From 8a0d94542f891e7329222966f0d03fc95e70d073 Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Fri, 12 May 2023 14:09:52 +0200
Subject: [PATCH 01/14] acosd implementation draft

---
 .../functions/trigonometric_funcs.slt.part    | 45 +++++++++++++++++++
 proto/expr.proto                              |  1 +
 src/expr/src/vector_op/trigonometric.rs       | 43 ++++++++++++++++++
 src/frontend/src/binder/expr/function.rs      |  1 +
 src/frontend/src/expr/pure.rs                 |  1 +
 src/tests/regress/data/sql/float8.sql         | 12 ++---
 6 files changed, 97 insertions(+), 6 deletions(-)

diff --git a/e2e_test/batch/functions/trigonometric_funcs.slt.part b/e2e_test/batch/functions/trigonometric_funcs.slt.part
index cd4b8e47ba2b1..8c7da6d21bb80 100644
--- a/e2e_test/batch/functions/trigonometric_funcs.slt.part
+++ b/e2e_test/batch/functions/trigonometric_funcs.slt.part
@@ -524,3 +524,48 @@ 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) - 120.00000000000001) < 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
diff --git a/proto/expr.proto b/proto/expr.proto
index 75c91931679a6..14c3be9187975 100644
--- a/proto/expr.proto
+++ b/proto/expr.proto
@@ -119,6 +119,7 @@ message ExprNode {
     SQRT = 258;
     DEGREES = 259;
     RADIANS = 260;
+    ACOSD = 261;
 
     // Boolean comparison
     IS_TRUE = 301;
diff --git a/src/expr/src/vector_op/trigonometric.rs b/src/expr/src/vector_op/trigonometric.rs
index 9887834a4bcba..457a4acb0e038 100644
--- a/src/expr/src/vector_op/trigonometric.rs
+++ b/src/expr/src/vector_op/trigonometric.rs
@@ -65,6 +65,7 @@ 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;
+static ACOS_0_5: f64 = 1.047_197_551_196_597_6;
 
 // 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.
@@ -314,6 +315,43 @@ 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);
+        90.0 - (asin_x / ASIN_0_5) * 30.0
+    } else {
+        let acos_x = f64::acos(x);
+        (acos_x / ACOS_0_5) * 60.0
+    }
+}
+
+#[function("acosd(float64) -> float64")]
+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() {
+        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(float64) -> float64")]
 pub fn degrees_f64(input: F64) -> F64 {
     input.0.to_degrees().into()
@@ -338,6 +376,9 @@ mod tests {
 
     /// 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, "{:?} != {:?}", lhs.0, rhs.0);
     }
@@ -433,6 +474,8 @@ mod tests {
         assert_similar(asind_f64(F64::from(0.5)), F64::from(30));
         assert_similar(asind_f64(F64::from(1)), F64::from(90));
 
+        // TODO: write some tests here for cosd here, matching the exact values
+
         // exact matches
         assert!(tand_f64(F64::from(-270)).0.is_infinite());
         assert_eq!(tand_f64(F64::from(-180)), 0.0);
diff --git a/src/frontend/src/binder/expr/function.rs b/src/frontend/src/binder/expr/function.rs
index a147e97803e85..cead16f5e9480 100644
--- a/src/frontend/src/binder/expr/function.rs
+++ b/src/frontend/src/binder/expr/function.rs
@@ -436,6 +436,7 @@ impl Binder {
                 ("cotd", raw_call(ExprType::Cotd)),
                 ("tand", raw_call(ExprType::Tand)),
                 ("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)),
diff --git a/src/frontend/src/expr/pure.rs b/src/frontend/src/expr/pure.rs
index e87a72fd7e861..919ccdf990ab9 100644
--- a/src/frontend/src/expr/pure.rs
+++ b/src/frontend/src/expr/pure.rs
@@ -155,6 +155,7 @@ impl ExprVisitor<bool> for ImpureAnalyzer {
             | expr_node::Type::Cosd
             | expr_node::Type::Cotd
             | expr_node::Type::Asind
+            | expr_node::Type::Acosd
             | expr_node::Type::Decode
             | expr_node::Type::Encode
             | expr_node::Type::Sha1
diff --git a/src/tests/regress/data/sql/float8.sql b/src/tests/regress/data/sql/float8.sql
index 17e4e61235564..3d389f5716e28 100644
--- a/src/tests/regress/data/sql/float8.sql
+++ b/src/tests/regress/data/sql/float8.sql
@@ -284,12 +284,12 @@ FROM (VALUES (0), (60), (90), (120), (180),
 --@ 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),

From e8383d473732d1bd1cb3eb8ee747c738ae8692f2 Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Fri, 12 May 2023 14:38:25 +0200
Subject: [PATCH 02/14] simplify if else statement

---
 src/expr/src/vector_op/trigonometric.rs | 13 +++++++------
 1 file changed, 7 insertions(+), 6 deletions(-)

diff --git a/src/expr/src/vector_op/trigonometric.rs b/src/expr/src/vector_op/trigonometric.rs
index 457a4acb0e038..7c148d21b2b71 100644
--- a/src/expr/src/vector_op/trigonometric.rs
+++ b/src/expr/src/vector_op/trigonometric.rs
@@ -65,7 +65,7 @@ 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;
-static ACOS_0_5: f64 = 1.047_197_551_196_597_6;
+static ACOS_0_5: f64 = 1.047_197_551_196_597_6; // TODO: maybe this num is incorrect?
 
