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histogram labels: bucket names repeat when the range is narrow next to its magnitude (years read 2K–2K) #1081

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histogram labels: bucket names repeat when the range is narrow next to its magnitude (years read 2K–2K)#1081
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Histograms

Description

@paddymul
paddymul
opened on Oct 6, 2026

Problem

fmt_num (histogram.py:19) picks an SI suffix from the largest bound and, after scaling, caps the decimals at 2 (line 30). A column whose spread is small next to its magnitude gets bucket names that repeat: years from 1990 to 2020 read 1.99K–1.99K, 2K–2K (three buckets) and 2.01K–2.01K, integers from 1,000,000 to 1,000,099 read 1M–1M for all twelve bars, and epoch seconds read 1.7B–1.7B. The plain branch caps at 6 decimals (line 33), which is #620's 0–0 for small numbers. pandas, polars and xorq all label with fmt_num.

The suffix stops at T, so a value above 1e15 prints every digit: a 1e30 fill value labels its tail 99–1000000000000000000T, and 1e308 makes a 300-character label. Separately, a bound of -0.5 rounded to 0 decimals keeps its sign, so an int8 column has buckets named -25<>-0 and -0<>24.

import pandas as pd
from buckaroo.customizations.histogram import fmt_tail_bucket
from buckaroo.customizations.pd_stats_v2 import PD_ANALYSIS_V2
from buckaroo.pluggable_analysis_framework.stat_pipeline import StatPipeline

def names(values):
    sd, _ = StatPipeline(PD_ANALYSIS_V2, unit_test=False).process_df(pd.DataFrame({"a": values}))
    return [b["name"] for b in sd["a"]["histogram"]]

print(names(list(range(1990, 2021)) * 10))
# ['1.99K–1.99K', '1.99K–1.99K', '1.99K–2K', '2K–2K', '2K–2K', '2K–2K', '2K–2.01K', '2.01K–2.01K', ...]
print(names([1_000_000 + i for i in range(100)]))
# ['1M–1M', '1M–1M', '1M–1M', ...]
print(fmt_tail_bucket(99.0, 1e30, 9.6))
# 99–1000000000000000000T

Suggested fix

Choose the decimals from the bucket width at the scale shown, so neighbouring edges differ. Skip the SI suffix when the width is small next to the magnitude (years would read 1990–1993). Switch to scientific notation past T.

Context

Found while probing histogram edge cases after #1069. Reproduces on main at e88ace9.

Activity

  1. paddymul
    added
    Histograms
    on Oct 6, 2026

  2. paddymul commented on Oct 7, 2026

    @paddymul
    paddymul
    on Oct 7, 2026
    CollaboratorAuthor

    Probe script for this issue. Save it as probe_1081.py in a buckaroo checkout and run uv run python probe_1081.py. The output below is from main at e88ace9. Each case prints the histogram from pandas (pd), polars (pl) and xorq (xo): the bar kinds, the sum of the population bars, the sum of the categorical bars and the NA bar, then each bar as name:kind=value, and below that the histogram_bins range, min, max, nan_per and distinct_count.

    probe_1081.py 
    """Histogram probe: runs columns through the pandas, polars and xorq stat pipelines and prints each histogram.

Each line is [bar kinds, population sum, categorical sum, NA, duplicate names] then the bars as name:kind=value.
"""
import logging
import warnings
from collections import Counter

logging.disable(logging.CRITICAL)
warnings.filterwarnings('ignore')

import numpy as np
import pandas as pd
import polars as pl
import pyarrow as pa
import xorq.api as xo

from buckaroo.customizations.pd_stats_v2 import PD_ANALYSIS_V2
from buckaroo.customizations.pl_stats_v2 import PL_ANALYSIS_V2
from buckaroo.customizations.xorq_stats_v2 import XORQ_STATS_V2
from buckaroo.pluggable_analysis_framework.stat_pipeline import StatPipeline
from buckaroo.pluggable_analysis_framework.xorq_stat_pipeline import XorqStatPipeline

