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// generated source. do not edit.
#![allow(non_upper_case_globals, unused_macros, unused_imports)]
use crate::low::macros::*;
// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0 OR ISC OR MIT-0
// ----------------------------------------------------------------------------
// Test bignums for coprimality, gcd(x,y) = 1
// Inputs x[m], y[n]; output function return; temporary buffer t[>=2*max(m,n)]
//
// extern uint64_t bignum_coprime(uint64_t m, const uint64_t *x, uint64_t n,
// const uint64_t *y, uint64_t *t);
//
// Test for whether two bignums are coprime (no common factor besides 1).
// This is equivalent to testing if their gcd is 1, but a bit faster than
// doing those two computations separately.
//
// Here bignum x is m digits long, y is n digits long and the temporary
// buffer t needs to be 2 * max(m,n) digits long. The return value is
// 1 if coprime(x,y) and 0 otherwise.
//
// Standard ARM ABI: X0 = m, X1 = x, X2 = n, X3 = y, X4 = t, returns X0
// ----------------------------------------------------------------------------
macro_rules! CHUNKSIZE {
() => {
"58"
};
}
// Pervasive variables
macro_rules! k {
() => {
"x9"
};
}
macro_rules! m {
() => {
"x4"
};
}
macro_rules! n {
() => {
"x5"
};
}
// Used via parameters in copy-in loop, then re-used as outer loop
// counter t and adaptive precision digit size l, which becomes a
// reduced version of k in later iterations but starts at l = k
macro_rules! x {
() => {
"x1"
};
}
macro_rules! y {
() => {
"x3"
};
}
macro_rules! t {
() => {
"x2"
};
}
macro_rules! l {
() => {
"x3"
};
}
// The matrix of update factors to apply to m and n
// Also used a couple of additional temporary variables for the swapping loop
// Also used as an extra down-counter in corrective negation loops
macro_rules! m_m {
() => {
"x6"
};
}
macro_rules! m_n {
() => {
"x7"
};
}
macro_rules! n_m {
() => {
"x8"
};
}
macro_rules! n_n {
() => {
"x1"
};
}
macro_rules! t3 {
() => {
"x6"
};
}
macro_rules! t4 {
() => {
"x7"
};
}
macro_rules! j {
() => {
"x6"
};
}
// General temporary variables and loop counters
macro_rules! i {
() => {
"x10"
};
}
macro_rules! t1 {
() => {
"x11"
};
}
macro_rules! t2 {
() => {
"x12"
};
}
// High and low proxies for the inner loop
// Then re-used for high and carry words during actual cross-multiplications
macro_rules! m_hi {
() => {
"x13"
};
}
macro_rules! n_hi {
() => {
"x14"
};
}
macro_rules! m_lo {
() => {
"x15"
};
}
macro_rules! n_lo {
() => {
"x16"
};
}
macro_rules! h1 {
() => {
"x13"
};
}
macro_rules! h2 {
() => {
"x14"
};
}
macro_rules! l1 {
() => {
"x15"
};
}
macro_rules! l2 {
() => {
"x16"
};
}
macro_rules! c1 {
() => {
"x17"
};
}
macro_rules! c2 {
() => {
"x19"
};
}
macro_rules! tt {
() => {
"x20"
};
}
/// Test bignums for coprimality, gcd(x,y) = 1
///
/// Inputs x[m], y[n]; output function return; temporary buffer t[>=2*max(m,n)]
///
/// Test for whether two bignums are coprime (no common factor besides 1).
/// This is equivalent to testing if their gcd is 1, but a bit faster than
/// doing those two computations separately.
