floating precision positive whole numbers using arbitrary mantissa / exponent sizes

myfloat.js

function tomyfloat(mbits, ebits, value) {
  if(mbits + ebits > 31) throw new Error('no support for > 31 bits')
  if(value < 0) throw new Error('no support for negative numbers')
  if(Math.floor(value) !== value) throw new Error('no support for decimal numbers (lol)')
  if(value >= (2**mbits-1)*2**(2**ebits-1)) return 2**(mbits+ebits)-1
  const bitstr = value.toString(2)
  const len = bitstr.length
  let m = parseInt(bitstr.substr(0, mbits), 2)
  let e = Math.min(2**ebits-1, Math.max(0, len - mbits))
  if( (m < 2**mbits-1 || e < 2**ebits-1) && Math.abs(value - (m+1)*2**e) < Math.abs(value - m*2**e)) m++
  if(m > 2**mbits-1) {m /= 2; e++}
  return parseInt(m.toString(2).padStart(mbits, 0) + e.toString(2).padStart(ebits, 0), 2)
}
function frommyfloat(mbits, ebits, value) {
  const m = (value & ((2**mbits-1) << ebits)) >> ebits
  const e = value & 2**ebits-1
  return m*2**e
}






// create an 8 bit number that can represent values from 0 to 15032385536
for(const target of [256, 12345, 1000000000000000000]) {
  const mbits = 3
  const ebits = 5
  const bits = tomyfloat(mbits, ebits, target)
  const value = frommyfloat(mbits, ebits, bits)
  
  console.log('target value:', target)
  console.log('actual value:', value, {m:(bits & ((2**mbits-1) << ebits)) >> ebits, e:bits & 2**ebits-1, bits:bits.toString(2)})
}

// copy paste into browser console for demo