function tabulateFloat16(precision) { function float16to32(sign, exponent, significand) { const value = new Float32Array(1); const bytes = new Uint8Array(value.buffer); if (exponent === 0x1f) { // Infinities and NaNs exponent = 0xff; } else if (exponent === 0x00) { // Subnormals. I'm not going to bother trying to do this via bitwise conversion. return ((sign > 0 ? -1 : 1) * (Math.pow(2, -14) * significand)) / 1024; } else { // Convert to float32's offset-binary for normals: exponent = exponent - 15 + 127; } // Float32 is 23 bits, Float16 is 0. We shift the significand over // so that we can convert to float32. significand <<= 13; bytes[3] = (sign > 0 ? 0x80 : 0x0) | ((exponent >> 1) & 0x7f); bytes[2] = ((exponent & 0x1) << 7) | ((significand & 0x7f0000) >> 16); bytes[1] = (significand & 0xff00) >> 8; bytes[0] = significand & 0xff; return value[0]; } var subnormals = { exponents: [], values: [], labels: [], label: 'Subnormals' }; var normals = { exponents: [], values: [], labels: [], label: 'Normals' }; var infinities = { exponents: [], values: [], labels: [], label: 'Infinities' }; var nans = { exponents: [], values: [], labels: [], label: 'NaNs' }; var zeros = { exponents: [], values: [], labels: [], label: 'Zeros' }; for (let i = 0, sign = 0; sign < 2; sign++) { for (let exponent = 0; exponent < 32; exponent++) { for ( let significand = 0; significand < 1024; significand += Math.pow(2, 10 - precision) ) { let destination = normals; if (exponent === 0 && significand === 0) { destination = zeros; } else if (exponent === 31) { destination = significand === 0 ? infinities : nans; } else if (exponent === 0) { destination = subnormals; } var value = float16to32(sign, exponent, significand); var valueDisplay = exponent < 31 ? value : (sign > 0 ? -1 : 1) * Math.pow(2, 16) * (1 + significand / 1024); var exponentDisplay = Math.max(-14, exponent - 15); if (exponent === 0 && significand === 0) { exponentDisplay = exponentDisplay + (sign > 0 ? -0.2 : 0.2); } var valueLabel = value; if (significand === 0 && exponent === 0) { valueLabel = sign > 0 ? '-0' : '+0'; } destination.exponents.push(exponentDisplay); destination.values.push(valueDisplay); destination.labels.push( `value = ${valueLabel}
sign bit = ${sign.toString( 2 )}₂
exponent = ${exponent .toString(2) .padStart( 5, '0' )}₂
significand = ${significand .toString(2) .padStart(10, '0')}₂` ); i++; } } } return { normals, subnormals, nans, infinities, zeros }; }