From 59eb20acb6382074cf9ab570c13f63c54a82d9ba Mon Sep 17 00:00:00 2001 From: Michael Griebling Date: Sat, 8 Jul 2023 16:39:09 -0400 Subject: [PATCH] Updated the documentation. --- .../css/chunk-384ef189.7ede1ea3.css | 9 + .../css/documentation-topic.29351f99.css | 9 + .../documentation-topic~topic.fccbd76c.css | 9 + ...opic~topic~tutorials-overview.1099452b.css | 9 + .../css/index.d5b499b0.css | 9 + .../css/topic.726a35dc.css | 9 + .../css/tutorials-overview.2a582c39.css | 9 + .../data/documentation/bigdecimal.json | 1 + .../bigdecimal/asincalculator.json | 1 + .../asincalculator/addfactor(_:).json | 1 + .../asincalculator/calculate(_:_:).json | 1 + .../asincalculator/calculateinpairs.json | 1 + .../asincalculator/calculatenextfactor().json | 1 + .../createpoweriterator(_:_:).json | 1 + .../bigdecimal/asincalculator/factors.json | 1 + .../asincalculator/getcurrentfactor().json | 1 + .../asincalculator/getfactor(_:).json | 1 + .../bigdecimal/asincalculator/init().json | 1 + 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input[type=text][data-v-483fdfd0]{font-size:1.11765rem;line-height:1.42105;font-weight:400;font-family:var(--typography-html-font,"Helvetica Neue","Helvetica","Arial",sans-serif)}}.quick-navigation__container[data-v-483fdfd0]{background-color:var(--color-fill);border:solid 1px var(--color-fill-gray);border-radius:var(--border-radius,4px);margin:0 .94118rem}.quick-navigation__container>[data-v-483fdfd0]{--input-text:var(--color-figure-gray-secondary)}.quick-navigation__filter[data-v-483fdfd0]{--input-border-color:var(--color-fill)}.quick-navigation__filter.focus+.quick-navigation__match-list[data-v-483fdfd0]{border-top:0}.quick-navigation__magnifier-icon-container[data-v-483fdfd0]{width:1.05882rem}.quick-navigation__magnifier-icon-container>[data-v-483fdfd0]{width:100%}.quick-navigation__magnifier-icon-container.blue 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(max-width:1023px){.aside[data-v-8b4eac40]{width:100%!important;overflow:hidden;min-width:0;max-width:100%;height:calc(var(--app-height) - var(--top-offset-mobile));position:fixed;top:var(--top-offset-mobile);bottom:0;z-index:9998;transform:translateX(-100%);transition:transform .15s ease-in;left:0}.aside[data-v-8b4eac40] .aside-animated-child{opacity:0}.aside.show-on-mobile[data-v-8b4eac40]{transform:translateX(0)}.aside.show-on-mobile[data-v-8b4eac40] .aside-animated-child{--index:0;opacity:1;transition:opacity .15s linear;transition-delay:calc(var(--index)*0.15s + .15s)}.aside.has-mobile-top-offset[data-v-8b4eac40]{border-top:1px solid var(--color-fill-gray-tertiary)}}.content[data-v-8b4eac40]{display:flex;flex-flow:column;min-width:0;flex:1 1 auto;height:100%}.resize-handle[data-v-8b4eac40]{position:absolute;cursor:col-resize;top:0;bottom:0;right:0;width:5px;height:100%;-webkit-user-select:none;-moz-user-select:none;user-select:none;z-index:1;transition:background-color 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.leaf-link[data-v-08a89c9e]:focus{outline:none}.leaf-link[data-v-08a89c9e]:hover{text-decoration:none}.leaf-link.bolded[data-v-08a89c9e]{font-weight:600}.leaf-link[data-v-08a89c9e]:after{content:"";position:absolute;top:0;left:0;right:0;bottom:0}.extended-content[data-v-08a89c9e]{font-size:.82353rem;line-height:1.42857;font-weight:400;font-family:var(--typography-html-font,"Helvetica Neue","Helvetica","Arial",sans-serif);color:var(--color-figure-gray-secondary);white-space:nowrap;overflow:hidden;text-overflow:ellipsis}.tree-toggle[data-v-08a89c9e]{overflow:hidden;position:absolute;width:100%;height:100%;padding-right:5px;box-sizing:border-box;z-index:1;display:flex;align-items:center;justify-content:flex-end}.chevron[data-v-08a89c9e]{width:10px}.chevron.animating[data-v-08a89c9e]{transition:transform .15s 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var(--color-grid);display:flex;align-items:center;height:3.05882rem;white-space:nowrap}.navigator-card .navigator-head .card-link[data-v-4a898368]{color:var(--color-text);font-size:.82353rem;line-height:1.42857;font-weight:400;font-family:var(--typography-html-font,"Helvetica Neue","Helvetica","Arial",sans-serif);font-weight:600;overflow:hidden;text-overflow:ellipsis}.navigator-card .navigator-head .badge[data-v-4a898368]{margin-top:0}.navigator-card .navigator-head.router-link-exact-active[data-v-4a898368]{background:var(--color-fill)}.navigator-card .navigator-head.router-link-exact-active .card-link[data-v-4a898368]{font-weight:700}.navigator-card .navigator-head[data-v-4a898368]:hover{background:var(--color-navigator-item-hover);text-decoration:none}@supports (padding:max(0px)){.navigator-card 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(max-width:767px){.close-card[data-v-4a898368]{padding-left:.94118rem;padding-right:.94118rem}@supports (padding:max(0px)){.close-card[data-v-4a898368]{padding-left:max(.94118rem,env(safe-area-inset-left))}}}.close-card .close-icon[data-v-4a898368]{width:19px;height:19px}@media only screen and (min-width:1024px){.close-card.hide-on-large[data-v-4a898368]{display:none}.close-card[data-v-4a898368]:hover{border-radius:var(--border-radius,4px);background:var(--color-fill-gray-quaternary)}.sidebar-hidden .close-card[data-v-4a898368]{transition:transform .3s ease-in 0s,visibility 0s linear .3s;visibility:hidden;transform:translateX(3.76471rem)}}[data-v-4a898368] .card-body{padding-right:0;flex:1 1 auto;min-height:0;height:100%}@media only screen and (max-width:1023px){[data-v-4a898368] .card-body{--card-vertical-spacing:0px}}.navigator-card-inner[data-v-4a898368]{display:flex;flex-flow:column;height:100%}.vue-recycle-scroller{position:relative}.vue-recycle-scroller.direction-vertical:not(.page-mode){overflow-y:auto}.vue-recycle-scroller.direction-horizontal:not(.page-mode){overflow-x:auto}.vue-recycle-scroller.direction-horizontal{display:-webkit-box;display:-ms-flexbox;display:flex}.vue-recycle-scroller__slot{-webkit-box-flex:1;-ms-flex:auto 0 0px;flex:auto 0 0}.vue-recycle-scroller__item-wrapper{-webkit-box-flex:1;-ms-flex:1;flex:1;-webkit-box-sizing:border-box;box-sizing:border-box;overflow:hidden;position:relative}.vue-recycle-scroller.ready .vue-recycle-scroller__item-view{position:absolute;top:0;left:0;will-change:transform}.vue-recycle-scroller.direction-vertical .vue-recycle-scroller__item-wrapper{width:100%}.vue-recycle-scroller.direction-horizontal .vue-recycle-scroller__item-wrapper{height:100%}.vue-recycle-scroller.ready.direction-vertical 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var(--card-horizontal-spacing);min-width:200px;box-sizing:border-box}.navigator-filter[data-v-a440d59c]{box-sizing:border-box;padding:15px var(--nav-filter-horizontal-padding);border-top:1px solid var(--color-grid);height:73px;display:flex;align-items:flex-end}.filter-on-top .navigator-filter[data-v-a440d59c]{border-top:none;align-items:flex-start}@supports (padding:max(0px)){.navigator-filter[data-v-a440d59c]{padding-left:max(var(--nav-filter-horizontal-padding),env(safe-area-inset-left));padding-right:max(var(--nav-filter-horizontal-padding),env(safe-area-inset-right))}}@media only screen and (max-width:1023px){.navigator-filter[data-v-a440d59c]{--nav-filter-horizontal-padding:20px;border:none;padding-top:10px;padding-bottom:10px;height:62px}}.navigator-filter .input-wrapper[data-v-a440d59c]{position:relative;flex:1;min-width:0}.navigator-filter .filter-component[data-v-a440d59c]{--input-vertical-padding:10px;--input-height:20px;--input-border-color:var(--color-grid);--input-text:var(--color-figure-gray-secondary)}.navigator-filter .filter-component[data-v-a440d59c] .filter__input{font-size:1rem;line-height:1.47059;font-weight:400;font-family:var(--typography-html-font,"Helvetica Neue","Helvetica","Arial",sans-serif)}.scroller[data-v-a440d59c]{height:100%;box-sizing:border-box;padding:var(--card-vertical-spacing) 0;padding-bottom:calc(var(--top-offset, 0px) + var(--card-vertical-spacing));transition:padding-bottom .15s ease-in}@media only screen and (max-width:1023px){.scroller[data-v-a440d59c]{padding-bottom:10em}}.scroller[data-v-a440d59c] .vue-recycle-scroller__item-wrapper{transform:translateZ(0)}.filter-wrapper[data-v-a440d59c]{position:sticky;bottom:0;background:var(--color-fill)}.sidebar-transitioning .filter-wrapper[data-v-a440d59c]{flex:1 0 73px;overflow:hidden}@media only screen and 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(max-width:735px){.title[data-v-c1de71de]{font-size:1.41176rem;line-height:1.33333;font-weight:400;font-family:var(--typography-html-font,"Helvetica Neue","Helvetica","Arial",sans-serif)}}.title p[data-v-c1de71de]{color:var(--colors-text,var(--color-text))}.assessments[data-v-c1de71de]{box-sizing:content-box;padding:0 1rem;background:var(--color-tutorial-assessments-background);margin-left:auto;margin-right:auto;width:980px;margin-bottom:80px}@media only screen and (max-width:1250px){.assessments[data-v-c1de71de]{width:692px}}@media only screen and (max-width:735px){.assessments[data-v-c1de71de]{width:87.5%}}.banner[data-v-c1de71de]{padding:40px 0;border-bottom:1px