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sql/stats: conversion of datums to and from quantile function values
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. The conversion of histograms to quantile functions will require conversion of histogram bounds (datums) to quantile values (float64s). And likewise, the inverse conversion from quantile functions back to histograms will require the inverse conversion of float64 quantile values back to datums. These conversions are a little different from our usual SQL conversions in `eval.PerformCast`, so we add them to a new quantile file in the `sql/stats` module. This code was originally part of cockroachdb#77070 but has been pulled out to simplify that PR. A few changes have been made: - `histogramValue` has been renamed to `FromQuantileValue`. - Support for `DECIMAL`, `TIME`, `TIMETZ`, and `INTERVAL` has been dropped. Clamping these types in `FromQuantileValue` was too complex for the first iteration of statistics forecasting. We expect the overwhelming majority of ascending keys to use INT or TIMESTAMP types. - Bugs in `FLOAT4`, `TIMESTAMP` and `TIMESTAMPTZ` conversions have been fixed. - We're now clamping timestamps to slightly tighter bounds to avoid the problems with infinite timestamps (see cockroachdb#41564). Assists: cockroachdb#79872 Release note: None
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| Original file line number | Diff line number | Diff line change |
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| // Copyright 2022 The Cockroach Authors. | ||
| // | ||
| // Use of this software is governed by the Business Source License | ||
| // included in the file licenses/BSL.txt. | ||
| // | ||
| // As of the Change Date specified in that file, in accordance with | ||
| // the Business Source License, use of this software will be governed | ||
| // by the Apache License, Version 2.0, included in the file | ||
| // licenses/APL.txt. | ||
|
|
||
| package stats | ||
|
|
||
| import ( | ||
| "math" | ||
| "time" | ||
|
|
||
| "github.com/cockroachdb/cockroach/pkg/sql/sem/tree" | ||
| "github.com/cockroachdb/cockroach/pkg/sql/types" | ||
| "github.com/cockroachdb/cockroach/pkg/util/timeutil" | ||
| "github.com/cockroachdb/cockroach/pkg/util/timeutil/pgdate" | ||
| "github.com/cockroachdb/errors" | ||
| ) | ||
|
|
||
| // We only create quantiles for types that make sense converted to float64. | ||
| // TODO(michae2): Add support for DECIMAL, TIME, TIMETZ, and INTERVAL. | ||
| func CanMakeQuantile(colType *types.T) bool { | ||
| if colType.UserDefined() { | ||
| return false | ||
| } | ||
| switch colType.Family() { | ||
| case types.IntFamily, | ||
| types.FloatFamily, | ||
| types.DateFamily, | ||
| types.TimestampFamily, | ||
| types.TimestampTZFamily: | ||
| return true | ||
| default: | ||
| return false | ||
| } | ||
| } | ||
|
|
||
| // ToQuantileValue converts from a datum to a float suitable for use in a quantile | ||
| // function. It differs from eval.PerformCast in a few ways: | ||
| // 1. It supports conversions that are not legal casts (e.g. DATE to FLOAT). | ||
| // 2. It errors on NaN and infinite values because they will break our model. | ||
| // FromQuantileValue is the inverse of this function, and together they should | ||
| // support round-trip conversions. | ||
| // TODO(michae2): Add support for DECIMAL, TIME, TIMETZ, and INTERVAL. | ||
| func ToQuantileValue(d tree.Datum) (float64, error) { | ||
| switch v := d.(type) { | ||
| case *tree.DInt: | ||
| return float64(*v), nil | ||
| case *tree.DFloat: | ||
| if math.IsNaN(float64(*v)) || math.IsInf(float64(*v), 0) { | ||
| return 0, tree.ErrFloatOutOfRange | ||
| } | ||
| return float64(*v), nil | ||
| case *tree.DDate: | ||
| if !v.IsFinite() { | ||
| return 0, tree.ErrFloatOutOfRange | ||
| } | ||
| // We use PG epoch instead of Unix epoch to simplify clamping when | ||
| // converting back. | ||
| return float64(v.PGEpochDays()), nil | ||
| case *tree.DTimestamp: | ||
| if v.Equal(pgdate.TimeInfinity) || v.Equal(pgdate.TimeNegativeInfinity) { | ||
| return 0, tree.ErrFloatOutOfRange | ||
| } | ||
| return float64(v.Unix()) + float64(v.Nanosecond())*1e-9, nil | ||
| case *tree.DTimestampTZ: | ||
| if v.Equal(pgdate.TimeInfinity) || v.Equal(pgdate.TimeNegativeInfinity) { | ||
| return 0, tree.ErrFloatOutOfRange | ||
| } | ||
| return float64(v.Unix()) + float64(v.Nanosecond())*1e-9, nil | ||