///
/// Here bignum x is m digits long, y is n digits long and the temporary
/// buffer t needs to be 2 * max(m,n) digits long. The return value is
/// 1 if coprime(x,y) and 0 otherwise.
pub(crate) fn bignum_coprime(x: &[u64], y: &[u64], t: &mut [u64]) -> bool {
let ret: u64;
debug_assert!(t.len() >= 2 * core::cmp::max(x.len(), y.len()));
// SAFETY: inline assembly. see [crate::low::inline_assembly_safety] for safety info.
unsafe {
core::arch::asm!(
// We make use of just a couple of additional registers
Q!(" stp " "x19, x20, [sp, #-16] !"),
// Compute k = max(m,n), and if this is zero skip to the end. Note that
// in this case x0 = m = 0 so we return the right answer of "false"
Q!(" cmp " "x0, x2"),
Q!(" csel " k!() ", x2, x0, cc"),
Q!(" cbz " k!() ", " Label!("bignum_coprime_end", 2, After)),
// Set up inside w two size-k buffers m and n
Q!(" lsl " i!() ", " k!() ", #3"),
Q!(" add " n!() ", " m!() ", " i!()),
// Copy the input x into the buffer m, padding with zeros as needed
Q!(" mov " i!() ", xzr"),
Q!(" cbz " "x0, " Label!("bignum_coprime_xpadloop", 3, After)),
Q!(Label!("bignum_coprime_xloop", 4) ":"),
Q!(" ldr " t1!() ", [x1, " i!() ", lsl #3]"),
Q!(" str " t1!() ", [" m!() ", " i!() ", lsl #3]"),
Q!(" add " i!() ", " i!() ", #1"),
Q!(" cmp " i!() ", x0"),
Q!(" bcc " Label!("bignum_coprime_xloop", 4, Before)),
Q!(" cmp " i!() ", " k!()),
Q!(" bcs " Label!("bignum_coprime_xskip", 5, After)),
Q!(Label!("bignum_coprime_xpadloop", 3) ":"),
Q!(" str " "xzr, [" m!() ", " i!() ", lsl #3]"),
Q!(" add " i!() ", " i!() ", #1"),
Q!(" cmp " i!() ", " k!()),
Q!(" bcc " Label!("bignum_coprime_xpadloop", 3, Before)),
Q!(Label!("bignum_coprime_xskip", 5) ":"),
// Copy the input y into the buffer n, padding with zeros as needed
Q!(" mov " i!() ", xzr"),
Q!(" cbz " "x2, " Label!("bignum_coprime_ypadloop", 6, After)),
Q!(Label!("bignum_coprime_yloop", 7) ":"),
Q!(" ldr " t1!() ", [x3, " i!() ", lsl #3]"),
Q!(" str " t1!() ", [" n!() ", " i!() ", lsl #3]"),
Q!(" add " i!() ", " i!() ", #1"),
Q!(" cmp " i!() ", x2"),
Q!(" bcc " Label!("bignum_coprime_yloop", 7, Before)),
Q!(" cmp " i!() ", " k!()),
Q!(" bcs " Label!("bignum_coprime_yskip", 8, After)),
Q!(Label!("bignum_coprime_ypadloop", 6) ":"),
Q!(" str " "xzr, [" n!() ", " i!() ", lsl #3]"),
Q!(" add " i!() ", " i!() ", #1"),
Q!(" cmp " i!() ", " k!()),
Q!(" bcc " Label!("bignum_coprime_ypadloop", 6, Before)),
Q!(Label!("bignum_coprime_yskip", 8) ":"),
// Set up the outer loop count of 64 * sum of input sizes.
// The invariant is that m * n < 2^t at all times.
Q!(" add " t!() ", x0, x2"),
Q!(" lsl " t!() ", " t!() ", #6"),
// Record for the very end the OR of the lowest words.
// If the bottom bit is zero we know both are even so the answer is false.
// But since this is constant-time code we still execute all the main part.
Q!(" ldr " "x0, [" m!() "]"),
Q!(" ldr " t3!() ", [" n!() "]"),
Q!(" orr " "x0, x0, " t3!()),
// Now if n is even trigger a swap of m and n. This ensures that if
// one or other of m and n is odd then we make sure now that n is,
// as expected by our invariant later on.
