From 4dab5d0c1a6393c82dbabb9e76ffea0ec982b4ff Mon Sep 17 00:00:00 2001
From: qntm <qntm@users.noreply.github.com>
Date: Sat, 20 Jul 2024 02:06:21 +0100
Subject: [PATCH] Adjust Second constructor

---
 src/munge.js           |  10 +-
 src/rat.js             |   2 +-
 src/second.js          |  18 +-
 test/converter.spec.js |  25 +--
 test/exact.spec.js     |  57 +++---
 test/munge.spec.js     | 452 ++++++++++++++++++++---------------------
 test/second.spec.js    |  55 ++---
 test/segment.spec.js   |   6 +-
 8 files changed, 306 insertions(+), 319 deletions(-)

diff --git a/src/munge.js b/src/munge.js
index 80176b0..de13cb7 100644
--- a/src/munge.js
+++ b/src/munge.js
@@ -34,7 +34,7 @@ export const MODELS = {
 }
 
 const NOV = 10
-const secondsPerDay = new Second(86_400n, 1n)
+const secondsPerDay = new Second(new Rat(86_400n, 1n))
 const mjdEpoch = {
   unix: Second.fromMillis(Date.UTC(1858, NOV, 17))
 }
@@ -63,20 +63,20 @@ export const munge = (data, model) => {
     // Convert from a floating point number to a precise ratio
     // Offsets are given in TAI seconds to seven decimal places, e.g. `1.422_818_0`.
     // So we have to do some rounding
-    offsetAtRoot.atomic = new Second(
+    offsetAtRoot.atomic = new Second(new Rat(
       BigInt(Math.round(offsetAtRoot.atomicFloat * 10_000_000)),
       BigInt(10_000_000)
-    )
+    ))
 
     root.unix = mjdEpoch.unix.plusS(secondsPerDay.timesR(new Rat(BigInt(root.mjds))))
 
     // Convert from a floating point number to a precise ratio
     // Drift rates are given in TAI seconds to seven decimal places, e.g. `0.001_123_2`
     // So we have to do some rounding
-    driftRate.atomicPerUnixDay = new Second(
+    driftRate.atomicPerUnixDay = new Second(new Rat(
       BigInt(Math.round(driftRate.atomicPerUnixDayFloat * 10_000_000)),
       BigInt(10_000_000)
-    )
+    ))
     driftRate.atomicPerUnix = driftRate.atomicPerUnixDay.divideS(secondsPerDay)
 
     const slope = {}
diff --git a/src/rat.js b/src/rat.js
index b561742..0df865d 100644
--- a/src/rat.js
+++ b/src/rat.js
@@ -17,7 +17,7 @@ export class Rat {
     const g2 = (de < 0) === (g < 0) ? g : -g
 
     this.nu = nu / g2 // sign of `this.nu` is the sign of the represented rational
-    this.de = de / g2 // non-negative
+    this.de = de / g2 // positive
   }
 
   plus (other) {
diff --git a/src/second.js b/src/second.js
index 8c17fe3..49e2e3d 100644
--- a/src/second.js
+++ b/src/second.js
@@ -1,28 +1,24 @@
 import { Rat } from './rat.js'
 
 export class Second {
-  constructor (nu, de) {
-    this.rat = new Rat(nu, de)
+  constructor (rat) {
+    this.rat = rat
   }
 
   plusS (other) {
-    const sum = this.rat.plus(other.rat)
-    return new Second(sum.nu, sum.de)
+    return new Second(this.rat.plus(other.rat))
   }
 
   minusS (other) {
-    const difference = this.rat.minus(other.rat)
-    return new Second(difference.nu, difference.de)
+    return new Second(this.rat.minus(other.rat))
   }
 
   timesR (other) {
-    const product = this.rat.times(other)
-    return new Second(product.nu, product.de)
+    return new Second(this.rat.times(other))
   }
 
   divideR (other) {
-    const quotient = this.rat.divide(other)
-    return new Second(quotient.nu, quotient.de)
+    return new Second(this.rat.divide(other))
   }
 
   divideS (other) {
@@ -51,7 +47,7 @@ Second.fromMillis = millis => {
     throw Error(`Not an integer: ${millis}`)
   }
 
-  return new Second(BigInt(millis), 1_000n)
+  return new Second(new Rat(BigInt(millis), 1_000n))
 }
 
 Second.END_OF_TIME = Symbol('end of time')
diff --git a/test/converter.spec.js b/test/converter.spec.js
index d035878..a9dfac8 100644
--- a/test/converter.spec.js
+++ b/test/converter.spec.js
@@ -3,6 +3,7 @@ import { describe, it } from 'mocha'
 import { Converter } from '../src/converter.js'
 import { MODELS } from '../src/munge.js'
 import { Range } from '../src/range.js'
+import { Rat } from '../src/rat.js'
 import { Second } from '../src/second.js'
 
 const JAN = 0
@@ -267,7 +268,7 @@ describe('Converter', () => {
           ])
         assert.deepStrictEqual(converter.unixToAtomic(Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1))),
           [
-            new Range(Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1)).plusS(new Second(1n, 86_400_000n)))
+            new Range(Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1)).plusS(new Second(new Rat(1n, 86_400_000n))))
           ])
 
