Convert From Dec To Bin #223

How to divide big floats

Unsigned BigInt Rounding

/** @typedef bigint UBigInt */

/** @type {(a: UBigInt) => (b: UBigInt) => readonly[UBigInt, UBigInt]} */
const uDiv = a => b => [a / b, a % b]

/** @type {(a: UBigInt) => (b: UBigInt) => UBigInt} */
const uRoundDiv = a => b => {
    const [d, r] = uDiv(a)(b)
    const sign = cmp(r << 1)(b)
    return d + (sign === 0 ? d & 1 : sign >> 1)
}

/** @typedef {readonly[UBigInt, UBigInt, UBigInt]} UFraction */

/** @type {(a: UFraction) => (x: UBigInt) => UFraction */
const uFractionDiv = ([d0, r0, c0]) => c1 => {
  const [d1, r1] = uDiv(d0)(c1)
  return [d1, c0 * r0 + r1, c0 * c1]
}

Convert From One Base To Another

Our floating point number is represented as $m*r^e$.

• $m$ is an integer and $m > 0$,
• $e$ is an integer,
• $r$ is an integer and $base > 1$.

Any $m*base^e$ can be converted to a fraction of two unsigned integers.

if $e >= 0$ then $\frac{mr^e}{1}$ else $\frac{m}{r ^{-e}}$

As a result, we have $a / b$, where

• $a$ is an integer and $a > 0$,
• $b$ is an iteger and $b > 0$.

Converting a fraction to a floating point number

Assume $a <= b$

Find $m$ and $e$ where $b <= r^e < br$

$$\frac{a}{b} = \frac{m + x/b}{r^e},$$

where $r^n <= m < r^{n+1}$