sql/stats: convert between histograms and quantile functions

To predict histograms in statistics forecasts, we will use linear
regression over quantile functions. (Quantile functions are another
representation of histogram data, in a form more amenable to statistical
manipulation.)

This commit defines quantile functions and adds methods to convert
between histograms and quantile functions.

This code was originally part of #77070 but has been pulled out to
simplify that PR. A few changes have been made:
- Common code has been factored into closures.
- More checks have been added for positive values.
- In `makeQuantile` we now trim leading empty buckets as well as
  trailing empty buckets.
- The logic in `quantile.toHistogram` to steal from `NumRange` if
  `NumEq` is zero now checks that `NumRange` will still be >= 1.
- More tests have been added.

Assists: #79872

Release note: None

pkg/sql/stats/histogram.go

@@ -11,8 +11,10 @@
 package stats
 
 import (
+	"fmt"
 	"math"
 	"sort"
+	"strings"
 
 	"github.com/cockroachdb/cockroach/pkg/settings"
 	"github.com/cockroachdb/cockroach/pkg/sql/opt/cat"
@@ -420,6 +422,23 @@ func (h histogram) toHistogramData(colType *types.T) (HistogramData, error) {
 	return histogramData, nil
 }
 
+// String prints a histogram to a string.
+func (h histogram) String() string {
+	var b strings.Builder
+	b.WriteString("{[")
+	for i, bucket := range h.buckets {
+		if i > 0 {
+			b.WriteRune(' ')
+		}
+		fmt.Fprintf(
+			&b, "{%v %v %v %v}",
+			bucket.NumEq, bucket.NumRange, bucket.DistinctRange, bucket.UpperBound.String(),
+		)
+	}
+	b.WriteString("]}")
+	return b.String()
+}
+
 // estimatedDistinctValuesInRange returns the estimated number of distinct
 // values in the range [lowerBound, upperBound), given that the total number
 // of values is numRange.