1 //! Simple variable-time big integer implementation
4 use core::marker::PhantomData;
6 const WORD_COUNT_4096: usize = 4096 / 64;
7 const WORD_COUNT_256: usize = 256 / 64;
8 const WORD_COUNT_384: usize = 384 / 64;
10 // RFC 5702 indicates RSA keys can be up to 4096 bits
11 #[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Ord)]
12 pub(super) struct U4096([u64; WORD_COUNT_4096]);
14 #[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Ord)]
15 pub(super) struct U256([u64; WORD_COUNT_256]);
17 #[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Ord)]
18 pub(super) struct U384([u64; WORD_COUNT_384]);
20 pub(super) trait Int: Clone + Ord + Sized {
23 fn from_be_bytes(b: &[u8]) -> Result<Self, ()>;
24 fn limbs(&self) -> &[u64];
27 const ZERO: U256 = U256([0; 4]);
28 const BYTES: usize = 32;
29 fn from_be_bytes(b: &[u8]) -> Result<Self, ()> { Self::from_be_bytes(b) }
30 fn limbs(&self) -> &[u64] { &self.0 }
33 const ZERO: U384 = U384([0; 6]);
34 const BYTES: usize = 48;
35 fn from_be_bytes(b: &[u8]) -> Result<Self, ()> { Self::from_be_bytes(b) }
36 fn limbs(&self) -> &[u64] { &self.0 }
39 /// Defines a *PRIME* Modulus
40 pub(super) trait PrimeModulus<I: Int> {
42 const R_SQUARED_MOD_PRIME: I;
43 const NEGATIVE_PRIME_INV_MOD_R: I;
46 #[derive(Clone, Debug, PartialEq, Eq)] // Ord doesn't make sense cause we have an R factor
47 pub(super) struct U256Mod<M: PrimeModulus<U256>>(U256, PhantomData<M>);
49 #[derive(Clone, Debug, PartialEq, Eq)] // Ord doesn't make sense cause we have an R factor
50 pub(super) struct U384Mod<M: PrimeModulus<U384>>(U384, PhantomData<M>);
52 macro_rules! debug_unwrap { ($v: expr) => { {
54 debug_assert!(v.is_ok());
57 Err(e) => return Err(e),
61 // Various const versions of existing slice utilities
62 /// Const version of `&a[start..end]`
63 const fn const_subslice<'a, T>(a: &'a [T], start: usize, end: usize) -> &'a [T] {
64 assert!(start <= a.len());
65 assert!(end <= a.len());
66 assert!(end >= start);
67 let mut startptr = a.as_ptr();
68 startptr = unsafe { startptr.add(start) };
69 let len = end - start;
70 // The docs for from_raw_parts do not mention any requirements that the pointer be valid if the
71 // length is zero, aside from requiring proper alignment (which is met here). Thus,
72 // one-past-the-end should be an acceptable pointer for a 0-length slice.
73 unsafe { alloc::slice::from_raw_parts(startptr, len) }
76 /// Const version of `dest[dest_start..dest_end].copy_from_slice(source)`
78 /// Once `const_mut_refs` is stable we can convert this to a function
79 macro_rules! copy_from_slice {
80 ($dest: ident, $dest_start: expr, $dest_end: expr, $source: ident) => { {
81 let dest_start = $dest_start;
82 let dest_end = $dest_end;
83 assert!(dest_start <= $dest.len());
84 assert!(dest_end <= $dest.len());
85 assert!(dest_end >= dest_start);
86 assert!(dest_end - dest_start == $source.len());
88 while i < $source.len() {
89 $dest[i + dest_start] = $source[i];
95 /// Const version of a > b
96 const fn slice_greater_than(a: &[u64], b: &[u64]) -> bool {
97 debug_assert!(a.len() == b.len());
98 let len = if a.len() <= b.len() { a.len() } else { b.len() };
101 if a[i] > b[i] { return true; }
102 else if a[i] < b[i] { return false; }
108 /// Const version of a == b
109 const fn slice_equal(a: &[u64], b: &[u64]) -> bool {
110 debug_assert!(a.len() == b.len());
111 let len = if a.len() <= b.len() { a.len() } else { b.len() };
114 if a[i] != b[i] { return false; }
120 /// Adds a single u64 valuein-place, returning an overflow flag, in which case one out-of-bounds
121 /// high bit is implicitly included in the result.
123 /// Once `const_mut_refs` is stable we can convert this to a function
124 macro_rules! add_u64 { ($a: ident, $b: expr) => { {
129 let (v, carry) = $a[i].overflowing_add(add);
132 if add == 0 { break; }
140 /// Negates the given u64 slice.
142 /// Once `const_mut_refs` is stable we can convert this to a function
143 macro_rules! negate { ($v: ident) => { {
146 $v[i] ^= 0xffff_ffff_ffff_ffff;
152 /// Doubles in-place, returning an overflow flag, in which case one out-of-bounds high bit is
153 /// implicitly included in the result.
155 /// Once `const_mut_refs` is stable we can convert this to a function
156 macro_rules! double { ($a: ident) => { {
157 { let _: &[u64] = &$a; } // Force type resolution
159 let mut carry = false;
162 let next_carry = ($a[i] & (1 << 63)) != 0;
163 let (v, _next_carry_2) = ($a[i] << 1).overflowing_add(carry as u64);
165 debug_assert!(!_next_carry_2, "Adding one to 0x7ffff..*2 is only 0xffff..");
167 // Note that we can ignore _next_carry_2 here as we never need it - it cannot be set if
168 // next_carry is not set and at max 0xffff..*2 + 1 is only 0x1ffff.. (i.e. we can not need
179 macro_rules! define_add { ($name: ident, $len: expr) => {
180 /// Adds two $len-64-bit integers together, returning a new $len-64-bit integer and an overflow
181 /// bit, with the same semantics as the std [`u64::overflowing_add`] method.
182 const fn $name(a: &[u64], b: &[u64]) -> ([u64; $len], bool) {
183 debug_assert!(a.len() == $len);
184 debug_assert!(b.len() == $len);
185 let mut r = [0; $len];
186 let mut carry = false;
187 let mut i = $len - 1;
189 let (v, mut new_carry) = a[i].overflowing_add(b[i]);
190 let (v2, new_new_carry) = v.overflowing_add(carry as u64);
191 new_carry |= new_new_carry;
202 define_add!(add_2, 2);
203 define_add!(add_3, 3);
204 define_add!(add_4, 4);
205 define_add!(add_6, 6);
206 define_add!(add_8, 8);
207 define_add!(add_12, 12);
208 define_add!(add_16, 16);
209 define_add!(add_32, 32);
210 define_add!(add_64, 64);
211 define_add!(add_128, 128);
213 macro_rules! define_sub { ($name: ident, $name_abs: ident, $len: expr) => {
214 /// Subtracts the `b` $len-64-bit integer from the `a` $len-64-bit integer, returning a new
215 /// $len-64-bit integer and an overflow bit, with the same semantics as the std
216 /// [`u64::overflowing_sub`] method.
217 const fn $name(a: &[u64], b: &[u64]) -> ([u64; $len], bool) {
218 debug_assert!(a.len() == $len);
219 debug_assert!(b.len() == $len);
220 let mut r = [0; $len];
221 let mut carry = false;
222 let mut i = $len - 1;
224 let (v, mut new_carry) = a[i].overflowing_sub(b[i]);
225 let (v2, new_new_carry) = v.overflowing_sub(carry as u64);
226 new_carry |= new_new_carry;
236 /// Subtracts the `b` $len-64-bit integer from the `a` $len-64-bit integer, returning a new
237 /// $len-64-bit integer representing the absolute value of the result, as well as a sign bit.
239 const fn $name_abs(a: &[u64], b: &[u64]) -> ([u64; $len], bool) {
240 let (mut res, neg) = $name(a, b);
248 define_sub!(sub_2, sub_abs_2, 2);
249 define_sub!(sub_3, sub_abs_3, 3);
250 define_sub!(sub_4, sub_abs_4, 4);
251 define_sub!(sub_6, sub_abs_6, 6);
252 define_sub!(sub_8, sub_abs_8, 8);
253 define_sub!(sub_12, sub_abs_12, 12);
254 define_sub!(sub_16, sub_abs_16, 16);
255 define_sub!(sub_32, sub_abs_32, 32);
256 define_sub!(sub_64, sub_abs_64, 64);
257 define_sub!(sub_128, sub_abs_128, 128);
259 /// Multiplies two 128-bit integers together, returning a new 256-bit integer.
261 /// This is the base case for our multiplication, taking advantage of Rust's native 128-bit int
262 /// types to do multiplication (potentially) natively.
263 const fn mul_2(a: &[u64], b: &[u64]) -> [u64; 4] {
264 debug_assert!(a.len() == 2);
265 debug_assert!(b.len() == 2);
267 // Gradeschool multiplication is way faster here.