solid;margin-bottom:40px;border-color:var(--colors-grid,var(--color-grid));text-align:center}.success[data-v-c1de71de]{text-align:center;padding-bottom:40px;font-size:1.88235rem;line-height:1.25;font-weight:400;font-family:var(--typography-html-font,"Helvetica 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.eyebrow{font-size:1.11765rem;line-height:1.21053;font-weight:400;font-family:var(--typography-html-font,"Helvetica Neue","Helvetica","Arial",sans-serif)}}[data-v-54daa228] .eyebrow a{color:inherit}[data-v-54daa228] .heading{font-size:1.88235rem;line-height:1.25;font-weight:400;font-family:var(--typography-html-font,"Helvetica Neue","Helvetica","Arial",sans-serif)}@media only screen and (max-width:1250px){[data-v-54daa228] .heading{font-size:1.64706rem;line-height:1.28571;font-weight:400;font-family:var(--typography-html-font,"Helvetica Neue","Helvetica","Arial",sans-serif)}}@media only screen and (max-width:735px){[data-v-54daa228] .heading{font-size:1.41176rem;line-height:1.33333;font-weight:400;font-family:var(--typography-html-font,"Helvetica Neue","Helvetica","Arial",sans-serif)}}.expanded-intro[data-v-54daa228]{margin-left:auto;margin-right:auto;width:980px;margin-top:40px}@media only screen and (max-width:1250px){.expanded-intro[data-v-54daa228]{width:692px}}@media only screen 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+++ b/Sources/BigDecimal/BigDecimal.docc/BigDecimal.doccarchive/data/documentation/bigdecimal.json @@ -0,0 +1 @@ +{"primaryContentSections":[{"kind":"content","content":[{"anchor":"overview","level":2,"type":"heading","text":"Overview"},{"type":"paragraph","inlineContent":[{"type":"text","text":"Its functionality falls in the following categories:"}]},{"type":"unorderedList","items":[{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Arithmetic: addition, subtraction, multiplication, division, remainder and"},{"type":"text","text":" "},{"type":"text","text":"exponentiation"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Constants: pi, zero, one, ten"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Functions: exp, log, log10, log2, pow, sqrt, root, factorial, gamma,"},{"type":"text","text":" "},{"type":"text","text":"trig + inverse, hyperbolic + inverse"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Rounding and scaling according to one of the rounding modes:"}]},{"type":"unorderedList","items":[{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"awayFromZero"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"down"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"towardZero"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"toNearestOrEven"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"toNearestOrAwayFromZero"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"up"}]}]}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Comparison: the six standard operators "},{"type":"codeVoice","code":"=="},{"type":"text","text":", "},{"type":"codeVoice","code":"!="},{"type":"text","text":", "},{"type":"codeVoice","code":"<"},{"type":"text","text":", "},{"type":"codeVoice","code":"<="},{"type":"text","text":", "},{"type":"codeVoice","code":">"},{"type":"text","text":", and "},{"type":"codeVoice","code":">="}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Conversion: to String, to Double, to Decimal (the Swift Foundation type), to"},{"type":"text","text":" "},{"type":"text","text":"Decimal32 \/ Decimal64 \/ Decimal128"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Support for Decimal32, Decimal64 and Decimal128 values stored as UInt32,"},{"type":"text","text":" "},{"type":"text","text":"UInt64 and UInt128 values respectively, using Densely Packed Decimal (DPD)"},{"type":"text","text":" "},{"type":"text","text":"encoding or Binary Integer Decimal (BID) encoding"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Support for Decimal32, Decimal64 and Decimal128 mathematical operations"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Supports the IEEE 754 concepts of Infinity and NaN (Not a Number) with the"},{"type":"text","text":" "},{"type":"text","text":"latter having a "},{"type":"codeVoice","code":"signaling"},{"type":"text","text":" option."}]}]}]},{"anchor":"Dependencies","level":2,"type":"heading","text":"Dependencies"},{"type":"paragraph","inlineContent":[{"type":"text","text":"BigDecimal requires Swift from macOS 13.3+, iOS 16.4+, macCatalyst 16.4+,"},{"type":"text","text":" "},{"type":"text","text":"tvOS 16.4+, or watchOS 9.4+. It also requires that the "},{"type":"codeVoice","code":"Int"},{"type":"text","text":" type be a 64-bit"},{"type":"text","text":" "},{"type":"text","text":"type."