 // 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.
@@ -324,11 +324,10 @@ fn acosd_q1(x: f64) -> f64 {
     // monotonic function over the full range.
     if x <= 0.5 {
         let asin_x = f64::asin(x);
-        90.0 - (asin_x / ASIN_0_5) * 30.0
-    } else {
-        let acos_x = f64::acos(x);
-        (acos_x / ACOS_0_5) * 60.0
+        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(float64) -> float64")]
@@ -336,7 +335,7 @@ 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() {
+    if input.0.is_nan() || input.0.is_infinite() || arg1 < -1.0 || arg1 > 1.0 {
         return F64::from(f64::NAN);
     }
 
@@ -385,6 +384,8 @@ mod tests {
 
     #[test]
     fn test_degrees() {
+        let ACOS_0_5_local = f64::acos(0.5);
+
         let d = F64::from(180);
         let pi = F64::from(PI);
 

From 8d8e0a21f391d46284bf56e8af04aa1d1f03fd7e Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Wed, 17 May 2023 15:13:58 +0100
Subject: [PATCH 03/14] fix bug + reduce accuracy

---
 .../functions/trigonometric_funcs.slt.part    |  2 +-
 src/expr/src/vector_op/trigonometric.rs       | 22 ++++++++++++-------
 2 files changed, 15 insertions(+), 9 deletions(-)

diff --git a/e2e_test/batch/functions/trigonometric_funcs.slt.part b/e2e_test/batch/functions/trigonometric_funcs.slt.part
index 8c7da6d21bb80..0665de5f4ed04 100644
--- a/e2e_test/batch/functions/trigonometric_funcs.slt.part
+++ b/e2e_test/batch/functions/trigonometric_funcs.slt.part
@@ -536,7 +536,7 @@ SELECT abs(acosd(-0.75) - 138.59037789072914) < 1e-14
 t
 
 query R
-SELECT abs(acosd(-0.5) - 120.00000000000001) < 1e-14
+SELECT abs(acosd(-0.5) - 120.0) < 1e-14
 ----
 t
 
diff --git a/src/expr/src/vector_op/trigonometric.rs b/src/expr/src/vector_op/trigonometric.rs
index 7c148d21b2b71..6277b2dfc21cb 100644
--- a/src/expr/src/vector_op/trigonometric.rs
+++ b/src/expr/src/vector_op/trigonometric.rs
@@ -58,6 +58,7 @@ pub fn atan2_f64(input_x: F64, input_y: F64) -> F64 {
 
 // Radians per degree, a.k.a. PI / 180
 static RADIANS_PER_DEGREE: f64 = 0.017_453_292_519_943_295;
+
 // Constants we use to get more accurate results.
 // 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;
@@ -65,7 +66,7 @@ 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;
-static ACOS_0_5: f64 = 1.047_197_551_196_597_6; // TODO: maybe this num is incorrect?
+static ACOS_0_5: f64 = 1.047_197_551_196_597_6;
 
 // 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.
@@ -286,7 +287,7 @@ pub fn asind_q1(x: f64) -> f64 {
     }
 
     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(float64) -> float64")]
@@ -299,7 +300,7 @@ 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);
     }
 
@@ -335,7 +336,7 @@ 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() || arg1 < -1.0 || arg1 > 1.0 {
+    if input.0.is_nan() || input.0.is_infinite() || !(-1.0..=1.0).contains(&arg1) {
         return F64::from(f64::NAN);
     }
 
@@ -370,7 +371,7 @@ mod tests {
     use crate::vector_op::trigonometric::*;
 
     fn precision() -> f64 {
-        1e-13
+        1e-12
     }
 
     /// numbers are equal within a rounding error
@@ -384,8 +385,6 @@ mod tests {
 
     #[test]
     fn test_degrees() {
-        let ACOS_0_5_local = f64::acos(0.5);
-
         let d = F64::from(180);
         let pi = F64::from(PI);
 
@@ -473,9 +472,16 @@ 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));
 
-        // TODO: write some tests here for cosd here, matching the exact values
+        // 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());

From 2cec3f5a39afd2d7a0caa4b59fabee78140ae086 Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Wed, 17 May 2023 15:39:48 +0100
Subject: [PATCH 04/14] retrigger