rng = np.random.default_rng(0)


def summarize(h):
    if not isinstance(h, list):
        return f'NOT-A-LIST {type(h).__name__}'
    if len(h) == 0:
        return 'EMPTY'
    kinds = Counter(k for b in h for k in b if k != 'name')
    parts = []
    for b in h:
        k = next((k for k in b if k != 'name'), '?')
        v = b.get(k)
        parts.append(f"{b['name']}:{k[:3]}={v:g}" if isinstance(v, (int, float, np.number)) else f"{b['name']}:{k}={v}")
    dups = [n for n, c in Counter(b['name'] for b in h).items() if c > 1]
    pop = sum(b.get('population', 0) for b in h)
    cat = sum(b.get(k, 0) for b in h for k in ('cat_pop', 'unique', 'longtail'))
    na = sum(b.get('NA', 0) for b in h)
    return f"[{dict(kinds)} pop={pop:g} cat={cat:g} NA={na:g}{' DUPNAMES=' + str(dups) if dups else ''}] " + ' | '.join(parts)


def bins_s(b):
    if not b:
        return 'bins=[]'
    arr = np.asarray(b, dtype=float)
    return f'bins={len(b)} [{arr[0]:.6g}..{arr[-1]:.6g}]' + ('' if np.isfinite(arr).all() else ' NONFINITE')


def run(backend, values, pd_dtype=None, pl_dtype=None, pa_type=None):
    if backend == 'pd':
        sd, errs = StatPipeline(PD_ANALYSIS_V2, unit_test=False).process_df(pd.DataFrame({'a': pd.Series(values, dtype=pd_dtype)}))
    elif backend == 'pl':
        sd, errs = StatPipeline(PL_ANALYSIS_V2, unit_test=False).process_df(pl.DataFrame({'a': pl.Series('a', values, dtype=pl_dtype, strict=False)}))
    else:
        table = xo.memtable(pa.table({'a': pa.array(values, type=pa_type)}), name='t')
        sd, errs = XorqStatPipeline(XORQ_STATS_V2, unit_test=False).process_table(table)
    return sd.get('a', {}), sorted({f'{e.stat_key}:{type(e.error).__name__}' for e in errs})


def case(name, values, pd_dtype=None, pl_dtype=None, pa_type=None, backends=('pd', 'pl', 'xo')):
    print(f'\n### {name}')
    for b in backends:
        try:
            c, errs = run(b, values, pd_dtype, pl_dtype, pa_type)
        except Exception as e:
            print(f'  {b}: RAISED {type(e).__name__}: {str(e)[:150]}')
            continue
        print(f"  {b}: {summarize(c.get('histogram'))}")
        print(f"      {bins_s(c.get('histogram_bins'))} min={c.get('min')!r:.30} max={c.get('max')!r:.30} "
              f"nan_per={c.get('nan_per')} distinct={c.get('distinct_count')}" + (f' ERRS={errs}' if errs else ''))