268 let (a0, a1) = (a[0] as u128, a[1] as u128);
269 let (b0, b1) = (b[0] as u128, b[1] as u128);
273 let (z1, i_carry_a) = z1i.overflowing_add(z1j);
276 add_mul_2_parts(z2, z1, z0, i_carry_a)
279 /// Adds the gradeschool multiplication intermediate parts to a final 256-bit result
280 const fn add_mul_2_parts(z2: u128, z1: u128, z0: u128, i_carry_a: bool) -> [u64; 4] {
281 let z2a = ((z2 >> 64) & 0xffff_ffff_ffff_ffff) as u64;
282 let z1a = ((z1 >> 64) & 0xffff_ffff_ffff_ffff) as u64;
283 let z0a = ((z0 >> 64) & 0xffff_ffff_ffff_ffff) as u64;
284 let z2b = (z2 & 0xffff_ffff_ffff_ffff) as u64;
285 let z1b = (z1 & 0xffff_ffff_ffff_ffff) as u64;
286 let z0b = (z0 & 0xffff_ffff_ffff_ffff) as u64;
290 let (k, j_carry) = z0a.overflowing_add(z1b);
292 let (mut j, i_carry_b) = z1a.overflowing_add(z2b);
294 (j, i_carry_c) = j.overflowing_add(j_carry as u64);
296 let i_carry = i_carry_a as u64 + i_carry_b as u64 + i_carry_c as u64;
297 let (i, must_not_overflow) = z2a.overflowing_add(i_carry);
298 debug_assert!(!must_not_overflow, "Two 2*64 bit numbers, multiplied, will not use more than 4*64 bits");
303 const fn mul_3(a: &[u64], b: &[u64]) -> [u64; 6] {
304 debug_assert!(a.len() == 3);
305 debug_assert!(b.len() == 3);
307 let (a0, a1, a2) = (a[0] as u128, a[1] as u128, a[2] as u128);
308 let (b0, b1, b2) = (b[0] as u128, b[1] as u128, b[2] as u128);
320 let r5 = ((m4 >> 0) & 0xffff_ffff_ffff_ffff) as u64;
322 let r4a = ((m4 >> 64) & 0xffff_ffff_ffff_ffff) as u64;
323 let r4b = ((m3a >> 0) & 0xffff_ffff_ffff_ffff) as u64;
324 let r4c = ((m3b >> 0) & 0xffff_ffff_ffff_ffff) as u64;
326 let r3a = ((m3a >> 64) & 0xffff_ffff_ffff_ffff) as u64;
327 let r3b = ((m3b >> 64) & 0xffff_ffff_ffff_ffff) as u64;
328 let r3c = ((m2a >> 0 ) & 0xffff_ffff_ffff_ffff) as u64;
329 let r3d = ((m2b >> 0 ) & 0xffff_ffff_ffff_ffff) as u64;
330 let r3e = ((m2c >> 0 ) & 0xffff_ffff_ffff_ffff) as u64;
332 let r2a = ((m2a >> 64) & 0xffff_ffff_ffff_ffff) as u64;
333 let r2b = ((m2b >> 64) & 0xffff_ffff_ffff_ffff) as u64;
334 let r2c = ((m2c >> 64) & 0xffff_ffff_ffff_ffff) as u64;
335 let r2d = ((m1a >> 0 ) & 0xffff_ffff_ffff_ffff) as u64;
336 let r2e = ((m1b >> 0 ) & 0xffff_ffff_ffff_ffff) as u64;
338 let r1a = ((m1a >> 64) & 0xffff_ffff_ffff_ffff) as u64;
339 let r1b = ((m1b >> 64) & 0xffff_ffff_ffff_ffff) as u64;
340 let r1c = ((m0 >> 0 ) & 0xffff_ffff_ffff_ffff) as u64;
342 let r0a = ((m0 >> 64) & 0xffff_ffff_ffff_ffff) as u64;
344 let (r4, r3_ca) = r4a.overflowing_add(r4b);
345 let (r4, r3_cb) = r4.overflowing_add(r4c);
346 let r3_c = r3_ca as u64 + r3_cb as u64;
348 let (r3, r2_ca) = r3a.overflowing_add(r3b);
349 let (r3, r2_cb) = r3.overflowing_add(r3c);
350 let (r3, r2_cc) = r3.overflowing_add(r3d);
351 let (r3, r2_cd) = r3.overflowing_add(r3e);
352 let (r3, r2_ce) = r3.overflowing_add(r3_c);
353 let r2_c = r2_ca as u64 + r2_cb as u64 + r2_cc as u64 + r2_cd as u64 + r2_ce as u64;
355 let (r2, r1_ca) = r2a.overflowing_add(r2b);
356 let (r2, r1_cb) = r2.overflowing_add(r2c);
357 let (r2, r1_cc) = r2.overflowing_add(r2d);
358 let (r2, r1_cd) = r2.overflowing_add(r2e);
359 let (r2, r1_ce) = r2.overflowing_add(r2_c);
360 let r1_c = r1_ca as u64 + r1_cb as u64 + r1_cc as u64 + r1_cd as u64 + r1_ce as u64;
362 let (r1, r0_ca) = r1a.overflowing_add(r1b);
363 let (r1, r0_cb) = r1.overflowing_add(r1c);
364 let (r1, r0_cc) = r1.overflowing_add(r1_c);
365 let r0_c = r0_ca as u64 + r0_cb as u64 + r0_cc as u64;
367 let (r0, must_not_overflow) = r0a.overflowing_add(r0_c);
368 debug_assert!(!must_not_overflow, "Two 3*64 bit numbers, multiplied, will not use more than 6*64 bits");
370 [r0, r1, r2, r3, r4, r5]
373 macro_rules! define_mul { ($name: ident, $len: expr, $submul: ident, $add: ident, $subadd: ident, $sub: ident, $subsub: ident) => {
374 /// Multiplies two $len-64-bit integers together, returning a new $len*2-64-bit integer.
375 const fn $name(a: &[u64], b: &[u64]) -> [u64; $len * 2] {
376 // We could probably get a bit faster doing gradeschool multiplication for some smaller
377 // sizes, but its easier to just have one variable-length multiplication, so we do
378 // Karatsuba always here.
379 debug_assert!(a.len() == $len);
380 debug_assert!(b.len() == $len);
382 let a0 = const_subslice(a, 0, $len / 2);
383 let a1 = const_subslice(a, $len / 2, $len);
384 let b0 = const_subslice(b, 0, $len / 2);
385 let b1 = const_subslice(b, $len / 2, $len);
387 let z2 = $submul(a0, b0);
388 let z0 = $submul(a1, b1);
390 let (z1a_max, z1a_min, z1a_sign) =
391 if slice_greater_than(&a1, &a0) { (a1, a0, true) } else { (a0, a1, false) };
392 let (z1b_max, z1b_min, z1b_sign) =
393 if slice_greater_than(&b1, &b0) { (b1, b0, true) } else { (b0, b1, false) };
395 let z1a = $subsub(z1a_max, z1a_min);
396 debug_assert!(!z1a.1, "z1a_max was selected to be greater than z1a_min");
397 let z1b = $subsub(z1b_max, z1b_min);
398 debug_assert!(!z1b.1, "z1b_max was selected to be greater than z1b_min");
399 let z1m_sign = z1a_sign == z1b_sign;
401 let z1m = $submul(&z1a.0, &z1b.0);
402 let z1n = $add(&z0, &z2);
403 let mut z1_carry = z1n.1;
404 let z1 = if z1m_sign {
405 let r = $sub(&z1n.0, &z1m);
406 if r.1 { z1_carry ^= true; }
409 let r = $add(&z1n.0, &z1m);
410 if r.1 { z1_carry = true; }
414 let l = const_subslice(&z0, $len / 2, $len);
415 let (k, j_carry) = $subadd(const_subslice(&z0, 0, $len / 2), const_subslice(&z1, $len / 2, $len));
416 let (mut j, i_carry_a) = $subadd(const_subslice(&z1, 0, $len / 2), const_subslice(&z2, $len / 2, $len));
417 let mut i_carry_b = false;
419 i_carry_b = add_u64!(j, 1);
421 let mut i = [0; $len / 2];
422 let i_source = const_subslice(&z2, 0, $len / 2);
423 copy_from_slice!(i, 0, $len / 2, i_source);
424 let i_carry = i_carry_a as u64 + i_carry_b as u64 + z1_carry as u64;
426 let must_not_overflow = add_u64!(i, i_carry);
427 debug_assert!(!must_not_overflow, "Two N*64 bit numbers, multiplied, will not use more than 2*N*64 bits");
430 let mut res = [0; $len * 2];
431 copy_from_slice!(res, $len * 2 * 0 / 4, $len * 2 * 1 / 4, i);
432 copy_from_slice!(res, $len * 2 * 1 / 4, $len * 2 * 2 / 4, j);
433 copy_from_slice!(res, $len * 2 * 2 / 4, $len * 2 * 3 / 4, k);
434 copy_from_slice!(res, $len * 2 * 3 / 4, $len * 2 * 4 / 4, l);
439 define_mul!(mul_4, 4, mul_2, add_4, add_2, sub_4, sub_2);
440 define_mul!(mul_6, 6, mul_3, add_6, add_3, sub_6, sub_3);
441 define_mul!(mul_8, 8, mul_4, add_8, add_4, sub_8, sub_4);
442 define_mul!(mul_16, 16, mul_8, add_16, add_8, sub_16, sub_8);
443 define_mul!(mul_32, 32, mul_16, add_32, add_16, sub_32, sub_16);
444 define_mul!(mul_64, 64, mul_32, add_64, add_32, sub_64, sub_32);
447 /// Squares a 128-bit integer, returning a new 256-bit integer.
449 /// This is the base case for our squaring, taking advantage of Rust's native 128-bit int
450 /// types to do multiplication (potentially) natively.
451 const fn sqr_2(a: &[u64]) -> [u64; 4] {
452 debug_assert!(a.len() == 2);
454 let (a0, a1) = (a[0] as u128, a[1] as u128);
456 let mut z1 = a0 * a1;
457 let i_carry_a = z1 & (1u128 << 127) != 0;
461 add_mul_2_parts(z2, z1, z0, i_carry_a)
464 macro_rules! define_sqr { ($name: ident, $len: expr, $submul: ident, $subsqr: ident, $subadd: ident) => {
465 /// Squares a $len-64-bit integers, returning a new $len*2-64-bit integer.
466 const fn $name(a: &[u64]) -> [u64; $len * 2] {
467 // Squaring is only 3 half-length multiplies/squares in gradeschool math, so use that.
