Struct LehmerMatrix
pub struct LehmerMatrix(pub u64, pub u64, pub u64, pub u64, pub bool);
Expand description
⚠️ Lehmer update matrix
Warning. This struct is not part of the stable API.
Signs are implicit, the boolean .4
encodes which of two sign
patterns applies. The signs and layout of the matrix are:
true false
[ .0 -.1] [-.0 .1]
[-.2 .3] [ .2 -.3]
Tuple Fields§
§0: u64
§1: u64
§2: u64
§3: u64
§4: bool
Implementations§
§impl Matrix
impl Matrix
pub const IDENTITY: Matrix = _
pub fn apply<const BITS: usize, const LIMBS: usize>(
&self,
a: &mut Uint<BITS, LIMBS>,
b: &mut Uint<BITS, LIMBS>,
)
pub fn apply<const BITS: usize, const LIMBS: usize>( &self, a: &mut Uint<BITS, LIMBS>, b: &mut Uint<BITS, LIMBS>, )
Applies the matrix to a Uint
.
pub const fn apply_u128(&self, a: u128, b: u128) -> (u128, u128)
pub const fn apply_u128(&self, a: u128, b: u128) -> (u128, u128)
Applies the matrix to a u128
.
pub fn from<const BITS: usize, const LIMBS: usize>(
a: Uint<BITS, LIMBS>,
b: Uint<BITS, LIMBS>,
) -> Matrix
pub fn from<const BITS: usize, const LIMBS: usize>( a: Uint<BITS, LIMBS>, b: Uint<BITS, LIMBS>, ) -> Matrix
pub fn from_u64(r0: u64, r1: u64) -> Matrix
pub fn from_u64(r0: u64, r1: u64) -> Matrix
Compute the Lehmer update matrix for small values.
This is essentially Euclids extended GCD algorithm for 64 bits.
§Panics
Panics if r0 < r1
.
pub fn from_u64_prefix(a0: u64, a1: u64) -> Matrix
pub fn from_u64_prefix(a0: u64, a1: u64) -> Matrix
Compute the largest valid Lehmer update matrix for a prefix.
Compute the Lehmer update matrix for a0 and a1 such that the matrix is valid for any two large integers starting with the bits of a0 and a1.
See also mpn_hgcd2
in GMP, but ours handles the double precision bit
separately in lehmer_double
.
https://gmplib.org/repo/gmp-6.1/file/tip/mpn/generic/hgcd2.c#l226
§Panics
Panics if a0
does not have the highest bit set.
Panics if a0 < a1
.
pub fn from_u128_prefix(r0: u128, r1: u128) -> Matrix
pub fn from_u128_prefix(r0: u128, r1: u128) -> Matrix
Compute the Lehmer update matrix in full 64 bit precision.
Jebelean solves this by starting in double-precission followed by single precision once values are small enough. Cohen instead runs a single precision round, refreshes the r0 and r1 values and continues with another single precision round on top. Our approach is similar to Cohen, but instead doing the second round on the same matrix, we start we a fresh matrix and multiply both in the end. This requires 8 additional multiplications, but allows us to use the tighter stopping conditions from Jebelean. It also seems the simplest out of these solutions.
Trait Implementations§
impl Copy for Matrix
impl Eq for Matrix
impl StructuralPartialEq for Matrix
Auto Trait Implementations§
impl Freeze for Matrix
impl RefUnwindSafe for Matrix
impl Send for Matrix
impl Sync for Matrix
impl Unpin for Matrix
impl UnwindSafe for Matrix
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Size: 40 bytes