case('years 1990..2020', list(range(1990, 2021)) * 10, pa_type=pa.int64())
case('offset 1,000,000 + 0..99', [1_000_000 + i for i in range(100)], pa_type=pa.int64())
case('epoch seconds, a minute apart', [1_704_067_200 + 60 * i for i in range(100)], pa_type=pa.int64())
case('epoch ns, an hour apart', [1_704_067_200_000_000_000 + 3_600_000_000_000 * i for i in range(100)], pa_type=pa.int64())
case('1e15..1e16', [1e15 + i * 1e14 for i in range(100)], pa_type=pa.float64())
case('1e30 fill value beside 0..99', [float(i) for i in range(100)] + [1e30], pa_type=pa.float64())
case('+-1e308 beside 0..99', [-1e308, 1e308] + [float(i) for i in range(100)], pa_type=pa.float64())
case('tiny i*1e-9 (#620)', [i * 1e-9 for i in range(100)], pa_type=pa.float64())
case('int8 -128..127 (the -0 bounds)', list(range(-128, 128)), pd_dtype='int8', pl_dtype=pl.Int8, pa_type=pa.int8())
    Output at e88ace9 
    ### years 1990..2020
  pd: [{'tail': 2, 'population': 10} pop=97 cat=0 NA=0 DUPNAMES=['1.99K–1.99K', '2K–2K', '2.01K–2.01K', '2.02K–2.02K']] 1.99K–1.99K:tai=1 | 1.99K–1.99K:pop=10 | 1.99K–2K:pop=10 | 2K–2K:pop=10 | 2K–2K:pop=10 | 2K–2K:pop=7 | 2K–2.01K:pop=10 | 2.01K–2.01K:pop=10 | 2.01K–2.01K:pop=10 | 2.01K–2.02K:pop=10 | 2.02K–2.02K:pop=10 | 2.02K–2.02K:tai=1
      bins=11 [1991..2019] min=np.int64(1990) max=np.int64(2020) nan_per=0.0 distinct=31
  pl: [{'tail': 2, 'population': 10} pop=97 cat=0 NA=0 DUPNAMES=['1.99K–1.99K', '2K–2K', '2.01K–2.01K', '2.02K–2.02K']] 1.99K–1.99K:tai=1 | 1.99K–1.99K:pop=10 | 1.99K–2K:pop=10 | 2K–2K:pop=10 | 2K–2K:pop=10 | 2K–2K:pop=7 | 2K–2.01K:pop=10 | 2.01K–2.01K:pop=10 | 2.01K–2.01K:pop=10 | 2.01K–2.02K:pop=10 | 2.02K–2.02K:pop=10 | 2.02K–2.02K:tai=1
      bins=11 [1991..2019] min=1990 max=2020 nan_per=0.0 distinct=31
  xo: [{'population': 10} pop=100.2 cat=0 NA=0 DUPNAMES=['2K–2K', '2.01K–2.01K']] 1.99K–1.99K:pop=9.7 | 1.99K–2K:pop=9.7 | 2K–2K:pop=9.7 | 2K–2K:pop=9.7 | 2K–2K:pop=9.7 | 2K–2.01K:pop=9.7 | 2.01K–2.01K:pop=9.7 | 2.01K–2.01K:pop=9.7 | 2.01K–2.02K:pop=9.7 | 2.02K–2.02K:pop=12.9
      bins=11 [1990..2020] min=1990 max=2020 nan_per=0.0 distinct=31

### offset 1,000,000 + 0..99
  pd: [{'tail': 2, 'population': 10} pop=98 cat=0 NA=0 DUPNAMES=['1M–1M']] 1M–1M:tai=1 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=9 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=9 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:tai=1
      bins=11 [1e+06..1.0001e+06] min=np.int64(1000000) max=np.int64(1000099) nan_per=0.0 distinct=100
  pl: [{'tail': 2, 'population': 10} pop=96 cat=0 NA=0 DUPNAMES=['1M–1M']] 1M–1M:tai=1 | 1M–1M:pop=10 | 1M–1M:pop=9 | 1M–1M:pop=10 | 1M–1M:pop=9 | 1M–1M:pop=10 | 1M–1M:pop=9 | 1M–1M:pop=10 | 1M–1M:pop=9 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:tai=1
      bins=11 [1e+06..1.0001e+06] min=1000000 max=1000099 nan_per=0.0 distinct=100
  xo: [{'population': 10} pop=100 cat=0 NA=0 DUPNAMES=['1M–1M']] 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=10 | 1M–1M:pop=10
      bins=11 [1e+06..1.0001e+06] min=1000000 max=1000099 nan_per=0.0 distinct=100

