plus(1, 0) = 1
plus(1, 1) = 2
plus(1, -1) = 0
plus(1, 31) = 32
plus(1, -31) = -30
plus(1, 2147483647) = -2147483648
plus(1, -2147483648) = -2147483647
plus(-1, 0) = -1
plus(-1, 1) = 0
plus(-1, -1) = -2
plus(-1, 31) = 30
plus(-1, -31) = -32
plus(-1, 2147483647) = 2147483646
plus(-1, -2147483648) = 2147483647
plus(31, 0) = 31
plus(31, 1) = 32
plus(31, -1) = 30
plus(31, 31) = 62
plus(31, -31) = 0
plus(31, 2147483647) = -2147483618
plus(31, -2147483648) = -2147483617
plus(-31, 0) = -31
plus(-31, 1) = -30
plus(-31, -1) = -32
plus(-31, 31) = 0
plus(-31, -31) = -62
plus(-31, 2147483647) = 2147483616
plus(-31, -2147483648) = 2147483617
plus(2147483647, 0) = 2147483647
plus(2147483647, 1) = -2147483648
plus(2147483647, -1) = 2147483646
plus(2147483647, 31) = -2147483618
plus(2147483647, -31) = 2147483616
plus(2147483647, 2147483647) = -2
plus(2147483647, -2147483648) = -1
plus(-2147483648, 0) = -2147483648
plus(-2147483648, 1) = -2147483647
plus(-2147483648, -1) = 2147483647
plus(-2147483648, 31) = -2147483617
plus(-2147483648, -31) = 2147483617
plus(-2147483648, 2147483647) = -1
plus(-2147483648, -2147483648) = 0

minus(1, 0) = 1
minus(1, 1) = 0
minus(1, -1) = 2
minus(1, 31) = -30
minus(1, -31) = 32
minus(1, 2147483647) = -2147483646
minus(1, -2147483648) = -2147483647
minus(-1, 0) = -1
minus(-1, 1) = -2
minus(-1, -1) = 0
minus(-1, 31) = -32
minus(-1, -31) = 30
minus(-1, 2147483647) = -2147483648
minus(-1, -2147483648) = 2147483647
minus(31, 0) = 31
minus(31, 1) = 30
minus(31, -1) = 32
minus(31, 31) = 0
minus(31, -31) = 62
minus(31, 2147483647) = -2147483616
minus(31, -2147483648) = -2147483617
minus(-31, 0) = -31
minus(-31, 1) = -32
minus(-31, -1) = -30
minus(-31, 31) = -62
minus(-31, -31) = 0
minus(-31, 2147483647) = 2147483618
minus(-31, -2147483648) = 2147483617
minus(2147483647, 0) = 2147483647
minus(2147483647, 1) = 2147483646
minus(2147483647, -1) = -2147483648
minus(2147483647, 31) = 2147483616
minus(2147483647, -31) = -2147483618
minus(2147483647, 2147483647) = 0
minus(2147483647, -2147483648) = -1
minus(-2147483648, 0) = -2147483648
minus(-2147483648, 1) = 2147483647
minus(-2147483648, -1) = -2147483647
minus(-2147483648, 31) = 2147483617
minus(-2147483648, -31) = -2147483617
minus(-2147483648, 2147483647) = 1
minus(-2147483648, -2147483648) = 0

times(1, 0) = 0
times(1, 1) = 1
times(1, -1) = -1
times(1, 31) = 31
times(1, -31) = -31
times(1, 2147483647) = 2147483647
times(1, -2147483648) = -2147483648
times(-1, 0) = 0
times(-1, 1) = -1
times(-1, -1) = 1
times(-1, 31) = -31
times(-1, -31) = 31
times(-1, 2147483647) = -2147483647
times(-1, -2147483648) = -2147483648
times(31, 0) = 0
times(31, 1) = 31
times(31, -1) = -31
times(31, 31) = 961
times(31, -31) = -961
times(31, 2147483647) = 2147483617
times(31, -2147483648) = -2147483648
times(-31, 0) = 0
times(-31, 1) = -31
times(-31, -1) = 31
times(-31, 31) = -961
times(-31, -31) = 961
times(-31, 2147483647) = -2147483617
times(-31, -2147483648) = -2147483648
times(2147483647, 0) = 0
times(2147483647, 1) = 2147483647
times(2147483647, -1) = -2147483647
times(2147483647, 31) = 2147483617
times(2147483647, -31) = -2147483617
times(2147483647, 2147483647) = 1
times(2147483647, -2147483648) = -2147483648
times(-2147483648, 0) = 0
times(-2147483648, 1) = -2147483648
times(-2147483648, -1) = -2147483648
times(-2147483648, 31) = -2147483648
times(-2147483648, -31) = -2147483648
times(-2147483648, 2147483647) = -2147483648
times(-2147483648, -2147483648) = 0

