use super::P16E1;
impl P16E1 {
pub const fn atan_pi(self) -> Self {
let ui_a = self.to_bits();
let mut f = ui_a as u64;
if (f & 0x7FFF) == 0 {
return self; // dispense with NaR and 0 cases
}
if (ui_a >> 15) != 0 {
f = 0x10000 - f; // f = |f|
}
let mut s: i32;
if f < 0x4000 {
// SE quadrant; regime bit is 0
if f > 4925 {
s = 14;
while (f & 0x2000) == 0 {
// decode regime
f <<= 1;
s -= 2;
}
if (f & 0x1000) != 0 {
s += 1; // decode exponent
}
f = (f & 0x0FFF) | 0x1000; // get 12-bit fraction and restore hidden bit
f <<= s;
f = poly(f);
} else {
// use small x approximation
s = 13;
while (f & 0x1000) == 0 {
// decode regime
f <<= 1;
s -= 2;
}
if (f & 0x800) != 0 {
s += 1; // decode exponent
}
f = (f & 0x7FF) | 0x800; // get 12-bit fraction and restore hidden bit
f = if s < 0 { f >> -s } else { f << s };
f = (f << 30) / ((((f * f) >> 34) * 67) + 843_314_118);
}
} else {
// NE quadrant; regime bit is 1
if f < 27_109 {
s = 0;
while (f & 0x2000) != 0 {
// decode regime
f <<= 1;
s += 2;
}
if (f & 0x1000) != 0 {
s += 1; // decode exponent
}
f = (f & 0x0FFF) | 0x1000; // get 12-bit fraction and restore hidden bit
f <<= s;
f = 0x_0100_0000_0000 / f; // fixed-point reciprocal
f = 0x_2000_0000 - poly(f);
} else {
s = -1;
while (f & 0x1000) != 0 {
// decode regime
f <<= 1;
s += 2;
}
if (f & 0x800) != 0 {
s += 1; // decode exponent
}
f = (f & 0x7FF) | 0x800; // get 12-bit fraction and restore hidden bit
f <<= s; // use large value approx. on fixed point:
f = 0x_2000_0000 - (0x_0002_8BE5_FF80_0000 / ((f << 13) + (0x_0AA5_5000 / f)));
}
}
// convert fixed-point to a posit
if f > 1 {
// leave f = 0 and f = minpos alone
s = 34;
while (f & 0x_2000_0000) == 0 {
f <<= 1;
s += 1;
}
f = (f ^ 0x_6000_0000) | (((1 ^ (s & 1)) as u64) << 29);
s >>= 1;
let bit = 1_u64 << (s - 1);
if (f & bit) != 0 {
// round to nearest, tie to even
if ((f & (bit - 1)) != 0) || ((f & (bit << 1)) != 0) {
f += bit;
}
}
f >>= s;
}
Self::from_bits((if (ui_a >> 15) != 0 { 0x10000 - f } else { f }) as u16)
}
}
#[inline]
const fn poly(f: u64) -> u64 {
let fsq = (f * f) >> 28;
let mut s = (fsq * 6_969) >> 24;
s = (fsq * (530_432 - s)) >> 28;
s = (fsq * (1_273_944 - s)) >> 28;
s = (fsq * (2_358_656 - s)) >> 27;
s = (fsq * (9_340_208 - s)) >> 29;
s = (fsq * (17_568_064 - s)) >> 24;
((f + 1) << 30) / (843_315_168 + s)
}