         // SMEAR MIDPOINT
@@ -279,7 +280,7 @@ describe('Converter', () => {
         // SMEAR ENDS, ATOMIC IS A FULL SECOND AHEAD (actually Unix is a full second behind)
         assert.deepStrictEqual(converter.unixToAtomic(Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 59, 999))),
           [
-            new Range(Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 59, 999)).plusS(new Second(86_399_999n, 86_400_000n)))
+            new Range(Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 59, 999)).plusS(new Second(new Rat(86_399_999n, 86_400_000n))))
           ])
         assert.deepStrictEqual(converter.unixToAtomic(Second.fromMillis(Date.UTC(1980, JAN, 1, 12, 0, 0, 0))),
           [
@@ -301,7 +302,7 @@ describe('Converter', () => {
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 0))),
           Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 0)))
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1))),
-          Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1)).minusS(new Second(1n, 86_401_000n)))
+          Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1)).minusS(new Second(new Rat(1n, 86_401_000n))))
 
         // SMEAR MIDPOINT
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1980, JAN, 1, 0, 0, 0, 500))),
@@ -309,7 +310,7 @@ describe('Converter', () => {
 
         // SMEAR ENDS, UNIX HAS DROPPED A FULL SECOND BEHIND
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1980, JAN, 1, 12, 0, 0, 999))),
-          Second.fromMillis(Date.UTC(1980, JAN, 1, 12, 0, 0, 999)).minusS(new Second(86_400_999n, 86_401_000n)))
+          Second.fromMillis(Date.UTC(1980, JAN, 1, 12, 0, 0, 999)).minusS(new Second(new Rat(86_400_999n, 86_401_000n))))
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1980, JAN, 1, 12, 0, 1, 0))),
           Second.fromMillis(Date.UTC(1980, JAN, 1, 12, 0, 0, 0)))
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1980, JAN, 1, 12, 0, 1, 1))),
@@ -482,7 +483,7 @@ describe('Converter', () => {
           ])
         assert.deepStrictEqual(converter.unixToAtomic(Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1))),
           [
-            new Range(Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1)).minusS(new Second(1n, 86_400_000n)))
+            new Range(Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1)).minusS(new Second(new Rat(1n, 86_400_000n))))
           ])
 
         // SMEAR MIDPOINT
@@ -494,7 +495,7 @@ describe('Converter', () => {
         // SMEAR ENDS, ATOMIC IS A FULL SECOND BEHIND (actually Unix is a full second ahead)
         assert.deepStrictEqual(converter.unixToAtomic(Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 59, 999))),
           [
-            new Range(Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 59, 999)).minusS(new Second(86_399_999n, 86_400_000n)))
+            new Range(Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 59, 999)).minusS(new Second(new Rat(86_399_999n, 86_400_000n))))
           ])
         assert.deepStrictEqual(converter.unixToAtomic(Second.fromMillis(Date.UTC(1980, JAN, 1, 12, 0, 0, 0))),
           [
@@ -516,7 +517,7 @@ describe('Converter', () => {
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 0))),
           Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 0)))
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1))),
-          Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1)).plusS(new Second(1n, 86_399_000n)))
+          Second.fromMillis(Date.UTC(1979, DEC, 31, 12, 0, 0, 1)).plusS(new Second(new Rat(1n, 86_399_000n))))
 
         // SMEAR MIDPOINT
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1979, DEC, 31, 23, 59, 59, 500))),
@@ -524,7 +525,7 @@ describe('Converter', () => {
 
         // SMEAR ENDS, UNIX HAS RUN A FULL SECOND FASTER THAN ATOMIC
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 58, 999))),
-          Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 58, 999)).plusS(new Second(86_398_999n, 86_399_000n)))
+          Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 58, 999)).plusS(new Second(new Rat(86_398_999n, 86_399_000n))))
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 59, 0))),
           Second.fromMillis(Date.UTC(1980, JAN, 1, 12, 0, 0, 0)))
         assert.deepStrictEqual(converter.atomicToUnix(Second.fromMillis(Date.UTC(1980, JAN, 1, 11, 59, 59, 1))),
@@ -543,9 +544,9 @@ describe('Converter', () => {
 
         assert.deepStrictEqual(converter.unixToAtomic(Second.fromMillis(1)),
           [
-            new Range(new Second(900n, 1_000_000n))
+            new Range(new Second(new Rat(900n, 1_000_000n)))
           ])
-        assert.deepStrictEqual(converter.atomicToUnix(new Second(900n, 1_000_000n)),
+        assert.deepStrictEqual(converter.atomicToUnix(new Second(new Rat(900n, 1_000_000n))),
           Second.fromMillis(1))
       })
 
@@ -558,9 +559,9 @@ describe('Converter', () => {
 
         assert.deepStrictEqual(converter.unixToAtomic(Second.fromMillis(-1)),
           [
-            new Range(new Second(-900n, 1_000_000n))
+            new Range(new Second(new Rat(-900n, 1_000_000n)))
           ])
-        assert.deepStrictEqual(converter.atomicToUnix(new Second(-900n, 1_000_000n)),
+        assert.deepStrictEqual(converter.atomicToUnix(new Second(new Rat(-900n, 1_000_000n))),
           Second.fromMillis(-1))
       })
     })
diff --git a/test/exact.spec.js b/test/exact.spec.js
index 0b06c64..504cb65 100644
--- a/test/exact.spec.js
+++ b/test/exact.spec.js
@@ -2,6 +2,7 @@ import assert from 'node:assert'
 import { describe, it } from 'mocha'
 import { TaiConverter, Second, MODELS, UNIX_START, UNIX_END } from '../src/exact.js'
 import { Range } from '../src/range.js'
+import { Rat } from '../src/rat.js'
 
