datafusion_functions/math/
cot.rs

1// Licensed to the Apache Software Foundation (ASF) under one
2// or more contributor license agreements.  See the NOTICE file
3// distributed with this work for additional information
4// regarding copyright ownership.  The ASF licenses this file
5// to you under the Apache License, Version 2.0 (the
6// "License"); you may not use this file except in compliance
7// with the License.  You may obtain a copy of the License at
8//
9//   http://www.apache.org/licenses/LICENSE-2.0
10//
11// Unless required by applicable law or agreed to in writing,
12// software distributed under the License is distributed on an
13// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
14// KIND, either express or implied.  See the License for the
15// specific language governing permissions and limitations
16// under the License.
17
18use std::any::Any;
19use std::sync::Arc;
20
21use arrow::array::AsArray;
22use arrow::datatypes::DataType::{Float32, Float64};
23use arrow::datatypes::{DataType, Float32Type, Float64Type};
24
25use datafusion_common::utils::take_function_args;
26use datafusion_common::{Result, ScalarValue, internal_err};
27use datafusion_expr::{ColumnarValue, Documentation, ScalarFunctionArgs};
28use datafusion_expr::{ScalarUDFImpl, Signature, Volatility};
29use datafusion_macros::user_doc;
30
31#[user_doc(
32    doc_section(label = "Math Functions"),
33    description = "Returns the cotangent of a number.",
34    syntax_example = r#"cot(numeric_expression)"#,
35    sql_example = r#"```sql
36> SELECT cot(1);
37+---------+
38| cot(1)  |
39+---------+
40| 0.64209 |
41+---------+
42```"#,
43    standard_argument(name = "numeric_expression", prefix = "Numeric")
44)]
45#[derive(Debug, PartialEq, Eq, Hash)]
46pub struct CotFunc {
47    signature: Signature,
48}
49
50impl Default for CotFunc {
51    fn default() -> Self {
52        CotFunc::new()
53    }
54}
55
56impl CotFunc {
57    pub fn new() -> Self {
58        use DataType::*;
59        Self {
60            // math expressions expect 1 argument of type f64 or f32
61            // priority is given to f64 because e.g. `sqrt(1i32)` is in IR (real numbers) and thus we
62            // return the best approximation for it (in f64).
63            // We accept f32 because in this case it is clear that the best approximation
64            // will be as good as the number of digits in the number
65            signature: Signature::uniform(
66                1,
67                vec![Float64, Float32],
68                Volatility::Immutable,
69            ),
70        }
71    }
72}
73
74impl ScalarUDFImpl for CotFunc {
75    fn as_any(&self) -> &dyn Any {
76        self
77    }
78
79    fn name(&self) -> &str {
80        "cot"
81    }
82
83    fn signature(&self) -> &Signature {
84        &self.signature
85    }
86
87    fn return_type(&self, arg_types: &[DataType]) -> Result<DataType> {
88        match arg_types[0] {
89            Float32 => Ok(Float32),
90            _ => Ok(Float64),
91        }
92    }
93
94    fn documentation(&self) -> Option<&Documentation> {
95        self.doc()
96    }
97
98    fn invoke_with_args(&self, args: ScalarFunctionArgs) -> Result<ColumnarValue> {
99        let return_field = args.return_field;
100        let [arg] = take_function_args(self.name(), args.args)?;
101
102        match arg {
103            ColumnarValue::Scalar(scalar) => {
104                if scalar.is_null() {
105                    return ColumnarValue::Scalar(ScalarValue::Null)
106                        .cast_to(return_field.data_type(), None);
107                }
108
109                match scalar {
110                    ScalarValue::Float64(Some(v)) => Ok(ColumnarValue::Scalar(
111                        ScalarValue::Float64(Some(compute_cot64(v))),
112                    )),
113                    ScalarValue::Float32(Some(v)) => Ok(ColumnarValue::Scalar(
114                        ScalarValue::Float32(Some(compute_cot32(v))),
115                    )),
116                    _ => {
117                        internal_err!(
118                            "Unexpected scalar type for cot: {:?}",
119                            scalar.data_type()
120                        )
121                    }
122                }
123            }
124            ColumnarValue::Array(array) => match array.data_type() {
125                Float64 => Ok(ColumnarValue::Array(Arc::new(
126                    array
127                        .as_primitive::<Float64Type>()