---
 src/expr/src/vector_op/trigonometric.rs | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/expr/src/vector_op/trigonometric.rs b/src/expr/src/vector_op/trigonometric.rs
index 427c1079964a4..4b03b9ae61cfd 100644
--- a/src/expr/src/vector_op/trigonometric.rs
+++ b/src/expr/src/vector_op/trigonometric.rs
@@ -450,7 +450,6 @@ 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

From 40cec342f9ad1f2be2676245fe97dd7bf6cf3e24 Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Thu, 18 May 2023 11:45:35 +0100
Subject: [PATCH 05/14] use lazy_static for constants

---
 src/expr/Cargo.toml                     |  1 +
 src/expr/src/vector_op/trigonometric.rs | 82 +++++++++++++++++++------
 2 files changed, 64 insertions(+), 19 deletions(-)

diff --git a/src/expr/Cargo.toml b/src/expr/Cargo.toml
index a8025d2dc8dd9..0f1dccbcc7501 100644
--- a/src/expr/Cargo.toml
+++ b/src/expr/Cargo.toml
@@ -30,6 +30,7 @@ futures-async-stream = { workspace = true }
 futures-util = "0.3"
 hex = "0.4.3"
 itertools = "0.10"
+lazy_static = "1"
 md5 = "0.7.0"
 num-traits = "0.2"
 ouroboros = "0.15"
diff --git a/src/expr/src/vector_op/trigonometric.rs b/src/expr/src/vector_op/trigonometric.rs
index 4b03b9ae61cfd..b1688b3d38ea2 100644
--- a/src/expr/src/vector_op/trigonometric.rs
+++ b/src/expr/src/vector_op/trigonometric.rs
@@ -12,6 +12,9 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
+use std::f64::consts::PI;
+
+use lazy_static::lazy_static;
 use risingwave_common::types::F64;
 use risingwave_expr_macro::function;
 
@@ -56,32 +59,73 @@ pub fn atan2_f64(input_x: F64, input_y: F64) -> F64 {
     input_x.0.atan2(input_y.0).into()
 }
 
-// Radians per degree, a.k.a. PI / 180
-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;
-static ACOS_0_5: f64 = 1.047_197_551_196_597_6;
+fn sind_30() -> f64 {
+    lazy_static! {
+        static ref SIND_30: f64 = f64::sin(30.0 * radians_per_degree());
+    }
+    *SIND_30
+}
+
+fn one_minus_cosd_60() -> f64 {
+    lazy_static! {
+        static ref ONE_MINUS_COSD_60: f64 = 1.0 - f64::cos(60.0 * radians_per_degree());
+    }
+    *ONE_MINUS_COSD_60
+}
+
+fn tand_45() -> f64 {
+    lazy_static! {
+        static ref TAND_45: f64 = f64::tan(45.0 * radians_per_degree());
+    }
+    *TAND_45
+}
+
+fn cotd_45() -> f64 {
+    lazy_static! {
+        static ref COTD_45: f64 =
+            f64::cos(45.0 * radians_per_degree()) / f64::sin(45.0 * radians_per_degree());
+    }
+    *COTD_45
+}
+
+fn asin_0_5() -> f64 {
+    lazy_static! {
+        static ref ASIN_0_5: f64 = f64::asin(0.5);
+    }
+    *ASIN_0_5
+}
+
+fn acos_0_5() -> f64 {
+    lazy_static! {
+        static ref ACOS_0_5: f64 = f64::acos(0.5);
+    }
+    *ACOS_0_5
+}
+
+fn radians_per_degree() -> f64 {
+    lazy_static! {
+        static ref RADIANS_PER_DEGREE: f64 = PI / 180.0;
+    }
+    *RADIANS_PER_DEGREE
+}
 
 // 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
+    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
 }
 
 // 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
+    let sin_x = f64::sin(x * radians_per_degree());
+    (sin_x / sind_30()) / 2.0
 }
 
 // returns the cosine of an angle in the first quadrant (0 to 90 degrees).
@@ -219,7 +263,7 @@ 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
@@ -259,7 +303,7 @@ 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
@@ -278,11 +322,11 @@ 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 / ACOS_0_5) * 60.0
+    90.0 - (acos_x / acos_0_5()) * 60.0
 }
 
 #[function("asind(float64) -> float64")]
@@ -320,10 +364,10 @@ fn acosd_q1(x: f64) -> f64 {
     // 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;
+        return 90.0 - (asin_x / asin_0_5()) * 30.0;
     }
     let acos_x = f64::acos(x);
-    (acos_x / ACOS_0_5) * 60.0
+    (acos_x / acos_0_5()) * 60.0
 }
 
 #[function("acosd(float64) -> float64")]

From 758b173f481525060598d3e701ac331f837f6676 Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Thu, 18 May 2023 11:49:49 +0100
Subject: [PATCH 06/14] lazy_static in cargo file

---
 Cargo.lock | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Cargo.lock b/Cargo.lock
index 37f10089c8623..bb52347e71d81 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -6089,6 +6089,7 @@ dependencies = [
  "futures-util",
  "hex",
  "itertools",
+ "lazy_static",
  "madsim-tokio",
  "md5",
  "num-traits",