 const JAN = 0
 const FEB = 1
@@ -48,51 +49,51 @@ describe('TaiConverter', () => {
         // 00:00:01.422_818 is in range, but rounds down to 00:00:01.422 which is not
         assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 0, 0))),
           [
-            new Range(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 422)).plusS(new Second(818_000_000n, 1_000_000_000_000n)))
+            new Range(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 422)).plusS(new Second(new Rat(818_000_000n, 1_000_000_000_000n))))
           ])
       })
 
       it('advances 15 TAI picoseconds per Unix millisecond', () => {
         assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 0, 1))),
           [
-            new Range(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 423)).plusS(new Second(818_000_015n, 1_000_000_000_000n)))
+            new Range(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 423)).plusS(new Second(new Rat(818_000_015n, 1_000_000_000_000n))))
           ])
         assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 0, 2))),
           [
-            new Range(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 424)).plusS(new Second(818_000_030n, 1_000_000_000_000n)))
+            new Range(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 424)).plusS(new Second(new Rat(818_000_030n, 1_000_000_000_000n))))
           ])
         assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 0, 3))),
           [
-            new Range(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 425)).plusS(new Second(818_000_045n, 1_000_000_000_000n)))
+            new Range(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 425)).plusS(new Second(new Rat(818_000_045n, 1_000_000_000_000n))))
           ])
       })
 
       it('advances 0.001_296 TAI seconds per Unix day', () => {
         assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, JAN, 2, 0, 0, 0, 0))),
           [
-            new Range(Second.fromMillis(Date.UTC(1961, JAN, 2, 0, 0, 1, 424)).plusS(new Second(114n, 1_000_000n)))
+            new Range(Second.fromMillis(Date.UTC(1961, JAN, 2, 0, 0, 1, 424)).plusS(new Second(new Rat(114n, 1_000_000n))))
           ])
       })
 
       it('makes certain TAI millisecond counts inaccessible', () => {
         assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(-283_984_666_668)),
           [
-            new Range(new Second(-283_984_665_245_000_000_020n, 1_000_000_000_000n))
+            new Range(new Second(new Rat(-283_984_665_245_000_000_020n, 1_000_000_000_000n)))
           ])
         assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(-283_984_666_667)),
           [
-            new Range(new Second(-283_984_665_244_000_000_005n, 1_000_000_000_000n))
+            new Range(new Second(new Rat(-283_984_665_244_000_000_005n, 1_000_000_000_000n)))
           ])
 
         // it's not possible to get a result of -283_984_665_244_XXX_XXX_XXXn
 
         assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(-283_984_666_666)),
           [
-            new Range(new Second(-283_984_665_242_999_999_990n, 1_000_000_000_000n))
+            new Range(new Second(new Rat(-283_984_665_242_999_999_990n, 1_000_000_000_000n)))
           ])
         assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(-283_984_666_665)),
           [
-            new Range(new Second(-283_984_665_241_999_999_975n, 1_000_000_000_000n))
+            new Range(new Second(new Rat(-283_984_665_241_999_999_975n, 1_000_000_000_000n)))
           ])
       })
     })
@@ -103,7 +104,7 @@ describe('TaiConverter', () => {
           NaN)
 
         // Actual start of TAI: 1961-01-01 00:00:01.422_818
-        assert.deepStrictEqual(taiConverter.atomicToUnix(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 422)).plusS(new Second(818n, 1_000_000n))),
+        assert.deepStrictEqual(taiConverter.atomicToUnix(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 422)).plusS(new Second(new Rat(818n, 1_000_000n)))),
           Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 0, 0)))
       })
 
@@ -143,7 +144,7 @@ describe('TaiConverter', () => {
         // Fun fact! There is about 105 leap milliseconds here!
         assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1972, JAN, 1, 0, 0, 0, 0))),
           [
-            new Range(Second.fromMillis(Date.UTC(1972, JAN, 1, 0, 0, 9, 892)).plusS(new Second(242n, 1_000_000n))),
+            new Range(Second.fromMillis(Date.UTC(1972, JAN, 1, 0, 0, 9, 892)).plusS(new Second(new Rat(242n, 1_000_000n)))),
             new Range(Second.fromMillis(Date.UTC(1972, JAN, 1, 0, 0, 10, 0)))
           ])
       })
@@ -188,15 +189,15 @@ describe('TaiConverter', () => {
       // TAI picosecond count rounds to -252_460_798_155 which is not in range
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, DEC, 31, 23, 59, 59, 999))),
         [
-          new Range(new Second(-252_460_798_155_142_000_015n, 1_000_000_000_000n))
+          new Range(new Second(new Rat(-252_460_798_155_142_000_015n, 1_000_000_000_000n)))
         ])
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1962, JAN, 1, 0, 0, 0, 0))),
         [
-          new Range(new Second(-252_460_798_154_142_000_000n, 1_000_000_000_000n))
+          new Range(new Second(new Rat(-252_460_798_154_142_000_000n, 1_000_000_000_000n)))
         ])
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1962, JAN, 1, 0, 0, 0, 1))),
         [
-          new Range(new Second(-252_460_798_153_141_999_987n, 1_000_000_000_000n))
+          new Range(new Second(new Rat(-252_460_798_153_141_999_987n, 1_000_000_000_000n)))
         ])
     })
 
