floating point

• How to Convert a Number to Binary
  Use repeated division by 2 for the integer part and repeated multiplication by 2 for the fraction, then normalize and round for IEEE 754.
• How to Find the Mantissa in a Floating-Point Binary Number
  To find a floating-point mantissa, split the IEEE 754 fields, restore the implicit leading bit for normal values, and account for subnormals.
• How to Compute the Sine of Huge Numbers
  For huge angles, compute sine by reducing the input modulo 2π. Learn why ordinary floating-point remainder can fail and when to use high precision.