Fixed-Point Decimals

To use in money, look at github.com/nikolaydubina/fpmoney

Be Precise. Using floats to represent currency is almost criminal. — Robert.C.Martin, "Clean Code" p.301

• int64 inside
• does not use float neither in parsing nor printing
• as fast as int64 in parsing, printing, arithmetics — 3x faser float, 20x faster shopspring/decimal, 30x faster fmt
• zero-overhead
• preventing error-prone fixed-point arithmetics
• Fuzz tests, Benchmarks
• JSON
• 200LOC

```go import fp "github.com/nikolaydubina/fpdecimal"

var BuySP500Price = fp.FromInt(9000)

input := []byte({"sp500": 9000.023})

type Stocks struct { SP500 fp.Decimal json:"sp500" } var v Stocks if err := json.Unmarshal(input, &v); err != nil { log.Fatal(err) }

var amountToBuy fp.Decimal if v.SP500.GreaterThan(BuySP500Price) { amountToBuy = amountToBuy.Add(v.SP500.Mul(fp.FromInt(2))) }

fmt.Println(amountToBuy) // Output: 18000.046 ```

Implementation

Parsing and Printing is expensive operation and requires a lot of code. However, if you know that your numbers are always small and simple and you do not care or do not permit lots of fractions like -1234.567, then parsing and printing can be greatly simplified. Code is heavily influenced by hot-path from Go core strconv package.

It is wrapped into struct to prevent bugs: - block multiplication by fpdecimal type, which leads to increase in decimal fractions and loose of precision - block additions of untyped constants, which leads to errors if you forget to scale by factor

Benchmarks

Parse $ go test -bench=BenchmarkParse -benchtime=5s -benchmem . goos: darwin goarch: arm64 pkg: github.com/nikolaydubina/fpdecimal BenchmarkParse/fromString/small-10 534307098 11.36 ns/op 0 B/op 0 allocs/op BenchmarkParse/fromString/large-10 254741558 23.42 ns/op 0 B/op 0 allocs/op BenchmarkParse/UnmarshalJSON/small-10 816873427 7.32 ns/op 0 B/op 0 allocs/op BenchmarkParse/UnmarshalJSON/large-10 272173255 22.16 ns/op 0 B/op 0 allocs/op BenchmarkParse_int_strconv_Atoi/small-10 1000000000 4.87 ns/op 0 B/op 0 allocs/op BenchmarkParse_int_strconv_Atoi/large-10 420536834 14.31 ns/op 0 B/op 0 allocs/op BenchmarkParse_int_strconv_ParseInt/small/int32-10 561137575 10.67 ns/op 0 B/op 0 allocs/op BenchmarkParse_int_strconv_ParseInt/small/int64-10 564200026 10.64 ns/op 0 B/op 0 allocs/op BenchmarkParse_int_strconv_ParseInt/large/int64-10 219626983 27.17 ns/op 0 B/op 0 allocs/op BenchmarkParse_float_strconv_ParseFloat/small/float32-10 345666214 17.36 ns/op 0 B/op 0 allocs/op BenchmarkParse_float_strconv_ParseFloat/small/float64-10 339620222 17.68 ns/op 0 B/op 0 allocs/op BenchmarkParse_float_strconv_ParseFloat/large/float32-10 128824344 46.68 ns/op 0 B/op 0 allocs/op BenchmarkParse_float_strconv_ParseFloat/large/float64-10 128140617 46.89 ns/op 0 B/op 0 allocs/op BenchmarkParse_float_fmt_Sscanf/small-10 21202892 281.6 ns/op 69 B/op 2 allocs/op BenchmarkParse_float_fmt_Sscanf/large-10 10074237 599.2 ns/op 88 B/op 3 allocs/op PASS ok github.com/nikolaydubina/fpdecimal 116.249s

Print $ go test -bench=BenchmarkPrint -benchtime=5s -benchmem . goos: darwin goarch: arm64 pkg: github.com/nikolaydubina/fpdecimal BenchmarkPrint/small-10 191982066 31.24 ns/op 8 B/op 1 allocs/op BenchmarkPrint/large-10 150874335 39.89 ns/op 24 B/op 1 allocs/op BenchmarkPrint_int_strconv_Itoa/small-10 446302868 13.39 ns/op 3 B/op 0 allocs/op BenchmarkPrint_int_strconv_Itoa/large-10 237484774 25.20 ns/op 18 B/op 1 allocs/op BenchmarkPrint_int_strconv_FormatInt/small-10 444861666 13.70 ns/op 3 B/op 0 allocs/op BenchmarkPrint_float_strconv_FormatFloat/small/float32-10 55003357 104.2 ns/op 31 B/op 2 allocs/op BenchmarkPrint_float_strconv_FormatFloat/small/float64-10 43565430 137.4 ns/op 31 B/op 2 allocs/op BenchmarkPrint_float_strconv_FormatFloat/large/float32-10 64069650 92.07 ns/op 48 B/op 2 allocs/op BenchmarkPrint_float_strconv_FormatFloat/large/float64-10 68441746 87.36 ns/op 48 B/op 2 allocs/op BenchmarkPrint_float_fmt_Sprintf/small-10 46503666 127.7 ns/op 16 B/op 2 allocs/op BenchmarkPrint_float_fmt_Sprintf/large-10 51764224 115.8 ns/op 28 B/op 2 allocs/op PASS ok github.com/nikolaydubina/fpdecimal 79.192s