@@ -205,8 +206,8 @@ describe('TaiConverter', () => {
       // The period between 1965-09-01 00:00:00 and 00:00:00.100 UTC happened twice!
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1965, SEP, 1, 0, 0, 0, 50))),
         [
-          new Range(new Second(-136_771_195_894_941_999_250n, 1_000_000_000_000n)),
-          new Range(new Second(-136_771_195_794_941_999_250n, 1_000_000_000_000n))
+          new Range(new Second(new Rat(-136_771_195_894_941_999_250n, 1_000_000_000_000n))),
+          new Range(new Second(new Rat(-136_771_195_794_941_999_250n, 1_000_000_000_000n)))
         ])
     })
 
@@ -216,11 +217,11 @@ describe('TaiConverter', () => {
       // Which means that 23:59:59.950 UTC *does* actually exist...
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, JUL, 31, 23, 59, 59, 949))),
         [
-          new Range(new Second(-265_679_998_353_430_000_765n, 1_000_000_000_000n))
+          new Range(new Second(new Rat(-265_679_998_353_430_000_765n, 1_000_000_000_000n)))
         ])
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, JUL, 31, 23, 59, 59, 950))),
         [
-          new Range(new Second(-265_679_998_352_430_000_750n, 1_000_000_000_000n))
+          new Range(new Second(new Rat(-265_679_998_352_430_000_750n, 1_000_000_000_000n)))
         ])
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, JUL, 31, 23, 59, 59, 951))),
         [])
@@ -229,11 +230,11 @@ describe('TaiConverter', () => {
         [])
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, AUG, 1, 0, 0, 0, 0))),
         [
-          new Range(new Second(-265_679_998_352_430_000_000n, 1_000_000_000_000n))
+          new Range(new Second(new Rat(-265_679_998_352_430_000_000n, 1_000_000_000_000n)))
         ])
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1961, AUG, 1, 0, 0, 0, 1))),
         [
-          new Range(new Second(-265_679_998_351_429_999_985n, 1_000_000_000_000n))
+          new Range(new Second(new Rat(-265_679_998_351_429_999_985n, 1_000_000_000_000n)))
         ])
     })
 
@@ -290,7 +291,7 @@ describe('TaiConverter', () => {
         1)
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1968, JAN, 31, 23, 59, 59, 900))),
         [
-          new Range(new Second(-60_479_993_814_318_003n, 1_000_000_000n))
+          new Range(new Second(new Rat(-60_479_993_814_318_003n, 1_000_000_000n)))
         ])
 
       assert.strictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1968, JAN, 31, 23, 59, 59, 901))).length,
@@ -471,7 +472,7 @@ describe('TaiConverter', () => {
     describe('atomicToUnix', () => {
       it('The NEW earliest instant in TAI', () => {
         // Actual start of TAI: 1961-01-01 00:00:01.422_818
-        assert.deepStrictEqual(taiConverter.atomicToUnix(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 422)).plusS(new Second(818n, 1_000_000n))),
+        assert.deepStrictEqual(taiConverter.atomicToUnix(Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 1, 422)).plusS(new Second(new Rat(818n, 1_000_000n)))),
           Second.fromMillis(Date.UTC(1961, JAN, 1, 0, 0, 0, 0)))
       })
 
@@ -482,7 +483,7 @@ describe('TaiConverter', () => {
 
       it('0.107_758 seconds added, start of 1972', () => {
         // stall begins at 1972-01-01 00:00:09.892_242 TAI
-        assert.deepStrictEqual(taiConverter.atomicToUnix(Second.fromMillis(Date.UTC(1972, JAN, 1, 0, 0, 9, 892)).plusS(new Second(242n, 1_000_000n))),
+        assert.deepStrictEqual(taiConverter.atomicToUnix(Second.fromMillis(Date.UTC(1972, JAN, 1, 0, 0, 9, 892)).plusS(new Second(new Rat(242n, 1_000_000n)))),
           Second.fromMillis(Date.UTC(1972, JAN, 1, 0, 0, 0, 0)))
         assert.deepStrictEqual(taiConverter.atomicToUnix(Second.fromMillis(Date.UTC(1972, JAN, 1, 0, 0, 9, 893))),
           Second.fromMillis(Date.UTC(1972, JAN, 1, 0, 0, 0, 0)))
@@ -547,11 +548,11 @@ describe('TaiConverter', () => {
       // Exact picosecond ratios
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1962, JAN, 1, 0, 0, 0, 0))),
         [
-          new Range(new Second(-252_460_798_154_142_000_000n, 1_000_000_000_000n))
+          new Range(new Second(new Rat(-252_460_798_154_142_000_000n, 1_000_000_000_000n)))
         ])
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(1962, JAN, 1, 0, 0, 0, 1))),
         [
-          new Range(new Second(-252_460_798_153_141_999_987n, 1_000_000_000_000n))
+          new Range(new Second(new Rat(-252_460_798_153_141_999_987n, 1_000_000_000_000n)))
         ])
     })
 
@@ -706,7 +707,7 @@ describe('TaiConverter', () => {
           const atomic = Second.fromMillis(63_072_010_000)
           assert.deepStrictEqual(taiConverter.unixToAtomic(taiConverter.atomicToUnix(atomic)),
             [
-              new Range(atomic.minusS(new Second(107_758n, 1_000_000n)), atomic)
+              new Range(atomic.minusS(new Second(new Rat(107_758n, 1_000_000n))), atomic)
             ])
         })
 
