Fix number patterns rounding unlike Excel and garbling large numbers

lib/runPart.ts

@@ -48,7 +48,8 @@ import {
   TOKEN_CURRENCY
 } from './constants.ts';
 import { pad } from './pad.ts';
-import { getExponent, getSignificand } from './numberProps.ts';
+import { roundDecimal, toDecimal, type Decimal } from './toDecimal.ts';
+import { getSignificand } from './numberProps.ts';
 import type { Partition } from './types.ts';
 import type { FormatOptions } from './options.ts';
 
@@ -105,38 +106,50 @@ export function runPart (value: number | string | bigint, part: Partition, opts:
   }
 
   // calc exponent
+  let dec: Decimal | undefined;
   if (part.exponential && typeof value === 'number') {
-    let v = Math.abs(value);
-    if (v) {
-      exp = getExponent(v, part.int_max);
+    // the significand has the number's own digits, so round those
+    dec = toDecimal(value);
+    if (dec.digits) {
+      exp = dec.point - 1;
+      if (part.int_max > 1) {
+        exp = Math.floor(exp / part.int_max) * part.int_max;
+      }
     }
     if (value && !part.integer) {
       // when there isn't an integer part, the exp gets shifted by 1
       exp++;
     }
-    v = getSignificand(v, exp);
-    if (part.int_max === 1 && round(v, part.frac_max) === 10) {
-      v = 1;
+    dec.point -= exp;
+    if (part.int_max === 1 && roundDecimal(dec, part.frac_max)[0] === '10') {
+      dec.point--;
       exp++;
     }
+    const v = getSignificand(Math.abs(value), exp);
     value = (value < 0) ? -v : v;
     mantissa += Math.abs(exp);
   }
 
-  // integer to text
-  if (part.integer && typeof value === 'number') {
-    const i = Math.abs(round(value, part.fractions ? 1 : part.frac_max));
-    integer += (i < 1) ? '' : Math.floor(i);
+  // integer and fraction to text
+  if (part.fractions) {
+    if (part.integer && typeof value === 'number') {
+      const i = Math.abs(round(value, 1));
+      integer += (i < 1) ? '' : Math.floor(i);
+    }
+  }
+  else if ((part.integer || part.dec_fractions) && typeof value === 'number') {
+    const digits = roundDecimal(dec ?? toDecimal(value), part.frac_max);
+    if (part.integer) {
+      integer = digits[0];
+    }
+    if (part.dec_fractions) {
+      fraction = digits[1];
+    }
   }
   // integer grouping
   const group_pri = opts.grouping[0] ?? 3;
   const group_sec = opts.grouping[1] ?? group_pri;
 
-  // fraction to text
-  if (part.dec_fractions && typeof value === 'number') {
-    fraction = String(round(value, part.frac_max)).split('.')[1] || '';
-  }
-
   // using vulgar fractions
   const fixed_slash = !part.error && (part.num_p.includes('0') || part.den_p.includes('0'));
 

