keen/bits

Functions for operating on the individual bits in nats / ints.

Bit indexes are counted from the right, so the least-siginificant digit is 0. So, the number 5 has bits 0 and 2 set, since 5 is 2**0 + 2**2.

~ nat8(a nat8)

Negates every bit. 0 bits become 1 bits and vice versa.

~ nat16(a nat16)

~ nat32(a nat32)

~ nat64(a nat64)

& nat8(a nat8, b nat8)

Intersection of bits; 'and's each corresponding bit in parallel. An output bit will be 1 iff both corresponding input bits are 1.

& nat16(a nat16, b nat16)

& nat32(a nat32, b nat32)

& nat64(a nat64, b nat64)

| nat8(a nat8, b nat8)

Union of bits; 'or's each corresponding bit in parallel. An output bit will be 1 iff either corresponding input bit is 1.

| nat16(a nat16, b nat16)

| nat32(a nat32, b nat32)

| nat64(a nat64, b nat64)

^ nat8(a nat8, b nat8)

Performs exclusive or of each bit in parallel. Output bits will be 1 iff the corresponding input bits are not equal.

^ nat16(a nat16, b nat16)

^ nat32(a nat32, b nat32)

^ nat64(a nat64, b nat64)

<< nat8(a nat8, b nat8)

Shifts the bits of 'a' left by 'b' bits. Does not rotate.

<< nat16(a nat16, b nat16)

<< nat32(a nat32, b nat32)

<< nat64(a nat64, b nat64)

rotate-left nat64(a nat64, amount nat64)

rotate-right nat64(a nat64, amount nat64)

>> nat8(a nat8, b nat8)

Shifts the bits of a right by b bits. Does not rotate.

>> nat16(a nat16, b nat16)

>> nat32(a nat32, b nat32)

>> nat64(a nat64, b nat64)

bits-intersect bool(a nat8, b nat8)

True iff the numbers have at least one bit in common.

bits-intersect bool(a nat16, b nat16)

bits-intersect bool(a nat32, b nat32)

bits-intersect bool(a nat64, b nat64)

has-all-bits bool(a nat8, b nat8)

True if for every 1 bit in b, the corresponding bit in a is also a 1.

has-all-bits bool(a nat16, b nat16)

has-all-bits bool(a nat32, b nat32)

has-all-bits bool(a nat64, b nat64)

nth-bit nat64(bit-index nat64)

Number with only the bit at bit-index set. Same as 1 << bit-index.

has-bit bool(a nat64, bit-index nat64)

True if the bit at bit-index is set.

add-bit nat64(a nat64, bit-index nat64)

Sets the bit at bit-index to 1.

sub-bit nat64(a nat64, bit-index nat64)

Sets the bit at bit-index to 0.

count-ones nat64(a nat64)

Returns the number of 1 bits in a.

bits-cat nat16(a nat8, b nat8)

bits-cat nat32(a nat16, b nat16)

bits-cat nat64(a nat32, b nat32)

Concatenates two 32-bit numbers to a 64-bit number. a will be the high bits and b will be the low bits.

high-n-bits nat32(n nat32)

Number with the highest n bits set.

high-n-bits nat64(n nat64)

low-n-bits nat32(n nat32)

Number with the lowest n bits set.

low-n-bits nat64(n nat64)

log-2-rounded-down nat64(a nat64)

is-power-of-two bool(a nat64)

round-up-to-power-of-two nat64(a nat64)