@@ -772,7 +773,7 @@ describe('TaiConverter', () => {
         ])
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(2016, DEC, 31, 12, 0, 0, 1))),
         [
-          new Range(Second.fromMillis(Date.UTC(2016, DEC, 31, 12, 0, 36, 1)).plusS(new Second(1n, 86_400_000n)))
+          new Range(Second.fromMillis(Date.UTC(2016, DEC, 31, 12, 0, 36, 1)).plusS(new Second(new Rat(1n, 86_400_000n))))
         ])
 
       // After 86_400 Unix milliseconds, exactly 86_401 TAI milliseconds have passed
@@ -790,7 +791,7 @@ describe('TaiConverter', () => {
       // SMEAR ENDS. After 24 Unix hours, 24 TAI hours and 1 second
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(2017, JAN, 1, 11, 59, 59, 999))),
         [
-          new Range(Second.fromMillis(Date.UTC(2017, JAN, 1, 12, 0, 35, 999)).plusS(new Second(86_399_999n, 86_400_000n)))
+          new Range(Second.fromMillis(Date.UTC(2017, JAN, 1, 12, 0, 35, 999)).plusS(new Second(new Rat(86_399_999n, 86_400_000n))))
         ])
       assert.deepStrictEqual(taiConverter.unixToAtomic(Second.fromMillis(Date.UTC(2017, JAN, 1, 12, 0, 0, 0))),
         [
diff --git a/test/munge.spec.js b/test/munge.spec.js
index 87dc080..09f434b 100644
--- a/test/munge.spec.js
+++ b/test/munge.spec.js
@@ -66,13 +66,13 @@ describe('munge', () => {
         [9_000, -3], // inserted leap second
         [13_000, -4] // removed leap second
       ], MODELS.OVERRUN), [new Segment(
-        { atomic: new Second(-5n, 1n), unix: new Second(-1n, 1n) },
-        { atomic: new Second(6n, 1n) }
+        { atomic: new Second(new Rat(-5n, 1n)), unix: new Second(new Rat(-1n, 1n)) },
+        { atomic: new Second(new Rat(6n, 1n)) }
       ), new Segment(
-        { atomic: new Second(6n, 1n), unix: new Second(9n, 1n) },
-        { atomic: new Second(9n, 1n) }
+        { atomic: new Second(new Rat(6n, 1n)), unix: new Second(new Rat(9n, 1n)) },
+        { atomic: new Second(new Rat(9n, 1n)) }
       ), new Segment(
-        { atomic: new Second(9n, 1n), unix: new Second(13n, 1n) }
+        { atomic: new Second(new Rat(9n, 1n)), unix: new Second(new Rat(13n, 1n)) }
       )])
     })
 
@@ -125,7 +125,7 @@ describe('munge', () => {
       assert.deepStrictEqual(munge([
         [Date.UTC(1961, JAN, 1), 1.422_818_0, 37_300, 0.001_296]
       ], MODELS.OVERRUN), [new Segment(
-        { atomic: new Second(-283_996_798_577_182n, 1_000_000n), unix: new Second(-283_996_800n, 1n) },
+        { atomic: new Second(new Rat(-283_996_798_577_182n, 1_000_000n)), unix: new Second(new Rat(-283_996_800n, 1n)) },
         { atomic: Second.END_OF_TIME },
         { unixPerAtomic: new Rat(86_400_000_000_000n, 86_400_000_000_000n + 1_296_000n) }
       )])
@@ -202,46 +202,46 @@ describe('munge', () => {
         return b.minusS(a)
       }), [
         // Exact ratio of microseconds
-        new Second(-50_000n, 1_000_000n),
-        new Second(0n, 1_000_000n),
-        new Second(100_000n, 1_000_000n),
-        new Second(0n, 1_000_000n),
-        new Second(100_000n, 1_000_000n),
-        new Second(100_000n, 1_000_000n),
-        new Second(100_000n, 1_000_000n),
-        new Second(100_000n, 1_000_000n),
-        new Second(100_000n, 1_000_000n),
-        new Second(100_000n, 1_000_000n),
-        new Second(0n, 1_000_000n),
-        new Second(-100_000n, 1_000_000n),
-        new Second(107_758n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
-        new Second(1_000_000n, 1_000_000n),
+        new Second(new Rat(-50_000n, 1_000_000n)),
+        new Second(new Rat(0n, 1_000_000n)),
+        new Second(new Rat(100_000n, 1_000_000n)),
+        new Second(new Rat(0n, 1_000_000n)),
+        new Second(new Rat(100_000n, 1_000_000n)),
+        new Second(new Rat(100_000n, 1_000_000n)),
+        new Second(new Rat(100_000n, 1_000_000n)),
+        new Second(new Rat(100_000n, 1_000_000n)),
+        new Second(new Rat(100_000n, 1_000_000n)),
+        new Second(new Rat(100_000n, 1_000_000n)),
+        new Second(new Rat(0n, 1_000_000n)),
+        new Second(new Rat(-100_000n, 1_000_000n)),
+        new Second(new Rat(107_758n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
+        new Second(new Rat(1_000_000n, 1_000_000n)),
         NaN // `Infinity - Infinity`
       ])
     })
@@ -251,7 +251,7 @@ describe('munge', () => {
         assert.deepStrictEqual(munge([
           [Date.UTC(1970, JAN, 1, 0, 0, 0, 1), -0.000_1]
         ], MODELS.OVERRUN), [new Segment(
-          { atomic: new Second(900n, 1_000_000n), unix: Second.fromMillis(1) } // ray start intentionally doesn't include TAI epoch
+          { atomic: new Second(new Rat(900n, 1_000_000n)), unix: Second.fromMillis(1) } // ray start intentionally doesn't include TAI epoch
         )])
       })
 
