Convert a boolean to an int64std/core/types/int64: V.
Convert a pair (histd/num/int64/hi: (i : int64) -> int64,lostd/num/int64/lo: (i : int64) -> int64) to an signed integer,
where (histd/num/int64/hi: (i : int64) -> int64,lostd/num/int64/lo: (i : int64) -> int64).int == histd/num/int64/hi: (i : int64) -> int64.int * 0x1_0000_0000_0000_0000 + lostd/num/int64/lo: (i : int64) -> int64.uint.
Create an int64std/core/types/int64: V from the given histd/num/int64/hi: (i : int64) -> int64 and lostd/num/int64/lo: (i : int64) -> int64 numbers lowest 32-bits.
Preserves the sign of histd/num/int64/hi: (i : int64) -> int64.
Convert a pair (histd/num/int64/hi: (i : int64) -> int64,lostd/num/int64/lo: (i : int64) -> int64) to an unsigned integer,
where (histd/num/int64/hi: (i : int64) -> int64,lostd/num/int64/lo: (i : int64) -> int64).uint == histd/num/int64/hi: (i : int64) -> int64.uint * 0x1_0000_0000_0000_0000 + lostd/num/int64/lo: (i : int64) -> int64.uint.
Create an int64std/core/types/int64: V i from the bits of lostd/num/int64/lo: (i : int64) -> int64 and histd/num/int64/hi: (i : int64) -> int64 such
that i.int = histd/num/int64/hi: (i : int64) -> int64.int * 0x1_0000_0000 + lostd/num/int64/lo: (i : int64) -> int64.uint.
Convert an intstd/core/types/int: V to int64std/core/types/int64: V but interpret the int as an unsigned 64-bit value.
i is clamped between 0 and 0xFFFF_FFFF_FFFF_FFFF.
0x7FFF_FFFF_FFFF_FFFF.uint64 == 0x7FFF_FFFF_FFFF_FFFF.int64 == max-int64std/num/int64/max-int64: int64
0x8000_0000_0000_0000.uint64 == -0x8000_0000_0000_0000.int64 == min-int64std/num/int64/min-int64: int64
0xFFFF_FFFF_FFFF_FFFF.uint64 == -1.int64.
Convert an int32std/core/types/int32: V to an int64std/core/types/int64: V (using sign extension).
Convert an int64std/core/types/int64: V to an intstd/core/types/int: V but interpret the int64std/core/types/int64: V as a 64-bit unsigned value.
Executes action for each integer between start upto end (including both start and end ).
If start > end the function returns without any call to action .
If action returns Juststd/core/types/Just: forall<a> (value : a) -> maybe<a>, the iteration is stopped and the result returned.
Are two 64-bit integers not equal?
Euclidean-0 modulus. See (/):(x : int64std/core/types/int64: V, y : int64std/core/types/int64: V) -> int64std/core/types/int64: V division for more information.
Multiply two 64-bit integers.
Add two 64-bit integers.
Subtract two 64-bit integers.
Euclidean-0 division.
Euclidean division is defined as: For any D and d where d!=0 , we have:
D == d*(D/d) + (D%d)
D%d is always positive where 0 <= D%d < abs(d)
Moreover, Euclidean-0 is a total function, for the case where d==0 we have
that D%0 == D and D/0 == 0 . So property (1) still holds, but not property (2).
Useful laws that hold for Euclidean-0 division:
D/(-d) == -(D/d)
D%(-d) == D%d
D/(2^n) == sarstd/num/int64/sar: (i : int64, shift : int) -> int64(D,n) (with 0 <= n <= 63)
D%(2n) == D & ((2n) - 1) (with 0 <= n <= 63)
Note that an interesting edge case is min-int64std/num/int64/min-int64: int64 / -1 which equals min-int64std/num/int64/min-int64: int64 since in modulo 64-bit
arithmetic min-int64std/num/int64/min-int64: int64 == -1 * min-int64std/num/int64/min-int64: int64 == -1 * (min-int64std/num/int64/min-int64: int64 / -1) + (min-int64std/num/int64/min-int64: int64 % -1) satisfying property (1).
Of course (min-int64std/num/int64/min-int64: int64 + 1) / -1 is again positive (namely max-int64std/num/int64/max-int64: int64).
See also Division and modulus for computer scientists, Daan Leijen, 2001 pdf .
Is the first 64-bit integer smaller than the second?
Is the first 64-bit integer smaller or equal to the second?
Are two 64-bit integers equal?
Is the first 64-bit integer larger than the second?
Is the first 64-bit integer larger or equal to the second?
Take the bitwise xor of two int64std/core/types/int64: Vs.
Negate an 64-bit integer.
Return the absolute value of an integer.
Raises an exception if the int64std/core/types/int64: V is min-int64std/num/int64/min-int64: int64
(since the negation of min-int64std/num/int64/min-int64: int64 equals itself and is still negative).
Return the absolute value of an integer.