From ee70fbe82067d93662565b108a09c3b2d7b99623 Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Thu, 27 Jun 2024 13:17:03 +0200
Subject: [PATCH 07/14] fix cargo file

---
 Cargo.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Cargo.toml b/Cargo.toml
index 3fe6abc8787ba..e2c75a4d84171 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -143,7 +143,7 @@ arrow-cast-iceberg = { package = "arrow-cast", version = "52" }
 # After apache/iceberg-rust#411 is merged, we move to the upstream version.
 iceberg = { git = "https://github.com/risingwavelabs/iceberg-rust.git", rev = "0c6e133e6f4655ff9ce4ad57b577dc7f692dd902" }
 iceberg-catalog-rest = { git = "https://github.com/risingwavelabs/iceberg-rust.git", rev = "0c6e133e6f4655ff9ce4ad57b577dc7f692dd902" }
-arrow-array = "50"
+arrow-array = "52"
 arrow-arith = "50"
 arrow-cast = "50"
 arrow-schema = "50"

From e4b7b688ff8e7d274dc0455aec1ec81784bf4b7d Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Thu, 27 Jun 2024 13:22:52 +0200
Subject: [PATCH 08/14] Fix cargo file

---
 Cargo.lock               | 4 ----
 Cargo.toml               | 2 +-
 src/batch/Cargo.toml     | 1 -
 src/common/Cargo.toml    | 2 --
 src/connector/Cargo.toml | 1 -
 5 files changed, 1 insertion(+), 9 deletions(-)

diff --git a/Cargo.lock b/Cargo.lock
index 37ba94e3fc3a3..ebf5f9d75b68c 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -10634,7 +10634,6 @@ version = "1.11.0-alpha"
 dependencies = [
  "anyhow",
  "arrow-array 50.0.0",
- "arrow-array 52.0.0",
  "arrow-schema 50.0.0",
  "assert_matches",
  "async-recursion",
@@ -10786,9 +10785,7 @@ dependencies = [
  "ahash 0.8.11",
  "anyhow",
  "arc-swap",
- "arrow-array 48.0.1",
  "arrow-array 50.0.0",
- "arrow-array 52.0.0",
  "arrow-buffer 48.0.1",
  "arrow-buffer 50.0.0",
  "arrow-buffer 52.0.0",
@@ -11096,7 +11093,6 @@ dependencies = [
  "anyhow",
  "apache-avro 0.16.0",
  "arrow-array 50.0.0",
- "arrow-array 52.0.0",
  "arrow-row 50.0.0",
  "arrow-schema 50.0.0",
  "arrow-schema 52.0.0",
diff --git a/Cargo.toml b/Cargo.toml
index e2c75a4d84171..3fe6abc8787ba 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -143,7 +143,7 @@ arrow-cast-iceberg = { package = "arrow-cast", version = "52" }
 # After apache/iceberg-rust#411 is merged, we move to the upstream version.
 iceberg = { git = "https://github.com/risingwavelabs/iceberg-rust.git", rev = "0c6e133e6f4655ff9ce4ad57b577dc7f692dd902" }
 iceberg-catalog-rest = { git = "https://github.com/risingwavelabs/iceberg-rust.git", rev = "0c6e133e6f4655ff9ce4ad57b577dc7f692dd902" }
-arrow-array = "52"
+arrow-array = "50"
 arrow-arith = "50"
 arrow-cast = "50"
 arrow-schema = "50"
diff --git a/src/batch/Cargo.toml b/src/batch/Cargo.toml
index ef4badfe07666..2ca8ed1be4e77 100644
--- a/src/batch/Cargo.toml
+++ b/src/batch/Cargo.toml
@@ -16,7 +16,6 @@ normal = ["workspace-hack"]
 [dependencies]
 anyhow = "1"
 arrow-array = { workspace = true }
-arrow-array-iceberg = { workspace = true }
 arrow-schema = { workspace = true }
 assert_matches = "1"
 async-recursion = "1"
diff --git a/src/common/Cargo.toml b/src/common/Cargo.toml
index ae6f67faf3aac..ba295b56f02ca 100644
--- a/src/common/Cargo.toml
+++ b/src/common/Cargo.toml
@@ -18,8 +18,6 @@ ahash = "0.8"
 anyhow = "1"
 arc-swap = "1"
 arrow-array = { workspace = true }
-arrow-array-deltalake = { workspace = true }
-arrow-array-iceberg = { workspace = true }
 arrow-buffer = { workspace = true }
 arrow-buffer-deltalake = { workspace = true }
 arrow-buffer-iceberg = { workspace = true }
diff --git a/src/connector/Cargo.toml b/src/connector/Cargo.toml
index 3d8bf618eca58..257b930556c94 100644
--- a/src/connector/Cargo.toml
+++ b/src/connector/Cargo.toml
@@ -17,7 +17,6 @@ normal = ["workspace-hack"]
 anyhow = "1"
 apache-avro = { workspace = true }
 arrow-array = { workspace = true }
-arrow-array-iceberg = { workspace = true }
 arrow-row = { workspace = true }
 arrow-schema = { workspace = true }
 arrow-schema-iceberg = { workspace = true }