}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"The BigDecimal package depends on the BigInt and UInt128 packages."}]},{"type":"codeListing","syntax":null,"code":["dependencies: ["," .package(url: \"https:\/\/github.com\/mgriebling\/BigInt.git\", from: \"2.0.0\"),"," .package(url: \"https:\/\/github.com\/mgriebling\/UInt128.git\", from: \"3.0.0\")","]"]},{"anchor":"Usage","level":2,"type":"heading","text":"Usage"},{"type":"paragraph","inlineContent":[{"type":"text","text":"In your project’s Package.swift file add a dependency like"}]},{"type":"codeListing","syntax":null,"code":["dependencies: ["," .package(url: \"https:\/\/github.com\/mgriebling\/BigDecimal.git\", from: \"2.0.0\"),","]"]},{"anchor":"Basics","level":2,"type":"heading","text":"Basics"},{"anchor":"Creating-BigDecimals","level":3,"type":"heading","text":"Creating BigDecimal’s"},{"type":"codeListing","syntax":"swift","code":["\/\/ From an integer","let x1 = BigDecimal(270) \/\/ = 270","let x2 = BigDecimal(270, -2) \/\/ = 2.70","let x3 = BigDecimal(314159265, -8) \/\/ = 3.14159265"," ","\/\/ From a BInt","let x4 = BigDecimal(BInt(314159265), -8) \/\/ = 3.14159265","let x5 = BigDecimal(BInt(100), -3) \/\/ = 0.100"," ","\/\/ From a string literal","let rnd1 = Rounding(.halfEven, 2)","let x6 = BigDecimal(\"0.123\").round(rnd1) \/\/ = 0.12","let x7 = BigDecimal(\"3.14159265\") \/\/ = 3.14159265"," ","\/\/ From a double","let rnd2 = Rounding(.halfEven, 9)","let x8 = BigDecimal(0.1).round(rnd2) \/\/ = 0.100000000","let x9 = BigDecimal(0.1) \/\/ = 0.1000000000000000055511151231257827021181583404541015625","let x10 = BigDecimal(3.14159265) \/\/ = 3.141592650000000208621031561051495373249053955078125","let x11 = BigDecimal(3.14159265).round(rnd2) \/\/ = 3.14159265","","\/\/ From Decimal32 \/ 64 \/ 128 encoded values","let x32 = BigDecimal(UInt32(0x223000f0), .dpd) \/\/ = 1.70","let x64 = BigDecimal(UInt64(0x22300000000000f0), .dpd) \/\/ = 1.70","let x128 = BigDecimal(UInt128(0x2207800000000000, 0x00000000000000f0), .dpd) \/\/ = 1.70"]},{"type":"paragraph","inlineContent":[{"type":"text","text":"Because Double values cannot represent all decimal values exactly,"},{"type":"text","text":" "},{"type":"text","text":"one sees that BigDecimal(0.1) is not exactly equal to 1 \/ 10 as one might expect."},{"type":"text","text":" "},{"type":"text","text":"On the other hand, BigDecimal(“0.1”) is in fact exactly equal to 1 \/ 10."}]},{"anchor":"Converting-BigDecimals","level":3,"type":"heading","text":"Converting BigDecimal’s"},{"type":"paragraph","inlineContent":[{"type":"reference","isActive":true,"identifier":"doc:\/\/BigDecimal\/documentation\/BigDecimal"},{"type":"text","text":" values can be converted to "},{"type":"codeVoice","code":"String"},{"type":"text","text":" values, "},{"type":"codeVoice","code":"Double"},{"type":"text","text":" values,"},{"type":"text","text":" "},{"type":"codeVoice","code":"Decimal"},{"type":"text","text":" (the Swift Foundation type) values, and "},{"type":"reference","isActive":true,"identifier":"doc:\/\/BigDecimal\/documentation\/BigDecimal\/Decimal32"},{"type":"text","text":", "},{"type":"reference","isActive":true,"identifier":"doc:\/\/BigDecimal\/documentation\/BigDecimal\/Decimal64"},{"type":"text","text":","},{"type":"text","text":" "},{"type":"text","text":"and "},{"type":"reference","isActive":true,"identifier":"doc:\/\/BigDecimal\/documentation\/BigDecimal\/Decimal128"},{"type":"text","text":" values."}]},{"anchor":"To-String","level":4,"type":"heading","text":"To String"},{"type":"codeListing","syntax":"swift","code":["let x1 = BigDecimal(\"2.1\").pow(3)","print(x1.asString()) \/\/ = 9.261"]},{"anchor":"To-Double","level":4,"type":"heading","text":"To Double"},{"type":"codeListing","syntax":"swift","code":["let x2 = BigDecimal(\"2.1\").pow(3)","print(x2.asDouble()) \/\/ = 9.261"]},{"anchor":"To-Decimal-the-Swift-Foundation-type","level":4,"type":"heading","text":"To Decimal (the Swift Foundation type)"},{"type":"codeListing","syntax":"swift","code":["let x3 = BigDecimal(\"1.70\")","let xd: Decimal = x3.asDecimal()","print(xd) \/\/ = 1.70"]},{"anchor":"To-Decimal32--64--128","level":4,"type":"heading","text":"To Decimal32 \/ 64 \/ 128"},{"type":"codeListing","syntax":"swift","code":["let x4 = BigDecimal(\"1.70\")","let x32: UInt32 = x4.asDecimal32(.dpd)","let x64: UInt64 = x4.asDecimal64(.dpd)","let x128: UInt128 = x4.asDecimal128(.dpd)","print(String(x32, radix: 16)) \/\/ = 223000f0","print(String(x64, radix: 16)) \/\/ = 22300000000000f0","print(String(x128, radix: 16)) \/\/ = 220780000000000000000000000000f0"]},{"anchor":"Comparing-BigDecimals","level":3,"type":"heading","text":"Comparing BigDecimal’s"},{"type":"paragraph","inlineContent":[{"type":"text","text":"The six standard operators == != < <= > >= are available to compare values."