1use diskann_vector::{MathematicalValue, PureDistanceFunction};
7use thiserror::Error;
8
9use crate::{
10 alloc::GlobalAllocator,
11 bits::{BitSlice, Dense, Representation, Unsigned},
12 distances,
13 distances::{InnerProduct, MV},
14 meta::{self, slice},
15};
16
17#[derive(Default, Debug, Clone, Copy, PartialEq, bytemuck::Zeroable, bytemuck::Pod)]
44#[repr(C)]
45pub struct MinMaxCompensation {
46 pub dim: u32, pub b: f32, pub n: f32, pub a: f32, pub norm_squared: f32, }
52
53const META_BYTES: usize = std::mem::size_of::<MinMaxCompensation>(); #[derive(Debug, Error, Clone, PartialEq, Eq)]
58pub enum MetaParseError {
59 #[error("Invalid size: {0}, must contain at least {META_BYTES} bytes")]
60 NotCanonical(usize),
61}
62
63impl MinMaxCompensation {
64 #[inline(always)]
80 pub fn read_dimension(bytes: &[u8]) -> Result<usize, MetaParseError> {
81 if bytes.len() < META_BYTES {
82 return Err(MetaParseError::NotCanonical(bytes.len()));
83 }
84
85 let dim_bytes: [u8; 4] = bytes.get(..4).map_or_else(
87 || Err(MetaParseError::NotCanonical(bytes.len())),
88 |slice| {
89 slice
90 .try_into()
91 .map_err(|_| MetaParseError::NotCanonical(bytes.len()))
92 },
93 )?;
94
95 let dim = u32::from_le_bytes(dim_bytes) as usize;
96
97 Ok(dim)
98 }
99}
100
101pub type Data<const NBITS: usize> = meta::Vector<NBITS, Unsigned, MinMaxCompensation, Dense>;
105
106pub type DataRef<'a, const NBITS: usize> =
110 meta::VectorRef<'a, NBITS, Unsigned, MinMaxCompensation, Dense>;
111
112#[derive(Debug, Error, Clone, Copy, PartialEq, Eq)]
113pub enum DecompressError {
114 #[error("expected src and dst length to be identical, instead src is {0}, and dst is {1}")]
115 LengthMismatch(usize, usize),
116}
117impl<const NBITS: usize> DataRef<'_, NBITS>
118where
119 Unsigned: Representation<NBITS>,
120{
121 pub fn decompress_into(&self, dst: &mut [f32]) -> Result<(), DecompressError> {
137 if dst.len() != self.len() {
138 return Err(DecompressError::LengthMismatch(self.len(), dst.len()));
139 }
140 let meta = self.meta();
141
142 dst.iter_mut().enumerate().for_each(|(i, d)| unsafe {
145 *d = self.vector().get_unchecked(i) as f32 * meta.a + meta.b
146 });
147 Ok(())
148 }
149}
150
151pub type DataMutRef<'a, const NBITS: usize> =
155 meta::VectorMut<'a, NBITS, Unsigned, MinMaxCompensation, Dense>;
156
157#[derive(Debug, Clone, Copy, Default, bytemuck::Zeroable, bytemuck::Pod)]
179#[repr(C)]
180pub struct FullQueryMeta {
181 pub sum: f32,
183 pub norm_squared: f32,
185}
186
187pub type FullQuery<A = GlobalAllocator> = slice::PolySlice<f32, FullQueryMeta, A>;
191
192pub type FullQueryRef<'a> = slice::SliceRef<'a, f32, FullQueryMeta>;
196
197pub type FullQueryMut<'a> = slice::SliceMut<'a, f32, FullQueryMeta>;
201
202#[inline(always)]
206fn kernel<const NBITS: usize, F>(
207 x: DataRef<'_, NBITS>,
208 y: DataRef<'_, NBITS>,
209 f: F,
210) -> distances::MathematicalResult<f32>
211where
212 Unsigned: Representation<NBITS>,
213 InnerProduct: for<'a, 'b> PureDistanceFunction<
214 BitSlice<'a, NBITS, Unsigned>,
215 BitSlice<'b, NBITS, Unsigned>,
216 distances::MathematicalResult<u32>,
217 >,
218 F: Fn(f32, &MinMaxCompensation, &MinMaxCompensation) -> f32,