From 090bc43fd6ecdfcee78c1e93c83d1912391f8caf Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Thu, 27 Jun 2024 14:44:23 +0200
Subject: [PATCH 09/14] remove lazy_static

---
 Cargo.lock                                | 46 ++++++-------
 src/batch/Cargo.toml                      |  1 +
 src/common/Cargo.toml                     |  2 +
 src/connector/Cargo.toml                  |  1 +
 src/expr/impl/Cargo.toml                  |  1 -
 src/expr/impl/src/scalar/trigonometric.rs | 81 ++++++-----------------
 6 files changed, 46 insertions(+), 86 deletions(-)

diff --git a/Cargo.lock b/Cargo.lock
index ebf5f9d75b68c..80cfce6eb09dc 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -926,9 +926,9 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "76cb6d108605c5489fff1ef9c520656946ad05ed0de3ea6d26d56bcb34bdb8c5"
 dependencies = [
  "anyhow",
- "arrow-array 52.0.0",
- "arrow-buffer 52.0.0",
- "arrow-schema 52.0.0",
+ "arrow-array 50.0.0",
+ "arrow-buffer 50.0.0",
+ "arrow-schema 50.0.0",
  "atomic-time",
  "rquickjs",
 ]
@@ -939,10 +939,10 @@ version = "0.0.1"
 source = "git+https://github.com/risingwavelabs/arrow-udf.git?rev=fa36365#fa3636559de986aa592da6e8b3fbfac7bdd4bb78"
 dependencies = [
  "anyhow",
- "arrow-array 52.0.0",
- "arrow-buffer 52.0.0",
- "arrow-data 52.0.0",
- "arrow-schema 52.0.0",
+ "arrow-array 50.0.0",
+ "arrow-buffer 50.0.0",
+ "arrow-data 50.0.0",
+ "arrow-schema 50.0.0",
  "arrow-udf-js-deno-runtime",
  "async-trait",
  "deno_core",
@@ -990,10 +990,10 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "4506efc6fbc200c083add2a7ed4e3616a859941a745e922320ae7051d90d12ec"
 dependencies = [
  "anyhow",
- "arrow-array 52.0.0",
- "arrow-buffer 52.0.0",
- "arrow-ipc 52.0.0",
- "arrow-schema 52.0.0",
+ "arrow-array 50.0.0",
+ "arrow-buffer 50.0.0",
+ "arrow-ipc 50.0.0",
+ "arrow-schema 50.0.0",
  "lazy_static",
  "pyo3",
  "pyo3-build-config",
@@ -1006,9 +1006,9 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "eb829e25925161d93617d4b053bae03fe51e708f2cce088d85df856011d4f369"
 dependencies = [
  "anyhow",
- "arrow-array 52.0.0",
- "arrow-ipc 52.0.0",
- "arrow-schema 52.0.0",
+ "arrow-array 50.0.0",
+ "arrow-ipc 50.0.0",
+ "arrow-schema 50.0.0",
  "async-trait",
  "base64 0.22.0",
  "genawaiter",
@@ -5898,7 +5898,7 @@ dependencies = [
  "http 0.2.9",
  "thiserror",
  "tokio",
- "tonic 0.11.0",
+ "tonic 0.10.2",
  "tower",
  "tracing",
  "trust-dns-resolver 0.23.2",
@@ -7098,11 +7098,11 @@ dependencies = [
 
 [[package]]
 name = "lazy_static"
-version = "1.5.0"
+version = "1.4.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "bbd2bcb4c963f2ddae06a2efc7e9f3591312473c50c6685e1f298068316e66fe"
+checksum = "e2abad23fbc42b3700f2f279844dc832adb2b2eb069b2df918f455c4e18cc646"
 dependencies = [
- "spin 0.9.8",
+ "spin 0.5.2",
 ]
 
