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// Copyright 2014 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 encoding
import (
// EncodeFloatAscending returns the resulting byte slice with the encoded float64
// appended to b. The encoded format for a float64 value f is, for positive f, the
// encoding of the 64 bits (in IEEE 754 format) re-interpreted as an int64 and
// encoded using EncodeUint64Ascending. For negative f, we keep the sign bit and
// invert all other bits, encoding this value using EncodeUint64Descending. This
// approach was inspired by in
// One of five single-byte prefix tags are appended to the front of the encoding.
// These tags enforce logical ordering of keys for both ascending and descending
// encoding directions. The tags split the encoded floats into five categories:
// - NaN for an ascending encoding direction
// - Negative valued floats
// - Zero (positive and negative)
// - Positive valued floats
// - NaN for a descending encoding direction
// This ordering ensures that NaNs are always sorted first in either encoding
// direction, and that after them a logical ordering is followed.
func EncodeFloatAscending(b []byte, f float64) []byte {
// Handle the simplistic cases first.
switch {
case math.IsNaN(f):
return append(b, floatNaN)
case f == 0:
// This encodes both positive and negative zero the same. Negative zero uses
// composite indexes to decode itself correctly.
return append(b, floatZero)
u := math.Float64bits(f)
if u&(1<<63) != 0 {
u = ^u
b = append(b, floatNeg)
} else {
b = append(b, floatPos)
return EncodeUint64Ascending(b, u)
// EncodeFloatDescending is the descending version of EncodeFloatAscending.
func EncodeFloatDescending(b []byte, f float64) []byte {
if math.IsNaN(f) {
return append(b, floatNaNDesc)
return EncodeFloatAscending(b, -f)
// DecodeFloatAscending returns the remaining byte slice after decoding and the decoded
// float64 from buf.
func DecodeFloatAscending(buf []byte) ([]byte, float64, error) {
if PeekType(buf) != Float {
return buf, 0, errors.Errorf("did not find marker")
switch buf[0] {
case floatNaN, floatNaNDesc:
return buf[1:], math.NaN(), nil
case floatNeg:
b, u, err := DecodeUint64Ascending(buf[1:])
if err != nil {
return b, 0, err
u = ^u
return b, math.Float64frombits(u), nil
case floatZero:
return buf[1:], 0, nil
case floatPos:
b, u, err := DecodeUint64Ascending(buf[1:])
if err != nil {
return b, 0, err
return b, math.Float64frombits(u), nil
return nil, 0, errors.Errorf("unknown prefix of the encoded byte slice: %q", buf)
// DecodeFloatDescending decodes floats encoded with EncodeFloatDescending.
func DecodeFloatDescending(buf []byte) ([]byte, float64, error) {
b, r, err := DecodeFloatAscending(buf)
return b, -r, err
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