Lesson 11 · Decoding 32-bit float samples

Decoding 32-bit float samples

Modern audio pipelines often store samples as 32-bit floats in the range -1.0 to 1.0, sidestepping clipping entirely. Today you decode IEEE 754 floats from their little-endian bytes.

The goal

Decode 32-bit little-endian IEEE 754 float samples into floating-point values.

Start here - the target

TO DO

Scenario: 32-bit little-endian bytes decode to IEEE 754 floats

Giventhe sixteen data bytes 00 00 80 3F 00 00 80 BF 00 00 00 00 00 00 00 3F

Whenthey are decoded as 32-bit float little-endian samples

Thenthe samples are [1.0, -1.0, 0.0, 0.5]

And00 00 80 3F is the bit pattern 0x3F800000, which is exactly 1.0

Background

Floating-point WAV (audioFormat 3, WAVE_FORMAT_IEEE_FLOAT) stores each sample as a 32-bit IEEE 754 float, normally in the nominal range -1.0 to +1.0 where 1.0 is full scale. The huge advantage is headroom: intermediate values can exceed 1.0 without clipping, so mixing and effects stay clean until you convert back to integers at the end. It is the native format of most audio software today.

Decoding is two steps: assemble the four little-endian bytes into a uint32 bit pattern exactly as you did for 32-bit integers, then reinterpret those same bits as a float rather than converting the number. 00 00 80 3F little-endian is 0x3F800000, and that bit pattern - sign 0, exponent representing 2^0, mantissa 0 - is precisely 1.0. The reinterpret (not a numeric cast) is the key move; every language has a “bits to float” primitive for it. With four integer depths plus float, you can now read any common PCM sample.

Make it work

// combine 4 LE bytes into a uint32, then reinterpret those bits as float32
func decodeF32(b []byte) []float64 {
  var out []float64
  for i := 0; i+3 < len(b); i += 4 {
    bits := uint32(b[i]) | uint32(b[i+1])<<8 | uint32(b[i+2])<<16 | uint32(b[i+3])<<24
    out = append(out, float64(math.Float32frombits(bits)))
  }
  return out
}

CheckpointDONE

You can decode 32-bit float samples. Commit and stop here.