Arithmetics $ go test -bench=BenchmarkArithmetic -benchtime=5s -benchmem . goos: darwin goarch: arm64 pkg: github.com/nikolaydubina/fpdecimal BenchmarkArithmetic/add-10 1000000000 0.316 ns/op 0 B/op 0 allocs/op BenchmarkArithmetic/div-10 1000000000 0.950 ns/op 0 B/op 0 allocs/op BenchmarkArithmetic/divmod-10 1000000000 1.890 ns/op 0 B/op 0 allocs/op BenchmarkArithmetic_int64/add-10 1000000000 0.314 ns/op 0 B/op 0 allocs/op BenchmarkArithmetic_int64/div-10 1000000000 0.316 ns/op 0 B/op 0 allocs/op BenchmarkArithmetic_int64/divmod-10 1000000000 1.261 ns/op 0 B/op 0 allocs/op BenchmarkArithmetic_int64/mod-10 1000000000 0.628 ns/op 0 B/op 0 allocs/op PASS ok github.com/nikolaydubina/fpdecimal 6.721s

References

• Fixed-Point Arithmetic Wiki
• shopspring/decimal

Appendix A: Comparison to other libraries

• https://github.com/shopspring/decimal solves arbitrary precision, fpdecimal solves only simple small decimals
• https://github.com/Rhymond/go-money solves typed number (currency), decodes through interface{} and float64, no precision in decoding, expects encoding to be in cents

Appendix B: Benchmarking shopspring/decimal

2022-05-28 $ go test -bench=. -benchtime=5s -benchmem ./... goos: darwin goarch: arm64 pkg: github.com/shopspring/decimal BenchmarkNewFromFloatWithExponent-10 59701516 97.7 ns/op 106 B/op 4 allocs/op BenchmarkNewFromFloat-10 14771503 410.3 ns/op 67 B/op 2 allocs/op BenchmarkNewFromStringFloat-10 16246342 375.2 ns/op 175 B/op 5 allocs/op Benchmark_FloorFast-10 1000000000 2.1 ns/op 0 B/op 0 allocs/op Benchmark_FloorRegular-10 53857244 106.3 ns/op 112 B/op 6 allocs/op Benchmark_DivideOriginal-10 7 715322768 ns/op 737406446 B/op 30652495 allocs/op Benchmark_DivideNew-10 22 262893689 ns/op 308046721 B/op 12054905 allocs/op BenchmarkDecimal_RoundCash_Five-10 9311530 636.5 ns/op 616 B/op 28 allocs/op Benchmark_Cmp-10 44 133191579 ns/op 24 B/op 1 allocs/op Benchmark_decimal_Decimal_Add_different_precision-10 31561636 176.6 ns/op 280 B/op 9 allocs/op Benchmark_decimal_Decimal_Sub_different_precision-10 36892767 164.4 ns/op 240 B/op 9 allocs/op Benchmark_decimal_Decimal_Add_same_precision-10 134831919 44.9 ns/op 80 B/op 2 allocs/op Benchmark_decimal_Decimal_Sub_same_precision-10 134902627 43.1 ns/op 80 B/op 2 allocs/op BenchmarkDecimal_IsInteger-10 92543083 66.1 ns/op 8 B/op 1 allocs/op BenchmarkDecimal_NewFromString-10 827455 7382 ns/op 3525 B/op 216 allocs/op BenchmarkDecimal_NewFromString_large_number-10 212538 28836 ns/op 16820 B/op 360 allocs/op BenchmarkDecimal_ExpHullAbraham-10 10000 572091 ns/op 486628 B/op 568 allocs/op BenchmarkDecimal_ExpTaylor-10 26343 222915 ns/op 431226 B/op 3172 allocs/op PASS ok github.com/shopspring/decimal 123.541sa

Appendix C: Why this is good fit for money?

There are only ~200 currencies in the world. All currencies have at most 3 decimal digits, thus it is sufficient to handle 3 decimal fractions. Next, currencies without decimal digits are typically 1000x larger than dollar, but even then maximum number that fits into int64 (without 3 decimal fractions) is 9 223 372 036 854 775.807 which is ~9 quadrillion. This should be enough for most operations with money.

Appendix D: Is it safe to use arithmetic operators in Go?

Sort of...

In one of iterations, I did Type Alias, but it required some effort to use it carefully.

Operations with defined types (variables) will fail. ```go var a int64 var b fpdecimal.FromInt(1000)

// does not compile a + b ```

However, untyped constants will be resolved to underlying type int64 and will be allowed.
```go const a 10000 var b fpdecimal.FromInt(1000)

// compiles a + b

// also compiles b - 42

// this one too b *= 23 ```

Is this a problem? * For multiplication and division - yes, it can be. You have to be careful not to multiply two fpdecimal numbers, since scaling factor will quadruple. Multiplying by constants is ok tho. * For addition substraction - yes, it can be. You have to be careful and remind yourself that constants would be reduced 1000x.

