fix: SSA typing for right shifts (#4302)

# Description

## Problem\*

Partial work towards #4275

## Summary\*

Previously, SSA was issuing (lhs_type, Field) DIV for right shifts.
However this is wrong if we support shifts by the bit size (`u1 >> 1`)

This is interpreted in acir_gen as an euclidean division with bit_size =
lhs_type.bit_size(). However, u1 >> 1 worked because of a + 1 that is in
euclidean division
https://github.com/noir-lang/noir/blob/0e073037b00212fd17fc8ca9c531b567614eb4c5/compiler/noirc_evaluator/src/ssa/acir_gen/acir_ir/acir_variable.rs#L703
(and it failed in unconstrained functions since they don't codegen that
extraneous + 1)

## Additional Context



## Documentation\*

Check one:
- [x] No documentation needed.
- [ ] Documentation included in this PR.
- [ ] **[Exceptional Case]** Documentation to be submitted in a separate
PR.

# PR Checklist\*

- [x] I have tested the changes locally.
- [x] I have formatted the changes with [Prettier](https://prettier.io/)
and/or `cargo fmt` on default settings.

---------

Co-authored-by: TomAFrench <tom@tomfren.ch>

compiler/noirc_evaluator/src/ssa/function_builder/mod.rs

@@ -336,11 +336,18 @@ impl FunctionBuilder {
         rhs: ValueId,
         bit_size: u32,
     ) -> ValueId {
+        let lhs_typ = self.type_of_value(lhs);
         let base = self.field_constant(FieldElement::from(2_u128));
         // we can safely cast to unsigned because overflow_checks prevent bit-shift with a negative value
         let rhs_unsigned = self.insert_cast(rhs, Type::unsigned(bit_size));
         let pow = self.pow(base, rhs_unsigned);
-        self.insert_binary(lhs, BinaryOp::Div, pow)
+        // We need at least one more bit for the case where rhs == bit_size
+        let div_type = Type::unsigned(bit_size + 1);
+        let casted_lhs = self.insert_cast(lhs, div_type.clone());
+        let casted_pow = self.insert_cast(pow, div_type);
+        let div_result = self.insert_binary(casted_lhs, BinaryOp::Div, casted_pow);
+        // We have to cast back to the original type
+        self.insert_cast(div_result, lhs_typ)
     }
 
     /// Computes lhs^rhs via square&multiply, using the bits decomposition of rhs

test_programs/execution_success/bit_shifts_runtime/src/main.nr

@@ -16,4 +16,5 @@ fn main(x: u64, y: u64) {
     assert(a << 7 == -128);
     assert(a << -a == -2);
 
+    assert(x >> x == 0);
 }

test_programs/execution_success/brillig_bit_shifts_runtime/Nargo.toml

@@ -0,0 +1,6 @@
+[package]
+name = "brillig_bit_shifts_runtime"
+type = "bin"
+authors = [""]
+
+[dependencies]

test_programs/execution_success/brillig_bit_shifts_runtime/Prover.toml

@@ -0,0 +1,2 @@
+x = 64
+y = 1

test_programs/execution_success/brillig_bit_shifts_runtime/src/main.nr

@@ -0,0 +1,20 @@
+unconstrained fn main(x: u64, y: u64) {
+    // runtime shifts on compile-time known values
+    assert(64 << y == 128);
+    assert(64 >> y == 32);
+    // runtime shifts on runtime values
+    assert(x << y == 128);
+    assert(x >> y == 32);
+
+    // Bit-shift with signed integers
+    let mut a :i8 = y as i8;
+    let mut b: i8 = x as i8;
+    assert(b << 1 == -128);
+    assert(b >> 2 == 16);
+    assert(b >> a == 32);
+    a = -a;
+    assert(a << 7 == -128);
+    assert(a << -a == -2);
+
+    assert(x >> x == 0);
+}