},{"type":"text","text":" "},{"type":"text","text":"The two operands may either be two "},{"type":"reference","isActive":true,"identifier":"doc:\/\/BigDecimal\/documentation\/BigDecimal"},{"type":"text","text":"’s or a "},{"type":"reference","isActive":true,"identifier":"doc:\/\/BigDecimal\/documentation\/BigDecimal"},{"type":"text","text":" and"},{"type":"text","text":" "},{"type":"text","text":"an integer. If neither of the operands is NaN, the operators perform as expected."},{"type":"text","text":" "},{"type":"text","text":"For example, -"},{"type":"reference","isActive":true,"identifier":"doc:\/\/BigDecimal\/documentation\/BigDecimal\/BigDecimal\/infinity"},{"type":"text","text":" is less than any finite number which in"},{"type":"text","text":" "},{"type":"text","text":"turn is less than +"},{"type":"reference","isActive":true,"identifier":"doc:\/\/BigDecimal\/documentation\/BigDecimal\/BigDecimal\/infinity"},{"type":"text","text":"."}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"Please see the section "},{"type":"emphasis","inlineContent":[{"type":"text","text":"About NaN’s"}]},{"type":"text","text":" for the rules governing comparison involving NaN’s."}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"The static function "},{"type":"codeVoice","code":"BigDecimal.maximum(x:y:)"},{"type":"text","text":" returns the non-NaN number if"},{"type":"text","text":" "},{"type":"text","text":"either x or y is NaN; otherwise it returns the larger of x and y."}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"The static function "},{"type":"codeVoice","code":"BigDecimal.minimum(x:y:)"},{"type":"text","text":" returns the non-NaN number if"},{"type":"text","text":" "},{"type":"text","text":"either x or y is NaN; otherwise it returns the smaller of x and y."}]},{"anchor":"Exact-Arithmetic","level":3,"type":"heading","text":"Exact Arithmetic"},{"type":"paragraph","inlineContent":[{"type":"text","text":"The ‘+’, ‘-’, and ‘*’ operators always produce exact results. The ‘\/’ operator"},{"type":"text","text":" "},{"type":"text","text":"truncates the exact result to an integer."}]},{"type":"codeListing","syntax":"swift","code":["let a = BigDecimal(\"25.1\")","let b = BigDecimal(\"12.0041\")","","print(a + b) \/\/ = 37.1041","print(a - b) \/\/ = 13.0959","print(a * b) \/\/ = 301.30291","print(a \/ b) \/\/ = 2"]},{"type":"paragraph","inlineContent":[{"type":"text","text":"The "},{"type":"emphasis","inlineContent":[{"type":"text","text":"quotientAndRemainder"}]},{"type":"text","text":" function produces an integer quotient and exact remainder"}]},{"type":"codeListing","syntax":"swift","code":["print(a.quotientAndRemainder(b)) \/\/ = (quotient: 2, remainder: 1.0918)"]},{"anchor":"Rounded-Arithmetic","level":3,"type":"heading","text":"Rounded Arithmetic"},{"type":"paragraph","inlineContent":[{"type":"text","text":"Rounding is controlled by Rounding objects that contain a rounding mode and a"},{"type":"text","text":" "},{"type":"text","text":"precision, which is the number of digits in the rounded result."}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"The rounding modes are:"}]},{"type":"unorderedList","items":[{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"awayFromZero - round away from 0"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"down - round towards -infinity"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"up - round towards +infinity"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"towardZero - round towards 0"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"toNearestOrEven - round to nearest, ties to even"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"toNearestOrAwayFromZero - round to nearest, ties away from 0"}]}]}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"The "},{"type":"emphasis","inlineContent":[{"type":"text","text":"add"}]},{"type":"text","text":", "},{"type":"emphasis","inlineContent":[{"type":"text","text":"subtract"}]},{"type":"text","text":" and "},{"type":"emphasis","inlineContent":[{"type":"text","text":"multiply"}]},{"type":"text","text":" methods have a Rounding parameter that"},{"type":"text","text":" "},{"type":"text","text":"controls how the result is rounded."