µδ code

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A binary maths hack, for use in DSP code and lossless compression

yann-guidon-ygdes

Yann Guidon / YGDES

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Step 1
Step 1: encoding
- Take A and B, two signed numbers made of N bits
- Compute the sum µ = A + B (with N+1 resolution)
- Compute the difference δ = A - B (with N+1 bits of resolution)
- Adjust the sign bit : µ = µ xor MSB(δ)
- Remove the LSB of µ : µ = µ shr 1 (µ now uses N bits)
- Remove the MSB of δ : δ = δ mod 2^N (δ now uses N bits)
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Step 2
Step 2: decoding
- Take the coded values µ and δ, with N bits each
- Restore the LSB of µ by copying it from δ: µ = (µ shl 1) + (δ mod 2)
- Restore A but drop the MSB: A = (µ + δ) mod 2^N
- Restore B but drop the MSB: B = (µ - δ) mod 2^N

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