468 debug_assert!(a.len() == $len);
470 let hi = const_subslice(a, 0, $len / 2);
471 let lo = const_subslice(a, $len / 2, $len);
473 let v0 = $subsqr(lo);
474 let mut v1 = $submul(hi, lo);
475 let i_carry_a = double!(v1);
476 let v2 = $subsqr(hi);
478 let l = const_subslice(&v0, $len / 2, $len);
479 let (k, j_carry) = $subadd(const_subslice(&v0, 0, $len / 2), const_subslice(&v1, $len / 2, $len));
480 let (mut j, i_carry_b) = $subadd(const_subslice(&v1, 0, $len / 2), const_subslice(&v2, $len / 2, $len));
482 let mut i = [0; $len / 2];
483 let i_source = const_subslice(&v2, 0, $len / 2);
484 copy_from_slice!(i, 0, $len / 2, i_source);
486 let mut i_carry_c = false;
488 i_carry_c = add_u64!(j, 1);
490 let i_carry = i_carry_a as u64 + i_carry_b as u64 + i_carry_c as u64;
492 let must_not_overflow = add_u64!(i, i_carry);
493 debug_assert!(!must_not_overflow, "Two N*64 bit numbers, multiplied, will not use more than 2*N*64 bits");
496 let mut res = [0; $len * 2];
497 copy_from_slice!(res, $len * 2 * 0 / 4, $len * 2 * 1 / 4, i);
498 copy_from_slice!(res, $len * 2 * 1 / 4, $len * 2 * 2 / 4, j);
499 copy_from_slice!(res, $len * 2 * 2 / 4, $len * 2 * 3 / 4, k);
500 copy_from_slice!(res, $len * 2 * 3 / 4, $len * 2 * 4 / 4, l);
505 // TODO: Write an optimized sqr_3 (though secp384r1 is barely used)
506 const fn sqr_3(a: &[u64]) -> [u64; 6] { mul_3(a, a) }
508 define_sqr!(sqr_4, 4, mul_2, sqr_2, add_2);
509 define_sqr!(sqr_6, 6, mul_3, sqr_3, add_3);
510 define_sqr!(sqr_8, 8, mul_4, sqr_4, add_4);
511 define_sqr!(sqr_16, 16, mul_8, sqr_8, add_8);
512 define_sqr!(sqr_32, 32, mul_16, sqr_16, add_16);
513 define_sqr!(sqr_64, 64, mul_32, sqr_32, add_32);
515 macro_rules! dummy_pre_push { ($name: ident, $len: expr) => {} }
516 macro_rules! vec_pre_push { ($name: ident, $len: expr) => { $name.push([0; $len]); } }
518 macro_rules! define_div_rem { ($name: ident, $len: expr, $sub: ident, $heap_init: expr, $pre_push: ident $(, $const_opt: tt)?) => {
519 /// Divides two $len-64-bit integers, `a` by `b`, returning the quotient and remainder
521 /// Fails iff `b` is zero.
522 $($const_opt)? fn $name(a: &[u64; $len], b: &[u64; $len]) -> Result<([u64; $len], [u64; $len]), ()> {
523 if slice_equal(b, &[0; $len]) { return Err(()); }
526 let mut pow2s = $heap_init;
527 let mut pow2s_count = 0;
528 while slice_greater_than(a, &b_pow) {
529 $pre_push!(pow2s, $len);
530 pow2s[pow2s_count] = b_pow;
532 let double_overflow = double!(b_pow);
533 if double_overflow { break; }
535 let mut quot = [0; $len];
537 let mut pow2 = pow2s_count as isize - 1;
539 let b_pow = pow2s[pow2 as usize];
540 let overflow = double!(quot);
541 debug_assert!(!overflow);
542 if slice_greater_than(&rem, &b_pow) {
543 let (r, carry) = $sub(&rem, &b_pow);
544 debug_assert!(!carry);
550 if slice_equal(&rem, b) {
551 let overflow = add_u64!(quot, 1);
552 debug_assert!(!overflow);
553 Ok((quot, [0; $len]))
561 define_div_rem!(div_rem_2, 2, sub_2, [[0; 2]; 2 * 64], dummy_pre_push, const);
562 define_div_rem!(div_rem_4, 4, sub_4, [[0; 4]; 4 * 64], dummy_pre_push, const); // Uses 8 KiB of stack
563 define_div_rem!(div_rem_6, 6, sub_6, [[0; 6]; 6 * 64], dummy_pre_push, const); // Uses 18 KiB of stack!
564 #[cfg(debug_assertions)]
565 define_div_rem!(div_rem_8, 8, sub_8, [[0; 8]; 8 * 64], dummy_pre_push, const); // Uses 32 KiB of stack!
566 #[cfg(debug_assertions)]
567 define_div_rem!(div_rem_12, 12, sub_12, [[0; 12]; 12 * 64], dummy_pre_push, const); // Uses 72 KiB of stack!
568 define_div_rem!(div_rem_64, 64, sub_64, Vec::new(), vec_pre_push); // Uses up to 2 MiB of heap
569 #[cfg(debug_assertions)]
570 define_div_rem!(div_rem_128, 128, sub_128, Vec::new(), vec_pre_push); // Uses up to 8 MiB of heap
572 macro_rules! define_mod_inv { ($name: ident, $len: expr, $div: ident, $add: ident, $sub_abs: ident, $mul: ident) => {
573 /// Calculates the modular inverse of a $len-64-bit number with respect to the given modulus,
575 const fn $name(a: &[u64; $len], m: &[u64; $len]) -> Result<[u64; $len], ()> {
576 if slice_equal(a, &[0; $len]) || slice_equal(m, &[0; $len]) { return Err(()); }
578 let (mut s, mut old_s) = ([0; $len], [0; $len]);
583 let (mut old_s_neg, mut s_neg) = (false, false);
585 while !slice_equal(&r, &[0; $len]) {
586 let (quot, new_r) = debug_unwrap!($div(&old_r, &r));
588 let new_sa = $mul(", &s);
589 debug_assert!(slice_equal(const_subslice(&new_sa, 0, $len), &[0; $len]), "S overflowed");
590 let (new_s, new_s_neg) = match (old_s_neg, s_neg) {
592 let (new_s, overflow) = $add(&old_s, const_subslice(&new_sa, $len, new_sa.len()));
593 debug_assert!(!overflow);
597 let (new_s, overflow) = $add(&old_s, const_subslice(&new_sa, $len, new_sa.len()));
598 debug_assert!(!overflow);
602 let (new_s, overflow) = $add(&old_s, const_subslice(&new_sa, $len, new_sa.len()));
603 debug_assert!(!overflow);
606 (false, false) => $sub_abs(&old_s, const_subslice(&new_sa, $len, new_sa.len())),
618 // At this point old_r contains our GCD and old_s our first Bézout's identity coefficient.
619 if !slice_equal(const_subslice(&old_r, 0, $len - 1), &[0; $len - 1]) || old_r[$len - 1] != 1 {
622 debug_assert!(slice_greater_than(m, &old_s));
624 let (modinv, underflow) = $sub_abs(m, &old_s);
625 debug_assert!(!underflow);
626 debug_assert!(slice_greater_than(m, &modinv));
635 define_mod_inv!(mod_inv_2, 2, div_rem_2, add_2, sub_abs_2, mul_2);
636 define_mod_inv!(mod_inv_4, 4, div_rem_4, add_4, sub_abs_4, mul_4);
637 define_mod_inv!(mod_inv_6, 6, div_rem_6, add_6, sub_abs_6, mul_6);
639 define_mod_inv!(mod_inv_8, 8, div_rem_8, add_8, sub_abs_8, mul_8);
642 /// Constructs a new [`U4096`] from a variable number of big-endian bytes.
643 pub(super) fn from_be_bytes(bytes: &[u8]) -> Result<U4096, ()> {
644 if bytes.len() > 4096/8 { return Err(()); }
645 let u64s = (bytes.len() + 7) / 8;
646 let mut res = [0; WORD_COUNT_4096];
649 let pos = (u64s - i) * 8;
650 let start = bytes.len().saturating_sub(pos);
651 let end = bytes.len() + 8 - pos;
652 b[8 + start - end..].copy_from_slice(&bytes[start..end]);
653 res[i + WORD_COUNT_4096 - u64s] = u64::from_be_bytes(b);
658 /// Naively multiplies `self` * `b` mod `m`, returning a new [`U4096`].
660 /// Fails iff m is 0 or self or b are greater than m.
661 #[cfg(debug_assertions)]
662 fn mulmod_naive(&self, b: &U4096, m: &U4096) -> Result<U4096, ()> {
663 if m.0 == [0; WORD_COUNT_4096] { return Err(()); }
664 if self > m || b > m { return Err(()); }
666 let mul = mul_64(&self.0, &b.0);
668 let mut m_zeros = [0; 128];
669 m_zeros[WORD_COUNT_4096..].copy_from_slice(&m.0);
670 let (_, rem) = div_rem_128(&mul, &m_zeros)?;
671 let mut res = [0; WORD_COUNT_4096];
672 debug_assert_eq!(&rem[..WORD_COUNT_4096], &[0; WORD_COUNT_4096]);
673 res.copy_from_slice(&rem[WORD_COUNT_4096..]);
677 /// Calculates `self` ^ `exp` mod `m`, returning a new [`U4096`].
679 /// Fails iff m is 0, even, or self or b are greater than m.
680 pub(super) fn expmod_odd_mod(&self, mut exp: u32, m: &U4096) -> Result<U4096, ()> {
681 #![allow(non_camel_case_types)]
683 if m.0 == [0; WORD_COUNT_4096] { return Err(()); }
684 if m.0[WORD_COUNT_4096 - 1] & 1 == 0 { return Err(()); }
685 if self > m { return Err(()); }
687 let mut t = [0; WORD_COUNT_4096];
688 if &m.0[..WORD_COUNT_4096 - 1] == &[0; WORD_COUNT_4096 - 1] && m.0[WORD_COUNT_4096 - 1] == 1 {
691 t[WORD_COUNT_4096 - 1] = 1;
692 if exp == 0 { return Ok(U4096(t)); }
694 // Because m is not even, using 2^4096 as the Montgomery R value is always safe - it is
695 // guaranteed to be co-prime with any non-even integer.
