diff options
Diffstat (limited to 'vendor/github.com/shopspring/decimal')
| -rw-r--r-- | vendor/github.com/shopspring/decimal/.gitignore | 9 | ||||
| -rw-r--r-- | vendor/github.com/shopspring/decimal/CHANGELOG.md | 76 | ||||
| -rw-r--r-- | vendor/github.com/shopspring/decimal/LICENSE | 45 | ||||
| -rw-r--r-- | vendor/github.com/shopspring/decimal/README.md | 139 | ||||
| -rw-r--r-- | vendor/github.com/shopspring/decimal/const.go | 63 | ||||
| -rw-r--r-- | vendor/github.com/shopspring/decimal/decimal-go.go | 415 | ||||
| -rw-r--r-- | vendor/github.com/shopspring/decimal/decimal.go | 2339 | ||||
| -rw-r--r-- | vendor/github.com/shopspring/decimal/rounding.go | 160 |
8 files changed, 3246 insertions, 0 deletions
diff --git a/vendor/github.com/shopspring/decimal/.gitignore b/vendor/github.com/shopspring/decimal/.gitignore new file mode 100644 index 0000000..ff36b98 --- /dev/null +++ b/vendor/github.com/shopspring/decimal/.gitignore @@ -0,0 +1,9 @@ +.git +*.swp + +# IntelliJ +.idea/ +*.iml + +# VS code +*.code-workspace diff --git a/vendor/github.com/shopspring/decimal/CHANGELOG.md b/vendor/github.com/shopspring/decimal/CHANGELOG.md new file mode 100644 index 0000000..432d0fd --- /dev/null +++ b/vendor/github.com/shopspring/decimal/CHANGELOG.md @@ -0,0 +1,76 @@ +## Decimal v1.4.0 +#### BREAKING +- Drop support for Go version older than 1.10 [#361](https://github.com/shopspring/decimal/pull/361) + +#### FEATURES +- Add implementation of natural logarithm [#339](https://github.com/shopspring/decimal/pull/339) [#357](https://github.com/shopspring/decimal/pull/357) +- Add improved implementation of power operation [#358](https://github.com/shopspring/decimal/pull/358) +- Add Compare method which forwards calls to Cmp [#346](https://github.com/shopspring/decimal/pull/346) +- Add NewFromBigRat constructor [#288](https://github.com/shopspring/decimal/pull/288) +- Add NewFromUint64 constructor [#352](https://github.com/shopspring/decimal/pull/352) + +#### ENHANCEMENTS +- Migrate to Github Actions [#245](https://github.com/shopspring/decimal/pull/245) [#340](https://github.com/shopspring/decimal/pull/340) +- Fix examples for RoundDown, RoundFloor, RoundUp, and RoundCeil [#285](https://github.com/shopspring/decimal/pull/285) [#328](https://github.com/shopspring/decimal/pull/328) [#341](https://github.com/shopspring/decimal/pull/341) +- Use Godoc standard to mark deprecated Equals and StringScaled methods [#342](https://github.com/shopspring/decimal/pull/342) +- Removed unnecessary min function for RescalePair method [#265](https://github.com/shopspring/decimal/pull/265) +- Avoid reallocation of initial slice in MarshalBinary (GobEncode) [#355](https://github.com/shopspring/decimal/pull/355) +- Optimize NumDigits method [#301](https://github.com/shopspring/decimal/pull/301) [#356](https://github.com/shopspring/decimal/pull/356) +- Optimize BigInt method [#359](https://github.com/shopspring/decimal/pull/359) +- Support scanning uint64 [#131](https://github.com/shopspring/decimal/pull/131) [#364](https://github.com/shopspring/decimal/pull/364) +- Add docs section with alternative libraries [#363](https://github.com/shopspring/decimal/pull/363) + +#### BUGFIXES +- Fix incorrect calculation of decimal modulo [#258](https://github.com/shopspring/decimal/pull/258) [#317](https://github.com/shopspring/decimal/pull/317) +- Allocate new(big.Int) in Copy method to deeply clone it [#278](https://github.com/shopspring/decimal/pull/278) +- Fix overflow edge case in QuoRem method [#322](https://github.com/shopspring/decimal/pull/322) + +## Decimal v1.3.1 + +#### ENHANCEMENTS +- Reduce memory allocation in case of initialization from big.Int [#252](https://github.com/shopspring/decimal/pull/252) + +#### BUGFIXES +- Fix binary marshalling of decimal zero value [#253](https://github.com/shopspring/decimal/pull/253) + +## Decimal v1.3.0 + +#### FEATURES +- Add NewFromFormattedString initializer [#184](https://github.com/shopspring/decimal/pull/184) +- Add NewNullDecimal initializer [#234](https://github.com/shopspring/decimal/pull/234) +- Add implementation of natural exponent function (Taylor, Hull-Abraham) [#229](https://github.com/shopspring/decimal/pull/229) +- Add RoundUp, RoundDown, RoundCeil, RoundFloor methods [#196](https://github.com/shopspring/decimal/pull/196) [#202](https://github.com/shopspring/decimal/pull/202) [#220](https://github.com/shopspring/decimal/pull/220) +- Add XML support for NullDecimal [#192](https://github.com/shopspring/decimal/pull/192) +- Add IsInteger method [#179](https://github.com/shopspring/decimal/pull/179) +- Add Copy helper method [#123](https://github.com/shopspring/decimal/pull/123) +- Add InexactFloat64 helper method [#205](https://github.com/shopspring/decimal/pull/205) +- Add CoefficientInt64 helper method [#244](https://github.com/shopspring/decimal/pull/244) + +#### ENHANCEMENTS +- Performance optimization of NewFromString init method [#198](https://github.com/shopspring/decimal/pull/198) +- Performance optimization of Abs and Round methods [#240](https://github.com/shopspring/decimal/pull/240) +- Additional tests (CI) for ppc64le architecture [#188](https://github.com/shopspring/decimal/pull/188) + +#### BUGFIXES +- Fix rounding in FormatFloat fallback path (roundShortest method, fix taken from Go main repository) [#161](https://github.com/shopspring/decimal/pull/161) +- Add slice range checks to UnmarshalBinary method [#232](https://github.com/shopspring/decimal/pull/232) + +## Decimal v1.2.0 + +#### BREAKING +- Drop support for Go version older than 1.7 [#172](https://github.com/shopspring/decimal/pull/172) + +#### FEATURES +- Add NewFromInt and NewFromInt32 initializers [#72](https://github.com/shopspring/decimal/pull/72) +- Add support for Go modules [#157](https://github.com/shopspring/decimal/pull/157) +- Add BigInt, BigFloat helper methods [#171](https://github.com/shopspring/decimal/pull/171) + +#### ENHANCEMENTS +- Memory usage optimization [#160](https://github.com/shopspring/decimal/pull/160) +- Updated travis CI golang versions [#156](https://github.com/shopspring/decimal/pull/156) +- Update documentation [#173](https://github.com/shopspring/decimal/pull/173) +- Improve code quality [#174](https://github.com/shopspring/decimal/pull/174) + +#### BUGFIXES +- Revert remove insignificant digits [#159](https://github.com/shopspring/decimal/pull/159) +- Remove 15 interval for RoundCash [#166](https://github.com/shopspring/decimal/pull/166) diff --git a/vendor/github.com/shopspring/decimal/LICENSE b/vendor/github.com/shopspring/decimal/LICENSE new file mode 100644 index 0000000..ad2148a --- /dev/null +++ b/vendor/github.com/shopspring/decimal/LICENSE @@ -0,0 +1,45 @@ +The MIT License (MIT) + +Copyright (c) 2015 Spring, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. + +- Based on https://github.com/oguzbilgic/fpd, which has the following license: +""" +The MIT License (MIT) + +Copyright (c) 2013 Oguz Bilgic + +Permission is hereby granted, free of charge, to any person obtaining a copy of +this software and associated documentation files (the "Software"), to deal in +the Software without restriction, including without limitation the rights to +use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of +the Software, and to permit persons to whom the Software is furnished to do so, +subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS +FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR +COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER +IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN +CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. +""" diff --git a/vendor/github.com/shopspring/decimal/README.md b/vendor/github.com/shopspring/decimal/README.md new file mode 100644 index 0000000..318c9df --- /dev/null +++ b/vendor/github.com/shopspring/decimal/README.md @@ -0,0 +1,139 @@ +# decimal + +[](https://github.com/shopspring/decimal/actions/workflows/ci.yml) +[](https://godoc.org/github.com/shopspring/decimal) +[](https://goreportcard.com/report/github.com/shopspring/decimal) + +Arbitrary-precision fixed-point decimal numbers in go. + +_Note:_ Decimal library can "only" represent numbers with a maximum of 2^31 digits after the decimal point. + +## Features + + * The zero-value is 0, and is safe to use without initialization + * Addition, subtraction, multiplication with no loss of precision + * Division with specified precision + * Database/sql serialization/deserialization + * JSON and XML serialization/deserialization + +## Install + +Run `go get github.com/shopspring/decimal` + +## Requirements + +Decimal library requires Go version `>=1.10` + +## Documentation + +http://godoc.org/github.com/shopspring/decimal + + +## Usage + +```go +package main + +import ( + "fmt" + "github.com/shopspring/decimal" +) + +func main() { + price, err := decimal.NewFromString("136.02") + if err != nil { + panic(err) + } + + quantity := decimal.NewFromInt(3) + + fee, _ := decimal.NewFromString(".035") + taxRate, _ := decimal.NewFromString(".08875") + + subtotal := price.Mul(quantity) + + preTax := subtotal.Mul(fee.Add(decimal.NewFromFloat(1))) + + total := preTax.Mul(taxRate.Add(decimal.NewFromFloat(1))) + + fmt.Println("Subtotal:", subtotal) // Subtotal: 408.06 + fmt.Println("Pre-tax:", preTax) // Pre-tax: 422.3421 + fmt.Println("Taxes:", total.Sub(preTax)) // Taxes: 37.482861375 + fmt.Println("Total:", total) // Total: 459.824961375 + fmt.Println("Tax rate:", total.Sub(preTax).Div(preTax)) // Tax rate: 0.08875 +} +``` + +## Alternative libraries + +When working with decimal numbers, you might face problems this library is not perfectly suited for. +Fortunately, thanks to the wonderful community we have a dozen other libraries that you can choose from. +Explore other alternatives to find the one that best fits your needs :) + +* [cockroachdb/apd](https://github.com/cockroachdb/apd) - arbitrary precision, mutable and rich API similar to `big.Int`, more performant than this library +* [alpacahq/alpacadecimal](https://github.com/alpacahq/alpacadecimal) - high performance, low precision (12 digits), fully compatible API with this library +* [govalues/decimal](https://github.com/govalues/decimal) - high performance, zero-allocation, low precision (19 digits) +* [greatcloak/decimal](https://github.com/greatcloak/decimal) - fork focusing on billing and e-commerce web application related use cases, includes out-of-the-box BSON marshaling support + +## FAQ + +#### Why don't you just use float64? + +Because float64 (or any binary floating point type, actually) can't represent +numbers such as `0.1` exactly. + +Consider this code: http://play.golang.org/p/TQBd4yJe6B You might expect that +it prints out `10`, but it actually prints `9.999999999999831`. Over time, +these small errors can really add up! + +#### Why don't you just use big.Rat? + +big.Rat is fine for representing rational numbers, but Decimal is better for +representing money. Why? Here's a (contrived) example: + +Let's say you use big.Rat, and you have two numbers, x and y, both +representing 1/3, and you have `z = 1 - x - y = 1/3`. If you print each one +out, the string output has to stop somewhere (let's say it stops at 3 decimal +digits, for simplicity), so you'll get 0.333, 0.333, and 0.333. But where did +the other 0.001 go? + +Here's the above example as code: http://play.golang.org/p/lCZZs0w9KE + +With Decimal, the strings being printed out represent the number exactly. So, +if you have `x = y = 1/3` (with precision 3), they will actually be equal to +0.333, and when you do `z = 1 - x - y`, `z` will be equal to .334. No money is +unaccounted for! + +You still have to be careful. If you want to split a number `N` 3 ways, you +can't just send `N/3` to three different people. You have to pick one to send +`N - (2/3*N)` to. That person will receive the fraction of a penny remainder. + +But, it is much easier to be careful with Decimal than with big.Rat. + +#### Why isn't the API similar to big.Int's? + +big.Int's API is built to reduce the number of memory allocations for maximal +performance. This makes sense for its use-case, but the trade-off is that the +API is awkward and easy to misuse. + +For example, to add two big.Ints, you do: `z := new(big.Int).Add(x, y)`. A +developer unfamiliar with this API might try to do `z := a.Add(a, b)`. This +modifies `a` and sets `z` as an alias for `a`, which they