| default: | ||
| return 0, errors.Errorf("cannot make quantile value from %v", d) | ||
| } | ||
| } | ||
|
|
||
| var ( | ||
| // QuantileMinTimestamp is an alternative minimum finite DTimestamp value to | ||
| // avoid the problems around TimeNegativeInfinity, see #41564. | ||
| QuantileMinTimestamp = tree.MinSupportedTime.Add(time.Second) | ||
| QuantileMinTimestampSec = float64(QuantileMinTimestamp.Unix()) | ||
| // QuantileMaxTimestamp is an alternative maximum finite DTimestamp value to | ||
| // avoid the problems around TimeInfinity, see #41564. | ||
| QuantileMaxTimestamp = tree.MaxSupportedTime.Add(-1 * time.Second).Truncate(time.Second) | ||
| QuantileMaxTimestampSec = float64(QuantileMaxTimestamp.Unix()) | ||
| ) | ||
|
|
||
| // FromQuantileValue converts from a quantile value back to a datum suitable for | ||
| // use in a histogram. It is the inverse of ToQuantileValue. It differs from | ||
| // eval.PerformCast in a few ways: | ||
| // 1. It supports conversions that are not legal casts (e.g. FLOAT to DATE). | ||
| // 2. It errors on NaN and infinite values because they indicate a problem with | ||
| // the regression model rather than valid values. | ||
| // 3. On overflow or underflow it clamps to maximum or minimum finite values | ||
| // rather than failing the conversion (and thus the entire histogram). | ||
| // TODO(michae2): Add support for DECIMAL, TIME, TIMETZ, and INTERVAL. | ||
| func FromQuantileValue(colType *types.T, val float64) (tree.Datum, error) { | ||
| if math.IsNaN(val) || math.IsInf(val, 0) { | ||
| return nil, tree.ErrFloatOutOfRange | ||
| } | ||
| switch colType.Family() { | ||
| case types.IntFamily: | ||
| i := math.Round(val) | ||
| // Clamp instead of truncating. | ||
| switch colType.Width() { | ||
| case 16: | ||
| if i <= math.MinInt16 { | ||
| return tree.NewDInt(tree.DInt(math.MinInt16)), nil | ||
| } | ||
| if i >= math.MaxInt16 { | ||
| return tree.NewDInt(tree.DInt(math.MaxInt16)), nil | ||
| } | ||
| case 32: | ||
| if i <= math.MinInt32 { | ||
| return tree.NewDInt(tree.DInt(math.MinInt32)), nil | ||
| } | ||
| if i >= math.MaxInt16 { | ||
| return tree.NewDInt(tree.DInt(math.MaxInt32)), nil | ||
| } | ||
| default: | ||
| if i <= math.MinInt64 { | ||
| return tree.NewDInt(tree.DInt(math.MinInt64)), nil | ||
| } | ||
| if i >= math.MaxInt64 { | ||
| return tree.NewDInt(tree.DInt(math.MaxInt64)), nil | ||
| } | ||
| } | ||
| return tree.NewDInt(tree.DInt(i)), nil | ||
| case types.FloatFamily: | ||
| switch colType.Width() { | ||
| case 32: | ||
| if val <= -math.MaxFloat32 { | ||
| val = -math.MaxFloat32 | ||
| } else if val >= math.MaxFloat32 { | ||
| val = math.MaxFloat32 | ||
| } else { | ||
| val = float64(float32(val)) | ||
| } | ||
| } | ||
| return tree.NewDFloat(tree.DFloat(val)), nil | ||
| case types.DateFamily: | ||
| days := math.Round(val) | ||
| // First clamp to int32. | ||
| if days <= math.MinInt32 { | ||
| days = math.MinInt32 | ||
| } else if days >= math.MaxInt32 { | ||
| days = math.MaxInt32 | ||
| } | ||
| // Then clamp to pgdate.Date. | ||
| return tree.NewDDate(pgdate.MakeDateFromPGEpochClampFinite(int32(days))), nil | ||
| case types.TimestampFamily: | ||
| sec, frac := math.Modf(val) | ||
| var t time.Time | ||
| // Clamp to (our alternative finite) DTimestamp bounds. | ||
| if sec <= QuantileMinTimestampSec { | ||
| t = QuantileMinTimestamp | ||
| } else if sec >= QuantileMaxTimestampSec { | ||
| t = QuantileMaxTimestamp | ||
| } else { | ||
| t = timeutil.Unix(int64(sec), int64(frac*1e9)) | ||
| } | ||
| roundTo := tree.TimeFamilyPrecisionToRoundDuration(colType.Precision()) | ||
| return tree.MakeDTimestamp(t, roundTo) | ||
| case types.TimestampTZFamily: | ||
| sec, frac := math.Modf(val) | ||
| var t time.Time | ||
| // Clamp to (our alternative finite) DTimestamp bounds. | ||
| if sec <= QuantileMinTimestampSec { | ||
| t = QuantileMinTimestamp | ||
| } else if sec >= QuantileMaxTimestampSec { | ||
| t = QuantileMaxTimestamp | ||
| } else { | ||
| t = timeutil.Unix(int64(sec), int64(frac*1e9)) | ||
| } | ||
| roundTo := tree.TimeFamilyPrecisionToRoundDuration(colType.Precision()) | ||
| return tree.MakeDTimestampTZ(t, roundTo) | ||
| default: | ||
| return nil, errors.Errorf("cannot convert quantile value to type %s", colType.Name()) | ||
| } | ||
| } |
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