lib/toDecimal.ts

@@ -0,0 +1,136 @@
+/**
+ * A non-negative decimal number: significant `digits` without leading or
+ * trailing zeros, and the position of the decimal point relative to the first
+ * of them. 1234.5 is `{ digits: '12345', point: 4 }`, 0.012 is
+ * `{ digits: '12', point: -1 }` and zero is `{ digits: '', point: 0 }`.
+ */
+export type Decimal = { digits: string, point: number };
+
+const CHAR_0 = 48;
+const CHAR_5 = 53;
+const CHAR_9 = 57;
+const MIN_NORMAL = 2 ** -1022;
+
+// read a non-negative number written by String() or toPrecision()
+function parseDecimal (str: string): Decimal {
+  let exp = 0;
+  const e = str.indexOf('e');
+  if (e >= 0) {
+    exp = +str.slice(e + 1);
+    str = str.slice(0, e);
+  }
+  const dot = str.indexOf('.');
+  const digits = dot >= 0 ? str.slice(0, dot) + str.slice(dot + 1) : str;
+  let start = 0;
+  while (digits.charCodeAt(start) === CHAR_0) {
+    start++;
+  }
+  let end = digits.length;
+  while (end > start && digits.charCodeAt(end - 1) === CHAR_0) {
+    end--;
+  }
+  if (start === end) {
+    return { digits: '', point: 0 };
+  }
+  return {
+    digits: digits.slice(start, end),
+    point: (dot >= 0 ? dot : digits.length) + exp - start
+  };
+}
+
+// Is the (non-negative) number exactly halfway between two decimals of 15
+// significant digits, when it has `point` integer digits?
+function isTie (num: number, point: number): boolean {
+  if (point >= 15) {
+    // A tie is an odd multiple of 5 * 10 ** (point - 16), so a multiple of
+    // 5 ** (point - 15). Beyond 5 ** 22 that won't fit in a double's mantissa.
+    if (point > 37) {
+      return false;
+    }
+    const unit = 10 ** (point - 15);
+    return num % unit === unit / 2;
+  }
+  // Below that, a tie has a fraction. A fraction of k binary digits is
+  // exactly k decimal digits, ending in 5, so a tie has 16 - point of them.
+  return (
+    Number.isInteger(num * 2 ** (16 - point)) &&
+    !Number.isInteger(num * 2 ** (15 - point))
+  );
+}
+
+/**
+ * Return the magnitude of a finite number as Excel sees it: its exact value
+ * rounded to 15 significant digits, a tie going toward zero.
+ *
+ * @param num The number to convert.
+ * @returns The decimal.
+ */
+export function toDecimal (num: number): Decimal {
+  const v = Math.abs(num);
+  if (v < MIN_NORMAL) {
+    // Excel has no subnormal numbers, so round their shortest representation
+    return roundDigits(parseDecimal(String(v)), 15);
+  }
+  // toPrecision rounds the exact value, but rounds a tie away from zero
+  const dec = parseDecimal(v.toPrecision(15));
+  if (
+    isTie(v, dec.point) ||
+    // rounding up to a power of 10 adds an integer digit
+    (dec.digits === '1' && isTie(v, dec.point - 1))
+  ) {
+    // a tie has 16 digits, and its shortest representation is exact
+    const exact = parseDecimal(String(v));
+    return parseDecimal(exact.digits.slice(0, 15) + 'e' + (exact.point - 15));
+  }
+  return dec;
+}
+
+// round a decimal to its first `keep` digits, a tie going away from zero
+function roundDigits (dec: Decimal, keep: number): Decimal {
+  const digits = dec.digits;
+  if (keep >= digits.length) {
+    return dec;
+  }
+  if (keep < 0) {
+    return { digits: '', point: 0 };
+  }
+  let end = keep;
+  if (digits.charCodeAt(keep) >= CHAR_5) {
+    // drop trailing nines, they carry into the digit before them
+    while (end > 0 && digits.charCodeAt(end - 1) === CHAR_9) {
+      end--;
+    }
+    if (!end) {
+      return { digits: '1', point: dec.point + 1 };
+    }
+    return {
+      digits: digits.slice(0, end - 1) + (+digits[end - 1] + 1),
+      point: dec.point
+    };
+  }
+  while (end > 0 && digits.charCodeAt(end - 1) === CHAR_0) {
+    end--;
+  }
+  return end ? { digits: digits.slice(0, end), point: dec.point } : { digits: '', point: 0 };
+}
+
+/**
+ * Round a decimal to a number of decimal places, a tie going away from zero,
+ * and return its integer and fraction digits. The integer digits are empty
+ * when the rounded number is below 1, and the fraction digits have no trailing
+ * zeros.
+ *
+ * @param dec The decimal to round.
+ * @param places The number of decimals to round to.
+ * @returns The integer and fraction digits.
+ */
+export function roundDecimal (dec: Decimal, places: number): [ string, string ] {
+  const { digits, point } = roundDigits(dec, dec.point + places);
+  if (!digits) {
+    return [ '', '' ];
+  }
+  return [
+    point > 0 ? digits.slice(0, point).padEnd(point, '0') : '',
+    point >= 0 ? digits.slice(point) : '0'.repeat(-point) + digits
+  ];
+}