might not expect. It +also modifies any other aliases to `a`. + +Here's an example of the subtle bugs you can introduce with big.Int's API: +https://play.golang.org/p/x2R_78pa8r + +In contrast, it's difficult to make such mistakes with decimal. Decimals +behave like other go numbers types: even though `a = b` will not deep copy +`b` into `a`, it is impossible to modify a Decimal, since all Decimal methods +return new Decimals and do not modify the originals. The downside is that +this causes extra allocations, so Decimal is less performant. My assumption +is that if you're using Decimals, you probably care more about correctness +than performance. + +## License + +The MIT License (MIT) + +This is a heavily modified fork of [fpd.Decimal](https://github.com/oguzbilgic/fpd), which was also released under the MIT License. diff --git a/vendor/github.com/shopspring/decimal/const.go b/vendor/github.com/shopspring/decimal/const.go new file mode 100644 index 0000000..e5d6fa8 --- /dev/null +++ b/vendor/github.com/shopspring/decimal/const.go @@ -0,0 +1,63 @@ +package decimal + +import ( + "strings" +) + +const ( + strLn10 = "2.302585092994045684017991454684364207601101488628772976033327900967572609677352480235997205089598298341967784042286248633409525465082806756666287369098781689482907208325554680843799894826233198528393505308965377732628846163366222287698219886746543667474404243274365155048934314939391479619404400222105101714174800368808401264708068556774321622835522011480466371565912137345074785694768346361679210180644507064800027750268491674655058685693567342067058113642922455440575892572420824131469568901675894025677631135691929203337658714166023010570308963457207544037084746994016826928280848118428931484852494864487192780967627127577539702766860595249671667418348570442250719796500471495105049221477656763693866297697952211071826454973477266242570942932258279850258550978526538320760672631716430950599508780752371033310119785754733154142180842754386359177811705430982748238504564801909561029929182431823752535770975053956518769751037497088869218020518933950723853920514463419726528728696511086257149219884997874887377134568620916705849807828059751193854445009978131146915934666241071846692310107598438319191292230792503747298650929009880391941702654416816335727555703151596113564846546190897042819763365836983716328982174407366009162177850541779276367731145041782137660111010731042397832521894898817597921798666394319523936855916447118246753245630912528778330963604262982153040874560927760726641354787576616262926568298704957954913954918049209069438580790032763017941503117866862092408537949861264933479354871737451675809537088281067452440105892444976479686075120275724181874989395971643105518848195288330746699317814634930000321200327765654130472621883970596794457943468343218395304414844803701305753674262153675579814770458031413637793236291560128185336498466942261465206459942072917119370602444929358037007718981097362533224548366988505528285966192805098447175198503666680874970496982273220244823343097169111136813588418696549323714996941979687803008850408979618598756579894836445212043698216415292987811742973332588607915912510967187510929248475023930572665446276200923068791518135803477701295593646298412366497023355174586195564772461857717369368404676577047874319780573853271810933883496338813069945569399346101090745616033312247949360455361849123333063704751724871276379140924398331810164737823379692265637682071706935846394531616949411701841938119405416449466111274712819705817783293841742231409930022911502362192186723337268385688273533371925103412930705632544426611429765388301822384091026198582888433587455960453004548370789052578473166283701953392231047527564998119228742789713715713228319641003422124210082180679525276689858180956119208391760721080919923461516952599099473782780648128058792731993893453415320185969711021407542282796298237068941764740642225757212455392526179373652434440560595336591539160312524480149313234572453879524389036839236450507881731359711238145323701508413491122324390927681724749607955799151363982881058285740538000653371655553014196332241918087621018204919492651483892" +) + +var ( + ln10 = newConstApproximation(strLn10) +) + +type constApproximation struct { + exact Decimal + approximations []Decimal +} + +func newConstApproximation(value string) constApproximation { + parts := strings.Split(value, ".") + coeff, fractional := parts[0], parts[1] + + coeffLen := len(coeff) + maxPrecision := len(fractional) + + var approximations []Decimal + for p := 1; p < maxPrecision; p *= 2 { + r := RequireFromString(value[:coeffLen+p]) + approximations = append(approximations, r) + } + + return constApproximation{ + RequireFromString(value), + approximations, + } +} + +// Returns the smallest approximation available that's at least as precise +// as the passed precision (places after decimal point), i.e. Floor[ log2(precision) ] + 1 +func (c constApproximation) withPrecision(precision int32) Decimal { + i := 0 + + if precision >= 1 { + i++ + } + + for precision >= 16 { + precision /= 16 + i += 4 + } + + for precision >= 2 { + precision /= 2 + i++ + } + + if i >= len(c.approximations) { + return c.exact + } + + return c.approximations[i] +} diff --git a/vendor/github.com/shopspring/decimal/decimal-go.go b/vendor/github.com/shopspring/decimal/decimal-go.go new file mode 100644 index 0000000..9958d69 --- /dev/null +++ b/vendor/github.com/shopspring/decimal/decimal-go.go @@ -0,0 +1,415 @@ +// Copyright 2009 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Multiprecision decimal numbers. +// For floating-point formatting only; not general purpose. +// Only operations are assign and (binary) left/right shift. +// Can do binary floating point in multiprecision decimal precisely +// because 2 divides 10; cannot do decimal floating point +// in multiprecision binary precisely. + +package decimal + +type decimal struct { + d [800]byte // digits, big-endian representation + nd int // number of digits used + dp int // decimal point + neg bool // negative flag + trunc bool // discarded nonzero digits beyond d[:nd] +} + +func (a *decimal) String() string { + n := 10 + a.nd + if a.dp > 0 { + n += a.dp + } + if a.dp < 0 { + n += -a.dp + } + + buf := make([]byte, n) + w := 0 + switch { + case a.nd == 0: + return "0" + + case a.dp <= 0: + // zeros fill space between decimal point and digits + buf[w] = '0' + w++ + buf[w] = '.' + w++ + w += digitZero(buf[w : w+-a.dp]) + w += copy(buf[w:], a.d[0:a.nd]) + + case a.dp < a.nd: + // decimal point in middle of digits + w += copy(buf[w:], a.d[0:a.dp]) + buf[w] = '.' + w++ + w += copy(buf[w:], a.d[a.dp:a.nd]) + + default: + // zeros fill space between digits and decimal point + w += copy(buf[w:], a.d[0:a.nd]) + w += digitZero(buf[w : w+a.dp-a.nd]) + } + return string(buf[0:w]) +} + +func digitZero(dst []byte) int { + for i := range dst { + dst[i] = '0' + } + return len(dst) +} + +// trim trailing zeros from number. +// (They are meaningless; the decimal point is tracked +// independent of the number of digits.) +func trim(a *decimal) { + for a.nd > 0 && a.d[a.nd-1] == '0' { + a.nd-- + } + if a.nd == 0 { + a.dp = 0 + } +} + +// Assign v to a. +func (a *decimal) Assign(v uint64) { + var buf [24]byte + + // Write reversed decimal in buf. + n := 0 + for v > 0 { + v1 := v / 10 + v -= 10 * v1 + buf[n] = byte(v + '0') + n++ + v = v1 + } + + // Reverse again to produce forward decimal in a.d. + a.nd = 0 + for n--; n >= 0; n-- { + a.d[a.nd] = buf[n] + a.nd++ + } + a.dp = a.nd + trim(a) +} + +// Maximum shift that we can do in one pass without overflow. +// A uint has 32 or 64 bits, and we have to be able to accommodate 9<<k. +const uintSize = 32 << (^uint(0) >> 63) +const maxShift = uintSize - 4 + +// Binary shift right (/ 2) by k bits. k <= maxShift to avoid overflow. +func rightShift(a *decimal, k uint) { + r := 0 // read pointer + w := 0 // write pointer + + // Pick up enough leading digits to cover first shift. + var n uint + for ; n>>k == 0; r++ { + if r >= a.nd { + if n == 0 { + // a == 0; shouldn't get here, but handle anyway. + a.nd = 0 + return + } + for n>>k == 0 { + n = n * 10 + r++ + } + break + } + c := uint(a.d[r]) + n = n*10 + c - '0' + } + a.dp -= r - 1 + + var mask uint = (1 << k) - 1 + + // Pick up a digit, put down a digit. + for ; r < a.nd; r++ { + c := uint(a.d[r]) + dig := n >> k + n &= mask + a.d[w] = byte(dig + '0') + w++ + n = n*10 + c - '0' + } + + // Put down extra digits. + for n > 0 { + dig := n >> k + n &= mask + if w < len(a.d) { + a.d[w] = byte(dig + '0') + w++ + } else if dig > 0 { + a.trunc = true + } + n = n * 10 + } + + a.nd = w + trim(a) +} + +// Cheat sheet for left shift: table indexed by shift count giving +// number of new digits that will be introduced by that shift. +// +// For example, leftcheats[4] = {2, "625"}. That means that +// if we are shifting by 4 (multiplying by 16), it will add 2 digits +// when the string prefix is "625" through "999", and one fewer digit +// if the string prefix is "000" through "624". +// +// Credit for this trick goes to Ken. + +type leftCheat struct { + delta int // number of new digits + cutoff string // minus one digit if original < a. +} + +var leftcheats = []leftCheat{ + // Leading digits of 1/2^i = 5^i. + // 5^23 is not an exact 64-bit floating point number, + // so have to use bc for the math. + // Go up to 60 to be large enough for 32bit and 64bit platforms. + /* + seq 60 | sed 's/^/5^/' | bc | + awk 'BEGIN{ print "\t{ 0, \"\" }," } + { + log2 = log(2)/log(10) + printf("\t{ %d, \"%s\" },\t// * %d\n", + int(log2*NR+1), $0, 2**NR) + }' + */ + {0, ""}, + {1, "5"}, // * 2 + {1, "25"}, // * 4 + {1, "125"}, // * 8 + {2, "625"}, // * 16 + {2, "3125"}, // * 32 + {2, "15625"}, // * 64 + {3, "78125"}, // * 128 + {3, "390625"}, // * 256 + {3, "1953125"}, // * 512 + {4, "9765625"}, // * 1024 + {4, "48828125"}, // * 2048 + {4, "244140625"}, // * 4096 + {4, "1220703125"}, // * 8192 + {5, "6103515625"}, // * 16384 + {5, "30517578125"}, // * 32768 + {5, "152587890625"}, // * 65536 + {6, "762939453125"}, // * 131072 + {6, "3814697265625"}, // * 262144 + {6, "19073486328125"}, // * 524288 + {7, "95367431640625"}, // * 1048576 + {7, "476837158203125"}, // * 2097152 + {7, "2384185791015625"}, // * 4194304 + {7, "11920928955078125"}, // * 8388608 + {8, "59604644775390625"}, // * 16777216 + {8, "298023223876953125"}, // * 33554432 + {8, "1490116119384765625"}, // * 67108864 + {9, "7450580596923828125"}, // * 134217728 + {9, "37252902984619140625"}, // * 268435456 + {9, "186264514923095703125"}, // * 536870912 + {10, "931322574615478515625"}, // * 1073741824 + {10, "4656612873077392578125"}, // * 2147483648 + {10, "23283064365386962890625"}, // * 4294967296 + {10, "116415321826934814453125"}, // * 8589934592 + {11, "582076609134674072265625"}, // * 17179869184 + {11, "2910383045673370361328125"}, // * 34359738368 + {11, "14551915228366851806640625"}, // * 68719476736 + {12, "72759576141834259033203125"}, // * 137438953472 + {12, "363797880709171295166015625"}, // * 274877906944 + {12, "1818989403545856475830078125"}, // * 549755813888 + {13, "9094947017729282379150390625"}, // * 1099511627776 + {13, "45474735088646411895751953125"}, // * 2199023255552 + {13, "227373675443232059478759765625"}, // * 4398046511104 + {13, "1136868377216160297393798828125"}, // * 8796093022208 + {14, "5684341886080801486968994140625"}, // * 17592186044416 + {14, "28421709430404007434844970703125"}, // * 35184372088832 + {14, "142108547152020037174224853515625"}, // * 70368744177664 + {15, "710542735760100185871124267578125"}, // * 140737488355328 + {15, "3552713678800500929355621337890625"}, // * 281474976710656 + {15, "17763568394002504646778106689453125"}, // * 562949953421312 + {16, "88817841970012523233890533447265625"}, // * 1125899906842624 + {16, "444089209850062616169452667236328125"}, // * 2251799813685248 + {16, "2220446049250313080847263336181640625"}, // * 4503599627370496 + {16, "11102230246251565404236316680908203125"}, // * 9007199254740992 + {17, "55511151231257827021181583404541015625"}, // * 18014398509481984 + {17, "277555756156289135105907917022705078125"}, // * 36028797018963968 + {17, "1387778780781445675529539585113525390625"}, // * 72057594037927936 + {18, "6938893903907228377647697925567626953125"}, // * 144115188075855872 + {18, "34694469519536141888238489627838134765625"}, // * 288230376151711744 + {18, "173472347597680709441192448139190673828125"}, // * 