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)]
468mod minmax_vector_tests {
469 use diskann_utils::Reborrow;
470 use rand::{
471 Rng, SeedableRng,
472 distr::{Distribution, Uniform},
473 rngs::StdRng,
474 };
475
476 use super::*;
477 use crate::{alloc::GlobalAllocator, scalar::bit_scale};
478
479 fn test_minmax_compensated_vectors<const NBITS: usize, R>(dim: usize, rng: &mut R)
480 where
481 Unsigned: Representation<NBITS>,
482 InnerProduct: for<'a, 'b> PureDistanceFunction<
483 BitSlice<'a, NBITS, Unsigned>,
484 BitSlice<'b, NBITS, Unsigned>,
485 distances::MathematicalResult<u32>,
486 >,
487 InnerProduct: for<'a, 'b> PureDistanceFunction<
488 &'a [f32],
489 BitSlice<'b, NBITS, Unsigned>,
490 distances::MathematicalResult<f32>,
491 >,
492 R: Rng,
493 {
494 assert!(dim <= bit_scale::<NBITS>() as usize);
495
496 let mut v1 = Data::<NBITS>::new_boxed(dim);
498 let mut v2 = Data::<NBITS>::new_boxed(dim);
499
500 let domain = Unsigned::domain_const::<NBITS>();
501 let code_distribution = Uniform::new_inclusive(*domain.start(), *domain.end()).unwrap();
502
503 {
505 let mut bitslice1 = v1.vector_mut();
506 let mut bitslice2 = v2.vector_mut();
507
508 for i in 0..dim {
509 bitslice1.set(i, code_distribution.sample(rng)).unwrap();
510 bitslice2.set(i, code_distribution.sample(rng)).unwrap();
511 }
512 }
513 let a_rnd = Uniform::new_inclusive(0.0, 2.0).unwrap();
514 let b_rnd = Uniform::new_inclusive(0.0, 2.0).unwrap();
515
516 let a1 = a_rnd.sample(rng);
520 let b1 = b_rnd.sample(rng);
521 let a2 = a_rnd.sample(rng);
522 let b2 = b_rnd.sample(rng);
523
524 let sum1: f32 = (0..dim).map(|i| v1.vector().get(i).unwrap() as f32).sum();
526 let sum2: f32 = (0..dim).map(|i| v2.vector().get(i).unwrap() as f32).sum();
527
528 let mut original1 = Vec::with_capacity(dim);
530 let mut original2 = Vec::with_capacity(dim);
531
532 for i in 0..dim {
534 let val1 = a1 * v1.vector().get(i).unwrap() as f32 + b1;
535 let val2 = a2 * v2.vector().get(i).unwrap() as f32 + b2;
536 original1.push(val1);
537 original2.push(val2);
538 }
539
540 let norm1_squared: f32 = original1.iter().map(|x| x * x).sum();
542 let norm2_squared: f32 = original2.iter().map(|x| x * x).sum();
543
544 v1.set_meta(MinMaxCompensation {
546 a: a1,
547 b: b1,
548 n: a1 * sum1,
549 norm_squared: norm1_squared,
550 dim: dim as u32,
551 });
552
553 v2.set_meta(MinMaxCompensation {
554 a: a2,
555 b: b2,
556 n: a2 * sum2,
557 norm_squared: norm2_squared,
558 dim: dim as u32,
559 });
560
561 let expected_ip = (0..dim).map(|i| original1[i] * original2[i]).sum::<f32>();
563
564 let computed_ip_f32: distances::Result<f32> =
566 MinMaxIP::evaluate(v1.reborrow(), v2.reborrow());
567 let computed_ip_f32 = computed_ip_f32.unwrap();
568 assert!(
569 (expected_ip - (-computed_ip_f32)).abs() / expected_ip.abs() < 1e-3,
570 "Inner product (f32) failed: expected {}, got {} on dim : {}",
571 -expected_ip,
572 computed_ip_f32,
573 dim
574 );
575
576 let expected_l2 = (0..dim)
578 .map(|i| original1[i] - original2[i])
579 .map(|x| x.powf(2.0))
580 .sum::<f32>();
581
582 let computed_l2_f32: distances::Result<f32> =
584 MinMaxL2Squared::evaluate(v1.reborrow(), v2.reborrow());
585 let computed_l2_f32 = computed_l2_f32.unwrap();
586 assert!(
587 ((computed_l2_f32 - expected_l2).abs() / expected_l2) < 1e-3,
588 "L2 distance (f32) failed: expected {}, got {} on dim : {}",
589 expected_l2,
590 computed_l2_f32,
591 dim
592 );
593
594 let expected_cosine = 1.0 - expected_ip / (norm1_squared.sqrt() * norm2_squared.sqrt());
595
596 let computed_cosine: distances::Result<f32> =
597 MinMaxCosine::evaluate(v1.reborrow(), v2.reborrow());
598 let computed_cosine = computed_cosine.unwrap();
599
600 {
601 let passed = (computed_cosine - expected_cosine).abs() < 1e-6
602 || ((computed_cosine - expected_cosine).abs() / expected_cosine) < 1e-3;
603
604 assert!(
605 passed,
606 "Cosine distance (f32) failed: expected {}, got {} on dim : {}",
607 expected_cosine, computed_cosine, dim
608 );
609 }
610
611 let cosine_normalized: distances::Result<f32> =
