign(y) */
m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */
ix &= 0x7fffffff;
iy &= 0x7fffffff;
/* when y = 0 */
if (iy == 0) {
switch (m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny; /* atan(+0,-anything) = pi */
case 3: return -pi-tiny; /* atan(-0,-anything) =-pi */
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi; /* atan(+0,-anything) = pi */
case 3: return -pi; /* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if (ix == 0)
return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
return m&1 ? -pi/2 : pi/2;
/* when x is INF */
if (ix == 0x7f800000) {
if (iy == 0x7f800000) {
switch (m) {
case 0: return pi_o_4+tiny; /* atan(+INF,+INF) */
case 1: return -pi_o_4-tiny; /* atan(-INF,+INF) */
case 2: return 3.0f*pi_o_4+tiny; /*atan(+INF,-INF)*/
case 3: return -3.0f*pi_o_4-tiny; /*atan(-INF,-INF)*/
case 0: return pi/4; /* atan(+INF,+INF) */
case 1: return -pi/4; /* atan(-INF,+INF) */
case 2: return 3*pi/4; /*atan(+INF,-INF)*/
case 3: return -3*pi/4; /*atan(-INF,-INF)*/
}
} else {
switch (m) {
case 0: return 0.0f; /* atan(+...,+INF) */
case 1: return -0.0f; /* atan(-...,+INF) */
case 2: return pi+tiny; /* atan(+...,-INF) */
case 3: return -pi-tiny; /* atan(-...,-INF) */
case 2: return pi; /* atan(+...,-INF) */
case 3: return -pi; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if (iy == 0x7f800000)
return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
/* |y/x| > 0x1p26 */
if (ix+(26<<23) < iy || iy == 0x7f800000)
return m&1 ? -pi/2 : pi/2;
/* compute y/x */
k = (iy-ix)>>23;
if (k > 26) { /* |y/x| > 2**26 */
z = pi_o_2 + 0.5f*pi_lo;
m &= 1;
} else if (k < -26 && hx < 0) /* 0 > |y|/x > -2**-26 */
/* z = atan(|y/x|) with correct underflow */
if ((m&2) && iy+(26<<23) < ix) /*|y/x| < 0x1p-26, x < 0 */
z = 0.0;
else /* safe to do y/x */
else
z = atanf(fabsf(y/x));
switch (m) {
case 0: return z; /* atan(+,+) */