576460752303423488 + {19, "867361737988403547205962240695953369140625"}, // * 1152921504606846976 +} + +// Is the leading prefix of b lexicographically less than s? +func prefixIsLessThan(b []byte, s string) bool { + for i := 0; i < len(s); i++ { + if i >= len(b) { + return true + } + if b[i] != s[i] { + return b[i] < s[i] + } + } + return false +} + +// Binary shift left (* 2) by k bits. k <= maxShift to avoid overflow. +func leftShift(a *decimal, k uint) { + delta := leftcheats[k].delta + if prefixIsLessThan(a.d[0:a.nd], leftcheats[k].cutoff) { + delta-- + } + + r := a.nd // read index + w := a.nd + delta // write index + + // Pick up a digit, put down a digit. + var n uint + for r--; r >= 0; r-- { + n += (uint(a.d[r]) - '0') << k + quo := n / 10 + rem := n - 10*quo + w-- + if w < len(a.d) { + a.d[w] = byte(rem + '0') + } else if rem != 0 { + a.trunc = true + } + n = quo + } + + // Put down extra digits. + for n > 0 { + quo := n / 10 + rem := n - 10*quo + w-- + if w < len(a.d) { + a.d[w] = byte(rem + '0') + } else if rem != 0 { + a.trunc = true + } + n = quo + } + + a.nd += delta + if a.nd >= len(a.d) { + a.nd = len(a.d) + } + a.dp += delta + trim(a) +} + +// Binary shift left (k > 0) or right (k < 0). +func (a *decimal) Shift(k int) { + switch { + case a.nd == 0: + // nothing to do: a == 0 + case k > 0: + for k > maxShift { + leftShift(a, maxShift) + k -= maxShift + } + leftShift(a, uint(k)) + case k < 0: + for k < -maxShift { + rightShift(a, maxShift) + k += maxShift + } + rightShift(a, uint(-k)) + } +} + +// If we chop a at nd digits, should we round up? +func shouldRoundUp(a *decimal, nd int) bool { + if nd < 0 || nd >= a.nd { + return false + } + if a.d[nd] == '5' && nd+1 == a.nd { // exactly halfway - round to even + // if we truncated, a little higher than what's recorded - always round up + if a.trunc { + return true + } + return nd > 0 && (a.d[nd-1]-'0')%2 != 0 + } + // not halfway - digit tells all + return a.d[nd] >= '5' +} + +// Round a to nd digits (or fewer). +// If nd is zero, it means we're rounding +// just to the left of the digits, as in +// 0.09 -> 0.1. +func (a *decimal) Round(nd int) { + if nd < 0 || nd >= a.nd { + return + } + if shouldRoundUp(a, nd) { + a.RoundUp(nd) + } else { + a.RoundDown(nd) + } +} + +// Round a down to nd digits (or fewer). +func (a *decimal) RoundDown(nd int) { + if nd < 0 || nd >= a.nd { + return + } + a.nd = nd + trim(a) +} + +// Round a up to nd digits (or fewer). +func (a *decimal) RoundUp(nd int) { + if nd < 0 || nd >= a.nd { + return + } + + // round up + for i := nd - 1; i >= 0; i-- { + c := a.d[i] + if c < '9' { // can stop after this digit + a.d[i]++ + a.nd = i + 1 + return + } + } + + // Number is all 9s. + // Change to single 1 with adjusted decimal point. + a.d[0] = '1' + a.nd = 1 + a.dp++ +} + +// Extract integer part, rounded appropriately. +// No guarantees about overflow. +func (a *decimal) RoundedInteger() uint64 { + if a.dp > 20 { + return 0xFFFFFFFFFFFFFFFF + } + var i int + n := uint64(0) + for i = 0; i < a.dp && i < a.nd; i++ { + n = n*10 + uint64(a.d[i]-'0') + } + for ; i < a.dp; i++ { + n *= 10 + } + if shouldRoundUp(a, a.dp) { + n++ + } + return n +} diff --git a/vendor/github.com/shopspring/decimal/decimal.go b/vendor/github.com/shopspring/decimal/decimal.go new file mode 100644 index 0000000..a37a230 --- /dev/null +++ b/vendor/github.com/shopspring/decimal/decimal.go @@ -0,0 +1,2339 @@ +// Package decimal implements an arbitrary precision fixed-point decimal. +// +// The zero-value of a Decimal is 0, as you would expect. +// +// The best way to create a new Decimal is to use decimal.NewFromString, ex: +// +// n, err := decimal.NewFromString("-123.4567") +// n.String() // output: "-123.4567" +// +// To use Decimal as part of a struct: +// +// type StructName struct { +// Number Decimal +// } +// +// Note: This can "only" represent numbers with a maximum of 2^31 digits after the decimal point. +package decimal + +import ( + "database/sql/driver" + "encoding/binary" + "fmt" + "math" + "math/big" + "regexp" + "strconv" + "strings" +) + +// DivisionPrecision is the number of decimal places in the result when it +// doesn't divide exactly. +// +// Example: +// +// d1 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3)) +// d1.String() // output: "0.6666666666666667" +// d2 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(30000)) +// d2.String() // output: "0.0000666666666667" +// d3 := decimal.NewFromFloat(20000).Div(decimal.NewFromFloat(3)) +// d3.String() // output: "6666.6666666666666667" +// decimal.DivisionPrecision = 3 +// d4 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3)) +// d4.String() // output: "0.667" +var DivisionPrecision = 16 + +// PowPrecisionNegativeExponent specifies the maximum precision of the result (digits after decimal point) +// when calculating decimal power. Only used for cases where the exponent is a negative number. +// This constant applies to Pow, PowInt32 and PowBigInt methods, PowWithPrecision method is not constrained by it. +// +// Example: +// +// d1, err := decimal.NewFromFloat(15.2).PowInt32(-2) +// d1.String() // output: "0.0043282548476454" +// +// decimal.PowPrecisionNegativeExponent = 24 +// d2, err := decimal.NewFromFloat(15.2).PowInt32(-2) +// d2.String() // output: "0.004328254847645429362881" +var PowPrecisionNegativeExponent = 16 + +// MarshalJSONWithoutQuotes should be set to true if you want the decimal to +// be JSON marshaled as a number, instead of as a string. +// WARNING: this is dangerous for decimals with many digits, since many JSON +// unmarshallers (ex: Javascript's) will unmarshal JSON numbers to IEEE 754 +// double-precision floating point numbers, which means you can potentially +// silently lose precision. +var MarshalJSONWithoutQuotes = false + +// ExpMaxIterations specifies the maximum number of iterations needed to calculate +// precise natural exponent value using ExpHullAbrham method. +var ExpMaxIterations = 1000 + +// Zero constant, to make computations faster. +// Zero should never be compared with == or != directly, please use decimal.Equal or decimal.Cmp instead. +var Zero = New(0, 1) + +var zeroInt = big.NewInt(0) +var oneInt = big.NewInt(1) +var twoInt = big.NewInt(2) +var fourInt = big.NewInt(4) +var fiveInt = big.NewInt(5) +var tenInt = big.NewInt(10) +var twentyInt = big.NewInt(20) + +var factorials = []Decimal{New(1, 0)} + +// Decimal represents a fixed-point decimal. It is immutable. +// number = value * 10 ^ exp +type Decimal struct { + value *big.Int + + // NOTE(vadim): this must be an int32, because we cast it to float64 during + // calculations. If exp is 64 bit, we might lose precision. + // If we cared about being able to represent every possible decimal, we + // could make exp a *big.Int but it would hurt performance and numbers + // like that are unrealistic. + exp int32 +} + +// New returns a new fixed-point decimal, value * 10 ^ exp. +func New(value int64, exp int32) Decimal { + return Decimal{ + value: big.NewInt(value), + exp: exp, + } +} + +// NewFromInt converts an int64 to Decimal. +// +// Example: +// +// NewFromInt(123).String() // output: "123" +// NewFromInt(-10).String() // output: "-10" +func NewFromInt(value int64) Decimal { + return Decimal{ + value: big.NewInt(value), + exp: 0, + } +} + +// NewFromInt32 converts an int32 to Decimal. +// +// Example: +// +// NewFromInt(123).String() // output: "123" +// NewFromInt(-10).String() // output: "-10" +func NewFromInt32(value int32) Decimal { + return Decimal{ + value: big.NewInt(int64(value)), + exp: 0, + } +} + +// NewFromUint64 converts an uint64 to Decimal. +// +// Example: +// +// NewFromUint64(123).String() // output: "123" +func NewFromUint64(value uint64) Decimal { + return Decimal{ + value: new(big.Int).SetUint64(value), + exp: 0, + } +} + +// NewFromBigInt returns a new Decimal from a big.Int, value * 10 ^ exp +func NewFromBigInt(value *big.Int, exp int32) Decimal { + return Decimal{ + value: new(big.Int).Set(value), + exp: exp, + } +} + +// NewFromBigRat returns a new Decimal from a big.Rat. The numerator and +// denominator are divided and rounded to the given precision. +// +// Example: +// +// d1 := NewFromBigRat(big.NewRat(0, 1), 0) // output: "0" +// d2 := NewFromBigRat(big.NewRat(4, 5), 1) // output: "0.8" +// d3 := NewFromBigRat(big.NewRat(1000, 3), 3) // output: "333.333" +// d4 := NewFromBigRat(big.NewRat(2, 7), 4) // output: "0.2857" +func NewFromBigRat(value *big.Rat, precision int32) Decimal { + return Decimal{ + value: new(big.Int).Set(value.Num()), + exp: 0, + }.DivRound(Decimal{ + value: new(big.Int).Set(value.Denom()), + exp: 0, + }, precision) +} + +// NewFromString returns a new Decimal from a string representation. +// Trailing zeroes are not trimmed. +// +// Example: +// +// d, err := NewFromString("-123.45") +// d2, err := NewFromString(".0001") +// d3, err := NewFromString("1.47000") +func NewFromString(value string) (Decimal, error) { + originalInput := value + var intString string + var exp int64 + + // Check if number is using scientific notation + eIndex := strings.IndexAny(value, "Ee") + if eIndex != -1 { + expInt, err := strconv.ParseInt(value[eIndex+1:], 10, 32) + if err != nil { + if e, ok := err.(*strconv.NumError); ok && e.Err == strconv.ErrRange { + return Decimal{}, fmt.Errorf("can't convert %s to decimal: fractional part too long", value) + } + return Decimal{}, fmt.Errorf("can't convert %s to decimal: exponent is not numeric", value) + } + value = value[:eIndex] + exp = expInt + } + + pIndex := -1 + vLen := len(value) + for i := 0; i < vLen; i++ { + if value[i] == '.' { + if pIndex > -1 { + return Decimal{}, fmt.Errorf("can't convert %s to decimal: too many .s", value) + } + pIndex = i + } + } + + if pIndex == -1 { + // There is no decimal point, we can just parse the original string as + // an int + intString = value + } else { + if pIndex+1 < vLen { + intString = value[:pIndex] + value[pIndex+1:] + } else { + intString = value[:pIndex] + } + expInt := -len(value[pIndex+1:]) + exp += int64(expInt) + } + + var dValue *big.Int + // strconv.ParseInt is faster than new(big.Int).SetString so this is just a shortcut for strings we know won't overflow + if len(intString) <= 18 { + parsed64, err := strconv.ParseInt(intString, 10, 64) + if err != nil { + return Decimal{}, fmt.Errorf("can't convert %s to decimal", value) + } + dValue = big.NewInt(parsed64) + } else { + dValue = new(big.Int) + _, ok := dValue.SetString(intString, 10) + if !ok { + return Decimal{}, fmt.Errorf("can't convert %s to decimal", value) + } + } + + if exp < math.MinInt32 || exp > math.MaxInt32 { + // NOTE(vadim): I doubt a string could realistically be this long + return Decimal{}, fmt.Errorf("can't convert %s to decimal: fractional part too long", originalInput) + } + + return Decimal{ + value: dValue, + exp: int32(exp), + }, nil +} + +// NewFromFormattedString returns a new Decimal from a formatted string representation. +// The second argument - replRegexp, is a regular expression that is used to find characters that should be +// removed from given decimal string representation. All matched characters will be replaced with an empty string. +// +// Example: +// +// r := regexp.MustCompile("[$,]") +// d1, err := NewFromFormattedString("$5,125.99", r) +// +// r2 := regexp.MustCompile("[_]") +// d2, err := NewFromFormattedString("1_000_000", r2) +// +// r3 := regexp.MustCompile("[USD\\s]") +// d3, err := NewFromFormattedString("5000 USD", r3) +func NewFromFormattedString(value string, replRegexp *regexp.Regexp) (Decimal, error) { + parsedValue := replRegexp.ReplaceAllString(value, "") + d, err := NewFromString(parsedValue) + if err != nil { + return Decimal{}, err + } + return d, nil +} + +// RequireFromString returns a new Decimal from a string representation +// or panics if NewFromString had returned an error. +// +// Example: +// +// d := RequireFromString("-123.45") +// d2 := RequireFromString(".0001") +func RequireFromString(value string) Decimal { + dec, err := NewFromString(value) + if err != nil { + panic(err) + } + return dec +} + +// NewFromFloat converts a float64 to Decimal. +// +// The converted number will contain the number of significant digits that can be +// represented in a float with reliable roundtrip. +// This is typically 15 digits, but may be more in some cases. +// See https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ for more information. +// +// For slightly faster conversion, use NewFromFloatWithExponent where you can specify the precision in absolute terms. +// +// NOTE: this will panic on NaN, +/-inf +func NewFromFloat(value float64) Decimal { + if value == 0 { + return New(0, 0) + } + return newFromFloat(value, math.Float64bits(value), &float64info) +} + +// NewFromFloat32 converts a float32 to Decimal. +// +// The converted number will contain the number of significant digits that can be +// represented in a float with reliable roundtrip. +// This is typically 6-8 digits depending on the input. +// See https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ for more information. +// +// For slightly faster conversion, use NewFromFloatWithExponent where you can specify the precision in absolute terms. +// +// NOTE: this will panic on NaN, +/-inf +func NewFromFloat32(value float32) Decimal { + if value == 0 { + return New(0, 0) + } + // XOR is workaround for https://github.com/golang/go/issues/26285 + a := math.Float32bits(value) ^ 0x80808080 + return newFromFloat(float64(value), uint64(a)^0x80808080, &float32info) +} + +func newFromFloat(val float64, bits uint64, flt *floatInfo) Decimal { + if math.IsNaN(val) || math.IsInf(val, 0) { + panic(fmt.Sprintf("Cannot create a Decimal from %v", val)) + } + exp := int(bits>>flt.mantbits) & (1<<flt.expbits - 1) + mant := bits & (uint64(1)<<flt.mantbits - 1) + + switch exp { + case 0: + // denormalized + exp++ + + default: + // add implicit top bit + mant |= uint64(1) << flt.mantbits + } + exp += flt.bias + + var d decimal + d.Assign(mant) + d.Shift(exp - int(flt.mantbits)) + d.neg = bits>>(flt.expbits+flt.mantbits) != 0 + + roundShortest(&d, mant, exp, flt) + // If less than 19 digits, we can do calculation in an int64. + if d.nd < 19 { + tmp := int64(0) + m := int64(1) + for i := d.nd - 1; i >= 0; i-- { + tmp += m * int64(d.d[i]-'0') + m *= 10 + } + if d.neg { + tmp *= -1 + } + return Decimal{value: big.NewInt(tmp), exp: int32(d.dp) - int32(d.nd)} + } + dValue := new(big.Int) + dValue, ok := dValue.SetString(string(d.d[:d.nd]), 10) + if ok { + return Decimal{value: dValue, exp: int32(d.dp) - int32(d.nd)} + } + + return NewFromFloatWithExponent(val, int32(d.dp)-int32(d.nd)) +} + +// NewFromFloatWithExponent converts a float64 to Decimal, with an arbitrary +// number of fractional digits. +// +// Example: +// +// NewFromFloatWithExponent(123.456, -2).String() // output: "123.46" +func NewFromFloatWithExponent(value float64, exp int32) Decimal { + if math.IsNaN(value) || math.IsInf(value, 0) { + panic(fmt.Sprintf("Cannot create a Decimal from %v", value)) + } + + bits := math.Float64bits(value) + mant := bits & (1<<52 - 1) + exp2 := int32((bits >> 52) & (1<<11 - 1)) + sign := bits >> 63 + + if exp2 == 0 { + // specials + if mant == 0 { + return Decimal{} + } + // subnormal + exp2++ + } else { + // normal + mant |= 1 << 52 + } + + exp2 -= 1023 + 52 + + // normalizing base-2 values + for mant&1 == 0 { + mant = mant >> 1 + exp2++ + } + + // maximum number of fractional base-10 digits to represent 2^N exactly cannot be more than -N if N<0 + if exp < 0 && exp < exp2 { + if exp2 < 0 { + exp = exp2 + } else { + exp = 0 + } + } + + // representing 10^M * 2^N as 5^M * 2^(M+N) + exp2 -= exp + + temp := big.NewInt(1) + dMant := big.NewInt(int64(mant)) + + // applying 5^M + if exp > 0 { + temp = temp.SetInt64(int64(exp)) + temp = temp.Exp(fiveInt, temp, nil) + } else if exp < 0 { + temp = temp.SetInt64(-int64(exp)) + temp = temp.Exp(fiveInt, temp, nil) + dMant = dMant.Mul(dMant, temp) + temp = temp.SetUint64(1) + } + + // applying 2^(M+N) + if exp2 > 0 { + dMant = dMant.Lsh(dMant, uint(exp2)) + } else if exp2 < 0 { + temp = temp.Lsh(temp, uint(-exp2)) + } + + // rounding and downscaling + if exp > 0 || exp2 < 0 { + halfDown := new(big.Int).Rsh(temp, 1) + dMant = dMant.Add(dMant, halfDown) + dMant = dMant.Quo(dMant, temp) + } + + if sign == 1 { + dMant = dMant.Neg(dMant) + } + + return Decimal{ + value: dMant, + exp: exp, + } +} + +// Copy returns a copy of decimal with the same value and exponent, but a different pointer to value. +func (d Decimal) Copy() Decimal { + d.ensureInitialized() + return Decimal{ + value: new(big.Int).Set(d.value), + exp: d.exp, + } +} + +// rescale returns a rescaled version of the decimal. Returned +// decimal may be less precise if the given exponent is bigger +// than the initial exponent of the Decimal. +// NOTE: this will truncate, NOT round +// +// Example: +// +// d := New(12345, -4) +// d2 := d.rescale(-1) +// d3 := d2.rescale(-4) +// println(d1) +// println(d2) +// println(d3) +// +// Output: +// +// 1.2345 +// 1.2 +// 1.2000 +func (d Decimal) rescale(exp int32) Decimal { + d.ensureInitialized() + + if d.exp == exp { + return Decimal{ + new(big.Int).Set(d.value), + d.exp, + } + } + + // NOTE(vadim): must convert exps to float64 before - to prevent overflow + diff := math.Abs(float64(exp) - float64(d.exp)) + value := new(big.Int).Set(d.value) + + expScale := new(big.Int).Exp(tenInt, big.NewInt(int64(diff)), nil) + if exp > d.exp { + value = value.Quo(value, expScale) + } else if exp < d.exp { + value = value.Mul(value, expScale) + } + + return Decimal{ + value: value, + exp: exp, + } +} + +// Abs returns the absolute value of the decimal. +func (d Decimal) Abs() Decimal { + if !d.IsNegative() { + return d + } + d.ensureInitialized() + d2Value := new(big.Int).Abs(d.value) + return Decimal{ + value: d2Value, + exp: d.exp, + } +} + +// Add returns d + d2. +func (d Decimal) Add(d2 Decimal) Decimal { + rd, rd2 := RescalePair(d, d2) + + d3Value := new(big.Int).Add(rd.value, rd2.value) + return Decimal{ + value: d3Value, + exp: rd.exp, + } +} + +// Sub returns d - d2. +func (d Decimal) Sub(d2 Decimal) Decimal { + rd, rd2 := RescalePair(d, d2) + + d3Value := new(big.Int).Sub(rd.value, rd2.value) + return Decimal{ + value: d3Value, + exp: rd.exp, + } +} + +// Neg returns -d. +func (d Decimal) Neg() Decimal { + d.ensureInitialized() + val := new(big.Int).Neg(d.value) + return Decimal{ + value: val, + exp: d.exp, + } +} + +// Mul returns d * d2. +func (d Decimal) Mul(d2 Decimal) Decimal { + d.ensureInitialized() + d2.ensureInitialized() + + expInt64 := int64(d.exp) + int64(d2.exp) + if expInt64 > math.MaxInt32 || expInt64 < math.MinInt32 { + // NOTE(vadim): better to panic than give incorrect results, as + // Decimals are usually used for money + panic(fmt.Sprintf("exponent %v overflows an int32!", expInt64)) + } + + d3Value := new(big.Int).Mul(d.value, d2.value) + return Decimal{ + value: d3Value, + exp: int32(expInt64), + } +} + +// Shift shifts the decimal in base 10. +// It shifts left when shift is positive and right if shift is negative. +// In simpler terms, the given value for shift is added to the exponent +// of the decimal. +func (d Decimal) Shift(shift int32) Decimal { + d.ensureInitialized() + return Decimal{ + value: new(big.Int).Set(d.value), + exp: d.exp + shift, + } +} + +// Div returns d / d2. If it doesn't divide exactly, the result will have +// DivisionPrecision digits after the decimal point. +func (d Decimal) Div(d2 Decimal) Decimal { + return d.DivRound(d2, int32(DivisionPrecision)) +} + +// QuoRem does division with remainder +// d.QuoRem(d2,precision) returns quotient q and remainder r such that +// +// d = d2 * q + r, q an integer multiple of 10^(-precision) +// 0 <= r < abs(d2) * 10 ^(-precision) if d>=0 +// 0 >= r > -abs(d2) * 10 ^(-precision) if d<0 +// +// Note that precision<0 is allowed as input. +func (d Decimal) QuoRem(d2 Decimal, precision int32) (Decimal, Decimal) { + d.ensureInitialized() + d2.ensureInitialized() + if d2.value.Sign() == 0 { + panic("decimal division by 0") + } + scale := -precision + e := int64(d.exp) - int64(d2.exp) - int64(scale) + if e > math.MaxInt32 || e < math.MinInt32 { + panic("overflow in decimal QuoRem") + } + var aa, bb, expo big.Int + var scalerest int32 + // d = a 10^ea + // d2 = b 10^eb + if e < 0 { + aa = *d.value + expo.SetInt64(-e) + bb.Exp(tenInt, &expo, nil) + bb.Mul(d2.value, &bb) + scalerest = d.exp + // now aa = a + // bb = b 10^(scale + eb - ea) + } else { + expo.SetInt64(e) + aa.Exp(tenInt, &expo, nil) + aa.Mul(d.value, &aa) + bb = *d2.value + scalerest = scale + d2.exp + // now aa = a ^ (ea - eb - scale) + // bb = b + } + var q, r big.Int + q.QuoRem(&aa, &bb, &r) + dq := Decimal{value: &q, exp: scale} + dr := Decimal{value: &r, exp: scalerest} + return dq, dr +} + +// DivRound divides and rounds to a given precision +// i.e. to an integer multiple of 10^(-precision) +// +// for a positive quotient digit 5 is rounded up, away from 0 +// if the quotient is negative then digit 5 is rounded down, away from 0 +// +// Note that precision<0 is allowed as input. +func (d Decimal) DivRound(d2 Decimal, precision int32) Decimal { + // QuoRem already checks initialization + q, r := d.QuoRem(d2, precision) + // the actual rounding decision is based on comparing r*10^precision and d2/2 + // instead compare 2 r 10 ^precision and d2 + var rv2 big.Int + rv2.Abs(r.value) + rv2.Lsh(&rv2, 1) + // now rv2 = abs(r.value) * 2 + r2 := Decimal{value: &rv2, exp: r.exp + precision} + // r2 is now 2 * r * 10 ^ precision + var c = r2.Cmp(d2.Abs()) + + if c < 0 { + return q + } + + if d.value.Sign()*d2.value.Sign() < 0 { + return q.Sub(New(1, -precision)) + } + + return q.Add(New(1, -precision)) +} + +// Mod returns d % d2. +func (d Decimal) Mod(d2 Decimal) Decimal { + _, r := d.QuoRem(d2, 0) + return r +} + +// Pow returns d to the power of d2. +// When exponent is negative the returned decimal will have maximum precision of PowPrecisionNegativeExponent places after decimal point. +// +// Pow returns 0 (zero-value of Decimal) instead of error for power operation edge cases, to handle those edge cases use PowWithPrecision +// Edge cases not handled by Pow: +// - 0 ** 0 => undefined value +// - 0 ** y, where y < 0 => infinity +// - x ** y, where x < 0 and y is non-integer decimal => imaginary value +// +// Example: +// +// d1 := decimal.NewFromFloat(4.0) +// d2 := decimal.NewFromFloat(4.0) +// res1 := d1.Pow(d2) +// res1.String() // output: "256" +// +// d3 := decimal.NewFromFloat(5.0) +// d4 := decimal.NewFromFloat(5.73) +// res2 := d3.Pow(d4) +// res2.String() // output: "10118.08037125" +func (d Decimal) Pow(d2 Decimal) Decimal { + baseSign := d.Sign() + expSign := d2.Sign() + + if baseSign == 0 { + if expSign == 0 { + return Decimal{} + } + if expSign == 1 { + return Decimal{zeroInt, 0} + } + if expSign == -1 { + return Decimal{} + } + } + + if expSign == 0 { + return Decimal{oneInt, 0} + } + + // TODO: optimize extraction of fractional part + one := Decimal{oneInt, 0} + expIntPart, expFracPart := d2.QuoRem(one, 0) + + if baseSign == -1 && !expFracPart.IsZero() { + return Decimal{} + } + + intPartPow, _ := d.PowBigInt(expIntPart.value) + + // if exponent is an integer we don't need to calculate d1**frac(d2) + if expFracPart.value.Sign() == 0 { + return intPartPow + } + + // TODO: optimize NumDigits for more performant precision adjustment + digitsBase := d.NumDigits() + digitsExponent := d2.NumDigits() + + precision := digitsBase + + if digitsExponent > precision { + precision += digitsExponent + } + + precision += 6 + + // Calculate x ** frac(y), where + // x ** frac(y) = exp(ln(x ** frac(y)) = exp(ln(x) * frac(y)) + fracPartPow, err := d.Abs().Ln(-d.exp + int32(precision)) + if err != nil { + return Decimal{} + } + + fracPartPow = fracPartPow.Mul(expFracPart) + + fracPartPow, err = fracPartPow.ExpTaylor(-d.exp + int32(precision)) + if err != nil { + return Decimal{} + } + + // Join integer and fractional part, + // base ** (expBase + expFrac) = base ** expBase * base ** expFrac + res := intPartPow.Mul(fracPartPow) + + return res +} + +// PowWithPrecision returns d to the power of d2. +// Precision parameter specifies minimum precision of the result (digits after decimal point). +// Returned decimal is not rounded to 'precision' places after decimal point. +// +// PowWithPrecision returns error when: +// - 0 ** 0 => undefined value +// - 0 ** y, where y < 0 => infinity +// - x ** y, where x < 0 and y is non-integer decimal => imaginary value +// +// Example: +// +// d1 := decimal.NewFromFloat(4.0) +// d2 := decimal.NewFromFloat(4.0) +// res1, err := d1.PowWithPrecision(d2, 2) +// res1.String() // output: "256" +// +// d3 := decimal.NewFromFloat(5.0) +// d4 := decimal.NewFromFloat(5.73) +// res2, err := d3.PowWithPrecision(d4, 5) +// res2.String() // output: "10118.080371595015625" +// +// d5 := decimal.NewFromFloat(-3.0) +// d6 := decimal.NewFromFloat(-6.0) +// res3, err := d5.PowWithPrecision(d6, 10) +// res3.String() // output: "0.0013717421" +func (d Decimal) PowWithPrecision(d2 Decimal, precision int32) (Decimal, error) { + baseSign := d.Sign() + expSign := d2.Sign() + + if baseSign == 0 { + if expSign == 0 { + return Decimal{}, fmt.Errorf("cannot represent undefined value of 0**0") + } + if expSign == 1 { + return Decimal{zeroInt, 0}, nil + } + if expSign == -1 { + return Decimal{}, fmt.Errorf("cannot represent infinity value of 0 ** y, where y < 0") + } + } + + if expSign == 0 { + return Decimal{oneInt, 0}, nil + } + + // TODO: optimize extraction of fractional part + one := Decimal{oneInt, 0} + expIntPart, expFracPart := d2.QuoRem(one, 0) + + if baseSign == -1 && !expFracPart.IsZero() { + return Decimal{}, fmt.Errorf("cannot represent imaginary value of x ** y, where x < 0 and y is non-integer decimal") + } + + intPartPow, _ := d.powBigIntWithPrecision(expIntPart.value, precision) + + // if exponent is an integer we don't need to calculate d1**frac(d2) + if expFracPart.value.Sign() == 0 { + return intPartPow, nil + } + + // TODO: optimize NumDigits for more performant precision adjustment + digitsBase := d.NumDigits() + digitsExponent := d2.NumDigits() + + if int32(digitsBase) > precision { + precision = int32(digitsBase) + } + if int32(digitsExponent) > precision { + precision += int32(digitsExponent) + } + // increase precision by 10 to compensate for errors in further calculations + precision += 10 + + // Calculate x ** frac(y), where + // x ** frac(y) = exp(ln(x ** frac(y)) = exp(ln(x) * frac(y)) + fracPartPow, err := d.Abs().Ln(precision) + if err != nil { + return Decimal{}, err + } + + fracPartPow = fracPartPow.Mul(expFracPart) + + fracPartPow, err = fracPartPow.ExpTaylor(precision) + if err != nil { + return Decimal{}, err + } + + // Join integer and fractional part, + // base ** (expBase + expFrac) = base ** expBase * base ** expFrac + res := intPartPow.Mul(fracPartPow) + + return res, nil +} + +// PowInt32 returns d to the power of exp, where exp is int32. +// Only returns error when d and exp is 0, thus result is undefined. +// +// When exponent is negative the returned decimal will have maximum precision of PowPrecisionNegativeExponent places after decimal point. +// +// Example: +// +// d1, err := decimal.NewFromFloat(4.0).PowInt32(4) +// d1.String() // output: "256" +// +// d2, err := decimal.NewFromFloat(3.13).PowInt32(5) +// d2.String() // output: "300.4150512793" +func (d Decimal) PowInt32(exp int32) (Decimal, error) { + if d.IsZero() && exp == 0 { + return Decimal{}, fmt.Errorf("cannot represent undefined value of 0**0") + } + + isExpNeg := exp < 0 + exp = abs(exp) + + n, result := d, New(1, 0) + + for exp > 0 { + if exp%2 == 1 { + result = result.Mul(n) + } + exp /= 2 + + if exp > 0 { + n = n.Mul(n) + } + } + + if isExpNeg { + return New(1, 0).DivRound(result, int32(PowPrecisionNegativeExponent)), nil + } + + return result, nil +} + +// PowBigInt returns d to the power of exp, where exp is big.Int. +// Only returns error when d and exp is 0, thus result is undefined. +// +// When exponent is negative the returned decimal will have maximum precision of PowPrecisionNegativeExponent places after decimal point. +// +// Example: +// +// d1, err := decimal.NewFromFloat(3.0).PowBigInt(big.NewInt(3)) +// d1.String() // output: "27" +// +// d2, err := decimal.NewFromFloat(629.25).PowBigInt(big.NewInt(5)) +// d2.String() // output: "98654323103449.5673828125" +func (d Decimal) PowBigInt(exp *big.Int) (Decimal, error) { + return d.powBigIntWithPrecision(exp, int32(PowPrecisionNegativeExponent)) +} + +func (d Decimal) powBigIntWithPrecision(exp *big.Int, precision int32) (Decimal, error) { + if d.IsZero() && exp.Sign() == 0 { + return Decimal{}, fmt.Errorf("cannot represent undefined value of 0**0") + } + + tmpExp := new(big.Int).Set(exp) + isExpNeg := exp.Sign() < 0 + + if isExpNeg { + tmpExp.Abs(tmpExp) + } + + n, result := d, New(1, 0) + + for tmpExp.Sign() > 0 { + if tmpExp.Bit(0) == 1 { + result = result.Mul(n) + } + tmpExp.Rsh(tmpExp, 1) + + if tmpExp.Sign() > 0 { + n = n.Mul(n) + } + } + + if isExpNeg { + return New(1, 0).DivRound(result, precision), nil + } + + return result, nil +} + +// ExpHullAbrham calculates the natural exponent of decimal (e to the power of d) using Hull-Abraham algorithm. +// OverallPrecision argument specifies the overall precision of the result (integer part + decimal part). +// +// ExpHullAbrham is faster than ExpTaylor for small precision values, but it is much slower for large precision values. +// +// Example: +// +// NewFromFloat(26.1).ExpHullAbrham(2).String() // output: "220000000000" +// NewFromFloat(26.1).ExpHullAbrham(20).String() // output: "216314672147.05767284" +func (d Decimal) ExpHullAbrham(overallPrecision uint32) (Decimal, error) { + // Algorithm based on Variable precision exponential function. + // ACM Transactions on Mathematical Software by T. E. Hull & A. Abrham. + if d.IsZero() { + return Decimal{oneInt, 0}, nil + } + + currentPrecision := overallPrecision + + // Algorithm does not work if currentPrecision * 23 < |x|. + // Precision is automatically increased in such cases, so the value can be calculated precisely. + // If newly calculated precision is higher than ExpMaxIterations the currentPrecision will not be changed. + f := d.Abs().InexactFloat64() + if ncp := f / 23; ncp > float64(currentPrecision) && ncp < float64(ExpMaxIterations) { + currentPrecision = uint32(math.Ceil(ncp)) + } + + // fail if abs(d) beyond an over/underflow threshold + overflowThreshold := New(23*int64(currentPrecision), 0) + if d.Abs().Cmp(overflowThreshold) > 0 { + return Decimal{}, fmt.Errorf("over/underflow threshold, exp(x) cannot be calculated precisely") + } + + // Return 1 if abs(d) small enough; this also avoids later over/underflow + overflowThreshold2 := New(9, -int32(currentPrecision)-1) + if d.Abs().Cmp(overflowThreshold2) <= 0 { + return Decimal{oneInt, d.exp}, nil + } + + // t is the smallest integer >= 0 such that the corresponding abs(d/k) < 1 + t := d.exp + int32(d.NumDigits()) // Add d.NumDigits because the paper assumes that d.value [0.1, 1) + + if t < 0 { + t = 0 + } + + k := New(1, t) // reduction factor + r := Decimal{new(big.Int).Set(d.value), d.exp - t} // reduced argument + p := int32(currentPrecision) + t + 2 // precision for calculating the sum + + // Determine n, the number of therms for calculating sum + // use first Newton step (1.435p - 1.182) / log10(p/abs(r)) + // for solving appropriate equation, along with directed + // roundings and simple rational bound for log10(p/abs(r)) + rf := r.Abs().InexactFloat64() + pf := float64(p) + nf := math.Ceil((1.453*pf - 1.182) / math.Log10(pf/rf)) + if nf > float64(ExpMaxIterations) || math.IsNaN(nf) { + return Decimal{}, fmt.Errorf("exact value cannot be calculated in <=ExpMaxIterations iterations") + } + n := int64(nf) + + tmp := New(0, 0) + sum := New(1, 0) + one := New(1, 0) + for i := n - 1; i > 0; i-- { + tmp.value.SetInt64(i) + sum = sum.Mul(r.DivRound(tmp, p)) + sum = sum.Add(one) + } + + ki := k.IntPart() + res := New(1, 0) + for i := ki; i > 0; i-- { + res = res.Mul(sum) + } + + resNumDigits := int32(res.NumDigits()) + + var roundDigits int32 + if resNumDigits > abs(res.exp) { + roundDigits = int32(currentPrecision) - resNumDigits - res.exp + } else { + roundDigits = int32(currentPrecision) + } + + res = res.Round(roundDigits) + + return res, nil +} + +// ExpTaylor calculates the natural exponent of decimal (e to the power of d) using Taylor series expansion. +// Precision argument specifies how precise the result must be (number of digits after decimal point). +// Negative precision is allowed. +// +// ExpTaylor is much faster for large precision values than ExpHullAbrham. +// +// Example: +// +// d, err := NewFromFloat(26.1).ExpTaylor(2).String() +// d.String() // output: "216314672147.06" +// +// NewFromFloat(26.1).ExpTaylor(20).String() +// d.String() // output: "216314672147.05767284062928674083" +// +// NewFromFloat(26.1).ExpTaylor(-10).String() +// d.String() // output: "220000000000" +func (d Decimal) ExpTaylor(precision int32) (Decimal, error) { + // Note(mwoss): Implementation can be optimized by exclusively using big.Int API only + if d.IsZero() { + return Decimal{oneInt, 0}.Round(precision), nil + } + + var epsilon Decimal + var divPrecision int32 + if precision < 0 { + epsilon = New(1, -1) + divPrecision = 8 + } else { + epsilon = New(1, -precision-1) + divPrecision = precision + 1 + } + + decAbs := d.Abs() + pow := d.Abs() + factorial := New(1, 0) + + result := New(1, 0) + + for i := int64(1); ; { + step := pow.DivRound(factorial, divPrecision) + result = result.Add(step) + + // Stop Taylor series when current step is smaller than epsilon + if step.Cmp(epsilon) < 0 { + break + } + + pow = pow.Mul(decAbs) + + i++ + + // Calculate next factorial number or retrieve cached value + if len(factorials) >= int(i) && !factorials[i-1].IsZero() { + factorial = factorials[i-1] + } else { + // To avoid any race conditions, firstly the zero value is appended to a slice to create + // a spot for newly calculated factorial. After that, the zero value is replaced by calculated + // factorial using the index notation. + factorial = factorials[i-2].Mul(New(i, 0)) + factorials = append(factorials, Zero) + factorials[i-1] = factorial + } + } + + if d.Sign() < 0 { + result = New(1, 0).DivRound(result, precision+1) + } + + result = result.Round(precision) + return result, nil +} + +// Ln calculates natural logarithm of d. +// Precision argument specifies how precise the result must be (number of digits after decimal point). +// Negative precision is allowed. +// +// Example: +// +// d1, err := NewFromFloat(13.3).Ln(2) +// d1.String() // output: "2.59" +// +// d2, err := NewFromFloat(579.161).Ln(10) +// d2.String() // output: "6.3615805046" +func (d Decimal) Ln(precision int32) (Decimal, error) { + // Algorithm based on The Use of Iteration Methods for Approximating the Natural Logarithm, + // James F. Epperson, The American Mathematical Monthly, Vol. 96, No. 9, November 1989, pp. 831-835. + if d.IsNegative() { + return Decimal{}, fmt.Errorf("cannot calculate natural logarithm for negative decimals") + } + + if d.IsZero() { + return Decimal{}, fmt.Errorf("cannot represent natural logarithm of 0, result: -infinity") + } + + calcPrecision := precision + 2 + z := d.Copy() + + var comp1, comp3, comp2, comp4, reduceAdjust Decimal + comp1 = z.Sub(Decimal{oneInt, 0}) + comp3 = Decimal{oneInt, -1} + + // for decimal in range [0.9, 1.1] where ln(d) is close to 0 + usePowerSeries := false + + if comp1.Abs().Cmp(comp3) <= 0 { + usePowerSeries = true + } else { + // reduce input decimal to range [0.1, 1) + expDelta := int32(z.NumDigits()) + z.exp + z.exp -= expDelta + + // Input decimal was reduced by factor of 10^expDelta, thus we will need to add + // ln(10^expDelta) = expDelta * ln(10) + // to the result to compensate that + ln10 := ln10.withPrecision(calcPrecision) + reduceAdjust = NewFromInt32(expDelta) + reduceAdjust = reduceAdjust.Mul(ln10) + + comp1 = z.Sub(Decimal{oneInt, 0}) + + if comp1.Abs().Cmp(comp3) <= 0 { + usePowerSeries = true + } else { + // initial estimate using floats + zFloat := z.InexactFloat64() + comp1 = NewFromFloat(math.Log(zFloat)) + } + } + + epsilon := Decimal{oneInt, -calcPrecision} + + if usePowerSeries { + // Power Series - https://en.wikipedia.org/wiki/Logarithm#Power_series + // Calculating n-th term of formula: ln(z+1) = 2 sum [ 1 / (2n+1) * (z / (z+2))^(2n+1) ] + // until the difference between current and next term is smaller than epsilon. + // Coverage quite fast for decimals close to 1.0 + + // z + 2 + comp2 = comp1.Add(Decimal{twoInt, 0}) + // z / (z + 2) + comp3 = comp1.DivRound(comp2, calcPrecision) + // 2 * (z / (z + 2)) + comp1 = comp3.Add(comp3) + comp2 = comp1.Copy() + + for n := 1; ; n++ { + // 2 * (z / (z+2))^(2n+1) + comp2 = comp2.Mul(comp3).Mul(comp3) + + // 1 / (2n+1) * 2 * (z / (z+2))^(2n+1) + comp4 = NewFromInt(int64(2*n + 1)) + comp4 = comp2.DivRound(comp4, calcPrecision) + + // comp1 = 2 sum [ 1 / (2n+1) * (z / (z+2))^(2n+1) ] + comp1 = comp1.Add(comp4) + + if comp4.Abs().Cmp(epsilon) <= 