Commit `53684aa7d7`

53684aa7d7e9ec4ddae59466cc2c00a5b23c56e6

parent: ff45d11a82

Verified · cmc

cmc <hello@cleberg.net> · 2026-10-07 23:22 UTC

Support the F formula flag: exact fractions

With ;F Calc keeps integer division exact, as calc-prefer-frac does:
fractions shown as n:d, exact through +, -, *, /, powers, vmean and the
variances, and exact square roots of square fractions; a float in the
expression gives a float.

Layout: unified · split

Sources/OrgCore/Compute/Calc.swift +80 −14

		@@ -26,6 +26,8 @@ public enum Calc {
26	26	/// A date form: the day number, with the time of day as a fraction.
27	27	case date(Value)
28	28	case nan
	29	/// An exact fraction, reduced, the denominator above 1 (`calc-prefer-frac`).
	30	case frac(Int, Int)
29	31	}
30	32
31	33	public enum FloatFormat: Equatable, Sendable {
		@@ -36,6 +38,8 @@ public enum Calc {
36	38	public var precision = 12
37	39	public var format = FloatFormat.float(8)
38	40	public var degrees = true
	41	/// `calc-prefer-frac`: dividing integers gives a fraction.
	42	public var preferFractions = false
39	43	public init() {}
40	44	}
41	45
		@@ -111,15 +115,48 @@ public enum Calc {
111	115	switch v {
112	116	case .int(let i): return (Int128(i), 0)
113	117	case .float(let m, let e): return (Int128(m), e)
	118	case .frac(let n, let d): return try parts(try divide(.int(n), .int(d)))
114	119	case .vector: throw Unsupported("vector arithmetic")
115	120	case .date, .nan: throw Unsupported("date arithmetic")
116	121	}
117	122	}
118	123
	124	/// An integer or a fraction as numerator and denominator.
	125	static func rational(_ v: Value) -> (Int, Int)? {
	126	switch v {
	127	case .int(let i): (i, 1)
	128	case .frac(let n, let d): (n, d)
	129	default: nil
	130	}
	131	}
	132
	133	/// `math-make-frac`: reduced, as an integer when it is one.
	134	static func fraction(_ n: Int, _ d: Int) throws -> Value {
	135	guard d != 0 else { throw Unsupported("division by zero") }
	136	guard n != .min, d != .min else { throw Unsupported("integer size") }
	137	func gcd(_ a: Int, _ b: Int) -> Int { b == 0 ? abs(a) : gcd(b, a % b) }
	138	let g = gcd(n, d)
	139	var (num, den) = (n / g, d / g)
	140	if den < 0 { (num, den) = (-num, -den) }
	141	return den == 1 ? .int(num) : .frac(num, den)
	142	}
	143
	144	/// Two rationals, one of them a fraction, combined exactly; nil otherwise.
	145	static func exact(_ a: Value, _ b: Value, _ op: (Int, Int, Int, Int) -> (Int, Int, Bool)) throws -> Value? {
	146	var fraction = false
	147	if case .frac = a { fraction = true }
	148	if case .frac = b { fraction = true }
	149	guard fraction, let (n1, d1) = rational(a), let (n2, d2) = rational(b) else { return nil }
	150	let (n, d, overflow) = op(n1, d1, n2, d2)
	151	if overflow { throw Unsupported("integer size") }
	152	return try self.fraction(n, d)
	153	}
	154
119	155	static func double(_ v: Value) throws -> Double {
120	156	switch v {
121	157	case .int(let i): return Double(i)
122	158	case .float(let m, let e): return Double(m) * pow(10, Double(e))
	159	case .frac(let n, let d): return Double(n) / Double(d)
123	160	case .vector: throw Unsupported("vector arithmetic")
124	161	case .date, .nan: throw Unsupported("date arithmetic")
125	162	}
		@@ -150,6 +187,13 @@ public enum Calc {
150	187	if overflow { throw Unsupported("integer size") }
151	188	return .int(sum)
152	189	}
	190	if let sum = try exact(a, b, { n1, d1, n2, d2 in
	191	let (p, o1) = n1.multipliedReportingOverflow(by: d2)
	192	let (q, o2) = n2.multipliedReportingOverflow(by: d1)
	193	let (n, o3) = p.addingReportingOverflow(q)
	194	let (d, o4) = d1.multipliedReportingOverflow(by: d2)
	195	return (n, d, o1 \|\| o2 \|\| o3 \|\| o4)
	196	}) { return sum }
153	197	let (m1, e1) = try parts(a)
154	198	let (m2, e2) = try parts(b)