### epoch seconds, a minute apart
  pd: [{'tail': 2, 'population': 10} pop=98 cat=0 NA=0 DUPNAMES=['1.7B–1.7B']] 1.7B–1.7B:tai=1 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=9 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=9 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:tai=1
      bins=11 [1.70407e+09..1.70407e+09] min=np.int64(1704067200) max=np.int64(1704073140) nan_per=0.0 distinct=100
  pl: [{'tail': 2, 'population': 10} pop=96 cat=0 NA=0 DUPNAMES=['1.7B–1.7B']] 1.7B–1.7B:tai=1 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=9 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=9 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=9 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=9 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:tai=1
      bins=11 [1.70407e+09..1.70407e+09] min=1704067200 max=1704073140 nan_per=0.0 distinct=100
  xo: [{'population': 10} pop=100 cat=0 NA=0 DUPNAMES=['1.7B–1.7B']] 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10 | 1.7B–1.7B:pop=10
      bins=11 [1.70407e+09..1.70407e+09] min=1704067200 max=1704073140 nan_per=0.0 distinct=100

### epoch ns, an hour apart
  pd: [{'tail': 2, 'population': 10} pop=98 cat=0 NA=0] 1704067T–1704071T:tai=1 | 1704071T–1704106T:pop=10 | 1704106T–1704141T:pop=10 | 1704141T–1704176T:pop=10 | 1704176T–1704210T:pop=9 | 1704210T–1704245T:pop=10 | 1704245T–1704280T:pop=10 | 1704280T–1704315T:pop=9 | 1704315T–1704350T:pop=10 | 1704350T–1704385T:pop=10 | 1704385T–1704420T:pop=10 | 1704420T–1704424T:tai=1
      bins=11 [1.70407e+18..1.70442e+18] min=np.int64(1704067200000000000) max=np.int64(1704423600000000000) nan_per=0.0 distinct=100
  pl: [{'tail': 2, 'population': 10} pop=96 cat=0 NA=0] 1704067T–1704071T:tai=1 | 1704074T–1704109T:pop=10 | 1704109T–1704143T:pop=9 | 1704143T–1704177T:pop=10 | 1704177T–1704211T:pop=9 | 1704211T–1704245T:pop=10 | 1704245T–1704280T:pop=9 | 1704280T–1704314T:pop=10 | 1704314T–1704348T:pop=9 | 1704348T–1704382T:pop=10 | 1704382T–1704416T:pop=10 | 1704420T–1704424T:tai=1
      bins=11 [1.70407e+18..1.70442e+18] min=1704067200000000000 max=1704423600000000000 nan_per=0.0 distinct=100
  xo: [{'population': 10} pop=100 cat=0 NA=0] 1704067T–1704103T:pop=10 | 1704103T–1704138T:pop=10 | 1704138T–1704174T:pop=10 | 1704174T–1704210T:pop=10 | 1704210T–1704245T:pop=10 | 1704245T–1704281T:pop=10 | 1704281T–1704317T:pop=10 | 1704317T–1704352T:pop=10 | 1704352T–1704388T:pop=10 | 1704388T–1704424T:pop=10
      bins=11 [1.70407e+18..1.70442e+18] min=1704067200000000000 max=1704423600000000000 nan_per=0.0 distinct=99 ERRS=['median:ArrowInvalid']