219{
220 let raw_product = InnerProduct::evaluate(x.vector(), y.vector())?;
221 let (xm, ym) = (x.meta(), y.meta());
222 let term0 = xm.a * ym.a * raw_product.into_inner() as f32;
223 let term1_x = xm.n * ym.b;
224 let term1_y = ym.n * xm.b;
225 let term2 = xm.b * ym.b * (x.len() as f32);
226
227 let v = term0 + term1_x + term1_y + term2;
228 Ok(MV::new(f(v, &xm, &ym)))
229}
230
231pub struct MinMaxIP;
232
233impl<const NBITS: usize>
234 PureDistanceFunction<DataRef<'_, NBITS>, DataRef<'_, NBITS>, distances::MathematicalResult<f32>>
235 for MinMaxIP
236where
237 Unsigned: Representation<NBITS>,
238 InnerProduct: for<'a, 'b> PureDistanceFunction<
239 BitSlice<'a, NBITS, Unsigned>,
240 BitSlice<'b, NBITS, Unsigned>,
241 distances::MathematicalResult<u32>,
242 >,
243{
244 fn evaluate(
245 x: DataRef<'_, NBITS>,
246 y: DataRef<'_, NBITS>,
247 ) -> distances::MathematicalResult<f32> {
248 kernel(x, y, |v, _, _| v)
249 }
250}
251
252impl<const NBITS: usize>
253 PureDistanceFunction<DataRef<'_, NBITS>, DataRef<'_, NBITS>, distances::Result<f32>>
254 for MinMaxIP
255where
256 Unsigned: Representation<NBITS>,
257 InnerProduct: for<'a, 'b> PureDistanceFunction<
258 BitSlice<'a, NBITS, Unsigned>,
259 BitSlice<'b, NBITS, Unsigned>,
260 distances::MathematicalResult<u32>,
261 >,
262{
263 fn evaluate(x: DataRef<'_, NBITS>, y: DataRef<'_, NBITS>) -> distances::Result<f32> {
264 let v: distances::MathematicalResult<f32> = Self::evaluate(x, y);
265 Ok(-v?.into_inner())
266 }
267}
268
269impl<const NBITS: usize>
270 PureDistanceFunction<FullQueryRef<'_>, DataRef<'_, NBITS>, distances::MathematicalResult<f32>>
271 for MinMaxIP
272where
273 Unsigned: Representation<NBITS>,
274 InnerProduct: for<'a, 'b> PureDistanceFunction<
275 &'a [f32],
276 BitSlice<'b, NBITS, Unsigned>,
277 distances::MathematicalResult<f32>,
278 >,
279{
280 fn evaluate(x: FullQueryRef<'_>, y: DataRef<'_, NBITS>) -> distances::MathematicalResult<f32> {
281 let raw_product: f32 = InnerProduct::evaluate(x.vector(), y.vector())?.into_inner();
282 Ok(MathematicalValue::new(
283 raw_product * y.meta().a + x.meta().sum * y.meta().b,
284 ))
285 }
286}
287
288impl<const NBITS: usize>
289 PureDistanceFunction<FullQueryRef<'_>, DataRef<'_, NBITS>, distances::Result<f32>> for MinMaxIP
290where
291 Unsigned: Representation<NBITS>,
292 InnerProduct: for<'a, 'b> PureDistanceFunction<
293 &'a [f32],
294 BitSlice<'b, NBITS, Unsigned>,
295 distances::MathematicalResult<f32>,
296 >,
297{
298 fn evaluate(x: FullQueryRef<'_>, y: DataRef<'_, NBITS>) -> distances::Result<f32> {
299 let v: distances::MathematicalResult<f32> = Self::evaluate(x, y);
300 Ok(-v?.into_inner())
301 }
302}
303
304pub struct MinMaxL2Squared;
305
306impl<const NBITS: usize>
307 PureDistanceFunction<DataRef<'_, NBITS>, DataRef<'_, NBITS>, distances::MathematicalResult<f32>>
308 for MinMaxL2Squared
309where
310 Unsigned: Representation<NBITS>,
311 InnerProduct: for<'a, 'b> PureDistanceFunction<
312 BitSlice<'a, NBITS, Unsigned>,
313 BitSlice<'b, NBITS, Unsigned>,
314 distances::MathematicalResult<u32>,
315 >,
316{
317 fn evaluate(
318 x: DataRef<'_, NBITS>,