Q!(" and " t3!() ", " t3!() ", #1"),
Q!(" sub " t3!() ", " t3!() ", #1"),
Q!(" mov " i!() ", xzr"),
Q!(Label!("bignum_coprime_swaploop", 9) ":"),
Q!(" ldr " t1!() ", [" m!() ", " i!() ", lsl #3]"),
Q!(" ldr " t2!() ", [" n!() ", " i!() ", lsl #3]"),
Q!(" eor " t4!() ", " t1!() ", " t2!()),
Q!(" and " t4!() ", " t4!() ", " t3!()),
Q!(" eor " t1!() ", " t1!() ", " t4!()),
Q!(" eor " t2!() ", " t2!() ", " t4!()),
Q!(" str " t1!() ", [" m!() ", " i!() ", lsl #3]"),
Q!(" str " t2!() ", [" n!() ", " i!() ", lsl #3]"),
Q!(" add " i!() ", " i!() ", #1"),
Q!(" cmp " i!() ", " k!()),
Q!(" bcc " Label!("bignum_coprime_swaploop", 9, Before)),
// Start of the main outer loop iterated t / CHUNKSIZE times
Q!(Label!("bignum_coprime_outerloop", 12) ":"),
// We need only bother with sharper l = min k (ceil(t/64)) digits
// Either both m and n fit in l digits, or m has become zero and so
// nothing happens in the loop anyway and this makes no difference.
Q!(" add " i!() ", " t!() ", #63"),
Q!(" lsr " l!() ", " i!() ", #6"),
Q!(" cmp " l!() ", " k!()),
Q!(" csel " l!() ", " k!() ", " l!() ", cs"),
// Select upper and lower proxies for both m and n to drive the inner
// loop. The lower proxies are simply the lowest digits themselves,
// m_lo = m[0] and n_lo = n[0], while the upper proxies are bitfields
// of the two inputs selected so their top bit (63) aligns with the
// most significant bit of *either* of the two inputs.
Q!(" mov " h1!() ", xzr"),
Q!(" mov " l1!() ", xzr"),
Q!(" mov " h2!() ", xzr"),
Q!(" mov " l2!() ", xzr"),
Q!(" mov " c2!() ", xzr"),
// and in this case h1 and h2 are those words
Q!(" mov " i!() ", xzr"),
Q!(Label!("bignum_coprime_toploop", 13) ":"),
Q!(" ldr " t1!() ", [" m!() ", " i!() ", lsl #3]"),
Q!(" ldr " t2!() ", [" n!() ", " i!() ", lsl #3]"),
Q!(" orr " c1!() ", " t1!() ", " t2!()),
Q!(" cmp " c1!() ", xzr"),
Q!(" and " c1!() ", " c2!() ", " h1!()),
Q!(" csel " l1!() ", " c1!() ", " l1!() ", ne"),
Q!(" and " c1!() ", " c2!() ", " h2!()),
Q!(" csel " l2!() ", " c1!() ", " l2!() ", ne"),
Q!(" csel " h1!() ", " t1!() ", " h1!() ", ne"),
Q!(" csel " h2!() ", " t2!() ", " h2!() ", ne"),
Q!(" csetm " c2!() ", ne"),
Q!(" add " i!() ", " i!() ", #1"),
Q!(" cmp " i!() ", " l!()),
Q!(" bcc " Label!("bignum_coprime_toploop", 13, Before)),
Q!(" orr " t1!() ", " h1!() ", " h2!()),
Q!(" clz " t2!() ", " t1!()),
Q!(" negs " c1!() ", " t2!()),
Q!(" lsl " h1!() ", " h1!() ", " t2!()),
Q!(" csel " l1!() ", " l1!() ", xzr, ne"),
Q!(" lsl " h2!() ", " h2!() ", " t2!()),
Q!(" csel " l2!() ", " l2!() ", xzr, ne"),
Q!(" lsr " l1!() ", " l1!() ", " c1!()),
Q!(" lsr " l2!() ", " l2!() ", " c1!()),
Q!(" orr " m_hi!() ", " h1!() ", " l1!()),
Q!(" orr " n_hi!() ", " h2!() ", " l2!()),
Q!(" ldr " m_lo!() ", [" m!() "]"),
Q!(" ldr " n_lo!() ", [" n!() "]"),
// Now the inner loop, with i as loop counter from CHUNKSIZE down.
