```
trait val _ArithmeticConvertible
fun i8(): I8 => compile_intrinsic
fun i16(): I16 => compile_intrinsic
fun i32(): I32 => compile_intrinsic
fun i64(): I64 => compile_intrinsic
fun i128(): I128 => compile_intrinsic
fun ilong(): ILong => compile_intrinsic
fun isize(): ISize => compile_intrinsic
fun u8(): U8 => compile_intrinsic
fun u16(): U16 => compile_intrinsic
fun u32(): U32 => compile_intrinsic
fun u64(): U64 => compile_intrinsic
fun u128(): U128 => compile_intrinsic
fun ulong(): ULong => compile_intrinsic
fun usize(): USize => compile_intrinsic
fun f32(): F32 => compile_intrinsic
fun f64(): F64 => compile_intrinsic
fun i8_unsafe(): I8 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun i16_unsafe(): I16 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun i32_unsafe(): I32 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun i64_unsafe(): I64 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun i128_unsafe(): I128 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun ilong_unsafe(): ILong =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun isize_unsafe(): ISize =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun u8_unsafe(): U8 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun u16_unsafe(): U16 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun u32_unsafe(): U32 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun u64_unsafe(): U64 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun u128_unsafe(): U128 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun ulong_unsafe(): ULong =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun usize_unsafe(): USize =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun f32_unsafe(): F32 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
fun f64_unsafe(): F64 =>
"""
Unsafe operation.
If the value doesn't fit in the destination type, the result is undefined.
"""
compile_intrinsic
trait val Real[A: Real[A] val] is
(Stringable & _ArithmeticConvertible & Comparable[A])
new val create(value: A)
new val from[B: (Number & Real[B] val)](a: B)
new val min_value()
new val max_value()
fun add(y: A): A => this + y
fun sub(y: A): A => this - y
fun mul(y: A): A => this * y
fun div(y: A): A =>
"""
Integer division, rounded towards zero.
"""
this / y
fun divrem(y: A): (A, A) => (this / y, this % y)
fun rem(y: A): A =>
"""
Calculate the remainder after integer division, rounded towards zero (`div`).
The result has the sign of the dividend.
"""
this % y
fun neg(): A => -this
fun fld(y: A): A
"""
Floored integer division, rounded towards negative infinity.
"""
fun mod(y: A): A
"""
Calculate the modulo after floored integer division, rounded towards negative infinity (`fld`).
The result has the sign of the divisor.
"""
fun eq(y: box->A): Bool => this == y
fun ne(y: box->A): Bool => this != y
fun lt(y: box->A): Bool => this < y
fun le(y: box->A): Bool => this <= y
fun ge(y: box->A): Bool => this >= y
fun gt(y: box->A): Bool => this > y
fun min(y: A): A
fun max(y: A): A
fun hash(): USize =>
var x = usize()
ifdef ilp32 then
x = (not x) + (x << 15)
x = x xor (x >> 12)
x = x + (x << 2)
x = x xor (x >> 4)
x = (x + (x << 3)) + (x << 11)
x = x xor (x >> 16)
x
else
hash64().usize()
end
fun hash64(): U64 =>
var x = u64()
x = (not x) + (x << 21)
x = x xor (x >> 24)
x = (x + (x << 3)) + (x << 8)
x = x xor (x >> 14)
x = (x + (x << 2)) + (x << 4)
x = x xor (x >> 28)
x = x + (x << 31)
x
fun _value(): A => compile_intrinsic
trait val Integer[A: Integer[A] val] is Real[A]
fun add_unsafe(y: A): A =>
"""
Unsafe operation.
If the operation overflows, the result is undefined.
"""
this +~ y
fun sub_unsafe(y: A): A =>
"""
Unsafe operation.
If the operation overflows, the result is undefined.
"""
this -~ y
fun mul_unsafe(y: A): A =>
"""
Unsafe operation.
If the operation overflows, the result is undefined.
"""
this *~ y
fun div_unsafe(y: A): A =>
"""
Integer division, rounded towards zero.
Unsafe operation.
If y is 0, the result is undefined.
If the operation overflows, the result is undefined.
"""
this /~ y
fun divrem_unsafe(y: A): (A, A) =>
"""
Calculates the quotient of this number and `y` and the remainder.
Unsafe operation.
If y is 0, the result is undefined.
If the operation overflows, the result is undefined.
"""
(this /~ y, this %~ y)
fun rem_unsafe(y: A): A =>
"""
Calculates the remainder of this number divided by `y`.
Unsafe operation.
If y is 0, the result is undefined.
If the operation overflows, the result is undefined.
"""
this %~ y
fun fld_unsafe(y: A): A
"""
Floored division, rounded towards negative infinity,
as opposed to `div` which rounds towards zero.
*Unsafe Operation*
If y is 0, the result is undefined.
If the operation overflows, the result is undefined.
