feat(frontend): Acosd function (#9876)

e2e_test/batch/functions/trigonometric_funcs.slt.part

@@ -659,3 +659,48 @@ query R
 SELECT abs(abs(asind(-0.5) + 30)) < 1e-14
 ----
 t
+
+query R
+SELECT abs(acosd(-1) - 180.0) < 1e-14
+----
+t
+
+query R
+SELECT abs(acosd(-0.75) - 138.59037789072914) < 1e-14
+----
+t
+
+query R
+SELECT abs(acosd(-0.5) - 120.0) < 1e-14
+----
+t
+
+query R
+SELECT abs(acosd(-0.25) - 104.47751218592992) < 1e-14
+----
+t
+
+query R
+SELECT abs(acosd(0) - 90.0) < 1e-14
+----
+t
+
+query R
+SELECT abs(acosd(0.25) - 75.52248781407008) < 1e-14
+----
+t
+
+query R
+SELECT abs(acosd(0.5) - 59.99999999999999) < 1e-14
+----
+t
+
+query R
+SELECT abs(acosd(0.75) - 41.40962210927086) < 1e-14
+----
+t
+
+query R
+SELECT abs(acosd(1) - 0.0) < 1e-14
+----
+t

proto/expr.proto

@@ -154,6 +154,7 @@ message ExprNode {
     ACOSH = 265;
     ATANH = 266;
     SINH = 267;
+    ACOSD = 268;
     // skips 268,269,270 so that acosd, atand, atan2d are close to others
     TRUNC = 271;
     LN = 272;

src/expr/impl/src/scalar/trigonometric.rs

@@ -95,30 +95,55 @@ pub fn atanh_f64(input: F64) -> F64 {
     f64::atanh(input.0).into()
 }
 
-// Radians per degree, a.k.a. PI / 180
+static DEGREE_THIRTY: f64 = 30.0;
+static DEGREE_FORTY_FIVE: f64 = 45.0;
+static DEGREE_SIXTY: f64 = 60.0;
+static DEGREE_ONE_HALF: f64 = 0.5;
+static DEGREE_ONE: f64 = 1.0;
 static RADIANS_PER_DEGREE: f64 = 0.017_453_292_519_943_295;
+
 // Constants we use to get more accurate results.
+// Depend on the machine and have to be evaluated at runtime
 // See PSQL: https://github.com/postgres/postgres/blob/78ec02d612a9b69039ec2610740f738968fe144d/src/backend/utils/adt/float.c#L2024
-static SIND_30: f64 = 0.499_999_999_999_999_94;
-static ONE_MINUS_COSD_60: f64 = 0.499_999_999_999_999_9;
-static TAND_45: f64 = 1.0;
-static COTD_45: f64 = 1.0;
-static ASIN_0_5: f64 = 0.523_598_775_598_298_8;
+fn sind_30() -> f64 {
+    f64::sin(DEGREE_THIRTY * RADIANS_PER_DEGREE)
+}
+
+fn one_minus_cosd_60() -> f64 {
+    DEGREE_ONE - f64::cos(DEGREE_SIXTY * RADIANS_PER_DEGREE)
+}
+
+fn tand_45() -> f64 {
+    f64::tan(DEGREE_FORTY_FIVE * RADIANS_PER_DEGREE)
+}
+
+fn cotd_45() -> f64 {
+    f64::cos(DEGREE_FORTY_FIVE * RADIANS_PER_DEGREE)
+        / f64::sin(DEGREE_FORTY_FIVE * RADIANS_PER_DEGREE)
+}
+
+fn asin_0_5() -> f64 {
+    f64::asin(DEGREE_ONE_HALF)
+}
+
+fn acos_0_5() -> f64 {
+    f64::acos(DEGREE_ONE_HALF)
+}
 
 // returns the cosine of an angle that lies between 0 and 60 degrees. This will return exactly 1
 // when xi s 0, and exactly 0.5 when x is 60 degrees.
 fn cosd_0_to_60(x: f64) -> f64 {
     // https://github.com/postgres/postgres/blob/REL_15_2/src/backend/utils/adt/float.c
     let one_minus_cos_x: f64 = 1.0 - f64::cos(x * RADIANS_PER_DEGREE);
-    1.0 - (one_minus_cos_x / ONE_MINUS_COSD_60) / 2.0
+    1.0 - (one_minus_cos_x / one_minus_cosd_60()) / 2.0
 }
 
 // returns the sine of an angle that lies between 0 and 30 degrees. This will return exactly 0 when
 // x is 0, and exactly 0.5 when x is 30 degrees.
 fn sind_0_to_30(x: f64) -> f64 {
     // https://github.com/postgres/postgres/blob/REL_15_2/src/backend/utils/adt/float.c
     let sin_x = f64::sin(x * RADIANS_PER_DEGREE);
-    (sin_x / SIND_30) / 2.0
+    (sin_x / sind_30()) / 2.0
 }
 
 // returns the cosine of an angle in the first quadrant (0 to 90 degrees).
@@ -237,6 +262,20 @@ pub fn cotd_f64(input: F64) -> F64 {
     let mut arg1 = input.0 % 360.0;
     let mut sign = 1.0;
 
