perf: reduce storage requirements for bounded btreemaps by ~25%.

[ielashi]

I did an analysis on how big node entries are. A node can have at most 11 entries, but ~70% of nodes contain <= 8 entries. With that information, I was able to reduce the page size in BTreeMap V2 in the case where the keys and values are both bounded, resulting in a storage saving of ~25%.

The report, generated by our new benchmarking framework, clearly shows the gains. V2 benchmarks saw a decline in the number of stable pages needed without compromising performance.

Benchmark: btreemap_insert_10mib_values
  measurements:
    instructions: 278228334 (0.00%) (no change)
    node_load_v2: 10377468 (0.00%) (no change)
    node_save_v2: 245958554 (0.00%) (no change)
    stable_memory_size: 33 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_blob_4_1024
  measurements:
    instructions: 938860652 (0.00%) (no change)
    node_load_v1: 246219371 (0.00%) (no change)
    node_save_v1: 370094431 (0.00%) (no change)
    stable_memory_size: 124 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_blob_4_1024_v2
  measurements:
    instructions: 1284860075 (-0.01%) (change within noise threshold)
    node_load_v2: 302568355 (0.00%) (no change)
    node_save_v2: 661255273 (-0.02%) (change within noise threshold)
    stable_memory_size: 93 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_insert_blob_8_1024
  measurements:
    instructions: 1084934108 (0.00%) (no change)
    node_load_v1: 286595797 (0.00%) (no change)
    node_save_v1: 394314301 (0.00%) (no change)
    stable_memory_size: 184 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_blob_8_1024_v2
  measurements:
    instructions: 1458496280 (-0.01%) (change within noise threshold)
    node_load_v2: 344800342 (0.00%) (change within noise threshold)
    node_save_v2: 711692000 (-0.03%) (change within noise threshold)
    stable_memory_size: 139 (improved by 24.46%)

---------------------------------------------------

Benchmark: btreemap_insert_blob_16_1024
  measurements:
    instructions: 1177421502 (0.00%) (no change)
    node_load_v1: 362914338 (0.00%) (no change)
    node_save_v1: 403464072 (0.00%) (no change)
    stable_memory_size: 216 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_blob_16_1024_v2
  measurements:
    instructions: 1588123192 (-0.02%) (change within noise threshold)
    node_load_v2: 440221819 (0.00%) (change within noise threshold)
    node_save_v2: 739898082 (-0.04%) (change within noise threshold)
    stable_memory_size: 162 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_insert_blob_32_1024
  measurements:
    instructions: 1224612399 (0.00%) (no change)
    node_load_v1: 390780802 (0.00%) (no change)
    node_save_v1: 415826600 (0.00%) (no change)
    stable_memory_size: 231 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_blob_32_1024_v2
  measurements:
    instructions: 1655605924 (-0.02%) (change within noise threshold)
    node_load_v2: 477569310 (0.00%) (no change)
    node_save_v2: 768954087 (-0.03%) (change within noise threshold)
    stable_memory_size: 174 (improved by 24.68%)

---------------------------------------------------

Benchmark: btreemap_insert_blob_64_1024
  measurements:
    instructions: 1464177820 (0.00%) (no change)
    node_load_v1: 595998298 (0.00%) (no change)
    node_save_v1: 418743231 (0.00%) (no change)
    stable_memory_size: 246 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_blob_64_1024_v2
  measurements:
    instructions: 1928636138 (-0.01%) (change within noise threshold)
    node_load_v2: 692235029 (0.00%) (no change)
    node_save_v2: 785237958 (-0.03%) (change within noise threshold)
    stable_memory_size: 184 (improved by 25.20%)

---------------------------------------------------

Benchmark: btreemap_insert_blob_128_1024
  measurements:
    instructions: 1730313092 (0.00%) (no change)
    node_load_v1: 818923030 (0.00%) (no change)
    node_save_v1: 424573804 (0.00%) (no change)
    stable_memory_size: 261 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_blob_128_1024_v2
  measurements:
    instructions: 2230592033 (-0.01%) (change within noise threshold)
    node_load_v2: 916541484 (0.00%) (no change)
    node_save_v2: 814064656 (-0.03%) (change within noise threshold)
    stable_memory_size: 196 (improved by 24.90%)

---------------------------------------------------

Benchmark: btreemap_insert_blob_256_1024
  measurements:
    instructions: 2255818313 (0.00%) (no change)
    node_load_v1: 1272224795 (0.00%) (no change)
    node_save_v1: 430174789 (0.00%) (no change)
    stable_memory_size: 293 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_blob_256_1024_v2
  measurements:
    instructions: 2794429751 (-0.01%) (change within noise threshold)
    node_load_v2: 1368657545 (0.00%) (no change)
    node_save_v2: 851897559 (-0.02%) (change within noise threshold)
    stable_memory_size: 220 (improved by 24.91%)