155	199	if m1 == 0 { return try makeFloat(m2, e2) }
		@@ -169,6 +213,7 @@ public enum Calc {
169	213	guard i != .min else { throw Unsupported("integer size") }
170	214	return .int(-i)
171	215	case .float(let m, let e): return .float(-m, e)
	216	case .frac(let n, let d): return .frac(-n, d)
172	217	case .vector: throw Unsupported("vector arithmetic")
173	218	case .date: throw Unsupported("date arithmetic")
174	219	case .nan: return .nan
		@@ -195,6 +240,11 @@ public enum Calc {
195	240	if overflow { throw Unsupported("integer size") }
196	241	return .int(product)
197	242	}
	243	if let product = try exact(a, b, { n1, d1, n2, d2 in
	244	let (n, o1) = n1.multipliedReportingOverflow(by: n2)
	245	let (d, o2) = d1.multipliedReportingOverflow(by: d2)
	246	return (n, d, o1 \|\| o2)
	247	}) { return product }
198	248	let (m1, e1) = try parts(a)
199	249	let (m2, e2) = try parts(b)
200	250	let (product, overflow) = m1.multipliedReportingOverflow(by: m2)
		@@ -202,8 +252,16 @@ public enum Calc {
202	252	return try makeFloat(product, e1 + e2)
203	253	}
204	254
205		static func divide(_ a: Value, _ b: Value) throws -> Value {
	255	static func divide(_ a: Value, _ b: Value, fractions: Bool = false) throws -> Value {
206	256	if isNaN(a, b) { return .nan }
	257	if fractions \|\| { if case .frac = a { return true }; if case .frac = b { return true }; return false }(),
	258	let (n1, d1) = rational(a), let (n2, d2) = rational(b) {
	259	guard n2 != 0 else { throw Unsupported("division by zero") }
	260	let (n, o1) = n1.multipliedReportingOverflow(by: d2)
	261	let (d, o2) = d1.multipliedReportingOverflow(by: n2)
	262	if o1 \|\| o2 { throw Unsupported("integer size") }
	263	return try fraction(n, d)
	264	}
207	265	if case .int(let x) = a, case .int(let y) = b {
208	266	guard y != 0 else { throw Unsupported("division by zero") }
209	267	if x % y == 0 { return .int(x / y) }
		@@ -223,8 +281,8 @@ public enum Calc {
223	281	}
224	282
225	283	/// `math-ipow`.
226		static func integerPower(_ a: Value, _ n: Int) throws -> Value {
227		if n < 0 { return try integerPower(try divide(.int(1), a), -n) }
	284	static func integerPower(_ a: Value, _ n: Int, fractions: Bool = false) throws -> Value {
	285	if n < 0 { return try integerPower(try divide(.int(1), a, fractions: fractions), -n) }
228	286	if n == 0 { return .int(1) }
229	287	if n == 1 { return a }
230	288	let square = try multiply(a, a)
		@@ -232,9 +290,9 @@ public enum Calc {
232	290	return try multiply(a, try integerPower(square, n / 2))
233	291	}
234	292
235		static func power(_ a: Value, _ b: Value) throws -> Value {
	293	static func power(_ a: Value, _ b: Value, fractions: Bool = false) throws -> Value {
236	294	if isNaN(a, b) { return .nan }
237		if case .int(let n) = b { return try integerPower(a, n) }
	295	if case .int(let n) = b { return try integerPower(a, n, fractions: fractions) }
238	296	let base = try double(a)
239	297	guard base >= 0 else { throw Unsupported("complex result") }
240	298	return try fromDouble(pow(base, try double(b)))
		@@ -254,6 +312,7 @@ public enum Calc {
254	312	static func format(_ value: Value, _ floatFormat: FloatFormat) throws -> String {
255	313	switch value {
256	314	case .int(let i): return String(i)
	315	case .frac(let n, let d): return "\(n):\(d)"
257	316	case .vector: throw Unsupported("vector result")
258	317	case .nan: return "nan"
259	318	case .date(let d): return "<" + (try formatDate(d)) + ">"
		@@ -577,10 +636,10 @@ public enum Calc {
577	636	case "+": return try add(a, b)
578	637	case "-": return try subtract(a, b)
579	638	case "*": return try multiply(a, b)
580		case "/": return try divide(a, b)
	639	case "/": return try divide(a, b, fractions: modes.preferFractions)
581	640	case "%": return try mod(a, b)
582	641	case "\\": return try idiv(a, b)