}]},{"anchor":"Examples","level":4,"type":"heading","text":"Examples"},{"type":"codeListing","syntax":"swift","code":["let a = BigDecimal(\"25.1E-2\")","let b = BigDecimal(\"12.0041E-3\")","let rnd = Rounding(.ceiling, 3)","\t","print(a + b) \/\/ = 0.2630041","print(a.add(b, rnd)) \/\/ = 0.264","print(a - b) \/\/ = 0.2389959","print(a.subtract(b, rnd)) \/\/ = 0.239","print(a * b) \/\/ = 0.0030130291","print(a.multiply(b, rnd)) \/\/ = 0.00302"]},{"anchor":"Precise-division","level":3,"type":"heading","text":"Precise division"},{"type":"paragraph","inlineContent":[{"type":"text","text":"The "},{"type":"emphasis","inlineContent":[{"type":"text","text":"divide"}]},{"type":"text","text":" method, that has an optional rounding parameter, performs division."},{"type":"text","text":" "},{"type":"text","text":"If the quotient has finite decimal expansion, the rounding parameter may or may not be present, it is used if it is there."},{"type":"text","text":" "},{"type":"text","text":"If the quotient has infinite decimal expansion, the rounding parameter must be present and is used to round the result."}]},{"anchor":"Examples","level":4,"type":"heading","text":"Examples"},{"type":"codeListing","syntax":"swift","code":["let x1 = BigDecimal(3)","let x2 = BigDecimal(48)","print(x1.divide(x2)) \/\/ = 0.0625","let rnd = Rounding(.ceiling, 2)","print(x1.divide(x2, rnd)) \/\/ = 0.063","\t","let x3 = BigDecimal(3)","let x4 = BigDecimal(49)","print(x3.divide(x4)) \/\/ = NaN because the quotient has infinite decimal expansion 0.06122448...","print(x3.divide(x4, rnd)) \/\/ = 0.062"]},{"anchor":"Data-Encoding","level":2,"type":"heading","text":"Data Encoding"},{"type":"paragraph","inlineContent":[{"type":"text","text":"BigDecimal’s can be encoded as Data objects (perhaps for long term storage) using the "},{"type":"emphasis","inlineContent":[{"type":"text","text":"asData"}]},{"type":"text","text":" method,"},{"type":"text","text":" "},{"type":"text","text":"and they can be regenerated from their Data encoding using the appropriate initializer."},{"type":"text","text":" "},{"type":"text","text":"The encoding rules are:"}]},{"type":"unorderedList","items":[{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"The encoding contains nine or more bytes. The first eight bytes is a"},{"type":"text","text":" "},{"type":"text","text":"Big Endian encoding of the signed exponent."},{"type":"text","text":" "},{"type":"text","text":"The remaining bytes is a Big Endian encoding of the signed significand."}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"NaN’s (and signaling NaNs) are encoded as a single byte = 0"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"positive infinity is encoded as a single byte = 1"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"negative infinity is encoded as a single byte = 2"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"negative zero is encoded as a single byte = 3"}]}]}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"It is also possible to encode BigDecimal’s using the "},{"type":"codeVoice","code":"JSONEncoder"},{"type":"text","text":" or as a"},{"type":"text","text":" "},{"type":"text","text":"property list using the "},{"type":"codeVoice","code":"PropertyListEncoder"},{"type":"text","text":" as in the second example."}]},{"anchor":"Examples","level":3,"type":"heading","text":"Examples"},{"type":"codeListing","syntax":"swift","code":["let x1 = BigDecimal(1000, 3) \/\/ = 1000000","print(Bytes(x1.asData())) \/\/ = [0, 0, 0, 0, 0, 0, 0, 3, 3, 232]","","let x2 = BigDecimal(1000, -3) \/\/ = 1.000","print(Bytes(x2.asData())) \/\/ = [255, 255, 255, 255, 255, 255, 255, 253, 3, 232]","","let x3 = BigDecimal(-1000, 3) \/\/ = -1000000","print(Bytes(x3.asData())) \/\/ = [0, 0, 0, 0, 0, 0, 0, 3, 252, 24]","","let x4 = BigDecimal(-1000, -3) \/\/ = -1.000","print(Bytes(x4.asData())) \/\/ = [255, 255, 255, 255, 255, 255, 255, 253, 252, 24]"]},{"type":"codeListing","syntax":"swift","code":["let encoder = JSONEncoder()","let x1 = BigDecimal(1000, 3) \/\/ = 1000000","if let encoded = try? encoder.encode(x1) {"," \/\/ save `encoded` data somewhere or",""," \/\/ extract the JSON string from the data"," if let json = String(data: encoded, encoding: .utf8) {"," print(json)"," }","}"]},{"anchor":"Decimal-Formats","level":2,"type":"heading","text":"Decimal Formats"},{"type":"paragraph","inlineContent":[{"type":"text","text":"Decimal values can be represented not only as BigDecimal’s but also as Double values,"},{"type":"text","text":" "},{"type":"text","text":"Decimal (the Swift Foundation type) values, and Decimal32 \/ 64 \/ 128 values."