612 MinMaxCosineNormalized::evaluate(v1.reborrow(), v2.reborrow());
613 let cosine_normalized = cosine_normalized.unwrap();
614 let expected_cos_normalized = 1.0 - expected_ip;
615 assert!(
616 ((expected_cos_normalized - cosine_normalized).abs() / expected_cos_normalized.abs())
617 < 1e-6,
618 "CosineNormalized distance (f32) failed: expected {}, got {} on dim : {}",
619 expected_cos_normalized,
620 cosine_normalized,
621 dim
622 );
623
624 let mut fp_query = FullQuery::new_in(dim, GlobalAllocator).unwrap();
626 fp_query.vector_mut().copy_from_slice(&original1);
627 *fp_query.meta_mut() = FullQueryMeta {
628 norm_squared: norm1_squared,
629 sum: original1.iter().sum::<f32>(),
630 };
631
632 let fp_ip: distances::Result<f32> = MinMaxIP::evaluate(fp_query.reborrow(), v2.reborrow());
633 let fp_ip = fp_ip.unwrap();
634 assert!(
635 (expected_ip - (-fp_ip)).abs() / expected_ip.abs() < 1e-3,
636 "Inner product (f32) failed: expected {}, got {} on dim : {}",
637 -expected_ip,
638 fp_ip,
639 dim
640 );
641
642 let fp_l2: distances::Result<f32> =
643 MinMaxL2Squared::evaluate(fp_query.reborrow(), v2.reborrow());
644 let fp_l2 = fp_l2.unwrap();
645 assert!(
646 ((fp_l2 - expected_l2).abs() / expected_l2) < 1e-3,
647 "L2 distance (f32) failed: expected {}, got {} on dim : {}",
648 expected_l2,
649 computed_l2_f32,
650 dim
651 );
652
653 let fp_cosine: distances::Result<f32> =
654 MinMaxCosine::evaluate(fp_query.reborrow(), v2.reborrow());
655 let fp_cosine = fp_cosine.unwrap();
656 let diff = (fp_cosine - expected_cosine).abs();
657 assert!(
658 (diff / expected_cosine) < 1e-3 || diff <= 1e-6,
659 "Cosine distance (f32) failed: expected {}, got {} on dim : {}",
660 expected_cosine,
661 fp_cosine,
662 dim
663 );
664
665 let fp_cos_norm: distances::Result<f32> =
666 MinMaxCosineNormalized::evaluate(fp_query.reborrow(), v2.reborrow());
667 let fp_cos_norm = fp_cos_norm.unwrap();
668 assert!(
669 (((1.0 - expected_ip) - fp_cos_norm).abs() / (1.0 - expected_ip)) < 1e-3,
670 "Cosine distance (f32) failed: expected {}, got {} on dim : {}",
671 (1.0 - expected_ip),
672 fp_cos_norm,
673 dim
674 );
675
676 let meta = v1.meta();
678 let v1_ref = DataRef::new(v1.vector(), &meta);
679 let dim = v1_ref.len();
680 let mut boxed = vec![0f32; dim + 1];
681
682 let pre = v1_ref.decompress_into(&mut boxed);
683 assert_eq!(
684 pre.unwrap_err(),
685 DecompressError::LengthMismatch(dim, dim + 1)
686 );
687 let pre = v1_ref.decompress_into(&mut boxed[..dim - 1]);
688 assert_eq!(
689 pre.unwrap_err(),
690 DecompressError::LengthMismatch(dim, dim - 1)
691 );
692 let pre = v1_ref.decompress_into(&mut boxed[..dim]);
693 assert!(pre.is_ok());
694
695 boxed
696 .iter()
697 .zip(original1.iter())
698 .for_each(|(x, y)| assert!((*x - *y).abs() <= 1e-6));
699
700 let mut bytes = vec![0u8; Data::canonical_bytes(dim)];
702 let mut data = DataMutRef::from_canonical_front_mut(bytes.as_mut_slice(), dim).unwrap();
703 data.set_meta(meta);
704
705 let pre = MinMaxCompensation::read_dimension(&bytes);
706 assert!(pre.is_ok());
707 let read_dim = pre.unwrap();
708 assert_eq!(read_dim, dim);
709
710 let pre = MinMaxCompensation::read_dimension(&[0_u8; 2]);
711 assert_eq!(pre.unwrap_err(), MetaParseError::NotCanonical(2));
712 }
713
714 cfg_if::cfg_if! {
715 if #[cfg(miri)] {
716 const TRIALS: usize = 2;
720 } else {
721 const TRIALS: usize = 10;
722 }
723 }
724
725 macro_rules! test_minmax_compensated {
726 ($name:ident, $nbits:literal, $seed:literal) => {
727 #[test]
728 fn $name() {
729 let mut rng = StdRng::seed_from_u64($seed);
730 for dim in 1..(bit_scale::<$nbits>() as usize) {
731 for _ in 0..TRIALS {
732 test_minmax_compensated_vectors::<$nbits, _>(dim, &mut rng);
733 }
734 }
735 }
736 };
737 }
738 test_minmax_compensated!(unsigned_minmax_compensated_test_u1, 1, 0xa32d5658097a1c35);
739 test_minmax_compensated!(unsigned_minmax_compensated_test_u2, 2, 0xaedf3d2a223b7b77);
740 test_minmax_compensated!(unsigned_minmax_compensated_test_u4, 4, 0xf60c0c8d1aadc126);
741 test_minmax_compensated!(unsigned_minmax_compensated_test_u8, 8, 0x09fa14c42a9d7d98);
742}