697 type mul_ty = fn(&[u64], &[u64]) -> [u64; WORD_COUNT_4096 * 2];
698 type sqr_ty = fn(&[u64]) -> [u64; WORD_COUNT_4096 * 2];
699 type add_double_ty = fn(&[u64], &[u64]) -> ([u64; WORD_COUNT_4096 * 2], bool);
700 type sub_ty = fn(&[u64], &[u64]) -> ([u64; WORD_COUNT_4096], bool);
701 let (word_count, log_bits, mul, sqr, add_double, sub) =
702 if m.0[..WORD_COUNT_4096 / 2] == [0; WORD_COUNT_4096 / 2] {
703 if m.0[..WORD_COUNT_4096 * 3 / 4] == [0; WORD_COUNT_4096 * 3 / 4] {
704 fn mul_16_subarr(a: &[u64], b: &[u64]) -> [u64; WORD_COUNT_4096 * 2] {
705 debug_assert_eq!(a.len(), WORD_COUNT_4096);
706 debug_assert_eq!(b.len(), WORD_COUNT_4096);
707 debug_assert_eq!(&a[..WORD_COUNT_4096 * 3 / 4], &[0; WORD_COUNT_4096 * 3 / 4]);
708 debug_assert_eq!(&b[..WORD_COUNT_4096 * 3 / 4], &[0; WORD_COUNT_4096 * 3 / 4]);
709 let mut res = [0; WORD_COUNT_4096 * 2];
710 res[WORD_COUNT_4096 + WORD_COUNT_4096 / 2..].copy_from_slice(
711 &mul_16(&a[WORD_COUNT_4096 * 3 / 4..], &b[WORD_COUNT_4096 * 3 / 4..]));
714 fn sqr_16_subarr(a: &[u64]) -> [u64; WORD_COUNT_4096 * 2] {
715 debug_assert_eq!(a.len(), WORD_COUNT_4096);
716 debug_assert_eq!(&a[..WORD_COUNT_4096 * 3 / 4], &[0; WORD_COUNT_4096 * 3 / 4]);
717 let mut res = [0; WORD_COUNT_4096 * 2];
718 res[WORD_COUNT_4096 + WORD_COUNT_4096 / 2..].copy_from_slice(
719 &sqr_16(&a[WORD_COUNT_4096 * 3 / 4..]));
722 fn add_32_subarr(a: &[u64], b: &[u64]) -> ([u64; WORD_COUNT_4096 * 2], bool) {
723 debug_assert_eq!(a.len(), WORD_COUNT_4096 * 2);
724 debug_assert_eq!(b.len(), WORD_COUNT_4096 * 2);
725 debug_assert_eq!(&a[..WORD_COUNT_4096 * 3 / 2], &[0; WORD_COUNT_4096 * 3 / 2]);
726 debug_assert_eq!(&b[..WORD_COUNT_4096 * 3 / 2], &[0; WORD_COUNT_4096 * 3 / 2]);
727 let (add, overflow) = add_32(&a[WORD_COUNT_4096 * 3 / 2..], &b[WORD_COUNT_4096 * 3 / 2..]);
728 let mut res = [0; WORD_COUNT_4096 * 2];
729 res[WORD_COUNT_4096 * 3 / 2..].copy_from_slice(&add);
732 fn sub_16_subarr(a: &[u64], b: &[u64]) -> ([u64; WORD_COUNT_4096], bool) {
733 debug_assert_eq!(a.len(), WORD_COUNT_4096);
734 debug_assert_eq!(b.len(), WORD_COUNT_4096);
735 debug_assert_eq!(&a[..WORD_COUNT_4096 * 3 / 4], &[0; WORD_COUNT_4096 * 3 / 4]);
736 debug_assert_eq!(&b[..WORD_COUNT_4096 * 3 / 4], &[0; WORD_COUNT_4096 * 3 / 4]);
737 let (sub, underflow) = sub_16(&a[WORD_COUNT_4096 * 3 / 4..], &b[WORD_COUNT_4096 * 3 / 4..]);
738 let mut res = [0; WORD_COUNT_4096];
739 res[WORD_COUNT_4096 * 3 / 4..].copy_from_slice(&sub);
742 (16, 10, mul_16_subarr as mul_ty, sqr_16_subarr as sqr_ty, add_32_subarr as add_double_ty, sub_16_subarr as sub_ty)
744 fn mul_32_subarr(a: &[u64], b: &[u64]) -> [u64; WORD_COUNT_4096 * 2] {
745 debug_assert_eq!(a.len(), WORD_COUNT_4096);
746 debug_assert_eq!(b.len(), WORD_COUNT_4096);
747 debug_assert_eq!(&a[..WORD_COUNT_4096 / 2], &[0; WORD_COUNT_4096 / 2]);
748 debug_assert_eq!(&b[..WORD_COUNT_4096 / 2], &[0; WORD_COUNT_4096 / 2]);
749 let mut res = [0; WORD_COUNT_4096 * 2];
750 res[WORD_COUNT_4096..].copy_from_slice(
751 &mul_32(&a[WORD_COUNT_4096 / 2..], &b[WORD_COUNT_4096 / 2..]));
754 fn sqr_32_subarr(a: &[u64]) -> [u64; WORD_COUNT_4096 * 2] {
755 debug_assert_eq!(a.len(), WORD_COUNT_4096);
756 debug_assert_eq!(&a[..WORD_COUNT_4096 / 2], &[0; WORD_COUNT_4096 / 2]);
757 let mut res = [0; WORD_COUNT_4096 * 2];
758 res[WORD_COUNT_4096..].copy_from_slice(
759 &sqr_32(&a[WORD_COUNT_4096 / 2..]));
762 fn add_64_subarr(a: &[u64], b: &[u64]) -> ([u64; WORD_COUNT_4096 * 2], bool) {
763 debug_assert_eq!(a.len(), WORD_COUNT_4096 * 2);
764 debug_assert_eq!(b.len(), WORD_COUNT_4096 * 2);
765 debug_assert_eq!(&a[..WORD_COUNT_4096], &[0; WORD_COUNT_4096]);
766 debug_assert_eq!(&b[..WORD_COUNT_4096], &[0; WORD_COUNT_4096]);
767 let (add, overflow) = add_64(&a[WORD_COUNT_4096..], &b[WORD_COUNT_4096..]);
768 let mut res = [0; WORD_COUNT_4096 * 2];
769 res[WORD_COUNT_4096..].copy_from_slice(&add);
772 fn sub_32_subarr(a: &[u64], b: &[u64]) -> ([u64; WORD_COUNT_4096], bool) {
773 debug_assert_eq!(a.len(), WORD_COUNT_4096);
774 debug_assert_eq!(b.len(), WORD_COUNT_4096);
775 debug_assert_eq!(&a[..WORD_COUNT_4096 / 2], &[0; WORD_COUNT_4096 / 2]);
776 debug_assert_eq!(&b[..WORD_COUNT_4096 / 2], &[0; WORD_COUNT_4096 / 2]);
777 let (sub, underflow) = sub_32(&a[WORD_COUNT_4096 / 2..], &b[WORD_COUNT_4096 / 2..]);
778 let mut res = [0; WORD_COUNT_4096];
779 res[WORD_COUNT_4096 / 2..].copy_from_slice(&sub);
782 (32, 11, mul_32_subarr as mul_ty, sqr_32_subarr as sqr_ty, add_64_subarr as add_double_ty, sub_32_subarr as sub_ty)
785 (64, 12, mul_64 as mul_ty, sqr_64 as sqr_ty, add_128 as add_double_ty, sub_64 as sub_ty)
788 let mut r = [0; WORD_COUNT_4096 * 2];
789 r[WORD_COUNT_4096 * 2 - word_count - 1] = 1;
791 let mut m_inv_pos = [0; WORD_COUNT_4096];
792 m_inv_pos[WORD_COUNT_4096 - 1] = 1;
793 let mut two = [0; WORD_COUNT_4096];
794 two[WORD_COUNT_4096 - 1] = 2;
795 for _ in 0..log_bits {
796 let mut m_m_inv = mul(&m_inv_pos, &m.0);
797 m_m_inv[..WORD_COUNT_4096 * 2 - word_count].fill(0);
798 let m_inv = mul(&sub(&two, &m_m_inv[WORD_COUNT_4096..]).0, &m_inv_pos);
799 m_inv_pos[WORD_COUNT_4096 - word_count..].copy_from_slice(&m_inv[WORD_COUNT_4096 * 2 - word_count..]);
801 m_inv_pos[..WORD_COUNT_4096 - word_count].fill(0);
803 // We want the negative modular inverse of m mod R, so subtract m_inv from R.
804 let mut m_inv = m_inv_pos;
806 m_inv[..WORD_COUNT_4096 - word_count].fill(0);
807 debug_assert_eq!(&mul(&m_inv, &m.0)[WORD_COUNT_4096 * 2 - word_count..],
809 &[0xffff_ffff_ffff_ffff; WORD_COUNT_4096][WORD_COUNT_4096 - word_count..]);
811 debug_assert_eq!(&m_inv[..WORD_COUNT_4096 - word_count], &[0; WORD_COUNT_4096][..WORD_COUNT_4096 - word_count]);
813 let mont_reduction = |mu: [u64; WORD_COUNT_4096 * 2]| -> [u64; WORD_COUNT_4096] {
814 debug_assert_eq!(&mu[..WORD_COUNT_4096 * 2 - word_count * 2],
815 &[0; WORD_COUNT_4096 * 2][..WORD_COUNT_4096 * 2 - word_count * 2]);
816 let mut mu_mod_r = [0; WORD_COUNT_4096];
817 mu_mod_r[WORD_COUNT_4096 - word_count..].copy_from_slice(&mu[WORD_COUNT_4096 * 2 - word_count..]);
818 let mut v = mul(&mu_mod_r, &m_inv);
819 v[..WORD_COUNT_4096 * 2 - word_count].fill(0); // mod R
820 let t0 = mul(&v[WORD_COUNT_4096..], &m.0);
821 let (t1, t1_extra_bit) = add_double(&t0, &mu);
822 let mut t1_on_r = [0; WORD_COUNT_4096];
823 debug_assert_eq!(&t1[WORD_COUNT_4096 * 2 - word_count..], &[0; WORD_COUNT_4096][WORD_COUNT_4096 - word_count..],
824 "t1 should be divisible by r");
825 t1_on_r[WORD_COUNT_4096 - word_count..].copy_from_slice(&t1[WORD_COUNT_4096 * 2 - word_count * 2..WORD_COUNT_4096 * 2 - word_count]);
826 if t1_extra_bit || t1_on_r >= m.0 {
828 (t1_on_r, underflow) = sub(&t1_on_r, &m.0);
829 debug_assert_eq!(t1_extra_bit, underflow);
834 // Calculate R^2 mod m as ((2^DOUBLES * R) mod m)^(log_bits - LOG2_DOUBLES) mod R
835 let mut r_minus_one = [0xffff_ffff_ffff_ffffu64; WORD_COUNT_4096];
836 r_minus_one[..WORD_COUNT_4096 - word_count].fill(0);
837 // While we do a full div here, in general R should be less than 2x m (assuming the RSA
838 // modulus used its full bit range and is 1024, 2048, or 4096 bits), so it should be cheap.
