1/* SPDX-License-Identifier: MIT OR Apache-2.0 */
2use crate::support::{CastFrom, Float, Int, MinInt};
3
4#[inline]
5pub fn fmod<F: Float>(x: F, y: F) -> F {
6 let _1 = F::Int::ONE;
7 let sx = x.to_bits() & F::SIGN_MASK;
8 let ux = x.to_bits() & !F::SIGN_MASK;
9 let uy = y.to_bits() & !F::SIGN_MASK;
10
11 // Cases that return NaN:
12 // NaN % _
13 // Inf % _
14 // _ % NaN
15 // _ % 0
16 let x_nan_or_inf = ux & F::EXP_MASK == F::EXP_MASK;
17 let y_nan_or_zero = uy.wrapping_sub(_1) & F::EXP_MASK == F::EXP_MASK;
18 if x_nan_or_inf | y_nan_or_zero {
19 return (x * y) / (x * y);
20 }
21
22 if ux < uy {
23 // |x| < |y|
24 return x;
25 }
26
27 let (num, ex) = into_sig_exp::<F>(ux);
28 let (div, ey) = into_sig_exp::<F>(uy);
29
30 // To compute `(num << ex) % (div << ey)`, first
31 // evaluate `rem = (num << (ex - ey)) % div` ...
32 let rem = reduction(num, ex - ey, div);
33 // ... so the result will be `rem << ey`
34
35 if rem.is_zero() {
36 // Return zero with the sign of `x`
37 return F::from_bits(sx);
38 };
39
40 // We would shift `rem` up by `ey`, but have to stop at `F::SIG_BITS`
41 let shift = ey.min(F::SIG_BITS - rem.ilog2());
42 // Anything past that is added to the exponent field
43 let bits = (rem << shift) + (F::Int::cast_from(ey - shift) << F::SIG_BITS);
44 F::from_bits(sx + bits)
45}
46
47/// Given the bits of a finite float, return a tuple of
48/// - the mantissa with the implicit bit (0 if subnormal, 1 otherwise)
49/// - the additional exponent past 1, (0 for subnormal, 0 or more otherwise)
50fn into_sig_exp<F: Float>(mut bits: F::Int) -> (F::Int, u32) {
51 bits &= !F::SIGN_MASK;
52 // Subtract 1 from the exponent, clamping at 0
53 let sat: ::Int = bits.checked_sub(F::IMPLICIT_BIT).unwrap_or(F::Int::ZERO);
54 (
55 bits - (sat & F::EXP_MASK),
56 u32::cast_from(sat >> F::SIG_BITS),
57 )
58}
59
60/// Compute the remainder `(x * 2.pow(e)) % y` without overflow.
61fn reduction<I: Int>(mut x: I, e: u32, y: I) -> I {
62 x %= y;
63 for _ in 0..e {
64 x <<= 1;
65 x = x.checked_sub(y).unwrap_or(default:x);
66 }
67 x
68}
69