"""
fun mod_unsafe(y: A): A
"""
Calculates the modulo of this number after floored division by `y`.
*Unsafe Operation.*
If y is 0, the result is undefined.
If the operation overflows, the result is undefined.
"""
fun add_partial(y: A): A ?
"""
Add y to this number.
If the operation overflows this function errors.
"""
fun sub_partial(y: A): A ?
"""
Subtract y from this number.
If the operation overflows/underflows this function errors.
"""
fun mul_partial(y: A): A ?
"""
Multiply y with this number.
If the operation overflows this function errors.
"""
fun div_partial(y: A): A ?
"""
Divides this number by `y`, rounds the result towards zero.
If y is `0` or the operation overflows, this function errors.
"""
fun rem_partial(y: A): A ?
"""
Calculates the remainder of this number divided by y.
The result has the sign of the dividend.
If y is `0` or the operation overflows, this function errors.
"""
fun divrem_partial(y: A): (A, A) ?
"""
Divides this number by y and calculates the remainder of the operation.
If y is `0` or the operation overflows, this function errors.
"""
fun fld_partial(y: A): A ?
"""
Floored integer division, rounded towards negative infinity.
If y is `0` or the operation overflows, this function errors
"""
fun mod_partial(y: A): A ?
"""
Calculates the modulo of this number and `y` after floored division (`fld`).
The result has the sign of the divisor.
If y is `0` or the operation overflows, this function errors.
"""
fun neg_unsafe(): A =>
"""
Unsafe operation.
If the operation overflows, the result is undefined.
"""
-~this
fun addc(y: A): (A, Bool)
"""
Add `y` to this integer and return the result and a flag indicating overflow.
"""
fun subc(y: A): (A, Bool)
"""
Subtract `y` from this integer and return the result and a flag indicating overflow.
"""
fun mulc(y: A): (A, Bool)
"""
Multiply `y` with this integer and return the result and a flag indicating overflow.
"""
fun divc(y: A): (A, Bool)
"""
Divide this integer by `y` and return the result and a flag indicating overflow or division by zero.
"""
fun remc(y: A): (A, Bool)
"""
Calculate the remainder of this number divided by `y` and return the result and a flag indicating division by zero or overflow.
The result will have the sign of the dividend.
"""
fun fldc(y: A): (A, Bool)
"""
Divide this integer by `y` and return the result, rounded towards negative infinity and a flag indicating overflow or division by zero.
"""
fun modc(y: A): (A, Bool)
"""
Calculate the modulo of this number after floored division by `y` and return the result and a flag indicating division by zero or overflow.
The result will have the sign of the divisor.
"""
fun op_and(y: A): A => this and y
fun op_or(y: A): A => this or y
fun op_xor(y: A): A => this xor y
fun op_not(): A => not this
fun bit_reverse(): A
"""
Reverse the order of the bits within the integer.
For example, 0b11101101 (237) would return 0b10110111 (183).
"""
fun bswap(): A
trait val SignedInteger[A: SignedInteger[A, B] val,
B: UnsignedInteger[B] val] is Integer[A]
fun abs(): B
fun shl(y: B): A => this << y
fun shr(y: B): A => this >> y
fun shl_unsafe(y: B): A =>
"""
Unsafe operation.
If bits differing from the final sign bit are shifted-out, the result is
undefined.
"""
this <<~ y
fun shr_unsafe(y: B): A =>
"""
Unsafe operation.
If non-zero bits are shifted-out, the result is undefined.
"""
this >>~ y
fun popcount(): B
fun clz(): B
fun ctz(): B
fun clz_unsafe(): B
"""
Unsafe operation.
If this is 0, the result is undefined.
"""
fun ctz_unsafe(): B
"""
Unsafe operation.
If this is 0, the result is undefined.
"""
fun bitwidth(): B
fun bytewidth(): USize
fun string(): String iso^ =>
_ToString._u64(abs().u64(), i64() < 0)
trait val UnsignedInteger[A: UnsignedInteger[A] val] is Integer[A]
fun abs(): A
fun shl(y: A): A => this << y
fun shr(y: A): A => this >> y
// both fld and mod behave the same as div and rem for unsigned integers
fun fld(y: A): A => this / y
fun fldc(y: A): (A, Bool) => this.divc(y)
fun fld_partial(y: A): A ? => this.div_partial(y)?
fun fld_unsafe(y: A): A => this.div_unsafe(y)
fun mod(y: A): A => this % y
fun modc(y: A): (A, Bool) => this.remc(y)
fun mod_partial(y: A): A ? => this.rem_partial(y)?
fun mod_unsafe(y: A): A => this.rem_unsafe(y)
fun shl_unsafe(y: A): A =>
"""
Unsafe operation.
If non-zero bits are shifted-out, the result is undefined.