},{"type":"text","text":" "},{"type":"text","text":"The strategy for working with other than BigDecimal values can be summarized as follows:"}]},{"type":"unorderedList","items":[{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"convert the input values to BigDecimal’s using the appropriate initializer"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"compute the results"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"convert the results back to the desired output format using the appropriate conversion function"}]}]}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"As an example, suppose you must compute the average value of three values a, b and c which are encoded as Decimal32 values using Densely Packed Decimal (DPD) encoding."},{"type":"text","text":" "},{"type":"text","text":"The result x must likewise be a Decimal32 value encoded using DPD."}]},{"type":"codeListing","syntax":"swift","code":["\/\/ Input values","let a = UInt32(0x223e1117) \/\/ = 7042.17 DPD encoded","let b = UInt32(0x22300901) \/\/ = 22.01 DPD encoded","let c = UInt32(0xa230cc00) \/\/ = -330.00 DPD encoded","\t","\/\/ Convert to BigDecimal's","let A = BigDecimal(a, .dpd)","let B = BigDecimal(b, .dpd)","let C = BigDecimal(c, .dpd)","\t","\/\/ Compute result","let X = (A + B + C).divide(3, Rounding.decimal32)","print(X) \/\/ = 2244.727","\t","\/\/ Convert result back to Decimal32","let x = X.asDecimal32(.dpd)","print(String(x, radix: 16)) \/\/ = 2a2513a7 (= 2244.727 DPD encoded)"]},{"anchor":"About-Infinities","level":2,"type":"heading","text":"About Infinities"},{"type":"paragraph","inlineContent":[{"type":"text","text":"The constants "},{"type":"codeVoice","code":"BigDecimal.infinity"},{"type":"text","text":" and "},{"type":"codeVoice","code":"-BigDecimal.infinity"},{"type":"text","text":" represent"},{"type":"text","text":" "},{"type":"text","text":"+Infinity and -Infinity respectively."},{"type":"text","text":" "},{"type":"codeVoice","code":"-infinity"},{"type":"text","text":" compares less than every finite number,"},{"type":"text","text":" "},{"type":"text","text":"and every finite number compares less than "},{"type":"codeVoice","code":"infinity"},{"type":"text","text":". Arithmetic operations"},{"type":"text","text":" "},{"type":"text","text":"involving infinite values is illustrated by the examples below:"}]},{"type":"codeListing","syntax":"swift","code":["let InfP = BigDecimal.infinity \/\/ Just to save some writing","let InfN = -BigDecimal.infinity","","print(InfP + 3) \/\/ +Infinity","print(InfN + 3) \/\/ -Infinity","print(InfP + InfP) \/\/ +Infinity","print(InfP - InfP) \/\/ NaN","print(InfP * 3) \/\/ +Infinity","print(InfP * InfP) \/\/ +Infinity","print(InfP * InfN) \/\/ -Infinity","print(InfP * 0) \/\/ NaN","print(InfP \/ 3) \/\/ +Infinity","print(InfP \/ 0) \/\/ +Infinity","print(1 \/ InfP) \/\/ 0","print(1 \/ InfN) \/\/ 0","print(InfP \/ InfP) \/\/ NaN","print(InfP < InfP) \/\/ false","print(InfP == InfP) \/\/ true","print(InfP != InfP) \/\/ false","print(InfP > InfP) \/\/ false","print(Rounding.decimal32.round(InfP)) \/\/ +Infinity","print(InfP.scale(4)) \/\/ +Infinity","print(InfP.scale(-4)) \/\/ +Infinity","print(InfP.withExponent(10, .up)) \/\/ NaN"]},{"anchor":"About-NaNs","level":2,"type":"heading","text":"About NaN’s"},{"type":"paragraph","inlineContent":[{"type":"text","text":"The IEEE 754 standard specifies two NaN’s, a quiet NaN (qNaN) and a signaling NaN (sNaN)."},{"type":"text","text":" "},{"type":"text","text":"The constant "},{"type":"emphasis","inlineContent":[{"type":"text","text":"BigDecimal.NaN"}]},{"type":"text","text":" corresponds to the quiet NaN and"},{"type":"text","text":" "},{"type":"codeVoice","code":"BigDecimal.signalingNan"},{"type":"text","text":" to the signaling NaN."}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"Arithmetic operations where one or more input is NaN, return NaN as result."},{"type":"text","text":" "},{"type":"text","text":"Comparing NaN values is illustrated by the example below:"}]},{"type":"codeListing","syntax":"swift","code":["let NaN = BigDecimal.NaN \/\/ Just to save some writing","\t","print(3 < NaN) \/\/ false","print(NaN < 3) \/\/ false","print(NaN < NaN) \/\/ false","print(3 <= NaN) \/\/ false","print(NaN <= 3) \/\/ false","print(NaN <= NaN) \/\/ false","print(3 > NaN) \/\/ false","print(NaN > 3) \/\/ false","print(NaN > NaN) \/\/ false","print(3 >= NaN) \/\/ false","print(NaN >= 3) \/\/ false","print(NaN >= NaN) \/\/ false","print(3 == NaN) \/\/ false","print(NaN == 3) \/\/ false","print(NaN == NaN) \/\/ false","print(3 != NaN) \/\/ true","print(NaN != 3) \/\/ true","print(NaN != NaN) \/\/ true !!!"]