---------------------------------------------------

Benchmark: btreemap_insert_blob_512_1024
  measurements:
    instructions: 3306816049 (0.00%) (no change)
    node_load_v1: 2162164471 (0.00%) (no change)
    node_save_v1: 447463180 (0.00%) (no change)
    stable_memory_size: 352 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_blob_512_1024_v2
  measurements:
    instructions: 3902055470 (-0.00%) (change within noise threshold)
    node_load_v2: 2249757429 (0.00%) (no change)
    node_save_v2: 953602203 (-0.01%) (change within noise threshold)
    stable_memory_size: 264 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_insert_u64_u64
  measurements:
    instructions: 771845193 (0.00%) (no change)
    node_load_v1: 274520203 (0.00%) (no change)
    node_save_v1: 266527196 (0.00%) (no change)
    stable_memory_size: 8 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_u64_u64_v2
  measurements:
    instructions: 848175865 (0.67%) (change within noise threshold)
    node_load_v2: 324943098 (1.24%) (change within noise threshold)
    node_save_v2: 295936099 (0.23%) (change within noise threshold)
    stable_memory_size: 7 (improved by 12.50%)

---------------------------------------------------

Benchmark: btreemap_insert_u64_blob_8
  measurements:
    instructions: 750190911 (0.00%) (no change)
    node_load_v1: 276866073 (0.00%) (no change)
    node_save_v1: 255664450 (0.00%) (no change)
    stable_memory_size: 8 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_u64_blob_8_v2
  measurements:
    instructions: 806917372 (0.11%) (change within noise threshold)
    node_load_v2: 320660408 (0.10%) (change within noise threshold)
    node_save_v2: 272412341 (0.12%) (change within noise threshold)
    stable_memory_size: 6 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_insert_blob_8_u64
  measurements:
    instructions: 684689096 (0.00%) (no change)
    node_load_v1: 277937358 (0.00%) (no change)
    node_save_v1: 189388784 (0.00%) (no change)
    stable_memory_size: 7 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_insert_blob_8_u64_v2
  measurements:
    instructions: 805533962 (0.84%) (change within noise threshold)
    node_load_v2: 358481378 (1.04%) (change within noise threshold)
    node_save_v2: 230438833 (0.29%) (change within noise threshold)
    stable_memory_size: 5 (improved by 28.57%)

---------------------------------------------------

Benchmark: btreemap_get_blob_4_1024
  measurements:
    instructions: 401718154 (0.00%) (no change)
    node_load_v1: 259275488 (0.00%) (no change)
    stable_memory_size: 124 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_blob_4_1024_v2
  measurements:
    instructions: 480241876 (0.00%) (no change)
    node_load_v2: 329436785 (0.00%) (no change)
    stable_memory_size: 93 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_get_blob_8_1024
  measurements:
    instructions: 473964224 (0.00%) (no change)
    node_load_v1: 304258691 (0.00%) (no change)
    stable_memory_size: 184 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_blob_8_1024_v2
  measurements:
    instructions: 549627424 (0.00%) (no change)
    node_load_v2: 371386524 (0.00%) (no change)
    stable_memory_size: 139 (improved by 24.46%)

---------------------------------------------------

Benchmark: btreemap_get_blob_16_1024
  measurements:
    instructions: 553966238 (0.00%) (no change)
    node_load_v1: 383794822 (0.00%) (no change)
    stable_memory_size: 216 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_blob_16_1024_v2
  measurements:
    instructions: 637391324 (0.00%) (no change)
    node_load_v2: 464133703 (0.00%) (no change)
    stable_memory_size: 162 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_get_blob_32_1024
  measurements:
    instructions: 591716960 (0.00%) (no change)
    node_load_v1: 410436451 (0.00%) (no change)
    stable_memory_size: 231 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_blob_32_1024_v2
  measurements:
    instructions: 679662006 (0.00%) (no change)
    node_load_v2: 495574095 (0.00%) (no change)
    stable_memory_size: 174 (improved by 24.68%)

---------------------------------------------------

Benchmark: btreemap_get_blob_64_1024
  measurements:
    instructions: 814621589 (0.00%) (no change)
    node_load_v1: 627796876 (0.00%) (no change)
    stable_memory_size: 246 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_blob_64_1024_v2
  measurements:
    instructions: 902934555 (0.00%) (no change)
    node_load_v2: 708745655 (0.00%) (no change)
    stable_memory_size: 184 (improved by 25.20%)