### 1e15..1e16
  pd: [{'tail': 2, 'population': 10} pop=98 cat=0 NA=0] 1000T–1099T:tai=1 | 1100T–2070T:pop=10 | 2070T–3040T:pop=10 | 3040T–4010T:pop=10 | 4010T–4980T:pop=9 | 4980T–5950T:pop=10 | 5950T–6920T:pop=10 | 6920T–7890T:pop=9 | 7890T–8860T:pop=10 | 8860T–9830T:pop=10 | 9830T–10800T:pop=10 | 10801T–10900T:tai=1
      bins=11 [1.1e+15..1.08e+16] min=np.float64(1000000000000000.0) max=np.float64(1.09e+16) nan_per=0.0 distinct=100
  pl: [{'tail': 2, 'population': 10} pop=96 cat=0 NA=0] 1000T–1100T:tai=1 | 1200T–2150T:pop=10 | 2150T–3100T:pop=9 | 3100T–4050T:pop=10 | 4050T–5000T:pop=9 | 5000T–5950T:pop=10 | 5950T–6900T:pop=9 | 6900T–7850T:pop=10 | 7850T–8800T:pop=9 | 8800T–9750T:pop=10 | 9750T–10700T:pop=10 | 10800T–10900T:tai=1
      bins=11 [1.2e+15..1.07e+16] min=1000000000000000.0 max=1.09e+16 nan_per=0.0 distinct=100
  xo: [{'population': 10} pop=100 cat=0 NA=0] 1000T–1990T:pop=10 | 1990T–2980T:pop=10 | 2980T–3970T:pop=10 | 3970T–4960T:pop=10 | 4960T–5950T:pop=10 | 5950T–6940T:pop=10 | 6940T–7930T:pop=10 | 7930T–8920T:pop=10 | 8920T–9910T:pop=10 | 9910T–10900T:pop=10
      bins=11 [1e+15..1.09e+16] min=1000000000000000.0 max=1.09e+16 nan_per=0.0 distinct=None

### 1e30 fill value beside 0..99
  pd: [{'tail': 2, 'population': 10} pop=97 cat=0 NA=0] 0–1:tai=1 | 2–11.6:pop=10 | 11.6–21.2:pop=10 | 21.2–30.8:pop=9 | 30.8–40.4:pop=10 | 40.4–50:pop=9 | 50–59.6:pop=10 | 59.6–69.2:pop=10 | 69.2–78.8:pop=9 | 78.8–88.4:pop=10 | 88.4–98:pop=10 | 99–1000000000000000000T:tai=1
      bins=11 [2..98] min=np.float64(0.0) max=np.float64(1e+30) nan_per=0.0 distinct=101
  pl: [{'tail': 2, 'population': 10} pop=97 cat=0 NA=0] 0–1:tai=1 | 2–11.6:pop=10 | 11.6–21.2:pop=10 | 21.2–30.8:pop=9 | 30.8–40.4:pop=10 | 40.4–50:pop=9 | 50–59.6:pop=10 | 59.6–69.2:pop=10 | 69.2–78.8:pop=9 | 78.8–88.4:pop=10 | 88.4–98:pop=10 | 99–1000000000000000000T:tai=1
      bins=11 [2..98] min=0.0 max=1e+30 nan_per=0.0 distinct=101
  xo: [{'population': 2} pop=100 cat=0 NA=0] 0T–100000000000000016T:pop=99 | 900000000000000000T–1000000000000000000T:pop=1
      bins=11 [0..1e+30] min=0.0 max=1e+30 nan_per=0.0 distinct=None

### +-1e308 beside 0..99
  pd: [{'tail': 2, 'population': 10} pop=98 cat=0 NA=0] -99999999999999998134867772062300415778155607198205813300984837204468478832795008398842977267828545807373626970040225815727702936870449359100155289601680494988872072239402046841988962644563396584878879514845800049027585211004144644909839626131908358862432902604247279245705105301413805838450032640T<>0:tai=1 | 1–10.7:pop=10 | 10.7–20.4:pop=10 | 20.4–30.1:pop=10 | 30.1–39.8:pop=9 | 39.8–49.5:pop=10 | 49.5–59.2:pop=10 | 59.2–68.9:pop=9 | 68.9–78.6:pop=10 | 78.6–88.3:pop=10 | 88.3–98:pop=10 | 99–99999999999999998134867772062300415778155607198205813300984837204468478832795008398842977267828545807373626970040225815727702936870449359100155289601680494988872072239402046841988962644563396584878879514845800049027585211004144644909839626131908358862432902604247279245705105301413805838450032640T:tai=1
      bins=11 [1..98] min=np.float64(-1e+308) max=np.float64(1e+308) nan_per=0.0 distinct=102
  pl: [{'tail': 2, 'population': 10} pop=98 cat=0 NA=0] -99999999999999998134867772062300415778155607198205813300984837204468478832795008398842977267828545807373626970040225815727702936870449359100155289601680494988872072239402046841988962644563396584878879514845800049027585211004144644909839626131908358862432902604247279245705105301413805838450032640T<>0:tai=1 | 1–10.7:pop=10 | 10.7–20.4:pop=10 | 20.4–30.1:pop=10 | 30.1–39.8:pop=9 | 39.8–49.5:pop=10 | 49.5–59.2:pop=10 | 59.2–68.9:pop=9 | 68.9–78.6:pop=10 | 78.6–88.3:pop=10 | 88.3–98:pop=10 | 99–99999999999999998134867772062300415778155607198205813300984837204468478832795008398842977267828545807373626970040225815727702936870449359100155289601680494988872072239402046841988962644563396584878879514845800049027585211004144644909839626131908358862432902604247279245705105301413805838450032640T:tai=1
      bins=11 [1..98] min=-1e+308 max=1e+308 nan_per=0.0 distinct=102
  xo: EMPTY
      bins=11 [nan..inf] NONFINITE min=-1e+308 max=1e+308 nan_per=0.0 distinct=None

