gnzlbg
227 lines
6.2 KiB
Rust
227 lines
6.2 KiB
Rust
use core::{f32, f64};
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use super::scalbn;
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const ZEROINFNAN: i32 = 0x7ff - 0x3ff - 52 - 1;
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struct Num {
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m: u64,
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e: i32,
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sign: i32,
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}
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#[inline]
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fn normalize(x: f64) -> Num {
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let x1p63: f64 = f64::from_bits(0x43e0000000000000); // 0x1p63 === 2 ^ 63
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let mut ix: u64 = x.to_bits();
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let mut e: i32 = (ix >> 52) as i32;
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let sign: i32 = e & 0x800;
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e &= 0x7ff;
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if e == 0 {
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ix = (x * x1p63).to_bits();
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e = (ix >> 52) as i32 & 0x7ff;
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e = if e != 0 { e - 63 } else { 0x800 };
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}
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ix &= (1 << 52) - 1;
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ix |= 1 << 52;
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ix <<= 1;
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e -= 0x3ff + 52 + 1;
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Num { m: ix, e, sign }
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}
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#[inline]
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fn mul(x: u64, y: u64) -> (u64, u64) {
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let t1: u64;
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let t2: u64;
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let t3: u64;
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let xlo: u64 = x as u32 as u64;
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let xhi: u64 = x >> 32;
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let ylo: u64 = y as u32 as u64;
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let yhi: u64 = y >> 32;
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t1 = xlo * ylo;
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t2 = xlo * yhi + xhi * ylo;
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t3 = xhi * yhi;
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let lo = t1.wrapping_add(t2 << 32);
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let hi = t3 + (t2 >> 32) + (t1 > lo) as u64;
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(hi, lo)
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}
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/// Floating multiply add (f64)
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///
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/// Computes `(x*y)+z`, rounded as one ternary operation:
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/// Computes the value (as if) to infinite precision and rounds once to the result format,
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/// according to the rounding mode characterized by the value of FLT_ROUNDS.
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#[inline]
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#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
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pub fn fma(x: f64, y: f64, z: f64) -> f64 {
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let x1p63: f64 = f64::from_bits(0x43e0000000000000); // 0x1p63 === 2 ^ 63
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let x0_ffffff8p_63 = f64::from_bits(0x3bfffffff0000000); // 0x0.ffffff8p-63
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/* normalize so top 10bits and last bit are 0 */
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let nx = normalize(x);
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let ny = normalize(y);
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let nz = normalize(z);
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if nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN {
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return x * y + z;
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}
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if nz.e >= ZEROINFNAN {
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if nz.e > ZEROINFNAN {
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/* z==0 */
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return x * y + z;
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}
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return z;
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}
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/* mul: r = x*y */
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let zhi: u64;
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let zlo: u64;
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let (mut rhi, mut rlo) = mul(nx.m, ny.m);
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/* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */
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/* align exponents */
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let mut e: i32 = nx.e + ny.e;
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let mut d: i32 = nz.e - e;
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/* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
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if d > 0 {
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if d < 64 {
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zlo = nz.m << d;
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zhi = nz.m >> (64 - d);
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} else {
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zlo = 0;
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zhi = nz.m;
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e = nz.e - 64;
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d -= 64;
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if d == 0 {
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} else if d < 64 {
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rlo = rhi << (64 - d) | rlo >> d | ((rlo << (64 - d)) != 0) as u64;
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rhi = rhi >> d;
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} else {
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rlo = 1;
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rhi = 0;
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}
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}
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} else {
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zhi = 0;
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d = -d;
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if d == 0 {
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zlo = nz.m;
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} else if d < 64 {
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zlo = nz.m >> d | ((nz.m << (64 - d)) != 0) as u64;
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} else {
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zlo = 1;
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}
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}
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/* add */
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let mut sign: i32 = nx.sign ^ ny.sign;
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let samesign: bool = (sign ^ nz.sign) == 0;
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let mut nonzero: i32 = 1;
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if samesign {
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/* r += z */
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rlo = rlo.wrapping_add(zlo);
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rhi += zhi + (rlo < zlo) as u64;
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} else {
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/* r -= z */
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let t = rlo;
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rlo -= zlo;
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rhi = rhi - zhi - (t < rlo) as u64;
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if (rhi >> 63) != 0 {
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rlo = (-(rlo as i64)) as u64;
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rhi = (-(rhi as i64)) as u64 - (rlo != 0) as u64;
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sign = (sign == 0) as i32;
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}
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nonzero = (rhi != 0) as i32;
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}
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/* set rhi to top 63bit of the result (last bit is sticky) */
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if nonzero != 0 {
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e += 64;
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d = rhi.leading_zeros() as i32 - 1;
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/* note: d > 0 */
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rhi = rhi << d | rlo >> (64 - d) | ((rlo << d) != 0) as u64;
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} else if rlo != 0 {
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d = rlo.leading_zeros() as i32 - 1;
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if d < 0 {
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rhi = rlo >> 1 | (rlo & 1);
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} else {
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rhi = rlo << d;
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}
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} else {
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/* exact +-0 */
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return x * y + z;
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}
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e -= d;
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/* convert to double */
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let mut i: i64 = rhi as i64; /* i is in [1<<62,(1<<63)-1] */
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if sign != 0 {
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i = -i;
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}
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let mut r: f64 = i as f64; /* |r| is in [0x1p62,0x1p63] */
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if e < -1022 - 62 {
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/* result is subnormal before rounding */
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if e == -1022 - 63 {
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let mut c: f64 = x1p63;
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if sign != 0 {
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c = -c;
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}
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if r == c {
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/* min normal after rounding, underflow depends
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on arch behaviour which can be imitated by
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a double to float conversion */
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let fltmin: f32 = (x0_ffffff8p_63 * f32::MIN_POSITIVE as f64 * r) as f32;
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return f64::MIN_POSITIVE / f32::MIN_POSITIVE as f64 * fltmin as f64;
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}
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/* one bit is lost when scaled, add another top bit to
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only round once at conversion if it is inexact */
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if (rhi << 53) != 0 {
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i = (rhi >> 1 | (rhi & 1) | 1 << 62) as i64;
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if sign != 0 {
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i = -i;
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}
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r = i as f64;
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r = 2. * r - c; /* remove top bit */
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/* raise underflow portably, such that it
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cannot be optimized away */
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{
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let tiny: f64 = f64::MIN_POSITIVE / f32::MIN_POSITIVE as f64 * r;
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r += (tiny * tiny) * (r - r);
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}
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}
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} else {
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/* only round once when scaled */
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d = 10;
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i = ((rhi >> d | ((rhi << (64 - d)) != 0) as u64) << d) as i64;
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if sign != 0 {
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i = -i;
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}
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r = i as f64;
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}
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}
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scalbn(r, e)
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn fma_segfault() {
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// These two inputs cause fma to segfault on release due to overflow:
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assert_eq!(
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fma(
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-0.0000000000000002220446049250313,
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-0.0000000000000002220446049250313,
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-0.0000000000000002220446049250313
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),
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-0.00000000000000022204460492503126,
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);
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assert_eq!(fma(-0.992, -0.992, -0.992), -0.00793599999988632,);
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}
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}
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