 [[package]]
@@ -9929,7 +9929,7 @@ dependencies = [
  "indoc",
  "libc",
  "memoffset",
- "parking_lot 0.12.1",
+ "parking_lot 0.11.2",
  "portable-atomic",
  "pyo3-build-config",
  "pyo3-ffi",
@@ -10634,6 +10634,7 @@ version = "1.11.0-alpha"
 dependencies = [
  "anyhow",
  "arrow-array 50.0.0",
+ "arrow-array 52.0.0",
  "arrow-schema 50.0.0",
  "assert_matches",
  "async-recursion",
@@ -10785,7 +10786,9 @@ dependencies = [
  "ahash 0.8.11",
  "anyhow",
  "arc-swap",
+ "arrow-array 48.0.1",
  "arrow-array 50.0.0",
+ "arrow-array 52.0.0",
  "arrow-buffer 48.0.1",
  "arrow-buffer 50.0.0",
  "arrow-buffer 52.0.0",
@@ -11093,6 +11096,7 @@ dependencies = [
  "anyhow",
  "apache-avro 0.16.0",
  "arrow-array 50.0.0",
+ "arrow-array 52.0.0",
  "arrow-row 50.0.0",
  "arrow-schema 50.0.0",
  "arrow-schema 52.0.0",
@@ -11412,7 +11416,6 @@ dependencies = [
  "icelake",
  "itertools 0.12.1",
  "jsonbb",
- "lazy_static",
  "linkme",
  "madsim-tokio",
  "md5",
@@ -15396,10 +15399,7 @@ dependencies = [
  "percent-encoding",
  "pin-project",
  "prost 0.12.1",
- "rustls-pemfile 2.1.1",
- "rustls-pki-types",
  "tokio",
- "tokio-rustls 0.25.0",
  "tokio-stream",
  "tower",
  "tower-layer",
diff --git a/src/batch/Cargo.toml b/src/batch/Cargo.toml
index 2ca8ed1be4e77..ef4badfe07666 100644
--- a/src/batch/Cargo.toml
+++ b/src/batch/Cargo.toml
@@ -16,6 +16,7 @@ normal = ["workspace-hack"]
 [dependencies]
 anyhow = "1"
 arrow-array = { workspace = true }
+arrow-array-iceberg = { workspace = true }
 arrow-schema = { workspace = true }
 assert_matches = "1"
 async-recursion = "1"
diff --git a/src/common/Cargo.toml b/src/common/Cargo.toml
index ba295b56f02ca..ae6f67faf3aac 100644
--- a/src/common/Cargo.toml
+++ b/src/common/Cargo.toml
@@ -18,6 +18,8 @@ ahash = "0.8"
 anyhow = "1"
 arc-swap = "1"
 arrow-array = { workspace = true }
+arrow-array-deltalake = { workspace = true }
+arrow-array-iceberg = { workspace = true }
 arrow-buffer = { workspace = true }
 arrow-buffer-deltalake = { workspace = true }
 arrow-buffer-iceberg = { workspace = true }
diff --git a/src/connector/Cargo.toml b/src/connector/Cargo.toml
index 257b930556c94..3d8bf618eca58 100644
--- a/src/connector/Cargo.toml
+++ b/src/connector/Cargo.toml
@@ -17,6 +17,7 @@ normal = ["workspace-hack"]
 anyhow = "1"
 apache-avro = { workspace = true }
 arrow-array = { workspace = true }
+arrow-array-iceberg = { workspace = true }
 arrow-row = { workspace = true }
 arrow-schema = { workspace = true }
 arrow-schema-iceberg = { workspace = true }
diff --git a/src/expr/impl/Cargo.toml b/src/expr/impl/Cargo.toml
index 8e7cb36dc27fc..0f69c91e34162 100644
--- a/src/expr/impl/Cargo.toml
+++ b/src/expr/impl/Cargo.toml
@@ -50,7 +50,6 @@ hex = "0.4"
 icelake = { workspace = true }
 itertools = { workspace = true }
 jsonbb = { workspace = true }
-lazy_static = "1.5.0"
 linkme = { version = "0.3", features = ["used_linker"] }
 md5 = "0.7"
 moka = { version = "0.12", features = ["sync"] }
diff --git a/src/expr/impl/src/scalar/trigonometric.rs b/src/expr/impl/src/scalar/trigonometric.rs
index f5ea625d7d2f3..b00078dc3bd5a 100644
--- a/src/expr/impl/src/scalar/trigonometric.rs
+++ b/src/expr/impl/src/scalar/trigonometric.rs
@@ -12,9 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-use std::f64::consts::PI;
-
-use lazy_static::lazy_static;
 use risingwave_common::types::F64;
 use risingwave_expr::function;
 
@@ -98,73 +95,33 @@ pub fn atanh_f64(input: F64) -> F64 {
     f64::atanh(input.0).into()
 }
 