---------------------------------------------------

Benchmark: btreemap_get_blob_128_1024
  measurements:
    instructions: 1036041908 (0.00%) (no change)
    node_load_v1: 839537545 (0.00%) (no change)
    stable_memory_size: 261 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_blob_128_1024_v2
  measurements:
    instructions: 1140173768 (0.00%) (no change)
    node_load_v2: 933785784 (0.00%) (no change)
    stable_memory_size: 196 (improved by 24.90%)

---------------------------------------------------

Benchmark: btreemap_get_u64_u64
  measurements:
    instructions: 412643077 (0.00%) (no change)
    node_load_v1: 290922161 (0.00%) (no change)
    stable_memory_size: 8 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_u64_u64_v2
  measurements:
    instructions: 477401878 (1.60%) (change within noise threshold)
    node_load_v2: 347289827 (1.76%) (change within noise threshold)
    stable_memory_size: 7 (improved by 12.50%)

---------------------------------------------------

Benchmark: btreemap_get_u64_blob_8
  measurements:
    instructions: 409579480 (0.00%) (no change)
    node_load_v1: 292395667 (0.00%) (no change)
    stable_memory_size: 8 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_u64_blob_8_v2
  measurements:
    instructions: 465392548 (0.00%) (no change)
    node_load_v2: 342799065 (0.00%) (no change)
    stable_memory_size: 6 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_get_blob_8_u64
  measurements:
    instructions: 426482546 (0.00%) (no change)
    node_load_v1: 294602061 (0.00%) (no change)
    stable_memory_size: 7 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_blob_8_u64_v2
  measurements:
    instructions: 523481237 (regressed by 2.27%)
    node_load_v2: 383093469 (regressed by 2.43%)
    stable_memory_size: 5 (improved by 28.57%)

---------------------------------------------------

Benchmark: btreemap_get_blob_256_1024
  measurements:
    instructions: 1523593515 (0.00%) (no change)
    node_load_v1: 1301924960 (0.00%) (no change)
    stable_memory_size: 293 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_blob_256_1024_v2
  measurements:
    instructions: 1628351182 (0.00%) (no change)
    node_load_v2: 1392993062 (0.00%) (no change)
    stable_memory_size: 220 (improved by 24.91%)

---------------------------------------------------

Benchmark: btreemap_get_blob_512_1024
  measurements:
    instructions: 2489215042 (0.00%) (no change)
    node_load_v1: 2219164452 (0.00%) (no change)
    stable_memory_size: 352 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_get_blob_512_1024_v2
  measurements:
    instructions: 2596163236 (0.00%) (no change)
    node_load_v2: 2312346281 (0.00%) (no change)
    stable_memory_size: 264 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_remove_blob_4_1024
  measurements:
    instructions: 1006445824 (0.00%) (no change)
    node_load_v1: 269171795 (0.00%) (no change)
    node_save_v1: 421165272 (0.00%) (no change)
    stable_memory_size: 124 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_blob_4_1024_v2
  measurements:
    instructions: 1417601784 (-0.00%) (change within noise threshold)
    node_load_v2: 334156300 (0.00%) (change within noise threshold)
    node_save_v2: 771175843 (-0.01%) (change within noise threshold)
    stable_memory_size: 93 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_remove_blob_8_1024
  measurements:
    instructions: 1300448303 (0.00%) (no change)
    node_load_v1: 325916114 (0.00%) (no change)
    node_save_v1: 562174712 (0.00%) (no change)
    stable_memory_size: 184 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_blob_8_1024_v2
  measurements:
    instructions: 1841887486 (-0.01%) (change within noise threshold)
    node_load_v2: 391438934 (0.00%) (no change)
    node_save_v2: 1045403922 (-0.01%) (change within noise threshold)
    stable_memory_size: 139 (improved by 24.46%)

---------------------------------------------------

Benchmark: btreemap_remove_blob_16_1024
  measurements:
    instructions: 1544917110 (0.00%) (no change)
    node_load_v1: 420249550 (0.00%) (no change)
    node_save_v1: 654430779 (0.00%) (no change)
    stable_memory_size: 216 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_blob_16_1024_v2
  measurements:
    instructions: 2218448732 (-0.01%) (change within noise threshold)
    node_load_v2: 513947291 (0.00%) (no change)
    node_save_v2: 1243769246 (-0.01%) (change within noise threshold)
    stable_memory_size: 162 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_remove_blob_32_1024
  measurements:
    instructions: 1622774819 (0.00%) (no change)
    node_load_v1: 443614945 (0.00%) (no change)
    node_save_v1: 681136613 (0.00%) (no change)
    stable_memory_size: 231 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_blob_32_1024_v2
  measurements:
    instructions: 2327559094 (-0.01%) (change within noise threshold)
    node_load_v2: 545935373 (-0.00%) (change within noise threshold)
    node_save_v2: 1295876421 (-0.01%) (change within noise threshold)
    stable_memory_size: 174 (improved by 24.68%)