583		case "^": return try power(a, b)
	642	case "^": return try power(a, b, fractions: modes.preferFractions)
584	643	case "\|": return .int(try truth(a) \|\| truth(b) ? 1 : 0)
585	644	case "&": return .int(try truth(a) && truth(b) ? 1 : 0)
586	645	default:
		@@ -640,7 +699,7 @@ public enum Calc {
640	699	func deviations(_ args: [Value]) throws -> (Value, Int) {
641	700	let items = try elements(args)
642	701	guard !items.isEmpty else { throw Unsupported("empty vector") }
643		let mean = try divide(try items.reduce(Value.int(0)) { try add($0, $1) }, .int(items.count))
	702	let mean = try divide(try items.reduce(Value.int(0)) { try add($0, $1) }, .int(items.count), fractions: modes.preferFractions)
644	703	let squares = try items.reduce(Value.int(0)) { sum, x in
645	704	let d = try subtract(x, mean)
646	705	return try add(sum, try multiply(d, d))
		@@ -678,7 +737,7 @@ public enum Calc {
678	737	case "vmean":
679	738	let items = try elements(args)
680	739	guard !items.isEmpty else { throw Unsupported("empty vector") }
681		return try divide(try items.reduce(Value.int(0)) { try add($0, $1) }, .int(items.count))
	740	return try divide(try items.reduce(Value.int(0)) { try add($0, $1) }, .int(items.count), fractions: modes.preferFractions)
682	741	case "vmax", "vmin":
683	742	let items = try elements(args)
684	743	guard var best = items.first else { throw Unsupported("empty vector") }
		@@ -700,7 +759,7 @@ public enum Calc {
700	759	let (squares, n) = try deviations(args)
701	760	let population = name == "vpvar" \|\| name == "vpsdev"
702	761	if !population, n < 2 { throw Unsupported("variance of one value") }
703		let variance = try divide(squares, .int(population ? n : n - 1))
	762	let variance = try divide(squares, .int(population ? n : n - 1), fractions: modes.preferFractions)
704	763	return name.hasSuffix("sdev") ? try root(variance) : variance
705	764	case "mod":
706	765	guard args.count == 2 else { throw Unsupported("arguments") }
		@@ -725,7 +784,8 @@ public enum Calc {
725	784	let x = try one(args)
726	785	return try compare(x, .int(0)) < 0 ? try negate(x) : x
727	786	case "floor", "ceil", "trunc":
728		let x = try one(args)
	787	var x = try one(args)
	788	if case .frac(let n, let d) = x { x = try divide(.int(n), .int(d)) }
729	789	if case .int = x { return x }
730	790	let d = try double(x)
731	791	let r = name == "floor" ? d.rounded(.down) : name == "ceil" ? d.rounded(.up) : d.rounded(.towardZero)
		@@ -733,7 +793,8 @@ public enum Calc {
733	793	return .int(i)
734	794	case "round":
735	795	guard args.count == 1 \|\| args.count == 2 else { throw Unsupported("arguments") }
736		let x = args[0]
	796	var x = args[0]
	797	if case .frac(let n, let d) = x { x = try divide(.int(n), .int(d)) }
737	798	if args.count == 2 {
738	799	guard case .int(let places) = args[1] else { throw Unsupported("arguments") }
739	800	guard case .float(let m, let e) = x else { return x }
		@@ -744,11 +805,16 @@ public enum Calc {
744	805	return .int(i)
745	806	case "sqrt":
746	807	let x = try one(args)
	808	func exactRoot(_ i: Int) -> Int? {
	809	guard i >= 0 else { return nil }
	810	let root = Int(Double(i).squareRoot().rounded())
	811	return root.multipliedReportingOverflow(by: root) == (i, false) ? root : nil
	812	}
747	813	if case .int(let i) = x {
748	814	guard i >= 0 else { throw Unsupported("complex result") }
749		let root = Int(Double(i).squareRoot().rounded())
750		if root * root == i { return .int(root) }
	815	if let root = exactRoot(i) { return .int(root) }
751	816	}
	817	if case .frac(let n, let d) = x, let rn = exactRoot(n), let rd = exactRoot(d) { return try fraction(rn, rd) }
752	818	let d = try double(x)
753	819	guard d >= 0 else { throw Unsupported("complex result") }
754	820	return try fromDouble(d.squareRoot())