839 // In cases with a nonstandard RSA modulus we may end up being pretty slow here, but we'll
841 // If we ever find a problem with this we should reduce R to be tigher on m, as we're
842 // wasting extra bits of calculation if R is too far from m.
843 let (_, mut r_mod_m) = debug_unwrap!(div_rem_64(&r_minus_one, &m.0));
844 let r_mod_m_overflow = add_u64!(r_mod_m, 1);
845 if r_mod_m_overflow || r_mod_m >= m.0 {
846 (r_mod_m, _) = sub_64(&r_mod_m, &m.0);
849 let mut r2_mod_m: [u64; 64] = r_mod_m;
850 const DOUBLES: usize = 32;
851 const LOG2_DOUBLES: usize = 5;
853 for _ in 0..DOUBLES {
854 let overflow = double!(r2_mod_m);
855 if overflow || r2_mod_m > m.0 {
856 (r2_mod_m, _) = sub_64(&r2_mod_m, &m.0);
859 for _ in 0..log_bits - LOG2_DOUBLES {
860 r2_mod_m = mont_reduction(sqr(&r2_mod_m));
862 // Clear excess high bits
863 for (m_limb, r2_limb) in m.0.iter().zip(r2_mod_m.iter_mut()) {
864 let clear_bits = m_limb.leading_zeros();
865 if clear_bits == 0 { break; }
866 *r2_limb &= !(0xffff_ffff_ffff_ffffu64 << (64 - clear_bits));
867 if *m_limb != 0 { break; }
869 debug_assert!(r2_mod_m < m.0);
871 // Calculate t * R and a * R as mont multiplications by R^2 mod m
872 let mut tr = mont_reduction(mul(&r2_mod_m, &t));
873 let mut ar = mont_reduction(mul(&r2_mod_m, &self.0));
875 #[cfg(debug_assertions)] {
876 debug_assert_eq!(r2_mod_m, U4096(r_mod_m).mulmod_naive(&U4096(r_mod_m), &m).unwrap().0);
877 debug_assert_eq!(&tr, &U4096(t).mulmod_naive(&U4096(r_mod_m), &m).unwrap().0);
878 debug_assert_eq!(&ar, &self.mulmod_naive(&U4096(r_mod_m), &m).unwrap().0);
883 tr = mont_reduction(mul(&tr, &ar));
886 ar = mont_reduction(sqr(&ar));
889 ar = mont_reduction(mul(&ar, &tr));
890 let mut resr = [0; WORD_COUNT_4096 * 2];
891 resr[WORD_COUNT_4096..].copy_from_slice(&ar);
892 Ok(U4096(mont_reduction(resr)))
896 const fn u64_from_bytes_a_panicking(b: &[u8]) -> u64 {
898 [a, b, c, d, e, f, g, h, ..] => {
899 ((*a as u64) << 8*7) |
900 ((*b as u64) << 8*6) |
901 ((*c as u64) << 8*5) |
902 ((*d as u64) << 8*4) |
903 ((*e as u64) << 8*3) |
904 ((*f as u64) << 8*2) |
905 ((*g as u64) << 8*1) |
912 const fn u64_from_bytes_b_panicking(b: &[u8]) -> u64 {
914 [_, _, _, _, _, _, _, _,
915 a, b, c, d, e, f, g, h, ..] => {
916 ((*a as u64) << 8*7) |
917 ((*b as u64) << 8*6) |
918 ((*c as u64) << 8*5) |
919 ((*d as u64) << 8*4) |
920 ((*e as u64) << 8*3) |
921 ((*f as u64) << 8*2) |
922 ((*g as u64) << 8*1) |
929 const fn u64_from_bytes_c_panicking(b: &[u8]) -> u64 {
931 [_, _, _, _, _, _, _, _,
932 _, _, _, _, _, _, _, _,
933 a, b, c, d, e, f, g, h, ..] => {
934 ((*a as u64) << 8*7) |
935 ((*b as u64) << 8*6) |
936 ((*c as u64) << 8*5) |
937 ((*d as u64) << 8*4) |
938 ((*e as u64) << 8*3) |
939 ((*f as u64) << 8*2) |
940 ((*g as u64) << 8*1) |
947 const fn u64_from_bytes_d_panicking(b: &[u8]) -> u64 {
949 [_, _, _, _, _, _, _, _,
950 _, _, _, _, _, _, _, _,
951 _, _, _, _, _, _, _, _,
952 a, b, c, d, e, f, g, h, ..] => {
953 ((*a as u64) << 8*7) |
954 ((*b as u64) << 8*6) |
955 ((*c as u64) << 8*5) |
956 ((*d as u64) << 8*4) |
957 ((*e as u64) << 8*3) |
958 ((*f as u64) << 8*2) |
959 ((*g as u64) << 8*1) |
966 const fn u64_from_bytes_e_panicking(b: &[u8]) -> u64 {
968 [_, _, _, _, _, _, _, _,
969 _, _, _, _, _, _, _, _,
970 _, _, _, _, _, _, _, _,
971 _, _, _, _, _, _, _, _,
972 a, b, c, d, e, f, g, h, ..] => {
973 ((*a as u64) << 8*7) |
974 ((*b as u64) << 8*6) |
975 ((*c as u64) << 8*5) |
976 ((*d as u64) << 8*4) |
977 ((*e as u64) << 8*3) |
978 ((*f as u64) << 8*2) |
979 ((*g as u64) << 8*1) |
986 const fn u64_from_bytes_f_panicking(b: &[u8]) -> u64 {
988 [_, _, _, _, _, _, _, _,
989 _, _, _, _, _, _, _, _,
990 _, _, _, _, _, _, _, _,
991 _, _, _, _, _, _, _, _,
992 _, _, _, _, _, _, _, _,
993 a, b, c, d, e, f, g, h, ..] => {
994 ((*a as u64) << 8*7) |
995 ((*b as u64) << 8*6) |
996 ((*c as u64) << 8*5) |
997 ((*d as u64) << 8*4) |
998 ((*e as u64) << 8*3) |
999 ((*f as u64) << 8*2) |
1000 ((*g as u64) << 8*1) |
1001 ((*h as u64) << 8*0)
1008 /// Constructs a new [`U256`] from a variable number of big-endian bytes.
1009 pub(super) fn from_be_bytes(bytes: &[u8]) -> Result<U256, ()> {
1010 if bytes.len() > 256/8 { return Err(()); }
1011 let u64s = (bytes.len() + 7) / 8;
1012 let mut res = [0; WORD_COUNT_256];
1015 let pos = (u64s - i) * 8;
1016 let start = bytes.len().saturating_sub(pos);
1017 let end = bytes.len() + 8 - pos;
1018 b[8 + start - end..].copy_from_slice(&bytes[start..end]);
1019 res[i + WORD_COUNT_256 - u64s] = u64::from_be_bytes(b);
1024 /// Constructs a new [`U256`] from a fixed number of big-endian bytes.
1025 pub(super) const fn from_32_be_bytes_panicking(bytes: &[u8; 32]) -> U256 {
1027 u64_from_bytes_a_panicking(bytes),
1028 u64_from_bytes_b_panicking(bytes),
1029 u64_from_bytes_c_panicking(bytes),
1030 u64_from_bytes_d_panicking(bytes),
1035 pub(super) const fn zero() -> U256 { U256([0, 0, 0, 0]) }
1036 pub(super) const fn one() -> U256 { U256([0, 0, 0, 1]) }
1037 pub(super) const fn three() -> U256 { U256([0, 0, 0, 3]) }
1040 impl<M: PrimeModulus<U256>> U256Mod<M> {
1041 const fn mont_reduction(mu: [u64; 8]) -> Self {
1042 #[cfg(debug_assertions)] {
1043 // Check NEGATIVE_PRIME_INV_MOD_R is correct. Since this is all const, the compiler
1044 // should be able to do it at compile time alone.
1045 let minus_one_mod_r = mul_4(&M::PRIME.0, &M::NEGATIVE_PRIME_INV_MOD_R.0);
1046 assert!(slice_equal(const_subslice(&minus_one_mod_r, 4, 8), &[0xffff_ffff_ffff_ffff; 4]));
1049 #[cfg(debug_assertions)] {
1050 // Check R_SQUARED_MOD_PRIME is correct. Since this is all const, the compiler
1051 // should be able to do it at compile time alone.
