Added classical functions to math library (#258)

This adds a few classical functions to the math namespace. Added new
project for library testing (thanks @swernli!)

1. Simple functions that are very convenient and their I, D, L variants
for completeness: Sign, Abs, Min, Max.
2. Inverse hyperbolic functions: ArcCosh , ArcSinh, ArcTanh.
3. Intrinsic Sqrt.
4. Intrinsic Log (base e), and derived Log10 and Lg (base 2).
5. ModulusI and ModulusL to compute remainder in canonical way (always
non-negative).
6. ExpModI and ExpModL to compute exponentiation with respect to
modulus.
7. GCD and extended GCD.

Many of these functions are used in Shor and Grover.

Not including
[ModPowL](https://github.com/microsoft/qsharp-runtime/blob/4976e913cf007f14958f5ab9a09db3a49fc57698/src/Simulation/QSharpFoundation/Math/Math.qs#L317)
- same intended functionality as
[ExpModL](https://github.com/microsoft/QuantumLibraries/blob/2214d89925e732bd3a10c642885699834cb975fa/Standard/src/Math/Functions.qs#L244)
and no use found.

---------

Co-authored-by: Dmitry Vasilevsky <dmitryv@microsoft.com>

Cargo.toml

@@ -9,6 +9,7 @@ members = [
     "compiler/qsc_hir",
     "compiler/qsc_passes",
     "katas",
+    "library/tests",
     "pip",
     "wasm",
 ]

compiler/qsc/src/interpret.rs

@@ -5,4 +5,7 @@ mod debug;
 pub mod stateful;
 pub mod stateless;
 
-pub use qsc_eval::{output, val::Value};
+pub use qsc_eval::{
+    output::{self, GenericReceiver},
+    val::Value,
+};

compiler/qsc_eval/src/intrinsic.rs

@@ -5,6 +5,7 @@
 mod tests;
 
 use crate::{output::Receiver, val::Value, Error, Reason, WithSpan};
+use num_bigint::BigInt;
 use qir_backend::{
     __quantum__qis__ccx__body, __quantum__qis__cx__body, __quantum__qis__cy__body,
     __quantum__qis__cz__body, __quantum__qis__h__body, __quantum__qis__m__body,
@@ -37,6 +38,11 @@ pub(crate) fn invoke_intrinsic(
                 Continue(Value::Double(val as f64))
             }
 
+            "IntAsBigInt" => {
+                let val: i64 = args.try_into().with_span(args_span)?;
+                Continue(Value::BigInt(BigInt::from(val)))
+            }
+
             "DumpMachine" => {
                 let (state, qubit_count) = capture_quantum_state();
                 match out.state(state, qubit_count) {
@@ -110,6 +116,16 @@ pub(crate) fn invoke_intrinsic(
                 Continue(Value::Double(val.tanh()))
             }
 
+            "Sqrt" => {
+                let val: f64 = args.try_into().with_span(args_span)?;
+                Continue(Value::Double(val.sqrt()))
+            }
+
+            "Log" => {
+                let val: f64 = args.try_into().with_span(args_span)?;
+                Continue(Value::Double(val.ln()))
+            }
+
             "DrawRandomInt" => match args.try_into_tuple().with_span(args_span)?.as_ref() {
                 [lo, hi] => invoke_draw_random_int(lo.clone(), hi.clone(), args_span),
                 args => Break(Reason::Error(Error::TupleArity(2, args.len(), args_span))),

compiler/qsc_eval/src/intrinsic/tests.rs

@@ -5,6 +5,7 @@ use std::f64::consts;
 
 use expect_test::{expect, Expect};
 use indoc::indoc;
+use num_bigint::BigInt;
 use qsc_frontend::compile::{self, compile, PackageStore, SourceMap};
 use qsc_passes::run_default_passes;
 
@@ -286,40 +287,32 @@ fn draw_random_int() {
 }
 
 #[test]
-fn check_bitsize_i() {
-    check_intrinsic_value("", "Microsoft.Quantum.Math.BitSizeI(0)", &Value::Int(0));
-    check_intrinsic_value("", "Microsoft.Quantum.Math.BitSizeI(1)", &Value::Int(1));
-    check_intrinsic_value("", "Microsoft.Quantum.Math.BitSizeI(2)", &Value::Int(2));
-    check_intrinsic_value("", "Microsoft.Quantum.Math.BitSizeI(3)", &Value::Int(2));
-    check_intrinsic_value(
-        "",
-        "Microsoft.Quantum.Math.BitSizeI(0x7FFFFFFFFFFFFFFF)",
-        &Value::Int(63),
-    );
+fn sqrt() {
+    check_intrinsic_value("", "Microsoft.Quantum.Math.Sqrt(0.0)", &Value::Double(0.0));
+    check_intrinsic_value("", "Microsoft.Quantum.Math.Sqrt(81.0)", &Value::Double(9.0));
 }
 
 #[test]
-fn check_fst_snd() {
-    check_intrinsic_value("", "Fst(7,6)", &Value::Int(7));
-    check_intrinsic_value("", "Snd(7,6)", &Value::Int(6));
-}
-
-#[test]
-fn check_index_range() {
+fn log() {
+    check_intrinsic_value("", "Microsoft.Quantum.Math.Log(1.0)", &Value::Double(0.0));
     check_intrinsic_value(
         "",
-        "Microsoft.Quantum.Arrays.IndexRange([7,6,5,4])::Start",
-        &Value::Int(0),
+        "Microsoft.Quantum.Math.Log(Microsoft.Quantum.Math.E())",
+        &Value::Double(1.0),
     );
+}
+
+#[test]
+fn int_as_bigint() {
     check_intrinsic_value(
         "",
-        "Microsoft.Quantum.Arrays.IndexRange([7,6,5,4])::Step",
-        &Value::Int(1),
+        "Microsoft.Quantum.Convert.IntAsBigInt(0)",
+        &Value::BigInt(BigInt::from(0)),
     );
     check_intrinsic_value(
         "",
-        "Microsoft.Quantum.Arrays.IndexRange([7,6,5,4])::End",
-        &Value::Int(3),
+        "Microsoft.Quantum.Convert.IntAsBigInt(-10000)",
+        &Value::BigInt(BigInt::from(-10000)),
     );
 }
 

library/convert.qs

@@ -7,4 +7,11 @@ namespace Microsoft.Quantum.Convert {
     function IntAsDouble(a : Int) : Double {
         body intrinsic;
     }
+
+    /// # Summary
+    /// Converts a given integer to an equivalent big integer.
+    function IntAsBigInt(a : Int) : BigInt {
+        body intrinsic;
+    }
+
 }