Sources/OrgCore/Compute/TableFormulas.swift +1

		@@ -537,6 +537,7 @@ extension EmacsBuffer {
537	537	case "N": mode.numbers = true
538	538	case "L": literal = true
539	539	case "E": mode.keepEmpty = true
	540	case "F": modes.preferFractions = true
540	541	case "D": modes.degrees = true
541	542	case "R": modes.degrees = false
542	543	default: throw Calc.Unsupported("format flag \(ns.substring(with: m.range))")

Tests/OrgCoreTests/TableFormulaTests.swift +2

		@@ -54,6 +54,8 @@ struct TableFormulaTests {
54	54	"\| \| a \| b \|\n\|---+---+---\|\n\| \| 2 \| \|\n\| \| 3 \| \|\n\| $ \| %=%.2f \| \|\n#+TBLFM: $3=$2/3;\n",
55	55	"\| a \| b \|\n\|---+---\|\n\| 4 \| \|\n\| 9 \| \|\n#+TBLFM: $2=vsdev(@I$1..@II$1)+fact(3)\n",
56	56	"\| a \| b \|\n\|---+---\|\n\| 1 \| \|\n\| 2 \| \|\n#+TBLFM: @-1$2=5\n",
	57	"\| a \| b \| f \|\n\|---+---+---\|\n\| 1 \| 3 \| \|\n\| 7 \| 2 \| \|\n\| -7 \| 2 \| \|\n\| 6 \| 3 \| \|\n\| 1 \| 0.5 \| \|\n\| 4 \| 6 \| \|\n#+TBLFM: $3=$1/$2;F\n",
	58	"\| a \|\n\|---\|\n\| \|\n\| \|\n\| \|\n\| \|\n\| \|\n\| \|\n\| \|\n\| \|\n\| \|\n#+TBLFM: @2$1=1/3+1/6;F::@3$1=(1/3)^2;F::@4$1=vsum([1/2,1/3]);F::@5$1=1/3*3;F::@6$1=sqrt(1/4);F::@7$1=vmean([1,2]);F::@8$1=2^-2;F::@9$1=abs(-1/3)+max(1/3,1/4);F::@10$1=round(7/2)+floor(7/2);F\n",
57	59	]
58	60
59	61	@Test func remoteFindsTablesByIDInOtherFiles() {

Commit 53684aa7d7

Commit `53684aa7d7`