Arithmetic

Arithmetic operations on two encrypted values of the same type. All arithmetic uses wrapping semantics, matching Solidity's unchecked behavior: on overflow or underflow, values wrap around the type boundary instead of reverting.

For overflow-safe variants, see Safe Arithmetic.

Supported types: euint16, euint256, eint16, eint256

Usage

euint256 total = Nox.add(balance, deposit);
euint256 remaining = Nox.sub(total, fee);
euint256 reward = Nox.mul(remaining, rate);
euint256 share = Nox.div(reward, participantCount);
Nox.allowThis(share);

add

function add(euint256 a, euint256 b) internal returns (euint256)

Wrapping addition. On overflow, the result wraps around the type boundary.

• Unsigned: (a + b) mod 2^N
• Signed: (a + b) mod 2^N, interpreted in two's complement. For example on Int8, adding past 127 continues from -128

Example (Uint8)	Result	Reason
200 + 100	44	Overflows, wraps around
255 + 1	0	Overflows to zero
100 + 50	150	No overflow

Example (Int8)	Result	Reason
100 + 100	-56	Overflows, wraps to negative
127 + 1	-128	Overflows to MIN
-50 + 30	-20	No overflow

sub

function sub(euint256 a, euint256 b) internal returns (euint256)

Wrapping subtraction. On underflow, the result wraps around the type boundary.

• Unsigned: when the result would be negative, it wraps around through MAX. For example on Uint8, 0 - 1 gives 255
• Signed: when the result goes below MIN, it wraps around through MAX. For example on Int8, -128 - 1 gives 127

Example (Uint8)	Result	Reason
0 - 1	255	Underflows, wraps to MAX
10 - 200	66	Underflows, wraps around
100 - 30	70	No underflow

Example (Int8)	Result	Reason
-128 - 1	127	Underflows, wraps to MAX
-100 - 100	56	Underflows, wraps to positive
50 - 30	20	No underflow

mul

function mul(euint256 a, euint256 b) internal returns (euint256)

Wrapping multiplication. On overflow, the result wraps around the type boundary.

• Unsigned: (a * b) mod 2^N
• Signed: (a * b) mod 2^N, interpreted in two's complement

Example (Uint8)	Result	Reason
3 * 100	44	Overflows, wraps around
16 * 16	0	Overflows to zero
10 * 5	50	No overflow

Example (Int8)	Result	Reason
-1 * -128	-128	Overflows, wraps back to MIN
10 * 20	-56	Overflows, wraps to negative
-5 * 3	-15	No overflow

div

function div(euint256 a, euint256 b) internal returns (euint256)

Integer division, truncated toward zero. Division by zero does not revert, it returns the maximum representable value of the type (saturates toward +infinity).

• Unsigned: returns 2^N - 1 (MAX_U). For example on Uint8, 10 / 0 gives 255
• Signed: returns 2^(N-1) - 1 (MAX_I). For example on Int8, 10 / 0 gives 127. Additionally, MIN / -1 wraps back to MIN because the true result (128) exceeds MAX_I (127)

Example (Uint8)	Result	Reason
10 / 0	255	Division by zero, returns MAX_U
7 / 2	3	Truncated toward zero
1 / 2	0	Truncated toward zero
0 / 5	0	Zero numerator

Example (Int8)	Result	Reason
10 / 0	127	Division by zero, returns MAX_I
-128 / -1	-128	Overflow, wraps back to MIN
7 / 2	3	Truncated toward zero
-7 / 2	-3	Truncated toward zero