Add Num.atan builtin

compiler/builtins/bitcode/src/lib.rs

@@ -45,3 +45,203 @@ pub fn pow_int_(mut base: i64, mut exp: i64) -> i64 {
 pub fn is_finite_(num: f64) -> bool {
     f64::is_finite(num)
 }
+
+/// Adapted from Rust's libm module, by the Rust core team,
+/// licensed under the Apache License, version 2.0 - https://www.apache.org/licenses/LICENSE-2.0
+/// https://github.com/rust-lang/libm/blob/master/LICENSE-APACHE
+///
+/// Thank you, Rust core team!
+
+// From https://github.com/rust-lang/libm/blob/master/src/math/mod.rs
+#[cfg(not(debug_assertions))]
+macro_rules! i {
+    ($array:expr, $index:expr) => {
+        unsafe { *$array.get_unchecked($index) }
+    };
+    ($array:expr, $index:expr, = , $rhs:expr) => {
+        unsafe {
+            *$array.get_unchecked_mut($index) = $rhs;
+        }
+    };
+    ($array:expr, $index:expr, += , $rhs:expr) => {
+        unsafe {
+            *$array.get_unchecked_mut($index) += $rhs;
+        }
+    };
+    ($array:expr, $index:expr, -= , $rhs:expr) => {
+        unsafe {
+            *$array.get_unchecked_mut($index) -= $rhs;
+        }
+    };
+    ($array:expr, $index:expr, &= , $rhs:expr) => {
+        unsafe {
+            *$array.get_unchecked_mut($index) &= $rhs;
+        }
+    };
+    ($array:expr, $index:expr, == , $rhs:expr) => {
+        unsafe { *$array.get_unchecked_mut($index) == $rhs }
+    };
+}
+
+#[cfg(debug_assertions)]
+macro_rules! i {
+    ($array:expr, $index:expr) => {
+        *$array.get($index).unwrap()
+    };
+    ($array:expr, $index:expr, = , $rhs:expr) => {
+        *$array.get_mut($index).unwrap() = $rhs;
+    };
+    ($array:expr, $index:expr, -= , $rhs:expr) => {
+        *$array.get_mut($index).unwrap() -= $rhs;
+    };
+    ($array:expr, $index:expr, += , $rhs:expr) => {
+        *$array.get_mut($index).unwrap() += $rhs;
+    };
+    ($array:expr, $index:expr, &= , $rhs:expr) => {
+        *$array.get_mut($index).unwrap() &= $rhs;
+    };
+    ($array:expr, $index:expr, == , $rhs:expr) => {
+        *$array.get_mut($index).unwrap() == $rhs
+    };
+}
+
+macro_rules! llvm_intrinsically_optimized {
+    (#[cfg($($clause:tt)*)] $e:expr) => {
+        #[cfg(all(feature = "unstable", $($clause)*))]
+        {
+            if true { // thwart the dead code lint
+                $e
+            }
+        }
+    };
+}
+
+macro_rules! force_eval {
+    ($e:expr) => {
+        unsafe {
+            ::core::ptr::read_volatile(&$e);
+        }
+    };
+}
+
+// From https://github.com/rust-lang/libm/blob/master/src/math/atan.rs
+
+// Clippy fails CI if we don't include overrides below. Since this is copied
+// straight from the libm crate, I figure they had a reason to include
+// the extra percision, so we just silence this warning.
+
+#[allow(clippy::excessive_precision)]
+const ATANHI: [f64; 4] = [
+    4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
+    7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
+    9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
+    1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
+];
+
+#[allow(clippy::excessive_precision)]
+const ATANLO: [f64; 4] = [
+    2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
+    3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
+    1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
+    6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
+];
+
+#[allow(clippy::excessive_precision)]
+const AT: [f64; 11] = [
+    3.33333333333329318027e-01,  /* 0x3FD55555, 0x5555550D */
+    -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
+    1.42857142725034663711e-01,  /* 0x3FC24924, 0x920083FF */
+    -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
+    9.09088713343650656196e-02,  /* 0x3FB745CD, 0xC54C206E */
+    -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
+    6.66107313738753120669e-02,  /* 0x3FB10D66, 0xA0D03D51 */
+    -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
+    4.97687799461593236017e-02,  /* 0x3FA97B4B, 0x24760DEB */
+    -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
+    1.62858201153657823623e-02,  /* 0x3F90AD3A, 0xE322DA11 */
+];
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fabs(x: f64) -> f64 {
+    // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+    // `f64.abs` native instruction, so we can leverage this for both code size
+    // and speed.
+    llvm_intrinsically_optimized! {
+        #[cfg(target_arch = "wasm32")] {
+            return unsafe { ::core::intrinsics::fabsf64(x) }
+        }
+    }
+    f64::from_bits(x.to_bits() & (u64::MAX / 2))
+}
+
+#[no_mangle]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atan_(x: f64) -> f64 {
+    let mut x = x;
+    let mut ix = (x.to_bits() >> 32) as u32;
+    let sign = ix >> 31;
+    ix &= 0x7fff_ffff;
+    if ix >= 0x4410_0000 {
+        if x.is_nan() {
+            return x;
+        }
+
+        let z = ATANHI[3] + f64::from_bits(0x0380_0000); // 0x1p-120f
+        return if sign != 0 { -z } else { z };
+    }
+
+    let id = if ix < 0x3fdc_0000 {
+        /* |x| < 0.4375 */
+        if ix < 0x3e40_0000 {
+            /* |x| < 2^-27 */
+            if ix < 0x0010_0000 {
+                /* raise underflow for subnormal x */
+                force_eval!(x as f32);
+            }
+
+            return x;
+        }
+
+        -1
+    } else {
+        x = fabs(x);
+        if ix < 0x3ff30000 {
+            /* |x| < 1.1875 */
+            if ix < 0x3fe60000 {
+                /* 7/16 <= |x| < 11/16 */
+                x = (2. * x - 1.) / (2. + x);
+                0
+            } else {
+                /* 11/16 <= |x| < 19/16 */
+                x = (x - 1.) / (x + 1.);
+                1
+            }
+        } else if ix < 0x40038000 {
+            /* |x| < 2.4375 */
+            x = (x - 1.5) / (1. + 1.5 * x);
+            2
+        } else {
+            /* 2.4375 <= |x| < 2^66 */
+            x = -1. / x;
+            3
+        }
+    };
+
+    let z = x * x;
+    let w = z * z;
+    /* break sum from i=0 to 10 AT[i]z**(i+1) into odd and even poly */
+    let s1 = z * (AT[0] + w * (AT[2] + w * (AT[4] + w * (AT[6] + w * (AT[8] + w * AT[10])))));
+    let s2 = w * (AT[1] + w * (AT[3] + w * (AT[5] + w * (AT[7] + w * AT[9]))));
+
+    if id < 0 {
+        return x - x * (s1 + s2);
+    }
+
+    let z = i!(ATANHI, id as usize) - (x * (s1 + s2) - i!(ATANLO, id as usize) - x);
+
+    if sign != 0 {
+        -z
+    } else {
+        z
+    }
+}