1052 let r_minus_one = [0xffff_ffff_ffff_ffff; 4];
1053 let (mut r_mod_prime, _) = sub_4(&r_minus_one, &M::PRIME.0);
1054 add_u64!(r_mod_prime, 1);
1055 let r_squared = sqr_4(&r_mod_prime);
1056 let mut prime_extended = [0; 8];
1057 let prime = M::PRIME.0;
1058 copy_from_slice!(prime_extended, 4, 8, prime);
1059 let (_, r_squared_mod_prime) = if let Ok(v) = div_rem_8(&r_squared, &prime_extended) { v } else { panic!() };
1060 assert!(slice_greater_than(&prime_extended, &r_squared_mod_prime));
1061 assert!(slice_equal(const_subslice(&r_squared_mod_prime, 4, 8), &M::R_SQUARED_MOD_PRIME.0));
1064 let mu_mod_r = const_subslice(&mu, 4, 8);
1065 let mut v = mul_4(&mu_mod_r, &M::NEGATIVE_PRIME_INV_MOD_R.0);
1066 const ZEROS: &[u64; 4] = &[0; 4];
1067 copy_from_slice!(v, 0, 4, ZEROS); // mod R
1068 let t0 = mul_4(const_subslice(&v, 4, 8), &M::PRIME.0);
1069 let (t1, t1_extra_bit) = add_8(&t0, &mu);
1070 let t1_on_r = const_subslice(&t1, 0, 4);
1071 let mut res = [0; 4];
1072 if t1_extra_bit || slice_greater_than(&t1_on_r, &M::PRIME.0) {
1074 (res, underflow) = sub_4(&t1_on_r, &M::PRIME.0);
1075 debug_assert!(t1_extra_bit == underflow);
1077 copy_from_slice!(res, 0, 4, t1_on_r);
1079 Self(U256(res), PhantomData)
1082 pub(super) const fn from_u256_panicking(v: U256) -> Self {
1083 assert!(v.0[0] <= M::PRIME.0[0]);
1084 if v.0[0] == M::PRIME.0[0] {
1085 assert!(v.0[1] <= M::PRIME.0[1]);
1086 if v.0[1] == M::PRIME.0[1] {
1087 assert!(v.0[2] <= M::PRIME.0[2]);
1088 if v.0[2] == M::PRIME.0[2] {
1089 assert!(v.0[3] < M::PRIME.0[3]);
1093 assert!(M::PRIME.0[0] != 0 || M::PRIME.0[1] != 0 || M::PRIME.0[2] != 0 || M::PRIME.0[3] != 0);
1094 Self::mont_reduction(mul_4(&M::R_SQUARED_MOD_PRIME.0, &v.0))
1097 pub(super) fn from_u256(mut v: U256) -> Self {
1098 debug_assert!(M::PRIME.0 != [0; 4]);
1099 debug_assert!(M::PRIME.0[0] > (1 << 63), "PRIME should have the top bit set");
1100 while v >= M::PRIME {
1101 let (new_v, spurious_underflow) = sub_4(&v.0, &M::PRIME.0);
1102 debug_assert!(!spurious_underflow);
1105 Self::mont_reduction(mul_4(&M::R_SQUARED_MOD_PRIME.0, &v.0))
1108 pub(super) fn from_modinv_of(v: U256) -> Result<Self, ()> {
1109 Ok(Self::from_u256(U256(mod_inv_4(&v.0, &M::PRIME.0)?)))
1112 /// Multiplies `self` * `b` mod `m`.
1114 /// Panics if `self`'s modulus is not equal to `b`'s
1115 pub(super) fn mul(&self, b: &Self) -> Self {
1116 Self::mont_reduction(mul_4(&self.0.0, &b.0.0))
1119 /// Doubles `self` mod `m`.
1120 pub(super) fn double(&self) -> Self {
1121 let mut res = self.0.0;
1122 let overflow = double!(res);
1123 if overflow || !slice_greater_than(&M::PRIME.0, &res) {
1125 (res, underflow) = sub_4(&res, &M::PRIME.0);
1126 debug_assert_eq!(overflow, underflow);
1128 Self(U256(res), PhantomData)
1131 /// Multiplies `self` by 3 mod `m`.
1132 pub(super) fn times_three(&self) -> Self {
1133 // TODO: Optimize this a lot
1134 self.mul(&U256Mod::from_u256(U256::three()))
1137 /// Multiplies `self` by 4 mod `m`.
1138 pub(super) fn times_four(&self) -> Self {
1139 // TODO: Optimize this somewhat?
1140 self.double().double()
1143 /// Multiplies `self` by 8 mod `m`.
1144 pub(super) fn times_eight(&self) -> Self {
1145 // TODO: Optimize this somewhat?
1146 self.double().double().double()
1149 /// Multiplies `self` by 8 mod `m`.
1150 pub(super) fn square(&self) -> Self {
1151 Self::mont_reduction(sqr_4(&self.0.0))
1154 /// Subtracts `b` from `self` % `m`.
1155 pub(super) fn sub(&self, b: &Self) -> Self {
1156 let (mut val, underflow) = sub_4(&self.0.0, &b.0.0);
1159 (val, overflow) = add_4(&val, &M::PRIME.0);
1160 debug_assert_eq!(overflow, underflow);
1162 Self(U256(val), PhantomData)
1165 /// Adds `b` to `self` % `m`.
1166 pub(super) fn add(&self, b: &Self) -> Self {
1167 let (mut val, overflow) = add_4(&self.0.0, &b.0.0);
1168 if overflow || !slice_greater_than(&M::PRIME.0, &val) {
1170 (val, underflow) = sub_4(&val, &M::PRIME.0);
1171 debug_assert_eq!(overflow, underflow);
1173 Self(U256(val), PhantomData)
1176 /// Returns the underlying [`U256`].
1177 pub(super) fn into_u256(self) -> U256 {
1178 let mut expanded_self = [0; 8];
1179 expanded_self[4..].copy_from_slice(&self.0.0);
1180 Self::mont_reduction(expanded_self).0
1185 /// Constructs a new [`U384`] from a variable number of big-endian bytes.
1186 pub(super) fn from_be_bytes(bytes: &[u8]) -> Result<U384, ()> {
1187 if bytes.len() > 384/8 { return Err(()); }
1188 let u64s = (bytes.len() + 7) / 8;
1189 let mut res = [0; WORD_COUNT_384];
1192 let pos = (u64s - i) * 8;
1193 let start = bytes.len().saturating_sub(pos);
1194 let end = bytes.len() + 8 - pos;
1195 b[8 + start - end..].copy_from_slice(&bytes[start..end]);
1196 res[i + WORD_COUNT_384 - u64s] = u64::from_be_bytes(b);
1201 /// Constructs a new [`U384`] from a fixed number of big-endian bytes.
1202 pub(super) const fn from_48_be_bytes_panicking(bytes: &[u8; 48]) -> U384 {
1204 u64_from_bytes_a_panicking(bytes),
1205 u64_from_bytes_b_panicking(bytes),
1206 u64_from_bytes_c_panicking(bytes),
1207 u64_from_bytes_d_panicking(bytes),
1208 u64_from_bytes_e_panicking(bytes),
1209 u64_from_bytes_f_panicking(bytes),
1214 pub(super) const fn zero() -> U384 { U384([0, 0, 0, 0, 0, 0]) }
1215 pub(super) const fn one() -> U384 { U384([0, 0, 0, 0, 0, 1]) }
1216 pub(super) const fn three() -> U384 { U384([0, 0, 0, 0, 0, 3]) }
1219 impl<M: PrimeModulus<U384>> U384Mod<M> {
1220 const fn mont_reduction(mu: [u64; 12]) -> Self {
1221 #[cfg(debug_assertions)] {
1222 // Check NEGATIVE_PRIME_INV_MOD_R is correct. Since this is all const, the compiler
1223 // should be able to do it at compile time alone.
1224 let minus_one_mod_r = mul_6(&M::PRIME.0, &M::NEGATIVE_PRIME_INV_MOD_R.0);
1225 assert!(slice_equal(const_subslice(&minus_one_mod_r, 6, 12), &[0xffff_ffff_ffff_ffff; 6]));
1228 #[cfg(debug_assertions)] {
1229 // Check R_SQUARED_MOD_PRIME is correct. Since this is all const, the compiler
1230 // should be able to do it at compile time alone.
1231 let r_minus_one = [0xffff_ffff_ffff_ffff; 6];
1232 let (mut r_mod_prime, _) = sub_6(&r_minus_one, &M::PRIME.0);
1233 add_u64!(r_mod_prime, 1);
1234 let r_squared = sqr_6(&r_mod_prime);
1235 let mut prime_extended = [0; 12];
1236 let prime = M::PRIME.0;
1237 copy_from_slice!(prime_extended, 6, 12, prime);
1238 let (_, r_squared_mod_prime) = if let Ok(v) = div_rem_12(&r_squared, &prime_extended) { v } else { panic!() };
1239 assert!(slice_greater_than(&prime_extended, &r_squared_mod_prime));
1240 assert!(slice_equal(const_subslice(&r_squared_mod_prime, 6, 12), &M::R_SQUARED_MOD_PRIME.0));
1243 let mu_mod_r = const_subslice(&mu, 6, 12);
1244 let mut v = mul_6(&mu_mod_r, &M::NEGATIVE_PRIME_INV_MOD_R.0);
1245 const ZEROS: &[u64; 6] = &[0; 6];
1246 copy_from_slice!(v, 0, 6, ZEROS); // mod R
1247 let t0 = mul_6(const_subslice(&v, 6, 12), &M::PRIME.0);
1248 let (t1, t1_extra_bit) = add_12(&t0, &mu);
1249 let t1_on_r = const_subslice(&t1, 0, 6);
1250 let mut res = [0; 6];
1251 if t1_extra_bit || slice_greater_than(&t1_on_r, &M::PRIME.0) {
1253 (res, underflow) = sub_6(&t1_on_r, &M::PRIME.0);
1254 debug_assert!(t1_extra_bit == underflow);
1256 copy_from_slice!(res, 0, 6, t1_on_r);
1258 Self(U384(res), PhantomData)
1261 pub(super) const fn from_u384_panicking(v: U384) -> Self {
1262 assert!(v.0[0] <= M::PRIME.0[0]);
1263 if v.0[0] == M::PRIME.0[0] {
1264 assert!(v.0[1] <= M::PRIME.0[1]);
1265 if v.0[1] == M::PRIME.0[1] {
1266 assert!(v.0[2] <= M::PRIME.0[2]);
1267 if v.0[2] == M::PRIME.0[2] {
1268 assert!(v.0[3] <= M::PRIME.0[3]);
1269 if v.0[3] == M::PRIME.0[3] {
1270 assert!(v.0[4] <= M::PRIME.0[4]);
1271 if v.0[4] == M::PRIME.0[4] {
1272 assert!(v.0[5] < M::PRIME.0[5]);
1278 assert!(M::PRIME.0[0] != 0 || M::PRIME.0[1] != 0 || M::PRIME.0[2] != 0
1279 || M::PRIME.0[3] != 0|| M::PRIME.0[4] != 0|| M::PRIME.0[5] != 0);
1280 Self::mont_reduction(mul_6(&M::R_SQUARED_MOD_PRIME.0, &v.0))
1283 pub(super) fn from_u384(mut v: U384) -> Self {
1284 debug_assert!(M::PRIME.0 != [0; 6]);
1285 debug_assert!(M::PRIME.0[0] > (1 << 63), "PRIME should have the top bit set");
1286 while v >= M::PRIME {
1287 let (new_v, spurious_underflow) = sub_6(&v.0, &M::PRIME.0);
1288 debug_assert!(!spurious_underflow);
1291 Self::mont_reduction(mul_6(&M::R_SQUARED_MOD_PRIME.0, &v.0))
1294 pub(super) fn from_modinv_of(v: U384) -> Result<Self, ()> {
1295 Ok(Self::from_u384(U384(mod_inv_6(&v.0, &M::PRIME.0)?)))
1298 /// Multiplies `self` * `b` mod `m`.