// This records a matrix of updates to apply to the initial
// values of m and n with, at stage j:
//
// sgn * m' = (m_m * m - m_n * n) / 2^j
// -sgn * n' = (n_m * m - n_n * n) / 2^j
//
// where "sgn" is either +1 or -1, and we lose track of which except
// that both instance above are the same. This throwing away the sign
// costs nothing (since we have to correct in general anyway because
// of the proxied comparison) and makes things a bit simpler. But it
// is simply the parity of the number of times the first condition,
// used as the swapping criterion, fires in this loop.
Q!(" mov " m_m!() ", #1"),
Q!(" mov " m_n!() ", xzr"),
Q!(" mov " n_m!() ", xzr"),
Q!(" mov " n_n!() ", #1"),
Q!(" mov " i!() ", # " CHUNKSIZE!()),
// Conceptually in the inner loop we follow these steps:
//
// * If m_lo is odd and m_hi < n_hi, then swap the four pairs
// (m_hi,n_hi); (m_lo,n_lo); (m_m,n_m); (m_n,n_n)
//
// * Now, if m_lo is odd (old or new, doesn't matter as initial n_lo is odd)
// m_hi := m_hi - n_hi, m_lo := m_lo - n_lo
// m_m := m_m + n_m, m_n := m_n + n_n
//
// * Halve and double them
// m_hi := m_hi / 2, m_lo := m_lo / 2
// n_m := n_m * 2, n_n := n_n * 2
//
// The actual computation computes updates before actually swapping and
// then corrects as needed. It also maintains the invariant ~ZF <=> odd(m_lo),
// since it seems to reduce the dependent latency. Set that up first.
Q!(" ands " "xzr, " m_lo!() ", #1"),
Q!(Label!("bignum_coprime_innerloop", 14) ":"),
// At the start of the loop ~ZF <=> m_lo is odd; mask values accordingly
// Set the flags for m_hi - [~ZF] * n_hi so we know to flip things.
Q!(" csel " t1!() ", " n_hi!() ", xzr, ne"),
Q!(" csel " t2!() ", " n_lo!() ", xzr, ne"),
Q!(" csel " c1!() ", " n_m!() ", xzr, ne"),
Q!(" csel " c2!() ", " n_n!() ", xzr, ne"),
Q!(" ccmp " m_hi!() ", " n_hi!() ", #0x2, ne"),
// Compute subtractive updates, trivial in the case ZF <=> even(m_lo).
Q!(" sub " t1!() ", " m_hi!() ", " t1!()),
Q!(" sub " t2!() ", " m_lo!() ", " t2!()),
// If the subtraction borrows, swap things appropriately, negating where
// we've already subtracted so things are as if we actually swapped first.
Q!(" csel " n_hi!() ", " n_hi!() ", " m_hi!() ", cs"),
Q!(" cneg " t1!() ", " t1!() ", cc"),
Q!(" csel " n_lo!() ", " n_lo!() ", " m_lo!() ", cs"),
Q!(" cneg " m_lo!() ", " t2!() ", cc"),
Q!(" csel " n_m!() ", " n_m!() ", " m_m!() ", cs"),
Q!(" csel " n_n!() ", " n_n!() ", " m_n!() ", cs"),
// Update and shift while setting oddness flag for next iteration
// We look at bit 1 of t2 (m_lo before possible negation), which is
// safe because it is even.