quotient(1, 1) = 1
quotient(1, -1) = -1
quotient(1, 31) = 0
quotient(1, -31) = 0
quotient(1, 2147483647) = 0
quotient(1, -2147483648) = 0
quotient(-1, 1) = -1
quotient(-1, -1) = 1
quotient(-1, 31) = 0
quotient(-1, -31) = 0
quotient(-1, 2147483647) = 0
quotient(-1, -2147483648) = 0
quotient(31, 1) = 31
quotient(31, -1) = -31
quotient(31, 31) = 1
quotient(31, -31) = -1
quotient(31, 2147483647) = 0
quotient(31, -2147483648) = 0
quotient(-31, 1) = -31
quotient(-31, -1) = 31
quotient(-31, 31) = -1
quotient(-31, -31) = 1
quotient(-31, 2147483647) = 0
quotient(-31, -2147483648) = 0
quotient(2147483647, 1) = 2147483647
quotient(2147483647, -1) = -2147483647
quotient(2147483647, 31) = 69273666
quotient(2147483647, -31) = -69273666
quotient(2147483647, 2147483647) = 1
quotient(2147483647, -2147483648) = 0
quotient(-2147483648, 1) = -2147483648
quotient(-2147483648, 31) = -69273666
quotient(-2147483648, -31) = 69273666
quotient(-2147483648, 2147483647) = -1
quotient(-2147483648, -2147483648) = 1

unchecked_quotient(1, 1) = 1
unchecked_quotient(1, -1) = -1
unchecked_quotient(1, 31) = 0
unchecked_quotient(1, -31) = 0
unchecked_quotient(1, 2147483647) = 0
unchecked_quotient(1, -2147483648) = 0
unchecked_quotient(-1, 1) = -1
unchecked_quotient(-1, -1) = 1
unchecked_quotient(-1, 31) = 0
unchecked_quotient(-1, -31) = 0
unchecked_quotient(-1, 2147483647) = 0
unchecked_quotient(-1, -2147483648) = 0
unchecked_quotient(31, 1) = 31
unchecked_quotient(31, -1) = -31
unchecked_quotient(31, 31) = 1
unchecked_quotient(31, -31) = -1
unchecked_quotient(31, 2147483647) = 0
unchecked_quotient(31, -2147483648) = 0
unchecked_quotient(-31, 1) = -31
unchecked_quotient(-31, -1) = 31
unchecked_quotient(-31, 31) = -1
unchecked_quotient(-31, -31) = 1
unchecked_quotient(-31, 2147483647) = 0
unchecked_quotient(-31, -2147483648) = 0
unchecked_quotient(2147483647, 1) = 2147483647
unchecked_quotient(2147483647, -1) = -2147483647
unchecked_quotient(2147483647, 31) = 69273666
unchecked_quotient(2147483647, -31) = -69273666
unchecked_quotient(2147483647, 2147483647) = 1
unchecked_quotient(2147483647, -2147483648) = 0
unchecked_quotient(-2147483648, 1) = -2147483648
unchecked_quotient(-2147483648, 31) = -69273666
unchecked_quotient(-2147483648, -31) = 69273666
unchecked_quotient(-2147483648, 2147483647) = -1
unchecked_quotient(-2147483648, -2147483648) = 1