319 y: DataRef<'_, NBITS>,
320 ) -> distances::MathematicalResult<f32> {
321 kernel(x, y, |v, xm, ym| {
322 -2.0 * v + xm.norm_squared + ym.norm_squared
323 })
324 }
325}
326
327impl<const NBITS: usize>
328 PureDistanceFunction<DataRef<'_, NBITS>, DataRef<'_, NBITS>, distances::Result<f32>>
329 for MinMaxL2Squared
330where
331 Unsigned: Representation<NBITS>,
332 InnerProduct: for<'a, 'b> PureDistanceFunction<
333 BitSlice<'a, NBITS, Unsigned>,
334 BitSlice<'b, NBITS, Unsigned>,
335 distances::MathematicalResult<u32>,
336 >,
337{
338 fn evaluate(x: DataRef<'_, NBITS>, y: DataRef<'_, NBITS>) -> distances::Result<f32> {
339 let v: distances::MathematicalResult<f32> = Self::evaluate(x, y);
340 Ok(v?.into_inner())
341 }
342}
343
344impl<const NBITS: usize>
345 PureDistanceFunction<FullQueryRef<'_>, DataRef<'_, NBITS>, distances::MathematicalResult<f32>>
346 for MinMaxL2Squared
347where
348 Unsigned: Representation<NBITS>,
349 InnerProduct: for<'a, 'b> PureDistanceFunction<
350 &'a [f32],
351 BitSlice<'b, NBITS, Unsigned>,
352 distances::MathematicalResult<f32>,
353 >,
354{
355 fn evaluate(x: FullQueryRef<'_>, y: DataRef<'_, NBITS>) -> distances::MathematicalResult<f32> {
356 let raw_product = InnerProduct::evaluate(x.vector(), y.vector())?.into_inner();
357
358 let ym = y.meta();
359 let compensated_ip = raw_product * ym.a + x.meta().sum * ym.b;
360 Ok(MV::new(
361 x.meta().norm_squared + ym.norm_squared - 2.0 * compensated_ip,
362 ))
363 }
364}
365
366impl<const NBITS: usize>
367 PureDistanceFunction<FullQueryRef<'_>, DataRef<'_, NBITS>, distances::Result<f32>>
368 for MinMaxL2Squared
369where
370 Unsigned: Representation<NBITS>,
371 InnerProduct: for<'a, 'b> PureDistanceFunction<
372 &'a [f32],
373 BitSlice<'b, NBITS, Unsigned>,
374 distances::MathematicalResult<f32>,
375 >,
376{
377 fn evaluate(x: FullQueryRef<'_>, y: DataRef<'_, NBITS>) -> distances::Result<f32> {
378 let v: distances::MathematicalResult<f32> = Self::evaluate(x, y);
379 Ok(v?.into_inner())
380 }
381}
382
383pub struct MinMaxCosine;
388
389impl<const NBITS: usize>
390 PureDistanceFunction<DataRef<'_, NBITS>, DataRef<'_, NBITS>, distances::Result<f32>>
391 for MinMaxCosine
392where
393 Unsigned: Representation<NBITS>,
394 MinMaxIP: for<'a, 'b> PureDistanceFunction<
395 DataRef<'a, NBITS>,
396 DataRef<'b, NBITS>,
397 distances::MathematicalResult<f32>,
398 >,
399{
400 fn evaluate(x: DataRef<'_, NBITS>, y: DataRef<'_, NBITS>) -> distances::Result<f32> {
402 let ip: MV<f32> = MinMaxIP::evaluate(x, y)?;
403 let (xm, ym) = (x.meta(), y.meta());
404 Ok(1.0 - ip.into_inner() / (xm.norm_squared.sqrt() * ym.norm_squared.sqrt()))
405 }
406}
407
408impl<const NBITS: usize>
409 PureDistanceFunction<FullQueryRef<'_>, DataRef<'_, NBITS>, distances::Result<f32>>
410 for MinMaxCosine
411where
412 Unsigned: Representation<NBITS>,
413 MinMaxIP: for<'a, 'b> PureDistanceFunction<
414 FullQueryRef<'a>,
415 DataRef<'b, NBITS>,
416 distances::MathematicalResult<f32>,
417 >,
418{
419 fn evaluate(x: FullQueryRef<'_>, y: DataRef<'_, NBITS>) -> distances::Result<f32> {
420 let ip: MathematicalValue<f32> = MinMaxIP::evaluate(x, y)?;