Returns 0 if the int64std/core/types/int64: V is min-int64std/num/int64/min-int64: int64
(since the negation of min-int64std/num/int64/min-int64: int64 equals itself and is still negative).
Take the bitwise and of two int64std/core/types/int64: Vs.
Bit gather (also known as pext or parallel bit extract).
For each 1-bit in mask m, extract the corresponding bit from i and write it
into contiguous lower bits in the result. The remaining bits in the result are zero.
bit-gatherstd/num/int64/bit-gather: (i : int64, m : int64) -> int64(0x1234.int64, 0x0F0F.int64).show-hex == "0x24".
Reverse the bits in an int64std/core/types/int64: V.
Bit scatter (also known as pdep or parallel bit deposit).
For each 1-bit in mask m, set the corresponding bit in the result from the
contiguous lower bits of i. Any bits not set according to the mask are set to zero.
bit-scatterstd/num/int64/bit-scatter: (i : int64, m : int64) -> int64(0x1234.int64, 0x0F0F.int64).show-hex == "0x304".
De-interleave the bits in i such that the odd bits are gathered in the
hi 32-bits of the result, and the even bits (starting at bit 0)
end up in the lo 32-bits of the result.
bit-unzipstd/num/int64/bit-unzip: (i : int64) -> int64(x).andstd/num/int64/and: (int64, int64) -> int64(0xFFFF_FFFF.int64) == bit-gatherstd/num/int64/bit-gather: (i : int64, m : int64) -> int64(x,0x5555_5555_5555_5555.int64).
Interleave the hi 32-bits with the lo 32-bits of the argument i such
that the hi bits are spread over the odd bits and the lo bits over the even bits
of the result (starting at bit 0).
bit-zipstd/num/int64/bit-zip: (i : int64) -> int64(x.andstd/num/int64/and: (int64, int64) -> int64(0xFFFF_FFFF.int64)) == bit-scatterstd/num/int64/bit-scatter: (i : int64, m : int64) -> int64(x,0x5555_5555_5555_5555.int64).
The number of bits in an int64std/core/types/int64: V (always 64).
Convert an int64std/core/types/int64: V to a boolean.
Reverse the bytes in an int64std/core/types/int64: V.
Truncated division (as in C). See also (/):(x : int64std/core/types/int64: V, y : int64std/core/types/int64: V) -> int64std/core/types/int64: V.
Carry-less multiplication (or xor multiplication).
See also https://en.wikipedia.org/wiki/Carry-less_product
Interesting cases:
- clmulstd/num/int64/clmul: (x : int64, y : int64) -> int64(x,x) : bit spread, where a zero bit is put in between each input bit.
clmulstd/num/int64/clmul: (x : int64, y : int64) -> int64(x,x) == bit-scatterstd/num/int64/bit-scatter: (i : int64, m : int64) -> int64(x,0x5555_5555_5555_5555.int64) == bit-zipstd/num/int64/bit-zip: (i : int64) -> int64(andstd/num/int64/and: (int64, int64) -> int64(x,0xFFFF_FFFF.int64))
- clmulstd/num/int64/clmul: (x : int64, y : int64) -> int64(x,-1.int32std/num/int64/int32: (i : int64) -> int32): prefix xor, where each bit is the parity of the corresponding input bit
and all input bits before it (the xor sum).
clmulstd/num/int64/clmul: (x : int64, y : int64) -> int64(x,-1.int64).shrstd/num/int64/shr: (i : int64, shift : int) -> int64(63).bool == x.paritystd/num/int64/parity: (i : int64) -> bool.
Wide carry-less multiplication (or xor multiplication) to (histd/num/int64/hi: (i : int64) -> int64,lostd/num/int64/lo: (i : int64) -> int64),
where (histd/num/int64/hi: (i : int64) -> int64,lostd/num/int64/lo: (i : int64) -> int64).int == histd/num/int64/hi: (i : int64) -> int64.int * 0x1_0000_0000_0000_0000 + lostd/num/int64/lo: (i : int64) -> int64.uint.
See also https://en.wikipedia.org/wiki/Carry-less_product.
Reverse carry-less multiplication.
Defined as clmulrstd/num/int64/clmulr: (x : int64, y : int64) -> int64(x,y) == clmulstd/num/int64/clmul: (x : int64, y : int64) -> int64(x.bit-reversestd/num/int64/bit-reverse: (i : int64) -> int64,y.bitreverse).bitreverse
Interesting cases:
- clmulrstd/num/int64/clmulr: (x : int64, y : int64) -> int64(x,x) == zipstd/core/list/zip: forall<a,b> (xs : list<a>, ys : list<b>) -> list<(a, b)>(x.andstd/num/int64/and: (int64, int64) -> int64(0xFFFF_FFFF_0000_0000.int64), and
- zipstd/core/list/zip: forall<a,b> (xs : list<a>, ys : list<b>) -> list<(a, b)>(x) == clmulstd/num/int64/clmul: (x : int64, y : int64) -> int64(x,x) | clmulrstd/num/int64/clmulr: (x : int64, y : int64) -> int64(x,x).