@@ -261,10 +261,10 @@ describe('munge', () => {
           [Date.UTC(1969, DEC, 31, 23, 59, 59, 999), 0.000_1],
           [Date.UTC(1970, JAN, 1, 0, 0, 0, 1), -0.001_1]
         ], MODELS.OVERRUN), [new Segment(
-          { atomic: new Second(-900n, 1_000_000n), unix: Second.fromMillis(-1) },
-          { atomic: new Second(-100n, 1_000_000n) }
+          { atomic: new Second(new Rat(-900n, 1_000_000n)), unix: Second.fromMillis(-1) },
+          { atomic: new Second(new Rat(-100n, 1_000_000n)) }
         ), new Segment(
-          { atomic: new Second(-100n, 1_000_000n), unix: Second.fromMillis(1) }
+          { atomic: new Second(new Rat(-100n, 1_000_000n)), unix: Second.fromMillis(1) }
         )])
       })
     })
@@ -289,14 +289,14 @@ describe('munge', () => {
         [9_000, -3], // inserted leap second
         [13_000, -4] // removed leap second
       ], MODELS.BREAK), [new Segment(
-        { atomic: new Second(-5n, 1n), unix: new Second(-1n, 1n) },
-        { atomic: new Second(5n, 1n) }
+        { atomic: new Second(new Rat(-5n, 1n)), unix: new Second(new Rat(-1n, 1n)) },
+        { atomic: new Second(new Rat(5n, 1n)) }
       ), new Segment(
         // this segment starts a full TAI second after the previous segment ended
-        { atomic: new Second(6n, 1n), unix: new Second(9n, 1n) },
-        { atomic: new Second(9n, 1n) }
+        { atomic: new Second(new Rat(6n, 1n)), unix: new Second(new Rat(9n, 1n)) },
+        { atomic: new Second(new Rat(9n, 1n)) }
       ), new Segment(
-        { atomic: new Second(9n, 1n), unix: new Second(13n, 1n) }
+        { atomic: new Second(new Rat(9n, 1n)), unix: new Second(new Rat(13n, 1n)) }
       )])
     })
   })
@@ -335,18 +335,18 @@ describe('munge', () => {
         [9_000, -3], // inserted leap second
         [13_000, -4] // removed leap second
       ], MODELS.STALL), [new Segment(
-        { atomic: new Second(-5n, 1n), unix: new Second(-1n, 1n) },
-        { atomic: new Second(5n, 1n) }
+        { atomic: new Second(new Rat(-5n, 1n)), unix: new Second(new Rat(-1n, 1n)) },
+        { atomic: new Second(new Rat(5n, 1n)) }
       ), new Segment(
         // Stall segment inserted here
-        { atomic: new Second(5n, 1n), unix: new Second(9n, 1n) },
-        { atomic: new Second(6n, 1n) },
+        { atomic: new Second(new Rat(5n, 1n)), unix: new Second(new Rat(9n, 1n)) },
+        { atomic: new Second(new Rat(6n, 1n)) },
         { unixPerAtomic: new Rat(0n) }
       ), new Segment(
-        { atomic: new Second(6n, 1n), unix: new Second(9n, 1n) },
-        { atomic: new Second(9n, 1n) }
+        { atomic: new Second(new Rat(6n, 1n)), unix: new Second(new Rat(9n, 1n)) },
+        { atomic: new Second(new Rat(9n, 1n)) }
       ), new Segment(
-        { atomic: new Second(9n, 1n), unix: new Second(13n, 1n) }
+        { atomic: new Second(new Rat(9n, 1n)), unix: new Second(new Rat(13n, 1n)) }
       )])
     })
 
@@ -399,7 +399,7 @@ describe('munge', () => {
       assert.deepStrictEqual(munge([
         [Date.UTC(1961, JAN, 1), 1.422_818_0, 37_300, 0.001_296]
       ], MODELS.STALL), [new Segment(
-        { atomic: new Second(-283_996_798_577_182n, 1_000_000n), unix: new Second(-283_996_800n, 1n) },
+        { atomic: new Second(new Rat(-283_996_798_577_182n, 1_000_000n)), unix: new Second(new Rat(-283_996_800n, 1n)) },
         { atomic: Second.END_OF_TIME },
         { unixPerAtomic: new Rat(86_400_000_000_000n, 86_400_000_000_000n + 1_296_000n) }
       )])
@@ -518,81 +518,81 @@ describe('munge', () => {
         return b.minusS(a)
       }), [
         // Exact ratio expressing milliseconds
-        new Second(-50n, 1_000n), // 0.05 TAI seconds removed from UTC
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(-100n, 1_000n), // 0.1 TAI seconds removed from UTC
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
-        new Second(0n, 1_000n),
+        new Second(new Rat(-50n, 1_000n)), // 0.05 TAI seconds removed from UTC
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(-100n, 1_000n)), // 0.1 TAI seconds removed from UTC
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
+        new Second(new Rat(0n, 1_000n)),
         NaN
       ])
     })
@@ -613,13 +613,13 @@ describe('munge', () => {
         [86_400_000, 1] // inserted leap second after one day
       ], MODELS.SMEAR), [new Segment(
         { atomic: Second.fromMillis(0), unix: Second.fromMillis(0) },
-        { atomic: new Second(43_200n, 1n) } // midday
+        { atomic: new Second(new Rat(43_200n, 1n)) } // midday
       ), new Segment(
-        { atomic: new Second(43_200n, 1n), unix: new Second(43_200n, 1n) }, // midday
-        { atomic: new Second(129_601n, 1n) }, // midday
+        { atomic: new Second(new Rat(43_200n, 1n)), unix: new Second(new Rat(43_200n, 1n)) }, // midday
+        { atomic: new Second(new Rat(129_601n, 1n)) }, // midday
         { unixPerAtomic: new Rat(86_400n, 86_401n) } // A full Unix day elapses, but a full TAI day plus one second elapses
       ), new Segment(
-        { atomic: new Second(129_601n, 1n), unix: new Second(129_600n, 1n) } // midday
+        { atomic: new Second(new Rat(129_601n, 1n)), unix: new Second(new Rat(129_600n, 1n)) } // midday
       )])
     })
 