1300 /// Panics if `self`'s modulus is not equal to `b`'s
1301 pub(super) fn mul(&self, b: &Self) -> Self {
1302 Self::mont_reduction(mul_6(&self.0.0, &b.0.0))
1305 /// Doubles `self` mod `m`.
1306 pub(super) fn double(&self) -> Self {
1307 let mut res = self.0.0;
1308 let overflow = double!(res);
1309 if overflow || !slice_greater_than(&M::PRIME.0, &res) {
1311 (res, underflow) = sub_6(&res, &M::PRIME.0);
1312 debug_assert_eq!(overflow, underflow);
1314 Self(U384(res), PhantomData)
1317 /// Multiplies `self` by 3 mod `m`.
1318 pub(super) fn times_three(&self) -> Self {
1319 // TODO: Optimize this a lot
1320 self.mul(&U384Mod::from_u384(U384::three()))
1323 /// Multiplies `self` by 4 mod `m`.
1324 pub(super) fn times_four(&self) -> Self {
1325 // TODO: Optimize this somewhat?
1326 self.double().double()
1329 /// Multiplies `self` by 8 mod `m`.
1330 pub(super) fn times_eight(&self) -> Self {
1331 // TODO: Optimize this somewhat?
1332 self.double().double().double()
1335 /// Multiplies `self` by 8 mod `m`.
1336 pub(super) fn square(&self) -> Self {
1337 Self::mont_reduction(sqr_6(&self.0.0))
1340 /// Subtracts `b` from `self` % `m`.
1341 pub(super) fn sub(&self, b: &Self) -> Self {
1342 let (mut val, underflow) = sub_6(&self.0.0, &b.0.0);
1345 (val, overflow) = add_6(&val, &M::PRIME.0);
1346 debug_assert_eq!(overflow, underflow);
1348 Self(U384(val), PhantomData)
1351 /// Adds `b` to `self` % `m`.
1352 pub(super) fn add(&self, b: &Self) -> Self {
1353 let (mut val, overflow) = add_6(&self.0.0, &b.0.0);
1354 if overflow || !slice_greater_than(&M::PRIME.0, &val) {
1356 (val, underflow) = sub_6(&val, &M::PRIME.0);
1357 debug_assert_eq!(overflow, underflow);
1359 Self(U384(val), PhantomData)
1362 /// Returns the underlying [`U384`].
1363 pub(super) fn into_u384(self) -> U384 {
1364 let mut expanded_self = [0; 12];
1365 expanded_self[6..].copy_from_slice(&self.0.0);
1366 Self::mont_reduction(expanded_self).0
1375 impl PrimeModulus<U256> for P256 {
1376 const PRIME: U256 = U256::from_32_be_bytes_panicking(&hex_lit::hex!(
1377 "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff"));
1378 const R_SQUARED_MOD_PRIME: U256 = U256::from_32_be_bytes_panicking(&hex_lit::hex!(
1379 "00000004fffffffdfffffffffffffffefffffffbffffffff0000000000000003"));
1380 const NEGATIVE_PRIME_INV_MOD_R: U256 = U256::from_32_be_bytes_panicking(&hex_lit::hex!(
1381 "ffffffff00000002000000000000000000000001000000000000000000000001"));
1385 impl PrimeModulus<U384> for P384 {
1386 const PRIME: U384 = U384::from_48_be_bytes_panicking(&hex_lit::hex!(
1387 "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff"));
1388 const R_SQUARED_MOD_PRIME: U384 = U384::from_48_be_bytes_panicking(&hex_lit::hex!(
1389 "000000000000000000000000000000010000000200000000fffffffe000000000000000200000000fffffffe00000001"));
1390 const NEGATIVE_PRIME_INV_MOD_R: U384 = U384::from_48_be_bytes_panicking(&hex_lit::hex!(
1391 "00000014000000140000000c00000002fffffffcfffffffafffffffbfffffffe00000000000000010000000100000001"));
1398 /// Read some bytes and use them to test bigint math by comparing results against the `ibig` crate.
1399 pub fn fuzz_math(input: &[u8]) {
1400 if input.len() < 32 || input.len() % 16 != 0 { return; }
1401 let split = core::cmp::min(input.len() / 2, 512);
1402 let (a, b) = input.split_at(core::cmp::min(input.len() / 2, 512));
1403 let b = &b[..split];
1405 let ai = ibig::UBig::from_be_bytes(&a);
1406 let bi = ibig::UBig::from_be_bytes(&b);
1408 let mut a_u64s = Vec::with_capacity(split / 8);
1409 for chunk in a.chunks(8) {
1410 a_u64s.push(u64::from_be_bytes(chunk.try_into().unwrap()));
1412 let mut b_u64s = Vec::with_capacity(split / 8);
1413 for chunk in b.chunks(8) {
1414 b_u64s.push(u64::from_be_bytes(chunk.try_into().unwrap()));
1417 macro_rules! test { ($mul: ident, $sqr: ident, $add: ident, $sub: ident, $div_rem: ident, $mod_inv: ident) => {
1418 let res = $mul(&a_u64s, &b_u64s);
1419 let mut res_bytes = Vec::with_capacity(input.len() / 2);
1421 res_bytes.extend_from_slice(&i.to_be_bytes());
1423 assert_eq!(ibig::UBig::from_be_bytes(&res_bytes), ai.clone() * bi.clone());
1425 debug_assert_eq!($mul(&a_u64s, &a_u64s), $sqr(&a_u64s));
1426 debug_assert_eq!($mul(&b_u64s, &b_u64s), $sqr(&b_u64s));
1428 let (res, carry) = $add(&a_u64s, &b_u64s);
1429 let mut res_bytes = Vec::with_capacity(input.len() / 2 + 1);
1430 if carry { res_bytes.push(1); } else { res_bytes.push(0); }
1432 res_bytes.extend_from_slice(&i.to_be_bytes());
1434 assert_eq!(ibig::UBig::from_be_bytes(&res_bytes), ai.clone() + bi.clone());
1436 let mut add_u64s = a_u64s.clone();
1437 let carry = add_u64!(add_u64s, 1);
1438 let mut res_bytes = Vec::with_capacity(input.len() / 2 + 1);
1439 if carry { res_bytes.push(1); } else { res_bytes.push(0); }
1440 for i in &add_u64s {
1441 res_bytes.extend_from_slice(&i.to_be_bytes());
1443 assert_eq!(ibig::UBig::from_be_bytes(&res_bytes), ai.clone() + 1);
1445 let mut double_u64s = b_u64s.clone();
1446 let carry = double!(double_u64s);
1447 let mut res_bytes = Vec::with_capacity(input.len() / 2 + 1);
1448 if carry { res_bytes.push(1); } else { res_bytes.push(0); }
1449 for i in &double_u64s {
1450 res_bytes.extend_from_slice(&i.to_be_bytes());
1452 assert_eq!(ibig::UBig::from_be_bytes(&res_bytes), bi.clone() * 2);
1454 let (quot, rem) = if let Ok(res) =
1455 $div_rem(&a_u64s[..].try_into().unwrap(), &b_u64s[..].try_into().unwrap()) {
1458 let mut quot_bytes = Vec::with_capacity(input.len() / 2);
1460 quot_bytes.extend_from_slice(&i.to_be_bytes());
1462 let mut rem_bytes = Vec::with_capacity(input.len() / 2);
1464 rem_bytes.extend_from_slice(&i.to_be_bytes());
1466 let (quoti, remi) = ibig::ops::DivRem::div_rem(ai.clone(), &bi);
1467 assert_eq!(ibig::UBig::from_be_bytes("_bytes), quoti);
1468 assert_eq!(ibig::UBig::from_be_bytes(&rem_bytes), remi);
1470 if ai != ibig::UBig::from(0u32) { // ibig provides a spurious modular inverse for 0
1471 let ring = ibig::modular::ModuloRing::new(&bi);
1472 let ar = ring.from(ai.clone());
1473 let invi = ar.inverse().map(|i| i.residue());
1475 if let Ok(modinv) = $mod_inv(&a_u64s[..].try_into().unwrap(), &b_u64s[..].try_into().unwrap()) {
1476 let mut modinv_bytes = Vec::with_capacity(input.len() / 2);
1478 modinv_bytes.extend_from_slice(&i.to_be_bytes());
1480 assert_eq!(invi.unwrap(), ibig::UBig::from_be_bytes(&modinv_bytes));
1482 assert!(invi.is_none());
1487 macro_rules! test_mod { ($amodp: expr, $bmodp: expr, $PRIME: expr, $len: expr, $into: ident, $div_rem_double: ident, $div_rem: ident, $mul: ident, $add: ident, $sub: ident) => {
1488 // Test the U256/U384Mod wrapper, which operates in Montgomery representation
1489 let mut p_extended = [0; $len * 2];
1490 p_extended[$len..].copy_from_slice(&$PRIME);
1492 let amodp_squared = $div_rem_double(&$mul(&a_u64s, &a_u64s), &p_extended).unwrap().1;
1493 assert_eq!(&amodp_squared[..$len], &[0; $len]);
1494 assert_eq!(&$amodp.square().$into().0, &amodp_squared[$len..]);