421 let (xm, ym) = (x.meta().norm_squared, y.meta());
422 Ok(1.0 - ip.into_inner() / (xm.sqrt() * ym.norm_squared.sqrt()))
423 }
425}
426
427pub struct MinMaxCosineNormalized;
428
429impl<const NBITS: usize>
430 PureDistanceFunction<DataRef<'_, NBITS>, DataRef<'_, NBITS>, distances::Result<f32>>
431 for MinMaxCosineNormalized
432where
433 Unsigned: Representation<NBITS>,
434 MinMaxIP: for<'a, 'b> PureDistanceFunction<
435 DataRef<'a, NBITS>,
436 DataRef<'b, NBITS>,
437 distances::MathematicalResult<f32>,
438 >,
439{
440 fn evaluate(x: DataRef<'_, NBITS>, y: DataRef<'_, NBITS>) -> distances::Result<f32> {
441 let ip: MathematicalValue<f32> = MinMaxIP::evaluate(x, y)?;
442 Ok(1.0 - ip.into_inner()) }
444}
445
446impl<const NBITS: usize>
447 PureDistanceFunction<FullQueryRef<'_>, DataRef<'_, NBITS>, distances::Result<f32>>
448 for MinMaxCosineNormalized
449where
450 Unsigned: Representation<NBITS>,
451 MinMaxIP: for<'a, 'b> PureDistanceFunction<
452 FullQueryRef<'a>,
453 DataRef<'b, NBITS>,
454 distances::MathematicalResult<f32>,
455 >,
456{
457 fn evaluate(x: FullQueryRef<'_>, y: DataRef<'_, NBITS>) -> distances::Result<f32> {
458 let ip: MathematicalValue<f32> = MinMaxIP::evaluate(x, y)?;
459 Ok(1.0 - ip.into_inner()) }
461}
462
463#[cfg(test)]
468#[cfg(not(miri))]
469mod minmax_vector_tests {
470 use diskann_utils::Reborrow;
471 use rand::{
472 Rng, SeedableRng,
473 distr::{Distribution, Uniform},
474 rngs::StdRng,
475 };
476
477 use super::*;
478 use crate::{alloc::GlobalAllocator, scalar::bit_scale};
479
480 fn test_minmax_compensated_vectors<const NBITS: usize, R>(dim: usize, rng: &mut R)
481 where
482 Unsigned: Representation<NBITS>,
483 InnerProduct: for<'a, 'b> PureDistanceFunction<
484 BitSlice<'a, NBITS, Unsigned>,
485 BitSlice<'b, NBITS, Unsigned>,
486 distances::MathematicalResult<u32>,
487 >,
488 InnerProduct: for<'a, 'b> PureDistanceFunction<
489 &'a [f32],
490 BitSlice<'b, NBITS, Unsigned>,
491 distances::MathematicalResult<f32>,
492 >,
493 R: Rng,
494 {
495 assert!(dim <= bit_scale::<NBITS>() as usize);
496
497 let mut v1 = Data::<NBITS>::new_boxed(dim);
499 let mut v2 = Data::<NBITS>::new_boxed(dim);
500
501 let domain = Unsigned::domain_const::<NBITS>();
502 let code_distribution = Uniform::new_inclusive(*domain.start(), *domain.end()).unwrap();
503
504 {
506 let mut bitslice1 = v1.vector_mut();
507 let mut bitslice2 = v2.vector_mut();
508
509 for i in 0..dim {
510 bitslice1.set(i, code_distribution.sample(rng)).unwrap();
511 bitslice2.set(i, code_distribution.sample(rng)).unwrap();
512 }
513 }
514 let a_rnd = Uniform::new_inclusive(0.0, 2.0).unwrap();
515 let b_rnd = Uniform::new_inclusive(0.0, 2.0).unwrap();
516
517 let a1 = a_rnd.sample(rng);
521 let b1 = b_rnd.sample(rng);
522 let a2 = a_rnd.sample(rng);
523 let b2 = b_rnd.sample(rng);
524
525 let sum1: f32 = (0..dim).map(|i| v1.vector().get(i).unwrap() as f32).sum();
527 let sum2: f32 = (0..dim).map(|i| v2.vector().get(i).unwrap() as f32).sum();
528
529 let mut original1 = Vec::with_capacity(dim);
531 let mut original2 = Vec::with_capacity(dim);
532
533 for i in 0..dim {
