feat: Update safe_math and move to libraries (#1803)

Fixes #1794 and address the wrong check in `mul`. 

Would prefer to add tests directly, but noir don't support failing tests
in noir yet, so there is really no good reason to do that currently. See
noir-lang/noir#1994

yarn-project/noir-libs/safe-math/Nargo.toml

@@ -0,0 +1,7 @@
+[package]
+name = "safe_math"
+authors = [""]
+compiler_version = "0.1"
+type = "lib"
+
+[dependencies]

yarn-project/noir-libs/safe-math/src/lib.nr

@@ -0,0 +1,3 @@
+mod safe_u120;
+
+use crate::safe_u120::SafeU120;

yarn-project/noir-libs/safe-math/src/safe_u120.nr

@@ -0,0 +1,82 @@
+struct SafeU120 {
+    value: u120,
+}
+
+impl SafeU120 {
+    fn is_zero(
+        self: Self,
+    ) -> bool {
+        self.value == 0
+    }
+
+    fn sub(
+      self: Self,
+      b: SafeU120,
+    ) -> SafeU120 {
+        assert(self.value >= b.value);
+        SafeU120 {
+            value: self.value - b.value
+        }
+    }
+
+    fn add(
+        self: Self,
+        b: SafeU120,
+    ) -> SafeU120 {
+        let c: u120 = self.value + b.value;
+        assert(c >= self.value);
+        SafeU120 {
+            value: c
+        }
+    }
+
+    fn mul(
+        self: Self,
+        b: SafeU120,
+    ) -> SafeU120 {
+        let c: u120 = self.value * b.value;
+        if b.value > 0 {
+            assert(c / b.value == self.value);
+        }
+        SafeU120 {
+            value: c
+        }
+    }
+
+    fn div(
+        self: Self,
+        b: SafeU120,
+    ) -> SafeU120 {
+        assert(b.value != 0);
+        SafeU120 {
+            value: self.value / b.value
+        }
+    }
+
+    fn mul_div(
+        self: Self,
+        b: SafeU120,
+        divisor: SafeU120
+    ) -> SafeU120 {
+        let c = SafeU120::mul(self, b);
+        SafeU120 {
+            value: c.value / divisor.value
+        }
+    }
+
+     fn mul_div_up(
+        self: Self,
+        b: SafeU120,
+        divisor: SafeU120
+    ) -> SafeU120 {
+        let c = SafeU120::mul(self, b);
+        let adder = ((self.value * b.value % divisor.value) as u120 > 0) as u120;
+        SafeU120 {
+            value: c.value / divisor.value + adder
+        }
+    }
+
+    // todo: implement mul_div with 240 bit intermediate values.
+}
+
+// Adding test in here is pretty useless as long as noir don't support failings tests.