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Start converting fma to a generic function #463

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Start converting fma to a generic function #463

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6 changes: 4 additions & 2 deletions etc/function-definitions.json
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Original file line number Diff line number Diff line change
Expand Up @@ -344,13 +344,15 @@
},
"fma": {
"sources": [
"src/math/fma.rs"
"src/math/fma.rs",
"src/math/generic/fma.rs"
],
"type": "f64"
},
"fmaf": {
"sources": [
"src/math/fmaf.rs"
"src/math/fmaf.rs",
"src/math/generic/fma.rs"
],
"type": "f32"
},
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192 changes: 3 additions & 189 deletions src/math/fma.rs
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Original file line number Diff line number Diff line change
@@ -1,195 +1,9 @@
use core::{f32, f64};

use super::scalbn;

const ZEROINFNAN: i32 = 0x7ff - 0x3ff - 52 - 1;

struct Num {
m: u64,
e: i32,
sign: i32,
}

fn normalize(x: f64) -> Num {
let x1p63: f64 = f64::from_bits(0x43e0000000000000); // 0x1p63 === 2 ^ 63

let mut ix: u64 = x.to_bits();
let mut e: i32 = (ix >> 52) as i32;
let sign: i32 = e & 0x800;
e &= 0x7ff;
if e == 0 {
ix = (x * x1p63).to_bits();
e = (ix >> 52) as i32 & 0x7ff;
e = if e != 0 { e - 63 } else { 0x800 };
}
ix &= (1 << 52) - 1;
ix |= 1 << 52;
ix <<= 1;
e -= 0x3ff + 52 + 1;
Num { m: ix, e, sign }
}

#[inline]
fn mul(x: u64, y: u64) -> (u64, u64) {
let t = (x as u128).wrapping_mul(y as u128);
((t >> 64) as u64, t as u64)
}

/// Floating multiply add (f64)
/// Fused multiply add (f64)
///
/// Computes `(x*y)+z`, rounded as one ternary operation:
/// Computes the value (as if) to infinite precision and rounds once to the result format,
/// according to the rounding mode characterized by the value of FLT_ROUNDS.
/// Computes `(x*y)+z`, rounded as one ternary operation (i.e. calculated with infinite precision).
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn fma(x: f64, y: f64, z: f64) -> f64 {
let x1p63: f64 = f64::from_bits(0x43e0000000000000); // 0x1p63 === 2 ^ 63
let x0_ffffff8p_63 = f64::from_bits(0x3bfffffff0000000); // 0x0.ffffff8p-63

/* normalize so top 10bits and last bit are 0 */
let nx = normalize(x);
let ny = normalize(y);
let nz = normalize(z);

if nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN {
return x * y + z;
}
if nz.e >= ZEROINFNAN {
if nz.e > ZEROINFNAN {
/* z==0 */
return x * y + z;
}
return z;
}

/* mul: r = x*y */
let zhi: u64;
let zlo: u64;
let (mut rhi, mut rlo) = mul(nx.m, ny.m);
/* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */

/* align exponents */
let mut e: i32 = nx.e + ny.e;
let mut d: i32 = nz.e - e;
/* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
if d > 0 {
if d < 64 {
zlo = nz.m << d;
zhi = nz.m >> (64 - d);
} else {
zlo = 0;
zhi = nz.m;
e = nz.e - 64;
d -= 64;
if d == 0 {
} else if d < 64 {
rlo = (rhi << (64 - d)) | (rlo >> d) | ((rlo << (64 - d)) != 0) as u64;
rhi = rhi >> d;
} else {
rlo = 1;
rhi = 0;
}
}
} else {
zhi = 0;
d = -d;
if d == 0 {
zlo = nz.m;
} else if d < 64 {
zlo = (nz.m >> d) | ((nz.m << (64 - d)) != 0) as u64;
} else {
zlo = 1;
}
}

/* add */
let mut sign: i32 = nx.sign ^ ny.sign;
let samesign: bool = (sign ^ nz.sign) == 0;
let mut nonzero: i32 = 1;
if samesign {
/* r += z */
rlo = rlo.wrapping_add(zlo);
rhi += zhi + (rlo < zlo) as u64;
} else {
/* r -= z */
let (res, borrow) = rlo.overflowing_sub(zlo);
rlo = res;
rhi = rhi.wrapping_sub(zhi.wrapping_add(borrow as u64));
if (rhi >> 63) != 0 {
rlo = (rlo as i64).wrapping_neg() as u64;
rhi = (rhi as i64).wrapping_neg() as u64 - (rlo != 0) as u64;
sign = (sign == 0) as i32;
}
nonzero = (rhi != 0) as i32;
}

/* set rhi to top 63bit of the result (last bit is sticky) */
if nonzero != 0 {
e += 64;
d = rhi.leading_zeros() as i32 - 1;
/* note: d > 0 */
rhi = (rhi << d) | (rlo >> (64 - d)) | ((rlo << d) != 0) as u64;
} else if rlo != 0 {
d = rlo.leading_zeros() as i32 - 1;
if d < 0 {
rhi = (rlo >> 1) | (rlo & 1);
} else {
rhi = rlo << d;
}
} else {
/* exact +-0 */
return x * y + z;
}
e -= d;

/* convert to double */
let mut i: i64 = rhi as i64; /* i is in [1<<62,(1<<63)-1] */
if sign != 0 {
i = -i;
}
let mut r: f64 = i as f64; /* |r| is in [0x1p62,0x1p63] */

if e < -1022 - 62 {
/* result is subnormal before rounding */
if e == -1022 - 63 {
let mut c: f64 = x1p63;
if sign != 0 {
c = -c;
}
if r == c {
/* min normal after rounding, underflow depends
on arch behaviour which can be imitated by
a double to float conversion */
let fltmin: f32 = (x0_ffffff8p_63 * f32::MIN_POSITIVE as f64 * r) as f32;
return f64::MIN_POSITIVE / f32::MIN_POSITIVE as f64 * fltmin as f64;
}
/* one bit is lost when scaled, add another top bit to
only round once at conversion if it is inexact */
if (rhi << 53) != 0 {
i = ((rhi >> 1) | (rhi & 1) | (1 << 62)) as i64;
if sign != 0 {
i = -i;
}
r = i as f64;
r = 2. * r - c; /* remove top bit */

/* raise underflow portably, such that it
cannot be optimized away */
{
let tiny: f64 = f64::MIN_POSITIVE / f32::MIN_POSITIVE as f64 * r;
r += (tiny * tiny) * (r - r);
}
}
} else {
/* only round once when scaled */
d = 10;
i = (((rhi >> d) | ((rhi << (64 - d)) != 0) as u64) << d) as i64;
if sign != 0 {
i = -i;
}
r = i as f64;
}
}
scalbn(r, e)
return super::generic::fma(x, y, z);
}

#[cfg(test)]
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