535 let val1 = a1 * v1.vector().get(i).unwrap() as f32 + b1;
536 let val2 = a2 * v2.vector().get(i).unwrap() as f32 + b2;
537 original1.push(val1);
538 original2.push(val2);
539 }
540
541 let norm1_squared: f32 = original1.iter().map(|x| x * x).sum();
543 let norm2_squared: f32 = original2.iter().map(|x| x * x).sum();
544
545 v1.set_meta(MinMaxCompensation {
547 a: a1,
548 b: b1,
549 n: a1 * sum1,
550 norm_squared: norm1_squared,
551 dim: dim as u32,
552 });
553
554 v2.set_meta(MinMaxCompensation {
555 a: a2,
556 b: b2,
557 n: a2 * sum2,
558 norm_squared: norm2_squared,
559 dim: dim as u32,
560 });
561
562 let expected_ip = (0..dim).map(|i| original1[i] * original2[i]).sum::<f32>();
564
565 let computed_ip_f32: distances::Result<f32> =
567 MinMaxIP::evaluate(v1.reborrow(), v2.reborrow());
568 let computed_ip_f32 = computed_ip_f32.unwrap();
569 assert!(
570 (expected_ip - (-computed_ip_f32)).abs() / expected_ip.abs() < 1e-3,
571 "Inner product (f32) failed: expected {}, got {} on dim : {}",
572 -expected_ip,
573 computed_ip_f32,
574 dim
575 );
576
577 let expected_l2 = (0..dim)
579 .map(|i| original1[i] - original2[i])
580 .map(|x| x.powf(2.0))
581 .sum::<f32>();
582
583 let computed_l2_f32: distances::Result<f32> =
585 MinMaxL2Squared::evaluate(v1.reborrow(), v2.reborrow());
586 let computed_l2_f32 = computed_l2_f32.unwrap();
587 assert!(
588 ((computed_l2_f32 - expected_l2).abs() / expected_l2) < 1e-3,
589 "L2 distance (f32) failed: expected {}, got {} on dim : {}",
590 expected_l2,
591 computed_l2_f32,
592 dim
593 );
594
595 let expected_cosine = 1.0 - expected_ip / (norm1_squared.sqrt() * norm2_squared.sqrt());
596
597 let computed_cosine: distances::Result<f32> =
598 MinMaxCosine::evaluate(v1.reborrow(), v2.reborrow());
599 let computed_cosine = computed_cosine.unwrap();
600
601 {
602 let passed = (computed_cosine - expected_cosine).abs() < 1e-6
603 || ((computed_cosine - expected_cosine).abs() / expected_cosine) < 1e-3;
604
605 assert!(
606 passed,
607 "Cosine distance (f32) failed: expected {}, got {} on dim : {}",
608 expected_cosine, computed_cosine, dim
609 );
610 }
611
612 let cosine_normalized: distances::Result<f32> =
613 MinMaxCosineNormalized::evaluate(v1.reborrow(), v2.reborrow());
614 let cosine_normalized = cosine_normalized.unwrap();
615 let expected_cos_normalized = 1.0 - expected_ip;
616 assert!(
617 ((expected_cos_normalized - cosine_normalized).abs() / expected_cos_normalized.abs())
618 < 1e-6,
619 "CosineNormalized distance (f32) failed: expected {}, got {} on dim : {}",
620 expected_cos_normalized,
621 cosine_normalized,
622 dim
623 );
624
625 let mut fp_query = FullQuery::new_in(dim, GlobalAllocator).unwrap();
627 fp_query.vector_mut().copy_from_slice(&original1);
628 *fp_query.meta_mut() = FullQueryMeta {
629 norm_squared: norm1_squared,
630 sum: original1.iter().sum::<f32>(),
631 };
632
633 let fp_ip: distances::Result<f32> = MinMaxIP::evaluate(fp_query.reborrow(), v2.reborrow());
634 let fp_ip = fp_ip.unwrap();
635 assert!(
636 (expected_ip - (-fp_ip)).abs() / expected_ip.abs() < 1e-3,
637 "Inner product (f32) failed: expected {}, got {} on dim : {}",
638 -expected_ip,
