TIP-39: Mana for IOTA 2.0

tips/TIP-0039/constraints.md

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+# Parameters constraints
+
+Due to the use of fixed point arithmetics, some contraints on the Mana parameters are needed to prevent overflowing of the variables used for the Mana decay and generation calculations.
+
+In particular, the function `Multiplication And Shift(valueHi, valueLo, multFactor, shiftFactor)` is applied to the following variables:
+
+- `Multiplication And Shift(Upper Bits(value, 32), Lower Bits(value, 32), Decay Factors(m), Decay Factors Exponent)`.
+- `Multiplication And Shift(Upper Bits(value, 32), Lower Bits(value, 32), slotIndexDiff * Generation Rate, Generation Rate Exponent)`.
+- `Multiplication And Shift(Upper Bits(Amount, 32), Lower Bits(Amount, 32), Decay Factor Epochs Sum * Generation Rate , Decay Factor Epochs Sum Exponent+generationRateExponent-slotsPerEpochExponent)`.
+By contruction, `Upper Bits(Amount, 32)` and `Upper Bits(Amount, 32)` will always use at most 32 bits (given that `Amount` uses at most 64 bits).
+
+Since `shiftFactor` must be an integer between 0 and 32, we have:
+
+- 0≤`Decay Factors Exponent`≤32.
+- 0≤`Generation Rate Exponent`≤32.
+- 0≤`Decay Factor Epochs Sum Exponent+generationRateExponent-slotsPerEpochExponent`≤32.
+- 0≤`generationRateExponent-slotsPerEpochExponent`≤32.
+
+The third variable `multFactor` must additionally use at most 32 bits, meaning that we have the following constraints:
+
+- `Decay Factors(m)`< <code>2<sup>32</sup></code> (which is equivalent, by contruction to 0≤`Decay Factors Exponent`≤3),
+- `slotIndexDiff * Generation Rate`< <code>2<sup>32</sup></code>,
+- `Decay Factor Epochs Sum * Generation Rate`< <code>2<sup>32</sup></code>.