compiler/builtins/src/std.rs

@@ -456,6 +456,12 @@ pub fn types() -> MutMap<Symbol, (SolvedType, Region)> {
         SolvedType::Func(vec![float_type()], Box::new(int_type())),
     );
 
+    // atan : Float -> Float
+    add_type(
+        Symbol::NUM_ATAN,
+        SolvedType::Func(vec![float_type()], Box::new(float_type())),
+    );
+
     // Bool module
 
     // and : Bool, Bool -> Bool

compiler/builtins/src/unique.rs

@@ -495,6 +495,12 @@ pub fn types() -> MutMap<Symbol, (SolvedType, Region)> {
         unique_function(vec![float_type(star1)], int_type(star2))
     });
 
+    // atan : Float -> Float
+    add_type(Symbol::NUM_ATAN, {
+        let_tvars! { star1, star2 };
+        unique_function(vec![float_type(star1)], float_type(star2))
+    });
+
     // Bool module
 
     // isEq or (==) : Attr * a, Attr * a -> Attr * Bool

compiler/can/src/builtins.rs

@@ -97,6 +97,7 @@ pub fn builtin_defs(var_store: &mut VarStore) -> MutMap<Symbol, Def> {
         Symbol::NUM_CEILING => num_ceiling,
         Symbol::NUM_POW_INT => num_pow_int,
         Symbol::NUM_FLOOR => num_floor,
+        Symbol::NUM_ATAN => num_atan,
     }
 }
 
@@ -765,6 +766,26 @@ fn num_floor(symbol: Symbol, var_store: &mut VarStore) -> Def {
     )
 }
 
