CALCULATOR
Negative Input Floor Remainder with Power-of-Two Modulus Calculator
Negative Input Floor Remainder with Power-of-Two Modulus Calculator — change the supplied values to calculate negative input floor remainder with power-of-two modulus.
Input is magnitude0.01..100 of a strictly negative number; listed positive power-of-two modulus1..128 and floor convention for negatives. Zero, positive and tiny-subnormal signed input directions are excluded. Binary scaling avoids decimal quotient ambiguity; no general modulus, arbitrary integer or cryptographic arithmetic claim.
Accepted inputs: Magnitude: 0.01 to 100 number; Modulus: choose 1 (1), 2 (2), 4 (4), 8 (8), 16 (16), 32 (32), 64 (64), 128 (128).
How the calculation works
x=−magnitude; r=x−m floor(x/m)
Choose the floor quotient so its remainder lies between zero and the positive modulus in exact arithmetic.
Worked example
With magnitude 7 number, modulus 4, negative input floor remainder with power-of-two modulus is 1 number.
Assumptions and limits
Input is magnitude0.01..100 of a strictly negative number; listed positive power-of-two modulus1..128 and floor convention for negatives. Zero, positive and tiny-subnormal signed input directions are excluded. Binary scaling avoids decimal quotient ambiguity; no general modulus, arbitrary integer or cryptographic arithmetic claim.