Q!(" ands " "xzr, " t2!() ", #2"),
Q!(" add " m_m!() ", " m_m!() ", " c1!()),
Q!(" add " m_n!() ", " m_n!() ", " c2!()),
Q!(" lsr " m_hi!() ", " t1!() ", #1"),
Q!(" lsr " m_lo!() ", " m_lo!() ", #1"),
Q!(" add " n_m!() ", " n_m!() ", " n_m!()),
Q!(" add " n_n!() ", " n_n!() ", " n_n!()),
// Next iteration; don't disturb the flags since they are used at entry
Q!(" sub " i!() ", " i!() ", #1"),
Q!(" cbnz " i!() ", " Label!("bignum_coprime_innerloop", 14, Before)),
// Now actually compute the updates to m and n corresponding to that matrix,
// and correct the signs if they have gone negative. First we compute the
// (k+1)-sized updates
//
// c1::h1::m = m_m * m - m_n * n
// c2::h2::n = n_m * m - n_n * n
//
// then for each one, sign-correct and shift by CHUNKSIZE
Q!(" mov " h1!() ", xzr"),
Q!(" mov " h2!() ", xzr"),
Q!(" mov " c1!() ", xzr"),
Q!(" mov " c2!() ", xzr"),
Q!(" mov " i!() ", xzr"),
Q!(Label!("bignum_coprime_crossloop", 15) ":"),
Q!(" ldr " t1!() ", [" m!() ", " i!() ", lsl #3]"),
Q!(" ldr " t2!() ", [" n!() ", " i!() ", lsl #3]"),
Q!(" mul " l1!() ", " m_m!() ", " t1!()),
Q!(" mul " l2!() ", " m_n!() ", " t2!()),
Q!(" adds " l1!() ", " l1!() ", " h1!()),
Q!(" umulh " h1!() ", " m_m!() ", " t1!()),
Q!(" adc " h1!() ", " h1!() ", xzr"),
Q!(" umulh " tt!() ", " m_n!() ", " t2!()),
Q!(" sub " c1!() ", " tt!() ", " c1!()),
Q!(" subs " l1!() ", " l1!() ", " l2!()),
Q!(" str " l1!() ", [" m!() ", " i!() ", lsl #3]"),
Q!(" sbcs " h1!() ", " h1!() ", " c1!()),
Q!(" csetm " c1!() ", cc"),
Q!(" mul " l1!() ", " n_m!() ", " t1!()),
Q!(" mul " l2!() ", " n_n!() ", " t2!()),
Q!(" adds " l1!() ", " l1!() ", " h2!()),
Q!(" umulh " h2!() ", " n_m!() ", " t1!()),
Q!(" adc " h2!() ", " h2!() ", xzr"),
Q!(" umulh " tt!() ", " n_n!() ", " t2!()),
Q!(" sub " c2!() ", " tt!() ", " c2!()),
Q!(" subs " l1!() ", " l1!() ", " l2!()),
Q!(" str " l1!() ", [" n!() ", " i!() ", lsl #3]"),
Q!(" sbcs " h2!() ", " h2!() ", " c2!()),
Q!(" csetm " c2!() ", cc"),
Q!(" add " i!() ", " i!() ", #1"),
Q!(" cmp " i!() ", " l!()),
Q!(" bcc " Label!("bignum_coprime_crossloop", 15, Before)),
// Write back m optionally negated and shifted right CHUNKSIZE bits
Q!(" adds " "xzr, " c1!() ", " c1!()),
Q!(" ldr " l1!() ", [" m!() "]"),
Q!(" mov " i!() ", xzr"),
Q!(" sub " j!() ", " l!() ", #1"),
Q!(" cbz " j!() ", " Label!("bignum_coprime_negskip1", 16, After)),
Q!(Label!("bignum_coprime_negloop1", 17) ":"),
Q!(" add " t1!() ", " i!() ", #8"),
Q!(" ldr " t2!() ", [" m!() ", " t1!() "]"),
Q!(" extr " l1!() ", " t2!() ", " l1!() ", # " CHUNKSIZE!()),
Q!(" eor " l1!() ", " l1!() ", " c1!()),
Q!(" adcs " l1!() ", " l1!() ", xzr"),
Q!(" str " l1!() ", [" m!() ", " i!() "]"),
Q!(" mov " l1!() ", " t2!()),
Q!(" add " i!() ", " i!() ", #8"),
Q!(" sub " j!() ", " j!() ", #1"),
Q!(" cbnz " j!() ", " Label!("bignum_coprime_negloop1", 17, Before)),