### tiny i*1e-9 (#620)
  pd: [{'tail': 2, 'population': 10} pop=98 cat=0 NA=0 DUPNAMES=['0–0']] 0–0:tai=1 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=9 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=9 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=10 | 0–0:tai=1
      bins=11 [1e-09..9.8e-08] min=np.float64(0.0) max=np.float64(9.9e-08) nan_per=0.0 distinct=100
  pl: [{'tail': 2, 'population': 10} pop=96 cat=0 NA=0 DUPNAMES=['0–0']] 0–0:tai=1 | 0–0:pop=10 | 0–0:pop=9 | 0–0:pop=10 | 0–0:pop=9 | 0–0:pop=10 | 0–0:pop=9 | 0–0:pop=10 | 0–0:pop=9 | 0–0:pop=10 | 0–0:pop=10 | 0–0:tai=1
      bins=11 [2e-09..9.7e-08] min=0.0 max=9.9e-08 nan_per=0.0 distinct=100
  xo: [{'population': 10} pop=100 cat=0 NA=0 DUPNAMES=['0–0']] 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=10 | 0–0:pop=10
      bins=11 [0..9.9e-08] min=0.0 max=9.9e-08 nan_per=0.0 distinct=None

### int8 -128..127 (the -0 bounds)
  pd: [{'tail': 2, 'population': 10} pop=100 cat=0 NA=0] 0<>-125:tai=1 | -125<>-100:pop=10 | -100<>-75:pop=10 | -75<>-50:pop=10 | -50<>-25:pop=10 | -25<>-0:pop=10 | -0<>24:pop=10 | 24–49:pop=10 | 49–74:pop=10 | 74–99:pop=10 | 99–124:pop=10 | 124–127:tai=1
      bins=11 [-125..124] min=np.int8(-128) max=np.int8(127) nan_per=0.0 distinct=256
  pl: [{'tail': 2, 'population': 10} pop=100 cat=0 NA=0] -128<>-125:tai=1 | -124<>-99:pop=10 | -99<>-75:pop=10 | -75<>-50:pop=10 | -50<>-25:pop=10 | -25<>-0:pop=10 | -0<>24:pop=10 | 24–49:pop=10 | 49–74:pop=10 | 74–98:pop=10 | 98–123:pop=10 | 124–127:tai=1
      bins=11 [-124..123] min=-128 max=127 nan_per=0.0 distinct=256
  xo: [{'population': 10} pop=100.4 cat=0 NA=0] -128<>-102:pop=10.2 | -102<>-77:pop=9.8 | -77<>-52:pop=10.2 | -52<>-26:pop=9.8 | -26<>-0:pop=10.2 | -0<>25:pop=9.8 | 25–50:pop=10.2 | 50–76:pop=9.8 | 76–102:pop=10.2 | 102–127:pop=10.2
      bins=11 [-128..127] min=-128 max=127 nan_per=0.0 distinct=254
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