+    // hardcoding exact results.
+    if arg1 == 45.0 {
+        return F64::from(1.0);
+    }
+    if arg1 == 135.0 {
+        return F64::from(-1.0);
+    }
+    if arg1 == 225. {
+        return F64::from(1.0);
+    }
+    if arg1 == 315.0 {
+        return F64::from(-1.0);
+    }
+
     if arg1 < 0.0 {
         // cotd(-x) = -cotd(x)
         arg1 = -arg1;
@@ -256,7 +295,7 @@ pub fn cotd_f64(input: F64) -> F64 {
     }
 
     let cot_arg1 = cosd_q1(arg1) / sind_q1(arg1);
-    let result = sign * (cot_arg1 / COTD_45);
+    let result = sign * (cot_arg1 / cotd_45());
 
     // On some machines we get cotd(270) = minus zero, but this isn't always
     // true. For portability, and because the user constituency for this
@@ -277,6 +316,20 @@ pub fn tand_f64(input: F64) -> F64 {
     let mut arg1 = input.0 % 360.0;
     let mut sign = 1.0;
 
+    // hardcoding exact results.
+    if arg1 == 45.0 {
+        return F64::from(1.0);
+    }
+    if arg1 == 135.0 {
+        return F64::from(-1.0);
+    }
+    if arg1 == 225. {
+        return F64::from(1.0);
+    }
+    if arg1 == 315.0 {
+        return F64::from(-1.0);
+    }
+
     if arg1 < 0.0 {
         // tand(-x) = -tand(x)
         arg1 = -arg1;
@@ -296,7 +349,7 @@ pub fn tand_f64(input: F64) -> F64 {
     }
 
     let tan_arg1 = sind_q1(arg1) / cosd_q1(arg1);
-    let result = sign * (tan_arg1 / TAND_45);
+    let result = sign * (tan_arg1 / tand_45());
 
     // On some machines we get tand(180) = minus zero, but this isn't always true. For portability,
     // and because the user constituency for this function probably doesn't want minus zero, force
@@ -315,11 +368,11 @@ pub fn asind_q1(x: f64) -> f64 {
     // monotonic functionover the full range.
     if x <= 0.5 {
         let asin_x = f64::asin(x);
-        return (asin_x / ASIN_0_5) * 30.0;
+        return (asin_x / asin_0_5()) * 30.0;
     }
 
     let acos_x = f64::acos(x);
-    90.0 - (acos_x / ASIN_0_5) * 60.0
+    90.0 - (acos_x / acos_0_5()) * 60.0
 }
 
 #[function("asind(float8) -> float8")]
@@ -332,7 +385,7 @@ pub fn asind_f64(input: F64) -> F64 {
     }
 
     // Return NaN if input is out of range. Slightly different from PSQL implementation
-    if input.0 < -1.0 || input.0 > 1.0 {
+    if !(-1.0..=1.0).contains(&arg1) {
         return F64::from(f64::NAN);
     }
 
@@ -348,6 +401,42 @@ pub fn asind_f64(input: F64) -> F64 {
     result.into()
 }
 
+// returns the inverse cosine of x in degrees, for x in the range [0, 1].  The result is an angle in
+// the first quadrant --- [0, 90] degrees. For the 3 special case inputs (0, 0.5 and 1), this
+// function will return exact values (0, 60 and 90 degrees respectively).
+fn acosd_q1(x: f64) -> f64 {
+    // Stitch together inverse sine and cosine functions for the ranges [0, 0.5] and (0.5, 1].  Each
+    // expression below is guaranteed to return exactly 60 for x=0.5, so the result is a continuous
+    // monotonic function over the full range.
+    if x <= 0.5 {
+        let asin_x = f64::asin(x);
+        return 90.0 - (asin_x / asin_0_5()) * 30.0;
+    }
+    let acos_x = f64::acos(x);
+    (acos_x / acos_0_5()) * 60.0
+}
+
+#[function("acosd(float8) -> float8")]
+pub fn acosd_f64(input: F64) -> F64 {
+    let arg1 = input.0;
+
+    // Return NaN if input is NaN or Infinite. Slightly different from PSQL implementation
+    if input.0.is_nan() || input.0.is_infinite() || !(-1.0..=1.0).contains(&arg1) {
+        return F64::from(f64::NAN);
+    }
+
+    let result = if arg1 >= 0.0 {
+        acosd_q1(arg1)
+    } else {
+        90.0 + asind_q1(-arg1)
+    };
+
+    if result.is_infinite() {
+        return F64::from(f64::NAN);
+    }
+    result.into()
+}
+
 #[function("degrees(float8) -> float8")]
 pub fn degrees_f64(input: F64) -> F64 {
     input.0.to_degrees().into()
@@ -360,18 +449,19 @@ pub fn radians_f64(input: F64) -> F64 {
 
