add toBits and fromBits to math

[ringabout]

It's not easy to support JS backend.

Todo in the following PR:

• signbits
• copysign

[Clyybber]

I don't think this should be in math.nim or in the stdlib at all because I don't see how it's better than writing the cast yourself.

[ringabout]

It's the basis of signbits and copysign function(Though I could not export them or use C ffi instead)
signbits and copysign are C99 function which are not in Nim yet. (copysign/signbits exists in many programming languages such as C/C++, Golang, Crystal, Zig, D etc)

As to toBits/fromBits

@bitCast in Zig

Float64bits in GoLang/VLang
https://golang.org/src/math/unsafe.go

toBits in Rust
https://doc.rust-lang.org/std/primitive.f64.html#method.to_bits

[ringabout]

So which is better?

func toBits*(x: float64): uint64 =
  ## Returns the IEEE 754 binary representation of float64.
  cast[ptr uint64](unsafeAddr x)[]

func toBits2*(x: float64): uint64 =
  ## Returns the IEEE 754 binary representation of float64.
  cast[uint64](x)

echo toBits(12.4)
echo toBits2(12.4)

N_LIB_PRIVATE N_NIMCALL(NU64, toBits)(NF x) {
	NU64 result;
	result = (NU64)0;
	result = (*((NU64*) ((&x))));
	return result;
}
N_LIB_PRIVATE N_NIMCALL(NU64, toBits2)(NF x) {
	NU64 result;
	union { NF source; NU64 dest; } LOC1;
	result = (NU64)0;
	LOC1.source = x;
	result = LOC1.dest;
	return result;
}

I prefer cast which looks more clear.

[timotheecour]

@xflywind

So which is better?

can you check generated asm in both cases? if cast[ptr uint64](unsafeAddr x)[] leads to better/more performant code than cast[uint64](x) then maybe there's a case for adding toBits

[ringabout]

@timotheecour

cast[ptr uint64](unsafeAddr x)[]

• Error: opcCastIntToPtr: regs[rb].kind: rkNodeAddr

This doesn't work in VM
but cast[uint64](x) works

[timotheecour]

@xflywind

It's not easy to support JS backend.

we can probably do something similar to toBitsImpl (#16592) for js backend, either returning a BigInt or returning array[2, uint32]

maybe this can be unified with a custom type:

when defined js:
  type Bits = array[2, uint32]
else:
  type Bits = uint

proc toBits(x: float): Bits =
  # now we can support c,vm,js

EDIT: see also asBigInt and BigUint64Array

  proc asBigInt(x: float): int64 =
    # result is a `BigInt` type in js, but we cheat the type system
    # and say it is a `int64` type.
    # TODO refactor it using bigInt once jsBigInt is ready, pending pr #1640
    asm """
    const buffer = new ArrayBuffer(8);
    const floatBuffer = new Float64Array(buffer);
    const uintBuffer = new BigUint64Array(buffer);
    floatBuffer[0] = `x`;
    `result` = uintBuffer[0];"""

(with safari support caveat for BigUint64Array timotheecour#509)