},{"type":"paragraph","inlineContent":[{"type":"text","text":"Because NaN != NaN is true, sorting a collection of BigDecimal’s doesn’t"},{"type":"text","text":" "},{"type":"text","text":"work if the collection contains one or more NaN’s. This is so, even if"},{"type":"text","text":" "},{"type":"text","text":"BigDecimal conforms to the Comparable protocol. Note: It is possible to"},{"type":"text","text":" "},{"type":"text","text":"sort values including NaNs using the "},{"type":"codeVoice","code":"isTotallyOrdered(belowOrEqualTo:)"},{"type":"text","text":" "},{"type":"text","text":"method."}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"The following example uses "},{"type":"codeVoice","code":"isTotallyOrdered(belowOrEqualTo:)"},{"type":"text","text":" to sort an"},{"type":"text","text":" "},{"type":"text","text":"array of floating-point values, including some that are NaN:"}]},{"type":"codeListing","syntax":"swift","code":["var numbers = [2.5, 21.25, 3.0, .nan, -9.5]","numbers.sort { !$1.isTotallyOrdered(belowOrEqualTo: $0) }","print(numbers)","\/\/ Prints \"[-9.5, 2.5, 3.0, 21.25, nan]\""]},{"type":"paragraph","inlineContent":[{"type":"text","text":"There is a static boolean variable "},{"type":"emphasis","inlineContent":[{"type":"text","text":"BigDecimal.NaNFlag"}]},{"type":"text","text":" which is set to"},{"type":"text","text":" "},{"type":"emphasis","inlineContent":[{"type":"text","text":"true"}]},{"type":"text","text":" whenever a NaN value is generated. It can be set to "},{"type":"emphasis","inlineContent":[{"type":"text","text":"false"}]},{"type":"text","text":" by"},{"type":"text","text":" "},{"type":"text","text":"application code. Therefore, to check if a sequence of code generates NaN,"},{"type":"text","text":" "},{"type":"text","text":"set NaNFlag to "},{"type":"emphasis","inlineContent":[{"type":"text","text":"false"}]},{"type":"text","text":" before the code and check it after the code. Since"},{"type":"text","text":" "},{"type":"text","text":"a BigDecimal has a stored property "},{"type":"emphasis","inlineContent":[{"type":"text","text":"isNaN"}]},{"type":"text","text":", it is of course also possible to"},{"type":"text","text":" "},{"type":"text","text":"check for a NaN value at any time."}]},{"anchor":"References","level":2,"type":"heading","text":"References"},{"type":"paragraph","inlineContent":[{"type":"text","text":"Algorithms from the following books and papers have been used in the implementation."},{"type":"text","text":" "},{"type":"text","text":"There are references in the source code where appropriate."}]},{"type":"unorderedList","items":[{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"[GRANLUND] - Moller and Granlund: Improved Division by Invariant Integers, 2011"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"[IEEE] - IEEE Standard for Floating-Point Arithmetic, 2019"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"[KNUTH] - Donald E. Knuth: Seminumerical Algorithms, Addison-Wesley 1971"}]}]}]},{"anchor":"Acknowledgement","level":2,"type":"heading","text":"Acknowledgement"},{"type":"orderedList","items":[{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Much of the original "},{"type":"reference","isActive":true,"identifier":"https:\/\/github.com\/leif-ibsen\/BigDecimal.git"},{"type":"text","text":" (pre-V2) was created by Leif Ibsen."}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Some unit test cases come from the "},{"type":"reference","isActive":true,"identifier":"http:\/\/speleotrove.com\/decimal"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Additional unit test cases and some algorithms are from the"},{"type":"text","text":" "},{"type":"reference","isActive":true,"identifier":"https:\/\/www.intel.com\/content\/www\/us\/en\/developer\/articles\/tool\/intel-decimal-floating-point-math-library.html"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"Floating point math functions are translated to Swift from the"},{"type":"text","text":" "},{"type":"reference","isActive":true,"identifier":"https:\/\/github.com\/eobermuhlner\/big-math"},{"type":"text","text":" implementation by Eric Obermühlner."}]}]}]}]}],"schemaVersion":{"major":0,"minor":3,"patch":0},"sections":[],"variants":[{"paths":["\/documentation\/bigdecimal"],"traits":[{"interfaceLanguage":"swift"}]}],"identifier":{"url":"doc:\/\/BigDecimal\/documentation\/BigDecimal","interfaceLanguage":"swift"},"abstract":[{"type":"text","text":"The BigDecimal package provides arbitrary-precision (with an adjustable upper"},{"type":"text","text":" "},{"type":"text","text":"limit for performance) and fixed-precision decimal arithmetic in 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