Q!(Label!("bignum_coprime_negskip1", 16) ":"),
Q!(" extr " l1!() ", " h1!() ", " l1!() ", # " CHUNKSIZE!()),
Q!(" eor " l1!() ", " l1!() ", " c1!()),
Q!(" adcs " l1!() ", " l1!() ", xzr"),
Q!(" str " l1!() ", [" m!() ", " i!() "]"),
// Write back n optionally negated and shifted right CHUNKSIZE bits
Q!(" adds " "xzr, " c2!() ", " c2!()),
Q!(" ldr " l1!() ", [" n!() "]"),
Q!(" mov " i!() ", xzr"),
Q!(" sub " j!() ", " l!() ", #1"),
Q!(" cbz " j!() ", " Label!("bignum_coprime_negskip2", 18, After)),
Q!(Label!("bignum_coprime_negloop2", 19) ":"),
Q!(" add " t1!() ", " i!() ", #8"),
Q!(" ldr " t2!() ", [" n!() ", " t1!() "]"),
Q!(" extr " l1!() ", " t2!() ", " l1!() ", # " CHUNKSIZE!()),
Q!(" eor " l1!() ", " l1!() ", " c2!()),
Q!(" adcs " l1!() ", " l1!() ", xzr"),
Q!(" str " l1!() ", [" n!() ", " i!() "]"),
Q!(" mov " l1!() ", " t2!()),
Q!(" add " i!() ", " i!() ", #8"),
Q!(" sub " j!() ", " j!() ", #1"),
Q!(" cbnz " j!() ", " Label!("bignum_coprime_negloop2", 19, Before)),
Q!(Label!("bignum_coprime_negskip2", 18) ":"),
Q!(" extr " l1!() ", " h2!() ", " l1!() ", # " CHUNKSIZE!()),
Q!(" eor " l1!() ", " l1!() ", " c2!()),
Q!(" adcs " l1!() ", " l1!() ", xzr"),
Q!(" str " l1!() ", [" n!() ", " i!() "]"),
// End of main loop. We can stop if t' <= 0 since then m * n < 2^0, which
// since n is odd (in the main cases where we had one or other input odd)
// means that m = 0 and n is the final gcd. Moreover we do in fact need to
// maintain strictly t > 0 in the main loop, or the computation of the
// optimized digit bound l could collapse to 0.
Q!(" subs " t!() ", " t!() ", # " CHUNKSIZE!()),
Q!(" bhi " Label!("bignum_coprime_outerloop", 12, Before)),
// Now compare n with 1 (OR of the XORs in t1)
Q!(" ldr " t1!() ", [" n!() "]"),
Q!(" eor " t1!() ", " t1!() ", #1"),
Q!(" cmp " k!() ", #1"),
Q!(" beq " Label!("bignum_coprime_finalcomb", 20, After)),
Q!(" mov " i!() ", #1"),
Q!(Label!("bignum_coprime_compareloop", 21) ":"),
Q!(" ldr " t2!() ", [" n!() ", " i!() ", lsl #3]"),
Q!(" orr " t1!() ", " t1!() ", " t2!()),
Q!(" add " i!() ", " i!() ", #1"),
Q!(" cmp " i!() ", " k!()),
Q!(" bcc " Label!("bignum_coprime_compareloop", 21, Before)),
// Now combine that with original oddness flag, which is still in x0
Q!(Label!("bignum_coprime_finalcomb", 20) ":"),
Q!(" cmp " t1!() ", xzr"),
Q!(" cset " t1!() ", eq"),
Q!(" and " "x0, x0, " t1!()),
Q!(Label!("bignum_coprime_end", 2) ":"),
Q!(" ldp " "x19, x20, [sp], #16"),
inout("x0") x.len() => ret,
inout("x1") x.as_ptr() => _,
inout("x2") y.len() => _,
inout("x3") y.as_ptr() => _,
inout("x4") t.as_mut_ptr() => _,
// clobbers
out("x10") _,
out("x11") _,
out("x12") _,
out("x13") _,
out("x14") _,
out("x15") _,
out("x16") _,
out("x17") _,
out("x20") _,
out("x5") _,
out("x6") _,
out("x7") _,
out("x8") _,
out("x9") _,
)
};
ret > 0
}