Both of this can be addressed at compile time by providing linter. This can be also addressed by wrapping into a struct and defining methods. Formed is hard to achieve in Go, due to lack of operator overload and lots of work required to write AST parser. Later has been implemented in this pacakge, and, as benchmarks show, without any extra memory or calls overhead as compared to int64.

Appendix E: Print into destination

To avoid mallocs, it is advantageous to print formatted value to pre-allocated destination. Similarly, to strconv.AppendInt, we provide AppendFixedPointDecimal. This is utilized in github.com/nikolaydubina/fpmoney package.

BenchmarkFixedPointDecimalToString/small-10 28522474 35.43 ns/op 24 B/op 1 allocs/op BenchmarkFixedPointDecimalToString/large-10 36883687 32.32 ns/op 24 B/op 1 allocs/op BenchmarkAppendFixedPointDecimal/small-10 38105520 30.51 ns/op 117 B/op 0 allocs/op BenchmarkAppendFixedPointDecimal/large-10 55147478 29.52 ns/op 119 B/op 0 allocs/op

Appendix F: DivMod notation

In early versions, Div and Mul operated on int and Div returned remainder. As recommended by @vanodevium and more in line with other common libraries, notation is changed. Bellow is survey as of 2023-05-18.

Go, https://pkg.go.dev/math/big go func (z *Int) Div(x, y *Int) *Int func (z *Int) DivMod(x, y, m *Int) (*Int, *Int) func (z *Int) Mod(x, y *Int) *Int

Go, github.com/shopspring/decimal go func (d Decimal) Div(d2 Decimal) Decimal // X no DivMod func (d Decimal) Mod(d2 Decimal) Decimal func (d Decimal) DivRound(d2 Decimal, precision int32) Decimal

Python, https://docs.python.org/3/library/decimal.html python divide(x, y) number divide_int(x, y) number // truncates divmod(x, y) number remainder(x, y) number

Pytorch, https://pytorch.org/docs/stable/generated/torch.div.html python torch.div(input, other, *, rounding_mode=None, out=None) → [Tensor] // discards remainder torch.remainder(input, other, *, out=None) → [Tensor] // remainder

numpy, https://numpy.org/doc/stable/reference/generated/numpy.divmod.html python np.divmod(x, y) (number, number) // is equivalent to (x // y, x % y np.mod(x, y) number np.remainder(x, y) number np.divide(x, y) number np.true_divide(x, y) number // same as divide np.floor_divide(x, y) number // rounding down

Appendix G: generics switch for decimal counting

Go does not support numerics in templates. However, defining multiple types each associated with specific number of decimals and passing them to functions and defining constraint as union of these types — is an attractive option. This does not work well since Go does not support switch case (casting generic) back to integer well.

Appendix H: string vs []byte in interface

The typical usage of parsing number is through some JSON or other mechanism. Those APIs are dealing with []byte. Now, conversion from []byte to string requires to copy data, since string is immutable. To improve performance, we are using []byte in signatures.

Using string BenchmarkParse/fromString/small-10 831217767 7.07 ns/op 0 B/op 0 allocs/op BenchmarkParse/fromString/large-10 275009497 21.79 ns/op 0 B/op 0 allocs/op BenchmarkParse/UnmarshalJSON/small-10 553035127 10.98 ns/op 0 B/op 0 allocs/op BenchmarkParse/UnmarshalJSON/large-10 248815030 24.14 ns/op 0 B/op 0 allocs/op

Using []byte BenchmarkParse/fromString/small-10 523937236 11.32 ns/op 0 B/op 0 allocs/op BenchmarkParse/fromString/large-10 257542226 23.23 ns/op 0 B/op 0 allocs/op BenchmarkParse/UnmarshalJSON/small-10 809793006 7.31 ns/op 0 B/op 0 allocs/op BenchmarkParse/UnmarshalJSON/large-10 272087984 22.04 ns/op 0 B/op 0 allocs/op

Appendix F: dynamic pkg level fraction digits

This is very bug prone. In fact, this was observd in production, issue.

Consider:

1. package A. init map with .FromInt
2. package B imports A and sets in init() num fraction digits
3. package B sees values in package A initialized with different fraction digits
4. 💥

Therefore, we are inlining fraction digits into most common fractions.

• 3 is enough to represent all currencies
• 3 is enough for SI units conversion ladder
• 6 is enough for 10cm x 10cm of (lat,long)