"""
this <<~ y
fun shr_unsafe(y: A): A =>
"""
Unsafe operation.
If non-zero bits are shifted-out, the result is undefined.
"""
this >>~ y
fun rotl(y: A): A =>
let y' = y % bitwidth()
if y' == y'.min_value() then
this._value()
else
(this << y') or (this >> (bitwidth() - y'))
end
fun rotr(y: A): A =>
let y' = y % bitwidth()
if y' == y'.min_value() then
this._value()
else
(this >> y') or (this << (bitwidth() - y'))
end
fun popcount(): A
fun clz(): A
fun ctz(): A
fun clz_unsafe(): A
"""
Count leading zeroes.
Unsafe operation.
If this is 0, the result is undefined.
"""
fun ctz_unsafe(): A
"""
Count trailing zeroes.
Unsafe operation.
If this is 0, the result is undefined.
"""
fun bitwidth(): A
fun bytewidth(): USize
fun string(): String iso^ =>
_ToString._u64(u64(), false)
trait val FloatingPoint[A: FloatingPoint[A] val] is Real[A]
new val min_normalised()
new val epsilon()
fun tag radix(): U8
fun tag precision2(): U8
fun tag precision10(): U8
fun tag min_exp2(): I16
fun tag min_exp10(): I16
fun tag max_exp2(): I16
fun tag max_exp10(): I16
fun add_unsafe(y: A): A =>
"""
Unsafe operation.
If any input or output of the operation is +/- infinity or NaN, the result
is undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this +~ y
fun sub_unsafe(y: A): A =>
"""
Unsafe operation.
If any input or output of the operation is +/- infinity or NaN, the result
is undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this -~ y
fun mul_unsafe(y: A): A =>
"""
Unsafe operation.
If any input or output of the operation is +/- infinity or NaN, the result
is undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this *~ y
fun div_unsafe(y: A): A =>
"""
Unsafe operation.
If any input or output of the operation is +/- infinity or NaN, the result
is undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this /~ y
fun fld_unsafe(y: A): A
"""
Unsafe operation.
If any input or output of the operation is +/- infinity or NaN, the result
is undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
fun divrem_unsafe(y: A): (A, A) =>
"""
Unsafe operation.
If any input or output of the operation is +/- infinity or NaN, the result
is undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
(this /~ y, this %~ y)
fun rem_unsafe(y: A): A =>
"""
Unsafe operation.
If any input or output of the operation is +/- infinity or NaN, the result
is undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this %~ y
fun mod_unsafe(y: A): A
"""
Unsafe operation.
If any input or output of the operation is +/- infinity or NaN, the result
is undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
fun neg_unsafe(): A =>
"""
Unsafe operation.
If any input or output of the operation is +/- infinity or NaN, the result
is undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
-~this
fun eq_unsafe(y: box->A): Bool =>
"""
Unsafe operation.
If any input of the operation is +/- infinity or NaN, the result is
undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this ==~ y
fun ne_unsafe(y: box->A): Bool =>
"""
Unsafe operation.
If any input of the operation is +/- infinity or NaN, the result is
undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this !=~ y
fun lt_unsafe(y: box->A): Bool =>
"""
Unsafe operation.
If any input of the operation is +/- infinity or NaN, the result is
undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this <~ y
fun le_unsafe(y: box->A): Bool =>
"""
Unsafe operation.
If any input of the operation is +/- infinity or NaN, the result is
undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this <=~ y
fun ge_unsafe(y: box->A): Bool =>
"""
Unsafe operation.
If any input of the operation is +/- infinity or NaN, the result is
undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this >=~ y
fun gt_unsafe(y: box->A): Bool =>
"""
Unsafe operation.
If any input of the operation is +/- infinity or NaN, the result is
undefined.
The operation isn't required to fully comply to IEEE 754 semantics.
"""
this >~ y
fun abs(): A
fun ceil(): A
fun floor(): A
fun round(): A
fun trunc(): A
fun finite(): Bool
fun infinite(): Bool
fun nan(): Bool
fun ldexp(x: A, exponent: I32): A
fun frexp(): (A, U32)
fun log(): A
fun log2(): A
fun log10(): A
fun logb(): A
fun pow(y: A): A
fun powi(y: I32): A
fun sqrt(): A
fun sqrt_unsafe(): A
"""
Unsafe operation.
If this is negative, the result is undefined.
"""
fun cbrt(): A
fun exp(): A
fun exp2(): A
fun cos(): A
fun sin(): A
fun tan(): A
fun cosh(): A
fun sinh(): A
fun tanh(): A
fun acos(): A
fun asin(): A
fun atan(): A
fun atan2(y: A): A
fun acosh(): A
fun asinh(): A
fun atanh(): A
fun copysign(sign: A): A
fun string(): String iso^ =>
_ToString._f64(f64())
type Number is (Int | Float)
type Int is (Signed | Unsigned)
```