1496 let abmodp = $div_rem_double(&$mul(&a_u64s, &b_u64s), &p_extended).unwrap().1;
1497 assert_eq!(&abmodp[..$len], &[0; $len]);
1498 assert_eq!(&$amodp.mul(&$bmodp).$into().0, &abmodp[$len..]);
1500 let (aplusb, aplusb_overflow) = $add(&a_u64s, &b_u64s);
1501 let mut aplusb_extended = [0; $len * 2];
1502 aplusb_extended[$len..].copy_from_slice(&aplusb);
1503 if aplusb_overflow { aplusb_extended[$len - 1] = 1; }
1504 let aplusbmodp = $div_rem_double(&aplusb_extended, &p_extended).unwrap().1;
1505 assert_eq!(&aplusbmodp[..$len], &[0; $len]);
1506 assert_eq!(&$amodp.add(&$bmodp).$into().0, &aplusbmodp[$len..]);
1508 let (mut aminusb, aminusb_underflow) = $sub(&a_u64s, &b_u64s);
1509 if aminusb_underflow {
1511 (aminusb, overflow) = $add(&aminusb, &$PRIME);
1513 (aminusb, overflow) = $add(&aminusb, &$PRIME);
1517 let aminusbmodp = $div_rem(&aminusb, &$PRIME).unwrap().1;
1518 assert_eq!(&$amodp.sub(&$bmodp).$into().0, &aminusbmodp);
1521 if a_u64s.len() == 2 {
1522 test!(mul_2, sqr_2, add_2, sub_2, div_rem_2, mod_inv_2);
1523 } else if a_u64s.len() == 4 {
1524 test!(mul_4, sqr_4, add_4, sub_4, div_rem_4, mod_inv_4);
1525 let amodp = U256Mod::<fuzz_moduli::P256>::from_u256(U256(a_u64s[..].try_into().unwrap()));
1526 let bmodp = U256Mod::<fuzz_moduli::P256>::from_u256(U256(b_u64s[..].try_into().unwrap()));
1527 test_mod!(amodp, bmodp, fuzz_moduli::P256::PRIME.0, 4, into_u256, div_rem_8, div_rem_4, mul_4, add_4, sub_4);
1528 } else if a_u64s.len() == 6 {
1529 test!(mul_6, sqr_6, add_6, sub_6, div_rem_6, mod_inv_6);
1530 let amodp = U384Mod::<fuzz_moduli::P384>::from_u384(U384(a_u64s[..].try_into().unwrap()));
1531 let bmodp = U384Mod::<fuzz_moduli::P384>::from_u384(U384(b_u64s[..].try_into().unwrap()));
1532 test_mod!(amodp, bmodp, fuzz_moduli::P384::PRIME.0, 6, into_u384, div_rem_12, div_rem_6, mul_6, add_6, sub_6);
1533 } else if a_u64s.len() == 8 {
1534 test!(mul_8, sqr_8, add_8, sub_8, div_rem_8, mod_inv_8);
1535 } else if input.len() == 512*2 + 4 {
1536 let mut e_bytes = [0; 4];
1537 e_bytes.copy_from_slice(&input[512 * 2..512 * 2 + 4]);
1538 let e = u32::from_le_bytes(e_bytes);
1539 let a = U4096::from_be_bytes(&a).unwrap();
1540 let b = U4096::from_be_bytes(&b).unwrap();
1542 let res = if let Ok(r) = a.expmod_odd_mod(e, &b) { r } else { return };
1543 let mut res_bytes = Vec::with_capacity(512);
1545 res_bytes.extend_from_slice(&i.to_be_bytes());
1548 let ring = ibig::modular::ModuloRing::new(&bi);
1549 let ar = ring.from(ai.clone());
1550 assert_eq!(ar.pow(&e.into()).residue(), ibig::UBig::from_be_bytes(&res_bytes));
1558 fn u64s_to_u128(v: [u64; 2]) -> u128 {
1561 r |= (v[0] as u128) << 64;
1565 fn u64s_to_i128(v: [u64; 2]) -> i128 {
1568 r |= (v[0] as i128) << 64;
1574 let mut zero = [0u64; 2];
1576 assert_eq!(zero, [0; 2]);
1578 let mut one = [0u64, 1u64];
1580 assert_eq!(u64s_to_i128(one), -1);
1582 let mut minus_one: [u64; 2] = [u64::MAX, u64::MAX];
1584 assert_eq!(minus_one, [0, 1]);
1589 let mut zero = [0u64; 2];
1590 assert!(!double!(zero));
1591 assert_eq!(zero, [0; 2]);
1593 let mut one = [0u64, 1u64];
1594 assert!(!double!(one));
1595 assert_eq!(one, [0, 2]);
1597 let mut u64_max = [0, u64::MAX];
1598 assert!(!double!(u64_max));
1599 assert_eq!(u64_max, [1, u64::MAX - 1]);
1601 let mut u64_carry_overflow = [0x7fff_ffff_ffff_ffffu64, 0x8000_0000_0000_0000];
1602 assert!(!double!(u64_carry_overflow));
1603 assert_eq!(u64_carry_overflow, [u64::MAX, 0]);
1605 let mut max = [u64::MAX; 4];
1606 assert!(double!(max));
1607 assert_eq!(max, [u64::MAX, u64::MAX, u64::MAX, u64::MAX - 1]);
1611 fn mul_min_simple_tests() {
1614 let res = mul_2(&a, &b);
1615 assert_eq!(res, [0, 3, 10, 8]);
1617 let a = [0x1bad_cafe_dead_beef, 2424];
1618 let b = [0x2bad_beef_dead_cafe, 4242];
1619 let res = mul_2(&a, &b);
1620 assert_eq!(res, [340296855556511776, 15015369169016130186, 4248480538569992542, 10282608]);
1622 let a = [0xf6d9_f8eb_8b60_7a6d, 0x4b93_833e_2194_fc2e];
1623 let b = [0xfdab_0000_6952_8ab4, 0xd302_0000_8282_0000];
1624 let res = mul_2(&a, &b);
1625 assert_eq!(res, [17625486516939878681, 18390748118453258282, 2695286104209847530, 1510594524414214144]);
1627 let a = [0x8b8b_8b8b_8b8b_8b8b, 0x8b8b_8b8b_8b8b_8b8b];
1628 let b = [0x8b8b_8b8b_8b8b_8b8b, 0x8b8b_8b8b_8b8b_8b8b];
1629 let res = mul_2(&a, &b);
1630 assert_eq!(res, [5481115605507762349, 8230042173354675923, 16737530186064798, 15714555036048702841]);
1632 let a = [0x0000_0000_0000_0020, 0x002d_362c_005b_7753];
1633 let b = [0x0900_0000_0030_0003, 0xb708_00fe_0000_00cd];
1634 let res = mul_2(&a, &b);
1635 assert_eq!(res, [1, 2306290405521702946, 17647397529888728169, 10271802099389861239]);
1637 let a = [0x0000_0000_7fff_ffff, 0xffff_ffff_0000_0000];
1638 let b = [0x0000_0800_0000_0000, 0x0000_1000_0000_00e1];
1639 let res = mul_2(&a, &b);
1640 assert_eq!(res, [1024, 0, 483183816703, 18446743107341910016]);
1642 let a = [0xf6d9_f8eb_ebeb_eb6d, 0x4b93_83a0_bb35_0680];
1643 let b = [0xfd02_b9b9_b9b9_b9b9, 0xb9b9_b9b9_b9b9_b9b9];
1644 let res = mul_2(&a, &b);
1645 assert_eq!(res, [17579814114991930107, 15033987447865175985, 488855932380801351, 5453318140933190272]);
1647 let a = [u64::MAX; 2];
1648 let b = [u64::MAX; 2];
1649 let res = mul_2(&a, &b);
1650 assert_eq!(res, [18446744073709551615, 18446744073709551614, 0, 1]);
1655 fn test(a: [u64; 2], b: [u64; 2]) {
1656 let a_int = u64s_to_u128(a);
1657 let b_int = u64s_to_u128(b);
1659 let res = add_2(&a, &b);
1660 assert_eq!((u64s_to_u128(res.0), res.1), a_int.overflowing_add(b_int));
1662 let res = sub_2(&a, &b);
1663 assert_eq!((u64s_to_u128(res.0), res.1), a_int.overflowing_sub(b_int));
1666 test([0; 2], [0; 2]);
1667 test([0x1bad_cafe_dead_beef, 2424], [0x2bad_cafe_dead_cafe, 4242]);
1668 test([u64::MAX; 2], [u64::MAX; 2]);
1669 test([u64::MAX, 0x8000_0000_0000_0000], [0, 0x7fff_ffff_ffff_ffff]);
1670 test([0, 0x7fff_ffff_ffff_ffff], [u64::MAX, 0x8000_0000_0000_0000]);
1671 test([u64::MAX, 0], [0, u64::MAX]);
1672 test([0, u64::MAX], [u64::MAX, 0]);
1673 test([u64::MAX; 2], [0; 2]);
1674 test([0; 2], [u64::MAX; 2]);
1678 fn mul_4_simple_tests() {
1681 assert_eq!(mul_4(&a, &b),
1682 [0, 2, 4, 6, 8, 6, 4, 2]);
1684 let a = [0x1bad_cafe_dead_beef, 2424, 0x1bad_cafe_dead_beef, 2424];
1685 let b = [0x2bad_beef_dead_cafe, 4242, 0x2bad_beef_dead_cafe, 4242];
1686 assert_eq!(mul_4(&a, &b),
1687 [340296855556511776, 15015369169016130186, 4929074249683016095, 11583994264332991364,
1688 8837257932696496860, 15015369169036695402, 4248480538569992542, 10282608]);
1690 let a = [u64::MAX; 4];
1691 let b = [u64::MAX; 4];
1692 assert_eq!(mul_4(&a, &b),
1693 [18446744073709551615, 18446744073709551615, 18446744073709551615,
1694 18446744073709551614, 0, 0, 0, 1]);
1698 fn double_simple_tests() {
1699 let mut a = [0xfff5_b32d_01ff_0000, 0x00e7_e7e7_e7e7_e7e7];
1700 assert!(double!(a));
1701 assert_eq!(a, [18440945635998695424, 130551405668716494]);
1703 let mut a = [u64::MAX, u64::MAX];
1704 assert!(double!(a));
1705 assert_eq!(a, [18446744073709551615, 18446744073709551614]);