整数运算

a = torch.tensor([-7, -7, 7, 7])
b = torch.tensor([2, -2, 2, -2])
fl, md = a // b, a % b
tr, fm = torch.div(a, b, rounding_mode="trunc"), torch.fmod(a, b)
print("a / b       ", vals(a / b), (a / b).dtype)
print("floor pair ok", bool(((fl * b + md) == a).all()))
print("trunc pair ok", bool(((tr * b + fm) == a).all()))

let a = Tensor::<1, Int>::from_ints([-7, -7, 7, 7], device);
let b = Tensor::<1, Int>::from_ints([2, -2, 2, -2], device);
let q = a.clone() / b.clone();
let r = a.clone() % b.clone();
let back = q.clone() * b.clone() + r.clone();

# PyTorch
a // b       [-4, 3, 3, -4] torch.int64
a % b        [1, -1, 1, -1]
div trunc    [-3, 3, 3, -3]
fmod         [-1, -1, 1, 1]
a / b        [-3.5, 3.5, 3.5, -3.5] torch.float32
floor pair ok True
trunc pair ok True
# burn（Flex；ndarray 和 Metal 逐行相同，只有 dtype 一行不同）
flex     dtype I32
flex     a / b        [-3, 3, 3, -3]
flex     a % b        [1, -1, 1, -1]
flex     a / 2, a % 2 [-3, -3, 3, 3] [1, 1, 1, 1]
flex     q*b + r      [-5, -7, 7, 5] (a = [-7, -7, 7, 7])
ndarray  dtype I64
metal    dtype I32

/// Python/PyTorch-style remainder: result has same sign as divisor.
#[inline]
fn remainder_int(a: i64, b: i64) -> i64 {
    let r = a.wrapping_rem(b);
    if r != 0 && (r < 0) != (b < 0) {
        r.wrapping_add(b)
    } else {
        r
    }
}

// floor division and truncating remainder, built from the two ops
let floor_div = (a.clone() - r.clone()) / b.clone();
let fmod = a.clone() - q.clone() * b.clone();

flex     (a - a%b)/b  [-4, 3, 3, -4]
flex     a - (a/b)*b  [-1, -1, 1, 1]

floor_div                n=  4  max|diff|=0.00e+00
remainder                n=  4  max|diff|=0.00e+00
trunc_div                n=  4  max|diff|=0.00e+00
fmod                     n=  4  max|diff|=0.00e+00
worst=0.00e+00 tol=0e+00 OK

x32 = torch.tensor([2**31 - 1], dtype=torch.int32)
print("int32 max + 1      ", vals(x32 + 1), (x32 + 1).dtype)
s = torch.tensor([2**30, 2**30], dtype=torch.int32)
print("int32 sum          ", vals(s.sum()), s.sum().dtype)
print("int32 cumsum       ", vals(s.cumsum(0)), s.cumsum(0).dtype)

let i32_opt = (device, DType::I32);
let x = Tensor::<1, Int>::from_data(TensorData::new(vec![i32::MAX], [1]), i32_opt);
let y = x + 1;
let s = Tensor::<1, Int>::from_data(TensorData::new(vec![1i32 << 30, 1 << 30], [2]), i32_opt);
let total = s.clone().sum();
let wide = s.cast(burn::tensor::IntDType::I64).sum();
// cumsum 单独一个进程跑

# PyTorch
int32 max + 1       [-2147483648] torch.int32
int32 sum           2147483648 torch.int64
int32 sum(dim=0)    2147483648 torch.int64
int32 cumsum        [1073741824, 2147483648] torch.int64
# burn（Flex，debug 和 release 相同；Metal 相同）
flex     i32 max + 1        I32 [-2147483648]
flex     i32 sum            I32 [-2147483648]
flex     i32 sum_dim(0)     [-2147483648]
flex     cast I64 then sum  I64 [2147483648]

torch.tensor([7]) // 0
torch.tensor([7]) % 0
torch.div(torch.tensor([7]), 0, rounding_mode="trunc")

let a = Tensor::<1, Int>::from_ints([7, -7], &device);
let z = Tensor::<1, Int>::from_ints([0, 0], &device);
println!("{} {:?} a / 0: {:?}", args[2], a.dtype(), vals(a / z));
// 另一次运行：a % z

# PyTorch
// 0 RuntimeError: ZeroDivisionError
% 0 RuntimeError: ZeroDivisionError
div trunc 0 RuntimeError: ZeroDivisionError
# burn，Flex（debug 和 release 相同）
thread 'main' (8544227) panicked at .../burn-flex-0.22.1/src/ops/int.rs:740:40:
attempt to divide by zero
# burn，ndarray（debug 和 release 相同）
thread 'main' (8544273) panicked at .../library/core/src/ops/function.rs:79:5:
attempt to divide by zero
# burn，Metal（debug 和 release 相同）
metal I32 a / 0: [-1, 1]
metal I32 a % 0: [7, -7]