+// Radians per degree, a.k.a. PI / 180
+static RADIANS_PER_DEGREE: f64 = 0.017_453_292_519_943_295;
 // Constants we use to get more accurate results.
+// TODO: use lazy_static
 // 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
-fn sind_30() -> f64 {
-    lazy_static! {
-        static ref SIND_30: f64 = f64::sin(30.0 * radians_per_degree());
-    }
-    *SIND_30
-}
-
-fn one_minus_cosd_60() -> f64 {
-    lazy_static! {
-        static ref ONE_MINUS_COSD_60: f64 = 1.0 - f64::cos(60.0 * radians_per_degree());
-    }
-    *ONE_MINUS_COSD_60
-}
-
-fn tand_45() -> f64 {
-    lazy_static! {
-        static ref TAND_45: f64 = f64::tan(45.0 * radians_per_degree());
-    }
-    *TAND_45
-}
-
-fn cotd_45() -> f64 {
-    lazy_static! {
-        static ref COTD_45: f64 =
-            f64::cos(45.0 * radians_per_degree()) / f64::sin(45.0 * radians_per_degree());
-    }
-    *COTD_45
-}
-
-fn asin_0_5() -> f64 {
-    lazy_static! {
-        static ref ASIN_0_5: f64 = f64::asin(0.5);
-    }
-    *ASIN_0_5
-}
-
-fn acos_0_5() -> f64 {
-    lazy_static! {
-        static ref ACOS_0_5: f64 = f64::acos(0.5);
-    }
-    *ACOS_0_5
-}
-
-fn radians_per_degree() -> f64 {
-    lazy_static! {
-        static ref RADIANS_PER_DEGREE: f64 = PI / 180.0;
-    }
-    *RADIANS_PER_DEGREE
-}
+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;
+static ACOS_0_5: f64 = 1.047_197_551_196_597_6;
 
 // 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
+    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
 }
 
 // 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
+    let sin_x = f64::sin(x * RADIANS_PER_DEGREE);
+    (sin_x / SIND_30) / 2.0
 }
 
 // returns the cosine of an angle in the first quadrant (0 to 90 degrees).
@@ -302,7 +259,7 @@ 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
@@ -342,7 +299,7 @@ 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
@@ -361,11 +318,11 @@ 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 / acos_0_5()) * 60.0
+    90.0 - (acos_x / ACOS_0_5) * 60.0
 }
 
 #[function("asind(float8) -> float8")]
@@ -403,10 +360,10 @@ fn acosd_q1(x: f64) -> f64 {
     // 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;
+        return 90.0 - (asin_x / ASIN_0_5) * 30.0;
     }
     let acos_x = f64::acos(x);
-    (acos_x / acos_0_5()) * 60.0
+    (acos_x / ACOS_0_5) * 60.0
 }
 
 #[function("acosd(float8) -> float8")]

From 80a9c340ec4b4a097f0e3b8fb2d94eead1351562 Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Thu, 27 Jun 2024 19:10:43 +0200
Subject: [PATCH 10/14] try more precise

---
 src/expr/impl/src/scalar/trigonometric.rs | 58 +++++++++++++++--------
 1 file changed, 39 insertions(+), 19 deletions(-)

diff --git a/src/expr/impl/src/scalar/trigonometric.rs b/src/expr/impl/src/scalar/trigonometric.rs
index b00078dc3bd5a..02a7e88d4b459 100644
--- a/src/expr/impl/src/scalar/trigonometric.rs
+++ b/src/expr/impl/src/scalar/trigonometric.rs
@@ -12,6 +12,8 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
+use std::f64::consts::PI;
+
 use risingwave_common::types::F64;
 use risingwave_expr::function;
 
@@ -95,33 +97,51 @@ pub fn atanh_f64(input: F64) -> F64 {
     f64::atanh(input.0).into()
 }
 
-// Radians per degree, a.k.a. PI / 180
-static RADIANS_PER_DEGREE: f64 = 0.017_453_292_519_943_295;
 // Constants we use to get more accurate results.
-// TODO: use lazy_static
 // 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;
-static ACOS_0_5: f64 = 1.047_197_551_196_597_6;
+fn sind_30() -> f64 {
+    f64::sin(30.0 * radians_per_degree())
+}
+
+fn one_minus_cosd_60() -> f64 {
+    1.0 - f64::cos(60.0 * radians_per_degree())
+}
+
+fn tand_45() -> f64 {
+    f64::tan(45.0 * radians_per_degree())
+}
+
+fn cotd_45() -> f64 {
+    f64::cos(45.0 * radians_per_degree()) / f64::sin(45.0 * radians_per_degree())
+}
+
+fn asin_0_5() -> f64 {
+    f64::asin(0.5)
+}
+
+fn acos_0_5() -> f64 {
+    f64::acos(0.5)
+}
+
+fn radians_per_degree() -> f64 {
+    PI / 180.0
+}
 
 // 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
+    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
 }
 
 // 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
+    let sin_x = f64::sin(x * radians_per_degree());
+    (sin_x / sind_30()) / 2.0
 }
 
 // returns the cosine of an angle in the first quadrant (0 to 90 degrees).
@@ -259,7 +279,7 @@ 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
@@ -299,7 +319,7 @@ 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
@@ -318,11 +338,11 @@ 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 / ACOS_0_5) * 60.0
+    90.0 - (acos_x / acos_0_5()) * 60.0
 }
 
 #[function("asind(float8) -> float8")]
@@ -360,10 +380,10 @@ fn acosd_q1(x: f64) -> f64 {
     // 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;
+        return 90.0 - (asin_x / asin_0_5()) * 30.0;
     }
     let acos_x = f64::acos(x);
-    (acos_x / ACOS_0_5) * 60.0
+    (acos_x / acos_0_5()) * 60.0
 }
 