639 fp_ip,
640 dim
641 );
642
643 let fp_l2: distances::Result<f32> =
644 MinMaxL2Squared::evaluate(fp_query.reborrow(), v2.reborrow());
645 let fp_l2 = fp_l2.unwrap();
646 assert!(
647 ((fp_l2 - expected_l2).abs() / expected_l2) < 1e-3,
648 "L2 distance (f32) failed: expected {}, got {} on dim : {}",
649 expected_l2,
650 computed_l2_f32,
651 dim
652 );
653
654 let fp_cosine: distances::Result<f32> =
655 MinMaxCosine::evaluate(fp_query.reborrow(), v2.reborrow());
656 let fp_cosine = fp_cosine.unwrap();
657 let diff = (fp_cosine - expected_cosine).abs();
658 assert!(
659 (diff / expected_cosine) < 1e-3 || diff <= 1e-6,
660 "Cosine distance (f32) failed: expected {}, got {} on dim : {}",
661 expected_cosine,
662 fp_cosine,
663 dim
664 );
665
666 let fp_cos_norm: distances::Result<f32> =
667 MinMaxCosineNormalized::evaluate(fp_query.reborrow(), v2.reborrow());
668 let fp_cos_norm = fp_cos_norm.unwrap();
669 assert!(
670 (((1.0 - expected_ip) - fp_cos_norm).abs() / (1.0 - expected_ip)) < 1e-3,
671 "Cosine distance (f32) failed: expected {}, got {} on dim : {}",
672 (1.0 - expected_ip),
673 fp_cos_norm,
674 dim
675 );
676
677 let meta = v1.meta();
679 let v1_ref = DataRef::new(v1.vector(), &meta);
680 let dim = v1_ref.len();
681 let mut boxed = vec![0f32; dim + 1];
682
683 let pre = v1_ref.decompress_into(&mut boxed);
684 assert_eq!(
685 pre.unwrap_err(),
686 DecompressError::LengthMismatch(dim, dim + 1)
687 );
688 let pre = v1_ref.decompress_into(&mut boxed[..dim - 1]);
689 assert_eq!(
690 pre.unwrap_err(),
691 DecompressError::LengthMismatch(dim, dim - 1)
692 );
693 let pre = v1_ref.decompress_into(&mut boxed[..dim]);
694 assert!(pre.is_ok());
695
696 boxed
697 .iter()
698 .zip(original1.iter())
699 .for_each(|(x, y)| assert!((*x - *y).abs() <= 1e-6));
700
701 let mut bytes = vec![0u8; Data::canonical_bytes(dim)];
703 let mut data = DataMutRef::from_canonical_front_mut(bytes.as_mut_slice(), dim).unwrap();
704 data.set_meta(meta);
705
706 let pre = MinMaxCompensation::read_dimension(&bytes);
707 assert!(pre.is_ok());
708 let read_dim = pre.unwrap();
709 assert_eq!(read_dim, dim);
710
711 let pre = MinMaxCompensation::read_dimension(&[0_u8; 2]);
712 assert_eq!(pre.unwrap_err(), MetaParseError::NotCanonical(2));
713 }
714
715 cfg_if::cfg_if! {
716 if #[cfg(miri)] {
717 const TRIALS: usize = 2;
721 } else {
722 const TRIALS: usize = 10;
723 }
724 }
725
726 macro_rules! test_minmax_compensated {
727 ($name:ident, $nbits:literal, $seed:literal) => {
728 #[test]
729 fn $name() {
730 let mut rng = StdRng::seed_from_u64($seed);
731 const MAX_DIM: usize = (bit_scale::<$nbits>() as usize);
732 for dim in 1..=MAX_DIM {
733 for _ in 0..TRIALS {
734 test_minmax_compensated_vectors::<$nbits, _>(dim, &mut rng);
735 }
736 }
737 }
738 };
739 }
740 test_minmax_compensated!(unsigned_minmax_compensated_test_u1, 1, 0xa33d5658097a1c35);
741 test_minmax_compensated!(unsigned_minmax_compensated_test_u2, 2, 0xaedf3d2a223b7b77);
742 test_minmax_compensated!(unsigned_minmax_compensated_test_u4, 4, 0xf60c0c8d1aadc126);
743 test_minmax_compensated!(unsigned_minmax_compensated_test_u8, 8, 0x09fa14c42a9d7d98);
744}