---------------------------------------------------

Benchmark: btreemap_remove_blob_64_1024
  measurements:
    instructions: 1917032351 (0.00%) (no change)
    node_load_v1: 675469604 (0.00%) (no change)
    node_save_v1: 700312977 (0.00%) (no change)
    stable_memory_size: 246 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_blob_64_1024_v2
  measurements:
    instructions: 2663779711 (-0.01%) (change within noise threshold)
    node_load_v2: 783139557 (0.00%) (no change)
    node_save_v2: 1347825662 (-0.01%) (change within noise threshold)
    stable_memory_size: 184 (improved by 25.20%)

---------------------------------------------------

Benchmark: btreemap_remove_blob_128_1024
  measurements:
    instructions: 2236575844 (0.00%) (no change)
    node_load_v1: 922607545 (0.00%) (no change)
    node_save_v1: 716920195 (0.00%) (no change)
    stable_memory_size: 261 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_blob_128_1024_v2
  measurements:
    instructions: 3031279182 (-0.00%) (change within noise threshold)
    node_load_v2: 1029479582 (0.00%) (no change)
    node_save_v2: 1412131798 (-0.01%) (change within noise threshold)
    stable_memory_size: 196 (improved by 24.90%)

---------------------------------------------------

Benchmark: btreemap_remove_blob_256_1024
  measurements:
    instructions: 2839195280 (0.00%) (no change)
    node_load_v1: 1421754484 (0.00%) (no change)
    node_save_v1: 722710062 (0.00%) (no change)
    stable_memory_size: 293 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_blob_256_1024_v2
  measurements:
    instructions: 3696334312 (-0.00%) (change within noise threshold)
    node_load_v2: 1528516744 (0.00%) (no change)
    node_save_v2: 1474999328 (-0.01%) (change within noise threshold)
    stable_memory_size: 220 (improved by 24.91%)

---------------------------------------------------

Benchmark: btreemap_remove_blob_512_1024
  measurements:
    instructions: 4124317339 (0.00%) (no change)
    node_load_v1: 2441544783 (0.00%) (no change)
    node_save_v1: 765030850 (0.00%) (no change)
    stable_memory_size: 352 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_blob_512_1024_v2
  measurements:
    instructions: 5148900105 (-0.00%) (change within noise threshold)
    node_load_v2: 2551454747 (0.00%) (change within noise threshold)
    node_save_v2: 1679737551 (-0.00%) (change within noise threshold)
    stable_memory_size: 264 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_remove_u64_u64
  measurements:
    instructions: 1110124274 (0.00%) (no change)
    node_load_v1: 314148033 (0.00%) (no change)
    node_save_v1: 483110284 (0.00%) (no change)
    stable_memory_size: 8 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_u64_u64_v2
  measurements:
    instructions: 1193726508 (1.02%) (change within noise threshold)
    node_load_v2: 372663005 (regressed by 2.18%)
    node_save_v2: 507231342 (0.68%) (change within noise threshold)
    stable_memory_size: 7 (improved by 12.50%)

---------------------------------------------------

Benchmark: btreemap_remove_u64_blob_8
  measurements:
    instructions: 1072866879 (0.00%) (no change)
    node_load_v1: 313757215 (0.00%) (no change)
    node_save_v1: 457702957 (0.00%) (no change)
    stable_memory_size: 8 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_u64_blob_8_v2
  measurements:
    instructions: 1131312211 (0.25%) (change within noise threshold)
    node_load_v2: 364893854 (0.54%) (change within noise threshold)
    node_save_v2: 464658073 (0.15%) (change within noise threshold)
    stable_memory_size: 6 (improved by 25.00%)

---------------------------------------------------

Benchmark: btreemap_remove_blob_8_u64
  measurements:
    instructions: 903826016 (0.00%) (no change)
    node_load_v1: 318747944 (0.00%) (no change)
    node_save_v1: 302202576 (0.00%) (no change)
    stable_memory_size: 7 (0.00%) (no change)

---------------------------------------------------

Benchmark: btreemap_remove_blob_8_u64_v2
  measurements:
    instructions: 1051368948 (1.19%) (change within noise threshold)
    node_load_v2: 405289279 (regressed by 2.05%)
    node_save_v2: 364434857 (0.84%) (change within noise threshold)
    stable_memory_size: 5 (improved by 28.57%)

---------------------------------------------------