 #[function("acosd(float8) -> float8")]

From 716133007232193205164a6473634f4b949613bf Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Thu, 27 Jun 2024 19:20:12 +0200
Subject: [PATCH 11/14] rm duplicate import

---
 src/expr/impl/src/scalar/trigonometric.rs | 2 --
 1 file changed, 2 deletions(-)

diff --git a/src/expr/impl/src/scalar/trigonometric.rs b/src/expr/impl/src/scalar/trigonometric.rs
index 02a7e88d4b459..47ad047766711 100644
--- a/src/expr/impl/src/scalar/trigonometric.rs
+++ b/src/expr/impl/src/scalar/trigonometric.rs
@@ -419,8 +419,6 @@ 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::*;

From ace278fbb1df71a64570bac73fcc495f12ee60d4 Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Fri, 28 Jun 2024 09:52:32 +0200
Subject: [PATCH 12/14] hardcode edge cases

---
 src/expr/impl/src/scalar/trigonometric.rs | 68 +++++++++++++++++++----
 1 file changed, 56 insertions(+), 12 deletions(-)

diff --git a/src/expr/impl/src/scalar/trigonometric.rs b/src/expr/impl/src/scalar/trigonometric.rs
index 47ad047766711..b4b1db192f490 100644
--- a/src/expr/impl/src/scalar/trigonometric.rs
+++ b/src/expr/impl/src/scalar/trigonometric.rs
@@ -97,42 +97,46 @@ pub fn atanh_f64(input: F64) -> F64 {
     f64::atanh(input.0).into()
 }
 
+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_769_2;
+
 // 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
 fn sind_30() -> f64 {
-    f64::sin(30.0 * radians_per_degree())
+    f64::sin(DEGREE_THIRTY * RADIANS_PER_DEGREE)
 }
 
 fn one_minus_cosd_60() -> f64 {
-    1.0 - f64::cos(60.0 * radians_per_degree())
+    DEGREE_ONE - f64::cos(DEGREE_SIXTY * RADIANS_PER_DEGREE)
 }
 
 fn tand_45() -> f64 {
-    f64::tan(45.0 * radians_per_degree())
+    f64::tan(DEGREE_FORTY_FIVE * RADIANS_PER_DEGREE)
 }
 
 fn cotd_45() -> f64 {
-    f64::cos(45.0 * radians_per_degree()) / f64::sin(45.0 * radians_per_degree())
+    f64::cos(DEGREE_FORTY_FIVE * RADIANS_PER_DEGREE)
+        / f64::sin(DEGREE_FORTY_FIVE * RADIANS_PER_DEGREE)
 }
 
 fn asin_0_5() -> f64 {
-    f64::asin(0.5)
+    f64::asin(DEGREE_ONE_HALF)
 }
 
 fn acos_0_5() -> f64 {
-    f64::acos(0.5)
-}
-
-fn radians_per_degree() -> f64 {
-    PI / 180.0
+    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());
+    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
 }
 
@@ -140,7 +144,7 @@ fn cosd_0_to_60(x: f64) -> f64 {
 // 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());
+    let sin_x = f64::sin(x * RADIANS_PER_DEGREE);
     (sin_x / sind_30()) / 2.0
 }
 
@@ -260,6 +264,20 @@ 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;
@@ -300,6 +318,20 @@ 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;
@@ -644,4 +676,16 @@ 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);
+    }
 }

From d62369681f64d46068bf39f6fc9fc6eea81e2d7c Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Fri, 28 Jun 2024 11:33:41 +0200
Subject: [PATCH 13/14] risedev c

---
 src/expr/impl/src/scalar/trigonometric.rs | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/src/expr/impl/src/scalar/trigonometric.rs b/src/expr/impl/src/scalar/trigonometric.rs
index b4b1db192f490..2dbaba23228f3 100644
--- a/src/expr/impl/src/scalar/trigonometric.rs
+++ b/src/expr/impl/src/scalar/trigonometric.rs
@@ -12,8 +12,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-use std::f64::consts::PI;
-
 use risingwave_common::types::F64;
 use risingwave_expr::function;
 
@@ -102,7 +100,7 @@ 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_769_2;
+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

From be412e2bb805d28e6c393946e8a8f22174c3a4ee Mon Sep 17 00:00:00 2001
From: CAJan93 <jan.mensch@gmx.net>
Date: Fri, 28 Jun 2024 15:48:18 +0200
Subject: [PATCH 14/14] use pi

---
 src/expr/impl/src/scalar/trigonometric.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/expr/impl/src/scalar/trigonometric.rs b/src/expr/impl/src/scalar/trigonometric.rs
index 2dbaba23228f3..325fc85538ffe 100644
--- a/src/expr/impl/src/scalar/trigonometric.rs
+++ b/src/expr/impl/src/scalar/trigonometric.rs
@@ -475,7 +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)));