mod(1, 1) = 0
mod(1, -1) = 0
mod(1, 31) = 1
mod(1, -31) = -30
mod(1, 2147483647) = 1
mod(1, -2147483648) = -2147483647
mod(-1, 1) = 0
mod(-1, -1) = 0
mod(-1, 31) = 30
mod(-1, -31) = -1
mod(-1, 2147483647) = 2147483646
mod(-1, -2147483648) = -1
mod(31, 1) = 0
mod(31, -1) = 0
mod(31, 31) = 0
mod(31, -31) = 0
mod(31, 2147483647) = 31
mod(31, -2147483648) = -2147483617
mod(-31, 1) = 0
mod(-31, -1) = 0
mod(-31, 31) = 0
mod(-31, -31) = 0
mod(-31, 2147483647) = 2147483616
mod(-31, -2147483648) = -31
mod(2147483647, 1) = 0
mod(2147483647, -1) = 0
mod(2147483647, 31) = 1
mod(2147483647, -31) = -30
mod(2147483647, 2147483647) = 0
mod(2147483647, -2147483648) = -1
mod(-2147483648, 1) = 0
mod(-2147483648, 31) = 29
mod(-2147483648, -31) = -2
mod(-2147483648, 2147483647) = 2147483646
mod(-2147483648, -2147483648) = 0

rem(1, 1) = 0
rem(1, -1) = 0
rem(1, 31) = 1
rem(1, -31) = 1
rem(1, 2147483647) = 1
rem(1, -2147483648) = 1
rem(-1, 1) = 0
rem(-1, -1) = 0
rem(-1, 31) = -1
rem(-1, -31) = -1
rem(-1, 2147483647) = -1
rem(-1, -2147483648) = -1
rem(31, 1) = 0
rem(31, -1) = 0
rem(31, 31) = 0
rem(31, -31) = 0
rem(31, 2147483647) = 31
rem(31, -2147483648) = 31
rem(-31, 1) = 0
rem(-31, -1) = 0
rem(-31, 31) = 0
rem(-31, -31) = 0
rem(-31, 2147483647) = -31
rem(-31, -2147483648) = -31
rem(2147483647, 1) = 0
rem(2147483647, -1) = 0
rem(2147483647, 31) = 1
rem(2147483647, -31) = 1
rem(2147483647, 2147483647) = 0
rem(2147483647, -2147483648) = 2147483647
rem(-2147483648, 1) = 0
rem(-2147483648, 31) = -2
rem(-2147483648, -31) = -2
rem(-2147483648, 2147483647) = -1
rem(-2147483648, -2147483648) = 0

unchecked_rem(1, 1) = 0
unchecked_rem(1, -1) = 0
unchecked_rem(1, 31) = 1
unchecked_rem(1, -31) = 1
unchecked_rem(1, 2147483647) = 1
unchecked_rem(1, -2147483648) = 1
unchecked_rem(-1, 1) = 0
unchecked_rem(-1, -1) = 0
unchecked_rem(-1, 31) = -1
unchecked_rem(-1, -31) = -1
unchecked_rem(-1, 2147483647) = -1
unchecked_rem(-1, -2147483648) = -1
unchecked_rem(31, 1) = 0
unchecked_rem(31, -1) = 0
unchecked_rem(31, 31) = 0
unchecked_rem(31, -31) = 0
unchecked_rem(31, 2147483647) = 31
unchecked_rem(31, -2147483648) = 31
unchecked_rem(-31, 1) = 0
unchecked_rem(-31, -1) = 0
unchecked_rem(-31, 31) = 0
unchecked_rem(-31, -31) = 0
unchecked_rem(-31, 2147483647) = -31
unchecked_rem(-31, -2147483648) = -31
unchecked_rem(2147483647, 1) = 0
unchecked_rem(2147483647, -1) = 0
unchecked_rem(2147483647, 31) = 1
unchecked_rem(2147483647, -31) = 1
unchecked_rem(2147483647, 2147483647) = 0
unchecked_rem(2147483647, -2147483648) = 2147483647
unchecked_rem(-2147483648, 1) = 0
unchecked_rem(-2147483648, 31) = -2
unchecked_rem(-2147483648, -31) = -2
unchecked_rem(-2147483648, 2147483647) = -1
unchecked_rem(-2147483648, -2147483648) = 0