test/bigint.spec.ts

@@ -2,7 +2,7 @@ import { expect, test } from 'vitest';
 import { format } from '../lib/index.ts';
 
 test('bigint', () => {
-  expect(format('0', Number.MAX_SAFE_INTEGER)).toBe(String(Number.MAX_SAFE_INTEGER));
+  expect(format('0', Number.MAX_SAFE_INTEGER)).toBe('9007199254740990');
   expect(format('0', 10n)).toBe('10');
 
   expect(format('General', 10n)).toBe('10');

test/numfmt.spec.ts

@@ -332,3 +332,48 @@ test('General rounds 10 and 11 digit numbers with a fraction', () => {
   expect(numfmt('General', -4403928373.5)).toBe('-4403928374');
   expect(numfmt('General', -99999999999.6)).toBe('-1E+11');
 });
+
+test('Fixed-point numbers are written out in full, never in exponent notation', () => {
+  expect(numfmt('#,##0', 2 ** 70)).toBe('1,180,591,620,717,410,000,000');
+  expect(numfmt('0', 1e21)).toBe('1000000000000000000000');
+  expect(numfmt('#,##0', -1e21)).toBe('-1,000,000,000,000,000,000,000');
+  expect(numfmt('0.00', 1.23456789012345e22)).toBe('12345678901234500000000.00');
+  expect(numfmt('#,##0', 1e300)).toBe('1' + ',000'.repeat(100));
+  expect(numfmt('0.0000000000', 1e-7)).toBe('0.0000001000');
+  expect(numfmt('0.00000000000000000000', 1.5e-19)).toBe('0.00000000000000000015');
+});
+
+test('Fixed-point numbers round as in Excel', () => {
+  // the exact value is first rounded to 15 significant digits, a tie going toward zero
+  expect(numfmt('0', 10 ** 15 + 5)).toBe('1000000000000000');
+  expect(numfmt('0', -(10 ** 15 + 5))).toBe('-1000000000000000');
+  expect(numfmt('0', 10 ** 15 + 15)).toBe('1000000000000010');
+  expect(numfmt('0', 246913578024691 / 2)).toBe('123456789012345');
+  expect(numfmt('0', 2.5 - 2 ** -51)).toBe('3');
+  expect(numfmt('#,##0', 2 ** 60 + 1)).toBe('1,152,921,504,606,850,000');
+  // a tie whose upper neighbour is a power of ten
+  expect(numfmt('0', 999999999999999.5)).toBe('999999999999999');
+  expect(numfmt('0.0', 99999999999999.25)).toBe('99999999999999.2');
+  // then that decimal is rounded to the pattern's last digit, a tie going away from zero
+  expect(numfmt('0.00', 1.005)).toBe('1.01');
+  expect(numfmt('0.00', 1.015)).toBe('1.02');
+  expect(numfmt('0.00', 0.285)).toBe('0.29');
+  expect(numfmt('0.0', -0.15)).toBe('-0.2');
+  expect(numfmt('0', 2.5)).toBe('3');
+  expect(numfmt('0', -2.5)).toBe('-3');
+  expect(numfmt('0.00', 0.125)).toBe('0.13');
+  expect(numfmt('0', 12345678901234.5)).toBe('12345678901235');
+});
+
+test('Exponent notation rounds as in Excel', () => {
+  expect(numfmt('0.00000000000000E+00', 3 * 2 ** 51 + 1)).toBe('6.75539944105574E+15');
+  expect(numfmt('0.00E+00', 1.005)).toBe('1.01E+00');
+  expect(numfmt('0.00E+00', 9.995)).toBe('1.00E+01');
+  expect(numfmt('0.00E+00', 501.5)).toBe('5.02E+02');
+});
+
+test('Subnormal numbers are rounded from their shortest representation', () => {
+  expect(numfmt('0.00E+00', 1e-320)).toBe('1.00E-320');
+  expect(numfmt('0E+00', 5e-324)).toBe('5E-324');
+  expect(numfmt('0.00000000000000E+00', 2.225073858507201e-308)).toBe('2.22507385850720E-308');
+});