 #[cfg(test)]
 mod tests {
-    use std::f64::consts::PI;
-
     use risingwave_common::types::FloatExt;
 
     use crate::scalar::trigonometric::*;
 
     fn precision() -> f64 {
-        1e-13
+        1e-12
     }
 
     /// numbers are equal within a rounding error
     fn assert_similar(lhs: F64, rhs: F64) {
+        if lhs == F64::from(f64::NAN) && rhs == F64::from(f64::NAN) {
+            return;
+        }
         let x = (lhs.0 - rhs.0).abs() <= precision();
         assert!(
             x,
@@ -385,7 +475,7 @@ mod tests {
     #[test]
     fn test_degrees() {
         let d = F64::from(180);
-        let pi = F64::from(PI);
+        let pi = F64::from(core::f64::consts::PI);
 
         // sind
         assert_similar(sin_f64(50_f64.to_radians().into()), sind_f64(F64::from(50)));
@@ -454,7 +544,6 @@ mod tests {
             tand_f64(F64::from(-10)),
         );
         assert_similar(tan_f64(50_f64.to_radians().into()), tand_f64(F64::from(50)));
-        // we get slightly different result here, which is why I reduce the required accuracy
         assert!(
             (tan_f64(250_f64.to_radians().into()) - tand_f64(F64::from(250)))
                 .0
@@ -471,8 +560,17 @@ mod tests {
         assert_similar(asind_f64(F64::from(-0.5)), F64::from(-30));
         assert_similar(asind_f64(F64::from(0)), F64::from(0));
         assert_similar(asind_f64(F64::from(0.5)), F64::from(30));
+        assert_similar(asind_f64(F64::from(0.75)), F64::from(48.590377890729));
         assert_similar(asind_f64(F64::from(1)), F64::from(90));
 
+        // acosd
+        assert_eq!(acosd_f64(F64::from(-1)), F64::from(180));
+        assert_similar(acosd_f64(F64::from(-0.75)), F64::from(138.59037789072914));
+        assert_eq!(acosd_f64(F64::from(-0.5)), F64::from(120));
+        assert_eq!(acosd_f64(F64::from(0.0)), F64::from(90));
+        assert_eq!(acosd_f64(F64::from(0.5)), F64::from(60));
+        assert_eq!(acosd_f64(F64::from(1)), F64::from(0));
+
         // exact matches
         assert!(tand_f64(F64::from(-270)).0.is_infinite());
         assert_eq!(tand_f64(F64::from(-180)), 0.0);
@@ -576,4 +674,16 @@ mod tests {
             atanh_f64(F64::from(x.powi(2) - 1.0) / F64::from(x.powi(2) + 1.0)),
         );
     }
+
+    #[test]
+    fn test_exact() {
+        assert_eq!(cotd_f64(F64::from(135.0)).0, -1.0);
+        assert_eq!(cotd_f64(F64::from(225.0)).0, 1.0);
+        assert_eq!(cotd_f64(F64::from(315.0)).0, -1.0);
+        assert_eq!(cotd_f64(F64::from(45.0)).0, 1.0);
+        assert_eq!(tand_f64(F64::from(45.0)).0, 1.0);
+        assert_eq!(tand_f64(F64::from(135.0)).0, -1.0);
+        assert_eq!(tand_f64(F64::from(225.0)).0, 1.0);
+        assert_eq!(tand_f64(F64::from(315.0)).0, -1.0);
+    }
 }

src/frontend/src/binder/expr/function.rs

@@ -1011,6 +1011,7 @@ impl Binder {
                 ("acosh", raw_call(ExprType::Acosh)),
                 ("atanh", raw_call(ExprType::Atanh)),
                 ("asind", raw_call(ExprType::Asind)),
+                ("acosd", raw_call(ExprType::Acosd)),
                 ("degrees", raw_call(ExprType::Degrees)),
                 ("radians", raw_call(ExprType::Radians)),
                 ("sqrt", raw_call(ExprType::Sqrt)),

src/frontend/src/expr/pure.rs

@@ -135,6 +135,7 @@ impl ExprVisitor for ImpureAnalyzer {
             | Type::Cot
             | Type::Asin
             | Type::Acos
+            | Type::Acosd
             | Type::Atan
             | Type::Atan2
             | Type::Sqrt

src/frontend/src/optimizer/plan_expr_visitor/strong.rs

@@ -188,6 +188,7 @@ impl Strong {
             | ExprType::Cot
             | ExprType::Asin
             | ExprType::Acos
+            | ExprType::Acosd
             | ExprType::Atan
             | ExprType::Atan2
             | ExprType::Sind

src/tests/regress/data/sql/float8.sql

@@ -284,12 +284,12 @@ SELECT x,
 FROM (VALUES (0), (45), (90), (135), (180),
       (225), (270), (315), (360)) AS t(x);
 
---@ SELECT x,
---@        asind(x),
---@        asind(x) IN (-90,-30,0,30,90) AS asind_exact,
---@        acosd(x),
---@        acosd(x) IN (0,60,90,120,180) AS acosd_exact
---@ FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
+SELECT x,
+       asind(x),
+       asind(x) IN (-90,-30,0,30,90) AS asind_exact,
+       acosd(x),
+       acosd(x) IN (0,60,90,120,180) AS acosd_exact
+FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
 
 --@ SELECT x,
 --@        atand(x),