+/// Num.atan : Float -> Float
+fn num_atan(symbol: Symbol, var_store: &mut VarStore) -> Def {
+    let arg_float_var = var_store.fresh();
+    let ret_float_var = var_store.fresh();
+
+    let body = RunLowLevel {
+        op: LowLevel::NumAtan,
+        args: vec![(arg_float_var, Var(Symbol::ARG_1))],
+        ret_var: ret_float_var,
+    };
+
+    defn(
+        symbol,
+        vec![(arg_float_var, Symbol::ARG_1)],
+        var_store,
+        body,
+        ret_float_var,
+    )
+}
+
 /// List.isEmpty : List * -> Bool
 fn list_is_empty(symbol: Symbol, var_store: &mut VarStore) -> Def {
     let list_var = var_store.fresh();

compiler/gen/src/llvm/build.rs

@@ -2106,7 +2106,7 @@ fn run_low_level<'a, 'ctx, 'env>(
             list_join(env, inplace, parent, list, outer_list_layout)
         }
         NumAbs | NumNeg | NumRound | NumSqrtUnchecked | NumSin | NumCos | NumCeiling | NumFloor
-        | NumToFloat | NumIsFinite => {
+        | NumToFloat | NumIsFinite | NumAtan => {
             debug_assert_eq!(args.len(), 1);
 
             let (arg, arg_layout) = load_symbol_and_layout(env, scope, &args[0]);
@@ -2659,6 +2659,7 @@ fn build_float_unary_op<'a, 'ctx, 'env>(
             "num_floor",
         ),
         NumIsFinite => call_bitcode_fn(NumIsFinite, env, &[arg.into()], "is_finite_"),
+        NumAtan => call_bitcode_fn(NumAtan, env, &[arg.into()], "atan_"),
         _ => {
             unreachable!("Unrecognized int unary operation: {:?}", op);
         }

compiler/gen/tests/gen_num.rs

@@ -686,6 +686,11 @@ mod gen_num {
         assert_evals_to!("Num.powInt 2 3", 8, i64);
     }
 
+    #[test]
+    fn atan() {
+        assert_evals_to!("Num.atan 10", 1.4711276743037347, f64);
+    }
+
     #[test]
     #[should_panic(expected = r#"Roc failed with message: "integer addition overflowed!"#)]
     fn int_overflow() {

compiler/module/src/low_level.rs

@@ -43,6 +43,7 @@ pub enum LowLevel {
     NumPowInt,
     NumFloor,
     NumIsFinite,
+    NumAtan,
     Eq,
     NotEq,
     And,

compiler/module/src/symbol.rs

@@ -646,6 +646,7 @@ define_builtins! {
         41 NUM_FLOOR: "floor"
         42 NUM_ADD_WRAP: "addWrap"
         43 NUM_ADD_CHECKED: "addChecked"
+        44 NUM_ATAN: "atan"
     }
     2 BOOL: "Bool" => {
         0 BOOL_BOOL: "Bool" imported // the Bool.Bool type alias

compiler/mono/src/borrow.rs

@@ -526,6 +526,6 @@ pub fn lowlevel_borrow_signature(arena: &Bump, op: LowLevel) -> &[bool] {
         | NumPowInt => arena.alloc_slice_copy(&[irrelevant, irrelevant]),
 
         NumAbs | NumNeg | NumSin | NumCos | NumSqrtUnchecked | NumRound | NumCeiling | NumFloor
-        | NumToFloat | Not | NumIsFinite => arena.alloc_slice_copy(&[irrelevant]),
+        | NumToFloat | Not | NumIsFinite | NumAtan => arena.alloc_slice_copy(&[irrelevant]),
     }
 }

compiler/solve/tests/solve_expr.rs

@@ -2430,6 +2430,18 @@ mod solve_expr {
         );
     }
 
+    #[test]
+    fn atan() {
+        infer_eq_without_problem(
+            indoc!(
+                r#"
+                Num.atan
+                "#
+            ),
+            "Float -> Float",
+        );
+    }
+
     #[test]
     fn reconstruct_path() {
         infer_eq_without_problem(

shell.nix

@@ -11,9 +11,9 @@ let
 in { pkgs ? pinnedPkgs }:
 
 let
-  isOsX = builtins.currentSystem == "x86_64-darwin";
+  isMacOS = builtins.currentSystem == "x86_64-darwin";
   darwin-frameworks =
-    if isOsX then
+    if isMacOS then
       with pkgs.darwin.apple_sdk.frameworks; [
         AppKit
         CoreFoundation
@@ -26,6 +26,7 @@ let
     else
       [ ];
   llvm = pkgs.llvm_10;
+  lld = pkgs.lld_10; # this should match llvm's version
   inputs =
     [
       pkgs.rustup
@@ -35,6 +36,8 @@ let
       pkgs.libffi
       pkgs.libxml2
       pkgs.zlib
+      # faster builds - see https://github.com/rtfeldman/roc/blob/trunk/BUILDING_FROM_SOURCE.md#use-lld-for-the-linker
+      lld
     ];
 in pkgs.mkShell {
   buildInputs = inputs ++ darwin-frameworks;