Count leading redundant sign bits (i.e. the number of bits following the most significant bit that are identical to it).
Count leading zero bits. Returns 64 if i is zero.
Truncated modulus (as in C). See also (%):(x : int64std/core/types/int64: V, y : int64std/core/types/int64: V) -> int64std/core/types/int64: V.
Count trailing zero bits. Returns 64 if i is zero.
Decrement a 64-bit integer.
Return the top 32-bits of an int64std/core/types/int64: V.
Preserves the sign.
Convenient shorthand to int64, e.g. 1234.i64std/num/int64/i64: (i : int) -> int64.
Full 64x64 to 128-bit signed multiply to (histd/num/int64/hi: (i : int64) -> int64,lostd/num/int64/lo: (i : int64) -> int64).
where imulstd/num/int64/imul: (i : int64, j : int64) -> (int64, int64)(x,y).int == x.int * y.int.
Increment a 64-bit integer.
Convert an int64_t to an intstd/core/types/int: V.
Clamp an int64std/core/types/int64: V to an int32std/core/types/int32: V
-1.int64.int32std/num/int64/int32: (i : int64) -> int32 == -1.int32std/num/int64/int32: (i : int64) -> int32
0x8000_0000.int64.int32std/num/int64/int32: (i : int64) -> int32 == 0x7FFF_FFFF.int32std/num/int64/int32: (i : int64) -> int32 (clamped).
Clamp an intstd/core/types/int: V to fit in an int64_t.
Returns true if the integer i is an even number.
Is the 64-bit integer negative?
Returns true if the integer i is an odd number.
Is the 64-bit integer positive? (i.e. larger than zero).
Is the 64-bit integer zero?
Return the low 32-bits of an int64std/core/types/int64: V.
Return the maximum of two integers.
The maximal integer value before overflow happens.
Return the minimum of two integers.
The minimal integer value before underflow happens.
Negate a 64-bit integer.
Bitwise not of an int64std/core/types/int64: V, i.e. flips all bits.
The 64-bit integer for 1.
Take the bitwise or of two int64std/core/types/int64: Vs.
Or-combine: for every byte b in the argument i, the corresponding
byte in the result becomes 0 if b==0, and 0xFF otherwise.
Is the popcountstd/num/int64/popcount: (i : int64) -> int even?
Count number of 1-bits.
Bitwise rotate an int64std/core/types/int64: V n % 64 bits to the left.
Bitwise rotate an int64std/core/types/int64: V n % 64 bits to the right.
Arithmetic shift an int64std/core/types/int64: V to the right by n % 64 bits. Shift in the sign bit from the left.
Shift an int64std/core/types/int64: V i to the left by n % 64 bits.
Convert an int64std/core/types/int64: V to a string.
Show an int64std/core/types/int64: V in hexadecimal notation
The width parameter specifies how wide the hex value is where '0' is used to align.
The use-capitals parameter (= Truestd/core/types/True: bool) determines if captical letters should be used to display the hexadecimal digits.
The pre (="0x") is an optional prefix for the number (goes between the sign and the number).
Show an int64std/core/types/int64: V in hexadecimal notation interpreted as an unsigned 64-bit value.
The width parameter specifies how wide the hex value is where '0' is used to align.
The use-capitals parameter (= Truestd/core/types/True: bool) determines if captical letters should be used to display the hexadecimal digits.
The pre (="0x") is an optional prefix for the number.
Logical shift an int64std/core/types/int64: V to the right by n % 64 bits. Shift in zeros from the left.
Compare a 64-integer to zero.
Clamp an int64std/core/types/int64: V to an int32std/core/types/int32: V but interpreting the int32std/core/types/int32: V as unsigned
(and thus clamp between 0 and 0xFFFFFFFF).
-1.int64.uint32std/num/int64/uint32: (i : int64) -> int32 == 0.int32std/num/int64/int32: (i : int64) -> int32 (clamped)
0xFFFFFFFF.int64.uint32std/num/int64/uint32: (i : int64) -> int32 == -1.int32std/num/int64/int32: (i : int64) -> int32.
Convert an int32std/core/types/int32: V to an int64std/core/types/int64: V interpreting the int32std/core/types/int32: V as unsigned.
Full 64x64 to 128-bit unsigned multiply to (histd/num/int64/hi: (i : int64) -> int64,lostd/num/int64/lo: (i : int64) -> int64).
where umulstd/num/int64/umul: (i : int64, j : int64) -> (int64, int64)(x,y).uint == x.uint * y.uint.
Take the bitwise xor of two int64std/core/types/int64: Vs.
The 64-bit integer for zero.
64-bit signed integers.
Using 64-bit signed two's complement representation with wrapping on overflow, e.g.
max-int64std/num/int64/max-int64: int64 + 1.int64 == min-int64std/num/int64/min-int64: int64.