mbutrovich opened a new issue, #11605:
URL: https://github.com/apache/arrow-rs/issues/11605
### Describe the bug
`multiply_fixed_point`, `multiply_fixed_point_checked` and
`multiply_fixed_point_dyn` round the product with the divisor
`10^(product_scale - required_scale)`. When that exponent is 77 or more, the
divisor does not fit in `i256` and wraps, and the results are wrong: a zero
product gives 1. When the exponent is above 127, computing it overflows `i8`,
which panics in debug builds. I did not check what a release build returns.
### To Reproduce
```rust
use arrow_arith::arithmetic::{multiply_fixed_point,
multiply_fixed_point_checked};
use arrow_array::Decimal128Array;
fn dec(v: Vec<i128>, p: u8, s: i8) -> Decimal128Array {
Decimal128Array::from(v).with_precision_and_scale(p, s).unwrap()
}
fn main() {
// Product scale 0, required scale -77
let a = dec(vec![0, 5, 5], 1, 0);
let b = dec(vec![0, 5, -5], 1, 0);
let r = multiply_fixed_point(&a, &b, -77).unwrap();
println!("{:?}", r.values()); // [1, 1, -1]
let r = multiply_fixed_point_checked(&a, &b, -77).unwrap();
println!("{:?}", r.values()); // [1, 1, -1]
// Product scale 38, required scale -90
let z = dec(vec![0], 1, 0);
let c = dec(vec![0], 38, 38);
let _ = multiply_fixed_point(&z, &c, -90);
// debug build: panics with "attempt to subtract with overflow"
}
```
### Expected behavior
`[0, 0, 0]` for both calls in the first case, because no product of two
`i128` values reaches `10^77 / 2`, so every product rounds to 0 at that scale.
Alternatively an error, as the
[docs](https://github.com/apache/arrow-rs/blob/dd240116c75a15a2a048a041c808d67f3f32a375/arrow-arith/src/arithmetic.rs#L130-L144)
specify for a required scale above the product scale. They do not restrict how
far below it the required scale can be, and `Decimal128(p, -77)` passes
`validate_decimal_precision_and_scale`.
### Additional context
[`get_fixed_point_info`](https://github.com/apache/arrow-rs/blob/dd240116c75a15a2a048a041c808d67f3f32a375/arrow-arith/src/arithmetic.rs#L35-L52)
computes `product_scale - required_scale` in `i8` and the divisor with
`i256::pow_wrapping`. `10^77` wraps to a negative `i256`, so `half` in
[`divide_and_round`](https://github.com/apache/arrow-rs/blob/dd240116c75a15a2a048a041c808d67f3f32a375/arrow-arith/src/arithmetic.rs#L174-L188)
is negative and every non-negative remainder rounds up. Should exponents above
76 return zeros, or an error?
Found with property-based tests that build arrays in every physical layout
the Arrow format allows, on `main` at `72887ed9`. The code is unchanged on
`main` at `dd240116`.
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