@@ -629,13 +629,13 @@ describe('munge', () => {
         [86_400_000, -1] // removed leap second after one day
       ], MODELS.SMEAR), [new Segment(
         { atomic: Second.fromMillis(0), unix: Second.fromMillis(0) },
-        { atomic: new Second(43_200n, 1n) } // midday
+        { atomic: new Second(new Rat(43_200n, 1n)) } // midday
       ), new Segment(
-        { atomic: new Second(43_200n, 1n), unix: new Second(43_200n, 1n) }, // midday
-        { atomic: new Second(129_599n, 1n) }, // midday
+        { atomic: new Second(new Rat(43_200n, 1n)), unix: new Second(new Rat(43_200n, 1n)) }, // midday
+        { atomic: new Second(new Rat(129_599n, 1n)) }, // midday
         { unixPerAtomic: new Rat(86_400n, 86_399n) } // A full Unix day elapses, but a full TAI day minus one second elapses
       ), new Segment(
-        { atomic: new Second(129_599n, 1n), unix: new Second(129_600n, 1n) } // midday
+        { atomic: new Second(new Rat(129_599n, 1n)), unix: new Second(new Rat(129_600n, 1n)) } // midday
       )])
     })
 
@@ -752,86 +752,86 @@ describe('munge', () => {
 
         return b.minusS(a)
       }), [
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
-        new Second(0n, 1n),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
+        new Second(new Rat(0n, 1n)),
         NaN
       ])
     })
diff --git a/test/second.spec.js b/test/second.spec.js
index 2f6ec4c..16f14c6 100644
--- a/test/second.spec.js
+++ b/test/second.spec.js
@@ -4,64 +4,53 @@ import { Rat } from '../src/rat.js'
 import { Second } from '../src/second.js'
 
 describe('Second', () => {
-  it('type checking', () => {
-    assert.throws(() => new Second(1, 2n), /numerator must be a BigInt/)
-    assert.throws(() => new Second(1n, 2), /denominator must be a BigInt/)
-    assert.throws(() => new Second(1n, 0), /denominator must be a BigInt/)
-    assert.throws(() => new Second(-1n, 0n), /denominator cannot be zero/)
-  })
-
-  it('defaults to an integer', () => {
-    assert.deepStrictEqual(new Second(1n), new Second(1n, 1n))
-  })
-
   it('adds', () => {
-    assert.deepStrictEqual(new Second(1n, 2n).plusS(new Second(1n, 3n)), new Second(5n, 6n))
-    assert.deepStrictEqual(new Second(1n, 2n).plusS(new Second(0n, 3n)), new Second(1n, 2n))
-    assert.deepStrictEqual(new Second(0n, 2n).plusS(new Second(1n, 3n)), new Second(1n, 3n))
+    assert.deepStrictEqual(new Second(new Rat(1n, 2n)).plusS(new Second(new Rat(1n, 3n))), new Second(new Rat(5n, 6n)))
+    assert.deepStrictEqual(new Second(new Rat(1n, 2n)).plusS(new Second(new Rat(0n, 3n))), new Second(new Rat(1n, 2n)))
+    assert.deepStrictEqual(new Second(new Rat(0n, 2n)).plusS(new Second(new Rat(1n, 3n))), new Second(new Rat(1n, 3n)))
   })
 
   it('subtracts', () => {
-    assert.deepStrictEqual(new Second(1n, 2n).minusS(new Second(1n, 3n)), new Second(1n, 6n))
-    assert.deepStrictEqual(new Second(1n, 2n).minusS(new Second(0n, 3n)), new Second(1n, 2n))
-    assert.deepStrictEqual(new Second(0n, 2n).minusS(new Second(1n, 3n)), new Second(-1n, 3n))
+    assert.deepStrictEqual(new Second(new Rat(1n, 2n)).minusS(new Second(new Rat(1n, 3n))), new Second(new Rat(1n, 6n)))
+    assert.deepStrictEqual(new Second(new Rat(1n, 2n)).minusS(new Second(new Rat(0n, 3n))), new Second(new Rat(1n, 2n)))
+    assert.deepStrictEqual(new Second(new Rat(0n, 2n)).minusS(new Second(new Rat(1n, 3n))), new Second(new Rat(-1n, 3n)))
   })
 