0 { + break + } + } + } else { + // Halley's Iteration. + // Calculating n-th term of formula: a_(n+1) = a_n - 2 * (exp(a_n) - z) / (exp(a_n) + z), + // until the difference between current and next term is smaller than epsilon + var prevStep Decimal + maxIters := calcPrecision*2 + 10 + + for i := int32(0); i < maxIters; i++ { + // exp(a_n) + comp3, _ = comp1.ExpTaylor(calcPrecision) + // exp(a_n) - z + comp2 = comp3.Sub(z) + // 2 * (exp(a_n) - z) + comp2 = comp2.Add(comp2) + // exp(a_n) + z + comp4 = comp3.Add(z) + // 2 * (exp(a_n) - z) / (exp(a_n) + z) + comp3 = comp2.DivRound(comp4, calcPrecision) + // comp1 = a_(n+1) = a_n - 2 * (exp(a_n) - z) / (exp(a_n) + z) + comp1 = comp1.Sub(comp3) + + if prevStep.Add(comp3).IsZero() { + // If iteration steps oscillate we should return early and prevent an infinity loop + // NOTE(mwoss): This should be quite a rare case, returning error is not necessary + break + } + + if comp3.Abs().Cmp(epsilon) <= 0 { + break + } + + prevStep = comp3 + } + } + + comp1 = comp1.Add(reduceAdjust) + + return comp1.Round(precision), nil +} + +// NumDigits returns the number of digits of the decimal coefficient (d.Value) +func (d Decimal) NumDigits() int { + if d.value == nil { + return 1 + } + + if d.value.IsInt64() { + i64 := d.value.Int64() + // restrict fast path to integers with exact conversion to float64 + if i64 <= (1<<53) && i64 >= -(1<<53) { + if i64 == 0 { + return 1 + } + return int(math.Log10(math.Abs(float64(i64)))) + 1 + } + } + + estimatedNumDigits := int(float64(d.value.BitLen()) / math.Log2(10)) + + // estimatedNumDigits (lg10) may be off by 1, need to verify + digitsBigInt := big.NewInt(int64(estimatedNumDigits)) + errorCorrectionUnit := digitsBigInt.Exp(tenInt, digitsBigInt, nil) + + if d.value.CmpAbs(errorCorrectionUnit) >= 0 { + return estimatedNumDigits + 1 + } + + return estimatedNumDigits +} + +// IsInteger returns true when decimal can be represented as an integer value, otherwise, it returns false. +func (d Decimal) IsInteger() bool { + // The most typical case, all decimal with exponent higher or equal 0 can be represented as integer + if d.exp >= 0 { + return true + } + // When the exponent is negative we have to check every number after the decimal place + // If all of them are zeroes, we are sure that given decimal can be represented as an integer + var r big.Int + q := new(big.Int).Set(d.value) + for z := abs(d.exp); z > 0; z-- { + q.QuoRem(q, tenInt, &r) + if r.Cmp(zeroInt) != 0 { + return false + } + } + return true +} + +// Abs calculates absolute value of any int32. Used for calculating absolute value of decimal's exponent. +func abs(n int32) int32 { + if n < 0 { + return -n + } + return n +} + +// Cmp compares the numbers represented by d and d2 and returns: +// +// -1 if d < d2 +// 0 if d == d2 +// +1 if d > d2 +func (d Decimal) Cmp(d2 Decimal) int { + d.ensureInitialized() + d2.ensureInitialized() + + if d.exp == d2.exp { + return d.value.Cmp(d2.value) + } + + rd, rd2 := RescalePair(d, d2) + + return rd.value.Cmp(rd2.value) +} + +// Compare compares the numbers represented by d and d2 and returns: +// +// -1 if d < d2 +// 0 if d == d2 +// +1 if d > d2 +func (d Decimal) Compare(d2 Decimal) int { + return d.Cmp(d2) +} + +// Equal returns whether the numbers represented by d and d2 are equal. +func (d Decimal) Equal(d2 Decimal) bool { + return d.Cmp(d2) == 0 +} + +// Deprecated: Equals is deprecated, please use Equal method instead. +func (d Decimal) Equals(d2 Decimal) bool { + return d.Equal(d2) +} + +// GreaterThan (GT) returns true when d is greater than d2. +func (d Decimal) GreaterThan(d2 Decimal) bool { + return d.Cmp(d2) == 1 +} + +// GreaterThanOrEqual (GTE) returns true when d is greater than or equal to d2. +func (d Decimal) GreaterThanOrEqual(d2 Decimal) bool { + cmp := d.Cmp(d2) + return cmp == 1 || cmp == 0 +} + +// LessThan (LT) returns true when d is less than d2. +func (d Decimal) LessThan(d2 Decimal) bool { + return d.Cmp(d2) == -1 +} + +// LessThanOrEqual (LTE) returns true when d is less than or equal to d2. +func (d Decimal) LessThanOrEqual(d2 Decimal) bool { + cmp := d.Cmp(d2) + return cmp == -1 || cmp == 0 +} + +// Sign returns: +// +// -1 if d < 0 +// 0 if d == 0 +// +1 if d > 0 +func (d Decimal) Sign() int { + if d.value == nil { + return 0 + } + return d.value.Sign() +} + +// IsPositive return +// +// true if d > 0 +// false if d == 0 +// false if d < 0 +func (d Decimal) IsPositive() bool { + return d.Sign() == 1 +} + +// IsNegative return +// +// true if d < 0 +// false if d == 0 +// false if d > 0 +func (d Decimal) IsNegative() bool { + return d.Sign() == -1 +} + +// IsZero return +// +// true if d == 0 +// false if d > 0 +// false if d < 0 +func (d Decimal) IsZero() bool { + return d.Sign() == 0 +} + +// Exponent returns the exponent, or scale component of the decimal. +func (d Decimal) Exponent() int32 { + return d.exp +} + +// Coefficient returns the coefficient of the decimal. It is scaled by 10^Exponent() +func (d Decimal) Coefficient() *big.Int { + d.ensureInitialized() + // we copy the coefficient so that mutating the result does not mutate the Decimal. + return new(big.Int).Set(d.value) +} + +// CoefficientInt64 returns the coefficient of the decimal as int64. It is scaled by 10^Exponent() +// If coefficient cannot be represented in an int64, the result will be undefined. +func (d Decimal) CoefficientInt64() int64 { + d.ensureInitialized() + return d.value.Int64() +} + +// IntPart returns the integer component of the decimal. +func (d Decimal) IntPart() int64 { + scaledD := d.rescale(0) + return scaledD.value.Int64() +} + +// BigInt returns integer component of the decimal as a BigInt. +func (d Decimal) BigInt() *big.Int { + scaledD := d.rescale(0) + return scaledD.value +} + +// BigFloat returns decimal as BigFloat. +// Be aware that casting decimal to BigFloat might cause a loss of precision. +func (d Decimal) BigFloat() *big.Float { + f := &big.Float{} + f.SetString(d.String()) + return f +} + +// Rat returns a rational number representation of the decimal. +func (d Decimal) Rat() *big.Rat { + d.ensureInitialized() + if d.exp <= 0 { + // NOTE(vadim): must negate after casting to prevent int32 overflow + denom := new(big.Int).Exp(tenInt, big.NewInt(-int64(d.exp)), nil) + return new(big.Rat).SetFrac(d.value, denom) + } + + mul := new(big.Int).Exp(tenInt, big.NewInt(int64(d.exp)), nil) + num := new(big.Int).Mul(d.value, mul) + return new(big.Rat).SetFrac(num, oneInt) +} + +// Float64 returns the nearest float64 value for d and a bool indicating +// whether f represents d exactly. +// For more details, see the documentation for big.Rat.Float64 +func (d Decimal) Float64() (f float64, exact bool) { + return d.Rat().Float64() +} + +// InexactFloat64 returns the nearest float64 value for d. +// It doesn't indicate if the returned value represents d exactly. +func (d Decimal) InexactFloat64() float64 { + f, _ := d.Float64() + return f +} + +// String returns the string representation of the decimal +// with the fixed point. +// +// Example: +// +// d := New(-12345, -3) +// println(d.String()) +// +// Output: +// +// -12.345 +func (d Decimal) String() string { + return d.string(true) +} + +// StringFixed returns a rounded fixed-point string with places digits after +// the decimal point. +// +// Example: +// +// NewFromFloat(0).StringFixed(2) // output: "0.00" +// NewFromFloat(0).StringFixed(0) // output: "0" +// NewFromFloat(5.45).StringFixed(0) // output: "5" +// NewFromFloat(5.45).StringFixed(1) // output: "5.5" +// NewFromFloat(5.45).StringFixed(2) // output: "5.45" +// NewFromFloat(5.45).StringFixed(3) // output: "5.450" +// NewFromFloat(545).StringFixed(-1) // output: "550" +func (d Decimal) StringFixed(places int32) string { + rounded := d.Round(places) + return rounded.string(false) +} + +// StringFixedBank returns a banker rounded fixed-point string with places digits +// after the decimal point. +// +// Example: +// +// NewFromFloat(0).StringFixedBank(2) // output: "0.00" +// NewFromFloat(0).StringFixedBank(0) // output: "0" +// NewFromFloat(5.45).StringFixedBank(0) // output: "5" +// NewFromFloat(5.45).StringFixedBank(1) // output: "5.4" +// NewFromFloat(5.45).StringFixedBank(2) // output: "5.45" +// NewFromFloat(5.45).StringFixedBank(3) // output: "5.450" +// NewFromFloat(545).StringFixedBank(-1) // output: "540" +func (d Decimal) StringFixedBank(places int32) string { + rounded := d.RoundBank(places) + return rounded.string(false) +} + +// StringFixedCash returns a Swedish/Cash rounded fixed-point string. For +// more details see the documentation at function RoundCash. +func (d Decimal) StringFixedCash(interval uint8) string { + rounded := d.RoundCash(interval) + return rounded.string(false) +} + +// Round rounds the decimal to places decimal places. +// If places < 0, it will round the integer part to the nearest 10^(-places). +// +// Example: +// +// NewFromFloat(5.45).Round(1).String() // output: "5.5" +// NewFromFloat(545).Round(-1).String() // output: "550" +func (d Decimal) Round(places int32) Decimal { + if d.exp == -places { + return d + } + // truncate to places + 1 + ret := d.rescale(-places - 1) + + // add sign(d) * 0.5 + if ret.value.Sign() < 0 { + ret.value.Sub(ret.value, fiveInt) + } else { + ret.value.Add(ret.value, fiveInt) + } + + // floor for positive numbers, ceil for negative numbers + _, m := ret.value.DivMod(ret.value, tenInt, new(big.Int)) + ret.exp++ + if ret.value.Sign() < 0 && m.Cmp(zeroInt) != 0 { + ret.value.Add(ret.value, oneInt) + } + + return ret +} + +// RoundCeil rounds the decimal towards +infinity. +// +// Example: +// +// NewFromFloat(545).RoundCeil(-2).String() // output: "600" +// NewFromFloat(500).RoundCeil(-2).String() // output: "500" +// NewFromFloat(1.1001).RoundCeil(2).String() // output: "1.11" +// NewFromFloat(-1.454).RoundCeil(1).String() // output: "-1.4" +func (d Decimal) RoundCeil(places int32) Decimal { + if d.exp >= -places { + return d + } + + rescaled := d.rescale(-places) + if d.Equal(rescaled) { + return d + } + + if d.value.Sign() > 0 { + rescaled.value.Add(rescaled.value, oneInt) + } + + return rescaled +} + +// RoundFloor rounds the decimal towards -infinity. +// +// Example: +// +// NewFromFloat(545).RoundFloor(-2).String() // output: "500" +// NewFromFloat(-500).RoundFloor(-2).String() // output: "-500" +// NewFromFloat(1.1001).RoundFloor(2).String() // output: "1.1" +// NewFromFloat(-1.454).RoundFloor(1).String() // output: "-1.5" +func (d Decimal) RoundFloor(places int32) Decimal { + if d.exp >= -places { + return d + } + + rescaled := d.rescale(-places) + if d.Equal(rescaled) { + return d + } + + if d.value.Sign() < 0 { + rescaled.value.Sub(rescaled.value, oneInt) + } + + return rescaled +} + +// RoundUp rounds the decimal away from zero. +// +// Example: +// +// NewFromFloat(545).RoundUp(-2).String() // output: "600" +// NewFromFloat(500).RoundUp(-2).String() // output: "500" +// NewFromFloat(1.1001).RoundUp(2).String() // output: "1.11" +// NewFromFloat(-1.454).RoundUp(1).String() // output: "-1.5" +func (d Decimal) RoundUp(places int32) Decimal { + if d.exp >= -places { + return d + } + + rescaled := d.rescale(-places) + if d.Equal(rescaled) { + return d + } + + if d.value.Sign() > 0 { + rescaled.value.Add(rescaled.value, oneInt) + } else if d.value.Sign() < 0 { + rescaled.value.Sub(rescaled.value, oneInt) + } + + return rescaled +} + +// RoundDown rounds the decimal towards zero. +// +// Example: +// +// NewFromFloat(545).RoundDown(-2).String() // output: "500" +// NewFromFloat(-500).RoundDown(-2).String() // output: "-500" +// NewFromFloat(1.1001).RoundDown(2).String() // output: "1.1" +// NewFromFloat(-1.454).RoundDown(1).String() // output: "-1.4" +func (d Decimal) RoundDown(places int32) Decimal { + if d.exp >= -places { + return d + } + + rescaled := d.rescale(-places) + if d.Equal(rescaled) { + return d + } + return rescaled +} + +// RoundBank rounds the decimal to places decimal places. +// If the final digit to round is equidistant from the nearest two integers the +// rounded value is taken as the even number +// +// If places < 0, it will round the integer part to the nearest 10^(-places). +// +// Examples: +// +// NewFromFloat(5.45).RoundBank(1).String() // output: "5.4" +// NewFromFloat(545).RoundBank(-1).String() // output: "540" +// NewFromFloat(5.46).RoundBank(1).String() // output: "5.5" +// NewFromFloat(546).RoundBank(-1).String() // output: "550" +// NewFromFloat(5.55).RoundBank(1).String() // output: "5.6" +// NewFromFloat(555).RoundBank(-1).String() // output: "560" +func (d Decimal) RoundBank(places int32) Decimal { + + round := d.Round(places) + remainder := d.Sub(round).Abs() + + half := New(5, -places-1) + if remainder.Cmp(half) == 0 && round.value.Bit(0) != 0 { + if round.value.Sign() < 0 { + round.value.Add(round.value, oneInt) + } else { + round.value.Sub(round.value, oneInt) + } + } + + return round +} + +// RoundCash aka Cash/Penny/öre rounding rounds decimal to a specific +// interval. The amount payable for a cash transaction is rounded to the nearest +// multiple of the minimum currency unit available. The following intervals are +// available: 5, 10, 25, 50 and 100; any other number throws a panic. +// +// 5: 5 cent rounding 3.43 => 3.45 +// 10: 10 cent rounding 3.45 => 3.50 (5 gets rounded up) +// 25: 25 cent rounding 3.41 => 3.50 +// 50: 50 cent rounding 3.75 => 4.00 +// 100: 100 cent rounding 3.50 => 4.00 +// +// For more details: https://en.wikipedia.org/wiki/Cash_rounding +func (d Decimal) RoundCash(interval uint8) Decimal { + var iVal *big.Int + switch interval { + case 5: + iVal = twentyInt + case 10: + iVal = tenInt + case 25: + iVal = fourInt + case 50: + iVal = twoInt + case 100: + iVal = oneInt + default: + panic(fmt.Sprintf("Decimal does not support this Cash rounding interval `%d`. Supported: 5, 10, 25, 50, 100", interval)) + } + dVal := Decimal{ + value: iVal, + } + + // TODO: optimize those calculations to reduce the high allocations (~29 allocs). + return d.Mul(dVal).Round(0).Div(dVal).Truncate(2) +} + +// Floor returns the nearest integer value less than or equal to d. +func (d Decimal) Floor() Decimal { + d.ensureInitialized() + + if d.exp >= 0 { + return d + } + + exp := big.NewInt(10) + + // NOTE(vadim): must negate after casting to prevent int32 overflow + exp.Exp(exp, big.NewInt(-int64(d.exp)), nil) + + z := new(big.Int).Div(d.value, exp) + return Decimal{value: z, exp: 0} +} + +// Ceil returns the nearest integer value greater than or equal to d. +func (d Decimal) Ceil() Decimal { + d.ensureInitialized() + + if d.exp >= 0 { + return d + } + + exp := big.NewInt(10) + + // NOTE(vadim): must negate after casting to prevent int32 overflow + exp.Exp(exp, big.NewInt(-int64(d.exp)), nil) + + z, m := new(big.Int).DivMod(d.value, exp, new(big.Int)) + if m.Cmp(zeroInt) != 0 { + z.Add(z, oneInt) + } + return Decimal{value: z, exp: 0} +} + +// Truncate truncates off digits from the number, without rounding. +// +// NOTE: precision is the last digit that will not be truncated (must be >= 0). +// +// Example: +// +// decimal.NewFromString("123.456").Truncate(2).String() // "123.45" +func (d Decimal) Truncate(precision int32) Decimal { + d.ensureInitialized() + if precision >= 0 && -precision > d.exp { + return d.rescale(-precision) + } + return d +} + +// UnmarshalJSON implements the json.Unmarshaler interface. +func (d *Decimal) UnmarshalJSON(decimalBytes []byte) error { + if string(decimalBytes) == "null" { + return nil + } + + str, err := unquoteIfQuoted(decimalBytes) + if err != nil { + return fmt.Errorf("error decoding string '%s': %s", decimalBytes, err) + } + + decimal, err := NewFromString(str) + *d = decimal + if err != nil { + return fmt.Errorf("error decoding string '%s': %s", str, err) + } + return nil +} + +// MarshalJSON implements the json.Marshaler interface. +func (d Decimal) MarshalJSON() ([]byte, error) { + var str string + if MarshalJSONWithoutQuotes { + str = d.String() + } else { + str = "\"" + d.String() + "\"" + } + return []byte(str), nil +} + +// UnmarshalBinary implements the encoding.BinaryUnmarshaler interface. As a string representation +// is already used when encoding to text, this method stores that string as []byte +func (d *Decimal) UnmarshalBinary(data []byte) error { + // Verify we have at least 4 bytes for the exponent. The GOB encoded value + // may be empty. + if len(data) < 4 { + return fmt.Errorf("error decoding binary %v: expected at least 4 bytes, got %d", data, len(data)) + } + + // Extract the exponent + d.exp = int32(binary.BigEndian.Uint32(data[:4])) + + // Extract the value + d.value = new(big.Int) + if err := d.value.GobDecode(data[4:]); err != nil { + return fmt.Errorf("error decoding binary %v: %s", data, err) + } + + return nil +} + +// MarshalBinary implements the encoding.BinaryMarshaler interface. +func (d Decimal) MarshalBinary() (data []byte, err error) { + // exp is written first, but encode value first to know output size + var valueData []byte + if valueData, err = d.value.GobEncode(); err != nil { + return nil, err + } + + // Write the exponent in front, since it's a fixed size + expData := make([]byte, 4, len(valueData)+4) + binary.BigEndian.PutUint32(expData, uint32(d.exp)) + + // Return the byte array + return append(expData, valueData...), nil +} + +// Scan implements the sql.Scanner interface for database deserialization. +func (d *Decimal) Scan(value interface{}) error { + // first try to see if the data is stored in database as a Numeric datatype + switch v := value.(type) { + + case float32: + *d = NewFromFloat(float64(v)) + return nil + + case float64: + // numeric in sqlite3 sends us float64 + *d = NewFromFloat(v) + return nil + + case int64: + // at least in sqlite3 when the value is 0 in db, the data is sent + // to us as an int64 instead of a float64 ... + *d = New(v, 0) + return nil + + case uint64: + // while clickhouse may send 0 in db as uint64 + *d = NewFromUint64(v) + return nil + + default: + // default is trying to interpret value stored as string + str, err := unquoteIfQuoted(v) + if err != nil { + return err + } + *d, err = NewFromString(str) + return err + } +} + +// Value implements the driver.Valuer interface for database serialization. +func (d Decimal) Value() (driver.Value, error) { + return d.String(), nil +} + +// UnmarshalText implements the encoding.TextUnmarshaler interface for XML +// deserialization. +func (d *Decimal) UnmarshalText(text []byte) error { + str := string(text) + + dec, err := NewFromString(str) + *d = dec + if err != nil { + return fmt.Errorf("error decoding string '%s': %s", str, err) + } + + return nil +} + +// MarshalText implements the encoding.TextMarshaler interface for XML +// serialization. +func (d Decimal) MarshalText() (text []byte, err error) { + return []byte(d.String()), nil +} + +// GobEncode implements the gob.GobEncoder interface for gob serialization. +func (d Decimal) GobEncode() ([]byte, error) { + return d.MarshalBinary() +} + +// GobDecode implements the gob.GobDecoder interface for gob serialization. +func (d *Decimal) GobDecode(data []byte) error { + return d.UnmarshalBinary(data) +} + +// StringScaled first scales the decimal then calls .String() on it. +// +// Deprecated: buggy and unintuitive. Use StringFixed instead. +func (d Decimal) StringScaled(exp int32) string { + return d.rescale(exp).String() +} + +func (d Decimal) string(trimTrailingZeros bool) string { + if d.exp >= 0 { + return d.rescale(0).value.String() + } + + abs := new(big.Int).Abs(d.value) + str := abs.String() + + var intPart, fractionalPart string + + // NOTE(vadim): this cast to int will cause bugs if d.exp == INT_MIN + // and you are on a 32-bit machine. Won't fix this super-edge case. + dExpInt := int(d.exp) + if len(str) > -dExpInt { + intPart = str[:len(str)+dExpInt] + fractionalPart = str[len(str)+dExpInt:] + } else { + intPart = "0" + + num0s := -dExpInt - len(str) + fractionalPart = strings.Repeat("0", num0s) + str + } + + if trimTrailingZeros { + i := len(fractionalPart) - 1 + for ; i >= 0; i-- { + if fractionalPart[i] != '0' { + break + } + } + fractionalPart = fractionalPart[:i+1] + } + + number := intPart + if len(fractionalPart) > 0 { + number += "." + fractionalPart + } + + if d.value.Sign() < 0 { + return "-" + number + } + + return number +} + +func (d *Decimal) ensureInitialized() { + if d.value == nil { + d.value = new(big.Int) + } +} + +// Min returns the smallest Decimal that was passed in the arguments. +// +// To call this function with an array, you must do: +// +// Min(arr[0], arr[1:]...) +// +// This makes it harder to accidentally call Min with 0 arguments. +func Min(first Decimal, rest ...Decimal) Decimal { + ans := first + for _, item := range rest { + if item.Cmp(ans) < 0 { + ans = item + } + } + return ans +} + +// Max returns the largest Decimal that was passed in the arguments. +// +// To call this function with an array, you must do: +// +// Max(arr[0], arr[1:]...) +// +// This makes it harder to accidentally call Max with 0 arguments. +func Max(first Decimal, rest ...Decimal) Decimal { + ans := first + for _, item := range rest { + if item.Cmp(ans) > 0 { + ans = item + } + } + return ans +} + +// Sum returns the combined total of the provided first and rest Decimals +func Sum(first Decimal, rest ...Decimal) Decimal { + total := first + for _, item := range rest { + total = total.Add(item) + } + + return total +} + +// Avg returns the average value of the provided first and rest Decimals +func Avg(first Decimal, rest ...Decimal) Decimal { + count := New(int64(len(rest)+1), 0) + sum := Sum(first, rest...) + return sum.Div(count) +} + +// RescalePair rescales two decimals to common exponential value (minimal exp of both decimals) +func RescalePair(d1 Decimal, d2 Decimal) (Decimal, Decimal) { + d1.ensureInitialized() + d2.ensureInitialized() + + if d1.exp < d2.exp { + return d1, d2.rescale(d1.exp) + } else if d1.exp > d2.exp { + return d1.rescale(d2.exp), d2 + } + + return d1, d2 +} + +func unquoteIfQuoted(value interface{}) (string, error) { + var bytes []byte + + switch v := value.(type) { + case string: + bytes = []byte(v) + case []byte: + bytes = v + default: + return "", fmt.Errorf("could not convert value '%+v' to byte array of type '%T'", value, value) + } + + // If the amount is quoted, strip the quotes + if len(bytes) > 2 && bytes[0] == '"' && bytes[len(bytes)-1] == '"' { + bytes = bytes[1 : len(bytes)-1] + } + return string(bytes), nil +} + +// NullDecimal represents a nullable decimal with compatibility for +// scanning null values from the database. +type NullDecimal struct { + Decimal Decimal + Valid bool +} + +func NewNullDecimal(d Decimal) NullDecimal { + return NullDecimal{ + Decimal: d, + Valid: true, + } +} + +// Scan implements the sql.Scanner interface for database deserialization. +func (d *NullDecimal) Scan(value interface{}) error { + if value == nil { + d.Valid = false + return nil + } + d.Valid = true + return d.Decimal.Scan(value) +} + +// Value implements the driver.Valuer interface for database serialization. +func (d NullDecimal) Value() (driver.Value, error) { + if !d.Valid { + return nil, nil + } + return d.Decimal.Value() +} + +// UnmarshalJSON implements the json.Unmarshaler interface. +func (d *NullDecimal) UnmarshalJSON(decimalBytes []byte) error { + if string(decimalBytes) == "null" { + d.Valid = false + return nil + } + d.Valid = true + return d.Decimal.UnmarshalJSON(decimalBytes) +} + +// MarshalJSON implements the json.Marshaler interface. +func (d NullDecimal) MarshalJSON() ([]byte, error) { + if !d.Valid { + return []byte("null"), nil + } + return d.Decimal.MarshalJSON() +} + +// UnmarshalText implements the encoding.TextUnmarshaler interface for XML +// deserialization +func (d *NullDecimal) UnmarshalText(text []byte) error { + str := string(text) + + // check for empty XML or XML without body e.g., <tag></tag> + if str == "" { + d.Valid = false + return nil + } + if err := d.Decimal.UnmarshalText(text); err != nil { + d.Valid = false + return err + } + d.Valid = true + return nil +} + +// MarshalText implements the encoding.TextMarshaler interface for XML +// serialization. +func (d NullDecimal) MarshalText() (text []byte, err error) { + if !d.Valid { + return []byte{}, nil + } + return d.Decimal.MarshalText() +} + +// Trig functions + +// Atan returns the arctangent, in radians, of x. +func (d Decimal) Atan() Decimal { + if d.Equal(NewFromFloat(0.0)) { + return d + } + if d.GreaterThan(NewFromFloat(0.0)) { + return d.satan() + } + return d.Neg().satan().Neg() +} + +func (d Decimal) xatan() Decimal { + P0 := NewFromFloat(-8.750608600031904122785e-01) + P1 := NewFromFloat(-1.615753718733365076637e+01) + P2 := NewFromFloat(-7.500855792314704667340e+01) + P3 := NewFromFloat(-1.228866684490136173410e+02) + P4 := NewFromFloat(-6.485021904942025371773e+01) + Q0 := NewFromFloat(2.485846490142306297962e+01) + Q1 := NewFromFloat(1.650270098316988542046e+02) + Q2 := NewFromFloat(4.328810604912902668951e+02) + Q3 := NewFromFloat(4.853903996359136964868e+02) + Q4 := NewFromFloat(1.945506571482613964425e+02) + z := d.Mul(d) + b1 := P0.Mul(z).Add(P1).Mul(z).Add(P2).Mul(z).Add(P3).Mul(z).Add(P4).Mul(z) + b2 := z.Add(Q0).Mul(z).Add(Q1).Mul(z).Add(Q2).Mul(z).Add(Q3).Mul(z).Add(Q4) + z = b1.Div(b2) + z = d.Mul(z).Add(d) + return z +} + +// satan reduces its argument (known to be positive) +// to the range [0, 0.66] and calls xatan. +func (d Decimal) satan() Decimal { + Morebits := NewFromFloat(6.123233995736765886130e-17) // pi/2 = PIO2 + Morebits + Tan3pio8 := NewFromFloat(2.41421356237309504880) // tan(3*pi/8) + pi := NewFromFloat(3.14159265358979323846264338327950288419716939937510582097494459) + + if d.LessThanOrEqual(NewFromFloat(0.66)) { + return d.xatan() + } + if d.GreaterThan(Tan3pio8) { + return pi.Div(NewFromFloat(2.0)).Sub(NewFromFloat(1.0).Div(d).xatan()).Add(Morebits) + } + return pi.Div(NewFromFloat(4.0)).Add((d.Sub(NewFromFloat(1.0)).Div(d.Add(NewFromFloat(1.0)))).xatan()).Add(NewFromFloat(0.5).Mul(Morebits)) +} + +// sin coefficients +var _sin = [...]Decimal{ + NewFromFloat(1.58962301576546568060e-10), // 0x3de5d8fd1fd19ccd + NewFromFloat(-2.50507477628578072866e-8), // 0xbe5ae5e5a9291f5d + NewFromFloat(2.75573136213857245213e-6), // 0x3ec71de3567d48a1 + NewFromFloat(-1.98412698295895385996e-4), // 0xbf2a01a019bfdf03 + NewFromFloat(8.33333333332211858878e-3), // 0x3f8111111110f7d0 + NewFromFloat(-1.66666666666666307295e-1), // 0xbfc5555555555548 +} + +// Sin returns the sine of the radian argument x. +func (d Decimal) Sin() Decimal { + PI4A := NewFromFloat(7.85398125648498535156e-1) // 0x3fe921fb40000000, Pi/4 split into three parts + PI4B := NewFromFloat(3.77489470793079817668e-8) // 0x3e64442d00000000, + PI4C := NewFromFloat(2.69515142907905952645e-15) // 0x3ce8469898cc5170, + M4PI := NewFromFloat(1.273239544735162542821171882678754627704620361328125) // 4/pi + + if d.Equal(NewFromFloat(0.0)) { + return d + } + // make argument positive but save the sign + sign := false + if d.LessThan(NewFromFloat(0.0)) { + d = d.Neg() + sign = true + } + + j := d.Mul(M4PI).IntPart() // integer part of x/(Pi/4), as integer for tests on the phase angle + y := NewFromFloat(float64(j)) // integer part of x/(Pi/4), as float + + // map zeros to origin + if j&1 == 1 { + j++ + y = y.Add(NewFromFloat(1.0)) + } + j &= 7 // octant modulo 2Pi radians (360 degrees) + // reflect in x axis + if j > 3 { + sign = !sign + j -= 4 + } + z := d.Sub(y.Mul(PI4A)).Sub(y.Mul(PI4B)).Sub(y.Mul(PI4C)) // Extended precision modular arithmetic + zz := z.Mul(z) + + if j == 1 || j == 2 { + w := zz.Mul(zz).Mul(_cos[0].Mul(zz).Add(_cos[1]).Mul(zz).Add(_cos[2]).Mul(zz).Add(_cos[3]).Mul(zz).Add(_cos[4]).Mul(zz).Add(_cos[5])) + y = NewFromFloat(1.0).Sub(NewFromFloat(0.5).Mul(zz)).Add(w) + } else { + y = z.Add(z.Mul(zz).Mul(_sin[0].Mul(zz).Add(_sin[1]).Mul(zz).Add(_sin[2]).Mul(zz).Add(_sin[3]).Mul(zz).Add(_sin[4]).Mul(zz).Add(_sin[5]))) + } + if sign { + y = y.Neg() + } + return y +} + +// cos coefficients +var _cos = [...]Decimal{ + NewFromFloat(-1.13585365213876817300e-11), // 0xbda8fa49a0861a9b + NewFromFloat(2.08757008419747316778e-9), // 0x3e21ee9d7b4e3f05 + NewFromFloat(-2.75573141792967388112e-7), // 0xbe927e4f7eac4bc6 + NewFromFloat(2.48015872888517045348e-5), // 0x3efa01a019c844f5 + NewFromFloat(-1.38888888888730564116e-3), // 0xbf56c16c16c14f91 + NewFromFloat(4.16666666666665929218e-2), // 0x3fa555555555554b +} + +// Cos returns the cosine of the radian argument x. +func (d Decimal) Cos() Decimal { + + PI4A := NewFromFloat(7.85398125648498535156e-1) // 0x3fe921fb40000000, Pi/4 split into three parts + PI4B := NewFromFloat(3.77489470793079817668e-8) // 0x3e64442d00000000, + PI4C := NewFromFloat(2.69515142907905952645e-15) // 0x3ce8469898cc5170, + M4PI := NewFromFloat(1.273239544735162542821171882678754627704620361328125) // 4/pi + + // make argument positive + sign := false + if d.LessThan(NewFromFloat(0.0)) { + d = d.Neg() + } + + j := d.Mul(M4PI).IntPart() // integer part of x/(Pi/4), as integer for tests on the phase angle + y := NewFromFloat(float64(j)) // integer part of x/(Pi/4), as float + + // map zeros to origin + if j&1 == 1 { + j++ + y = y.Add(NewFromFloat(1.0)) + } + j &= 7 // octant modulo 2Pi radians (360 degrees) + // reflect in x axis + if j > 3 { + sign = !sign + j -= 4 + } + if j > 1 { + sign = !sign + } + + z := d.Sub(y.Mul(PI4A)).Sub(y.Mul(PI4B)).Sub(y.Mul(PI4C)) // Extended precision modular arithmetic + zz := z.Mul(z) + + if j == 1 || j == 2 { + y = z.Add(z.Mul(zz).Mul(_sin[0].Mul(zz).Add(_sin[1]).Mul(zz).Add(_sin[2]).Mul(zz).Add(_sin[3]).Mul(zz).Add(_sin[4]).Mul(zz).Add(_sin[5]))) + } else { + w := zz.Mul(zz).Mul(_cos[0].Mul(zz).Add(_cos[1]).Mul(zz).Add(_cos[2]).Mul(zz).Add(_cos[3]).Mul(zz).Add(_cos[4]).Mul(zz).Add(_cos[5])) + y = NewFromFloat(1.0).Sub(NewFromFloat(0.5).Mul(zz)).Add(w) + } + if sign { + y = y.Neg() + } + return y +} + +var _tanP = [...]Decimal{ + NewFromFloat(-1.30936939181383777646e+4), // 0xc0c992d8d24f3f38 + NewFromFloat(1.15351664838587416140e+6), // 0x413199eca5fc9ddd + NewFromFloat(-1.79565251976484877988e+7), // 0xc1711fead3299176 +} +var _tanQ = [...]Decimal{ + NewFromFloat(1.00000000000000000000e+0), + NewFromFloat(1.36812963470692954678e+4), //0x40cab8a5eeb36572 + NewFromFloat(-1.32089234440210967447e+6), //0xc13427bc582abc96 + NewFromFloat(2.50083801823357915839e+7), //0x4177d98fc2ead8ef + NewFromFloat(-5.38695755929454629881e+7), //0xc189afe03cbe5a31 +} + +// Tan returns the tangent of the radian argument x. +func (d Decimal) Tan() Decimal { + + PI4A := NewFromFloat(7.85398125648498535156e-1) // 0x3fe921fb40000000, Pi/4 split into three parts + PI4B := NewFromFloat(3.77489470793079817668e-8) // 0x3e64442d00000000, + PI4C := NewFromFloat(2.69515142907905952645e-15) // 0x3ce8469898cc5170, + M4PI := NewFromFloat(1.273239544735162542821171882678754627704620361328125) // 4/pi + + if d.Equal(NewFromFloat(0.0)) { + return d + } + + // make argument positive but save the sign + sign := false + if d.LessThan(NewFromFloat(0.0)) { + d = d.Neg() + sign = true + } + + j := d.Mul(M4PI).IntPart() // integer part of x/(Pi/4), as integer for tests on the phase angle + y := NewFromFloat(float64(j)) // integer part of x/(Pi/4), as float + + // map zeros to origin + if j&1 == 1 { + j++ + y = y.Add(NewFromFloat(1.0)) + } + + z := d.Sub(y.Mul(PI4A)).Sub(y.Mul(PI4B)).Sub(y.Mul(PI4C)) // Extended precision modular arithmetic + zz := z.Mul(z) + + if zz.GreaterThan(NewFromFloat(1e-14)) { + w := zz.Mul(_tanP[0].Mul(zz).Add(_tanP[1]).Mul(zz).Add(_tanP[2])) + x := zz.Add(_tanQ[1]).Mul(zz).Add(_tanQ[2]).Mul(zz).Add(_tanQ[3]).Mul(zz).Add(_tanQ[4]) + y = z.Add(z.Mul(w.Div(x))) + } else { + y = z + } + if j&2 == 2 { + y = NewFromFloat(-1.0).Div(y) + } + if sign { + y = y.Neg() + } + return y +} diff --git a/vendor/github.com/shopspring/decimal/rounding.go b/vendor/github.com/shopspring/decimal/rounding.go new file mode 100644 index 0000000..d4b0cd0 --- /dev/null +++ b/vendor/github.com/shopspring/decimal/rounding.go @@ -0,0 +1,160 @@ +// Copyright 2009 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Multiprecision decimal numbers. +// For floating-point formatting only; not general purpose. +// Only operations are assign and (binary) left/right shift. +// Can do binary floating point in multiprecision decimal precisely +// because 2 divides 10; cannot do decimal floating point +// in multiprecision binary precisely. + +package decimal + +type floatInfo struct { + mantbits uint + expbits uint + bias int +} + +var float32info = floatInfo{23, 8, -127} +var float64info = floatInfo{52, 11, -1023} + +// roundShortest rounds d (= mant * 2^exp) to the shortest number of digits +// that will let the original floating point value be precisely reconstructed. +func roundShortest(d *decimal, mant uint64, exp int, flt *floatInfo) { + // If mantissa is zero, the number is zero; stop now. + if mant == 0 { + d.nd = 0 + return + } + + // Compute upper and lower such that any decimal number + // between upper and lower (possibly inclusive) + // will round to the original floating point number. + + // We may see at once that the number is already shortest. + // + // Suppose d is not denormal, so that 2^exp <= d < 10^dp. + // The closest shorter number is at least 10^(dp-nd) away. + // The lower/upper bounds computed below are at distance + // at most 2^(exp-mantbits). + // + // So the number is already shortest if 10^(dp-nd) > 2^(exp-mantbits), + // or equivalently log2(10)*(dp-nd) > exp-mantbits. + // It is true if 332/100*(dp-nd) >= exp-mantbits (log2(10) > 3.32). + minexp := flt.bias + 1 // minimum possible exponent + if exp > minexp && 332*(d.dp-d.nd) >= 100*(exp-int(flt.mantbits)) { + // The number is already shortest. + return + } + + // d = mant << (exp - mantbits) + // Next highest floating point number is mant+1 << exp-mantbits. + // Our upper bound is halfway between, mant*2+1 << exp-mantbits-1. + upper := new(decimal) + upper.Assign(mant*2 + 1) + upper.Shift(exp - int(flt.mantbits) - 1) + + // d = mant << (exp - mantbits) + // Next lowest floating point number is mant-1 << exp-mantbits, + // unless mant-1 drops the significant bit and exp is not the minimum exp, + // in which case the next lowest is mant*2-1 << exp-mantbits-1. + // Either way, call it mantlo << explo-mantbits. + // Our lower bound is halfway between, mantlo*2+1 << explo-mantbits-1. + var mantlo uint64 + var explo int + if mant > 1<<flt.mantbits || exp == minexp { + mantlo = mant - 1 + explo = exp + } else { + mantlo = mant*2 - 1 + explo = exp - 1 + } + lower := new(decimal) + lower.Assign(mantlo*2 + 1) + lower.Shift(explo - int(flt.mantbits) - 1) + + // The upper and lower bounds are possible outputs only if + // the original mantissa is even, so that IEEE round-to-even + // would round to the original mantissa and not the neighbors. + inclusive := mant%2 == 0 + + // As we walk the digits we want to know whether rounding up would fall + // within the upper bound. This is tracked by upperdelta: + // + // If upperdelta == 0, the digits of d and upper are the same so far. + // + // If upperdelta == 1, we saw a difference of 1 between d and upper on a + // previous digit and subsequently only 9s for d and 0s for upper. + // (Thus rounding up may fall outside the bound, if it is exclusive.) + // + // If upperdelta == 2, then the difference is greater than 1 + // and we know that rounding up falls within the bound. + var upperdelta uint8 + + // Now we can figure out the minimum number of digits required. + // Walk along until d has distinguished itself from upper and lower. + for ui := 0; ; ui++ { + // lower, d, and upper may have the decimal points at different + // places. In this case upper is the longest, so we iterate from + // ui==0 and start li and mi at (possibly) -1. + mi := ui - upper.dp + d.dp + if mi >= d.nd { + break + } + li := ui - upper.dp + lower.dp + l := byte('0') // lower digit + if li >= 0 && li < lower.nd { + l = lower.d[li] + } + m := byte('0') // middle digit + if mi >= 0 { + m = d.d[mi] + } + u := byte('0') // upper digit + if ui < upper.nd { + u = upper.d[ui] + } + + // Okay to round down (truncate) if lower has a different digit + // or if lower is inclusive and is exactly the result of rounding + // down (i.e., and we have reached the final digit of lower). + okdown := l != m || inclusive && li+1 == lower.nd + + switch { + case upperdelta == 0 && m+1 < u: + // Example: + // m = 12345xxx + // u = 12347xxx + upperdelta = 2 + case upperdelta == 0 && m != u: + // Example: + // m = 12345xxx + // u = 12346xxx + upperdelta = 1 + case upperdelta == 1 && (m != '9' || u != '0'): + // Example: + // m = 1234598x + // u = 1234600x + upperdelta = 2 + } + // Okay to round up if upper has a different digit and either upper + // is inclusive or upper is bigger than the result of rounding up. + okup := upperdelta > 0 && (inclusive || upperdelta > 1 || ui+1 < upper.nd) + + // If it's okay to do either, then round to the nearest one. + // If it's okay to do only one, do it. + switch { + case okdown && okup: + d.Round(mi + 1) + return + case okdown: + d.RoundDown(mi + 1) + return + case okup: + d.RoundUp(mi + 1) + return + } + } +} |