left_shift(1, 0) = 1
left_shift(1, 1) = 2
left_shift(1, -1) = 0
left_shift(1, 31) = -2147483648
left_shift(1, -31) = 0
left_shift(-1, 0) = -1
left_shift(-1, 1) = -2
left_shift(-1, -1) = -1
left_shift(-1, 31) = -2147483648
left_shift(-1, -31) = -1
left_shift(31, 0) = 31
left_shift(31, 1) = 62
left_shift(31, -1) = 15
left_shift(31, 31) = -2147483648
left_shift(31, -31) = 0
left_shift(-31, 0) = -31
left_shift(-31, 1) = -62
left_shift(-31, -1) = -16
left_shift(-31, 31) = -2147483648
left_shift(-31, -31) = -1
left_shift(2147483647, 0) = 2147483647
left_shift(2147483647, 1) = -2
left_shift(2147483647, -1) = 1073741823
left_shift(2147483647, 31) = -2147483648
left_shift(2147483647, -31) = 0
left_shift(-2147483648, 0) = -2147483648
left_shift(-2147483648, 1) = 0
left_shift(-2147483648, -1) = -1073741824
left_shift(-2147483648, 31) = 0
left_shift(-2147483648, -31) = -1

unchecked_left_shift(1, 0) = 1
unchecked_left_shift(1, 1) = 2
unchecked_left_shift(1, 31) = -2147483648
unchecked_left_shift(-1, 0) = -1
unchecked_left_shift(-1, 1) = -2
unchecked_left_shift(-1, 31) = -2147483648
unchecked_left_shift(31, 0) = 31
unchecked_left_shift(31, 1) = 62
unchecked_left_shift(31, 31) = -2147483648
unchecked_left_shift(-31, 0) = -31
unchecked_left_shift(-31, 1) = -62
unchecked_left_shift(-31, 31) = -2147483648
unchecked_left_shift(2147483647, 0) = 2147483647
unchecked_left_shift(2147483647, 1) = -2
unchecked_left_shift(2147483647, 31) = -2147483648
unchecked_left_shift(-2147483648, 0) = -2147483648
unchecked_left_shift(-2147483648, 1) = 0
unchecked_left_shift(-2147483648, 31) = 0

right_shift(1, 0) = 1
right_shift(1, 1) = 0
right_shift(1, -1) = 2
right_shift(1, 31) = 0
right_shift(1, -31) = -2147483648
right_shift(-1, 0) = -1
right_shift(-1, 1) = -1
right_shift(-1, -1) = -2
right_shift(-1, 31) = -1
right_shift(-1, -31) = -2147483648
right_shift(31, 0) = 31
right_shift(31, 1) = 15
right_shift(31, -1) = 62
right_shift(31, 31) = 0
right_shift(31, -31) = -2147483648
right_shift(-31, 0) = -31
right_shift(-31, 1) = -16
right_shift(-31, -1) = -62
right_shift(-31, 31) = -1
right_shift(-31, -31) = -2147483648
right_shift(2147483647, 0) = 2147483647
right_shift(2147483647, 1) = 1073741823
right_shift(2147483647, -1) = -2
right_shift(2147483647, 31) = 0
right_shift(2147483647, -31) = -2147483648
right_shift(-2147483648, 0) = -2147483648
right_shift(-2147483648, 1) = -1073741824
right_shift(-2147483648, -1) = 0
right_shift(-2147483648, 31) = -1
right_shift(-2147483648, -31) = 0

unchecked_right_shift(1, 0) = 1
unchecked_right_shift(1, 1) = 0
unchecked_right_shift(1, 31) = 0
unchecked_right_shift(-1, 0) = -1
unchecked_right_shift(-1, 1) = -1
unchecked_right_shift(-1, 31) = -1
unchecked_right_shift(31, 0) = 31
unchecked_right_shift(31, 1) = 15
unchecked_right_shift(31, 31) = 0
unchecked_right_shift(-31, 0) = -31
unchecked_right_shift(-31, 1) = -16
unchecked_right_shift(-31, 31) = -1
unchecked_right_shift(2147483647, 0) = 2147483647
unchecked_right_shift(2147483647, 1) = 1073741823
unchecked_right_shift(2147483647, 31) = 0
unchecked_right_shift(-2147483648, 0) = -2147483648
unchecked_right_shift(-2147483648, 1) = -1073741824
unchecked_right_shift(-2147483648, 31) = -1