   it('multiplies', () => {
-    assert.deepStrictEqual(new Second(6n, 5n).timesR(new Rat(4n, 5n)), new Second(24n, 25n))
-    assert.deepStrictEqual(new Second(6n, 5n).timesR(new Rat(0n, 5n)), new Second(0n, 25n))
-    assert.deepStrictEqual(new Second(0n, 5n).timesR(new Rat(4n, 5n)), new Second(0n, 25n))
+    assert.deepStrictEqual(new Second(new Rat(6n, 5n)).timesR(new Rat(4n, 5n)), new Second(new Rat(24n, 25n)))
+    assert.deepStrictEqual(new Second(new Rat(6n, 5n)).timesR(new Rat(0n, 5n)), new Second(new Rat(0n, 25n)))
+    assert.deepStrictEqual(new Second(new Rat(0n, 5n)).timesR(new Rat(4n, 5n)), new Second(new Rat(0n, 25n)))
   })
 
   it('divides', () => {
-    assert.deepStrictEqual(new Second(6n, 5n).divideS(new Second(4n, 5n)), new Rat(30n, 20n))
-    assert.deepStrictEqual(new Second(0n, 5n).divideS(new Second(4n, 5n)), new Rat(0n, 20n))
+    assert.deepStrictEqual(new Second(new Rat(6n, 5n)).divideS(new Second(new Rat(4n, 5n))), new Rat(30n, 20n))
+    assert.deepStrictEqual(new Second(new Rat(0n, 5n)).divideS(new Second(new Rat(4n, 5n))), new Rat(0n, 20n))
   })
 
   it('greater than', () => {
-    assert.strictEqual(new Second(-1n, 3n).gtS(new Second(1n, -2n)), true)
-    assert.strictEqual(new Second(0n).gtS(new Second(1n)), false)
+    assert.strictEqual(new Second(new Rat(-1n, 3n)).gtS(new Second(new Rat(1n, -2n))), true)
+    assert.strictEqual(new Second(new Rat(0n)).gtS(new Second(new Rat(1n))), false)
   })
 
   it('equal', () => {
-    assert.strictEqual(new Second(-1n, 3n).eqS(new Second(4n, -12n)), true)
-    assert.strictEqual(new Second(0n).eqS(new Second(-1n)), false)
-    assert.strictEqual(new Second(0n).eqS(new Second(-0n)), true)
+    assert.strictEqual(new Second(new Rat(-1n, 3n)).eqS(new Second(new Rat(4n, -12n))), true)
+    assert.strictEqual(new Second(new Rat(0n)).eqS(new Second(new Rat(-1n))), false)
+    assert.strictEqual(new Second(new Rat(0n)).eqS(new Second(new Rat(-0n))), true)
   })
 
   it('less than or equal', () => {
-    assert.strictEqual(new Second(-2n, -3n).leS(new Second(-2n, -3n)), true)
-    assert.strictEqual(new Second(-2n, -3n).leS(new Second(2n, 3n)), true)
-    assert.strictEqual(new Second(9n, 12n).leS(new Second(6n, 8n)), true)
-    assert.strictEqual(new Second(9n, 13n).leS(new Second(6n, 8n)), true)
+    assert.strictEqual(new Second(new Rat(-2n, -3n)).leS(new Second(new Rat(-2n, -3n))), true)
+    assert.strictEqual(new Second(new Rat(-2n, -3n)).leS(new Second(new Rat(2n, 3n))), true)
+    assert.strictEqual(new Second(new Rat(9n, 12n)).leS(new Second(new Rat(6n, 8n))), true)
+    assert.strictEqual(new Second(new Rat(9n, 13n)).leS(new Second(new Rat(6n, 8n))), true)
   })
 
   it('fromMillis', () => {
-    assert.deepStrictEqual(Second.fromMillis(123), new Second(123n, 1_000n))
+    assert.deepStrictEqual(Second.fromMillis(123), new Second(new Rat(123n, 1_000n)))
     assert.throws(() => Second.fromMillis(Infinity))
   })
 
   it('toMillis', () => {
-    assert.strictEqual(new Second(123n, 1_000n).toMillis(), 123)
+    assert.strictEqual(new Second(new Rat(123n, 1_000n)).toMillis(), 123)
   })
 })
diff --git a/test/segment.spec.js b/test/segment.spec.js
index 967392e..f943253 100644
--- a/test/segment.spec.js
+++ b/test/segment.spec.js
@@ -22,14 +22,14 @@ describe('Segment', () => {
     assert.throws(() => new Segment(
       { atomic: Second.fromMillis(0), unix: Second.fromMillis(0) },
       { atomic: Second.fromMillis(1_000) },
-      { unixPerAtomic: new Second(1n, 1n) }
+      { unixPerAtomic: new Second(new Rat(1n, 1n)) }
     ), /slope must be a `Rat`/)
   })
 
   it('disallows rays which run backwards', () => {
     assert.throws(() => new Segment(
       { atomic: Second.fromMillis(0), unix: Second.fromMillis(0) },
-      { atomic: new Second(-1n, 1_000_000_000_000n) }
+      { atomic: new Second(new Rat(-1n, 1_000_000_000_000n)) }
     ), /segment length must be positive/)
   })
 
@@ -121,7 +121,7 @@ describe('Segment', () => {
       assert.strictEqual(segment.atomicOnSegment(Second.fromMillis(1_999)),
         true)
       assert.deepStrictEqual(segment.atomicToUnix(Second.fromMillis(1_999)),
-        new Second(1_999n, 2_000n)) // truncates to 999ms
+        new Second(new Rat(1_999n, 2_000n))) // truncates to 999ms
     })
 
     it('end point', () => {