128                        .unary::<_, Float64Type>(compute_cot64),
129                ))),
130                Float32 => Ok(ColumnarValue::Array(Arc::new(
131                    array
132                        .as_primitive::<Float32Type>()
133                        .unary::<_, Float32Type>(compute_cot32),
134                ))),
135                other => {
136                    internal_err!("Unexpected data type {other:?} for function cot")
137                }
138            },
139        }
140    }
141}
142
143fn compute_cot32(x: f32) -> f32 {
144    let a = f32::tan(x);
145    1.0 / a
146}
147
148fn compute_cot64(x: f64) -> f64 {
149    let a = f64::tan(x);
150    1.0 / a
151}
152
153#[cfg(test)]
154mod test {
155    use std::sync::Arc;
156
157    use arrow::array::{ArrayRef, Float32Array, Float64Array};
158    use arrow::datatypes::{DataType, Field};
159    use datafusion_common::ScalarValue;
160    use datafusion_common::cast::{as_float32_array, as_float64_array};
161    use datafusion_common::config::ConfigOptions;
162    use datafusion_expr::{ColumnarValue, ScalarFunctionArgs, ScalarUDFImpl};
163
164    use crate::math::cot::CotFunc;
165
166    #[test]
167    fn test_cot_f32() {
168        let array = Arc::new(Float32Array::from(vec![12.1, 30.0, 90.0, -30.0]));
169        let arg_fields = vec![Field::new("a", DataType::Float32, false).into()];
170        let args = ScalarFunctionArgs {
171            args: vec![ColumnarValue::Array(Arc::clone(&array) as ArrayRef)],
172            arg_fields,
173            number_rows: array.len(),
174            return_field: Field::new("f", DataType::Float32, true).into(),
175            config_options: Arc::new(ConfigOptions::default()),
176        };
177        let result = CotFunc::new()
178            .invoke_with_args(args)
179            .expect("failed to initialize function cot");
180
181        match result {
182            ColumnarValue::Array(arr) => {
183                let floats = as_float32_array(&arr)
184                    .expect("failed to convert result to a Float32Array");
185
186                let expected = Float32Array::from(vec![
187                    -1.986_460_4,
188                    -0.156_119_96,
189                    -0.501_202_8,
190                    0.156_119_96,
191                ]);
192
193                let eps = 1e-6;
194                assert_eq!(floats.len(), 4);
195                assert!((floats.value(0) - expected.value(0)).abs() < eps);
196                assert!((floats.value(1) - expected.value(1)).abs() < eps);
197                assert!((floats.value(2) - expected.value(2)).abs() < eps);
198                assert!((floats.value(3) - expected.value(3)).abs() < eps);
199            }
200            ColumnarValue::Scalar(_) => {
201                panic!("Expected an array value")
202            }
203        }
204    }
205
206    #[test]
207    fn test_cot_f64() {
208        let array = Arc::new(Float64Array::from(vec![12.1, 30.0, 90.0, -30.0]));
209        let arg_fields = vec![Field::new("a", DataType::Float64, false).into()];
210        let args = ScalarFunctionArgs {
211            args: vec![ColumnarValue::Array(Arc::clone(&array) as ArrayRef)],
212            arg_fields,
213            number_rows: array.len(),
214            return_field: Field::new("f", DataType::Float64, true).into(),
215            config_options: Arc::new(ConfigOptions::default()),
216        };
217        let result = CotFunc::new()
218            .invoke_with_args(args)
219            .expect("failed to initialize function cot");
220
221        match result {
222            ColumnarValue::Array(arr) => {
223                let floats = as_float64_array(&arr)
224                    .expect("failed to convert result to a Float64Array");
225
226                let expected = Float64Array::from(vec![
227                    -1.986_458_685_881_4,
228                    -0.156_119_952_161_6,
229                    -0.501_202_783_380_1,
230                    0.156_119_952_161_6,
231                ]);
232
233                let eps = 1e-12;
234                assert_eq!(floats.len(), 4);
235                assert!((floats.value(0) - expected.value(0)).abs() < eps);
236                assert!((floats.value(1) - expected.value(1)).abs() < eps);
237                assert!((floats.value(2) - expected.value(2)).abs() < eps);
238                assert!((floats.value(3) - expected.value(3)).abs() < eps);
239            }
240            ColumnarValue::Scalar(_) => {
241                panic!("Expected an array value")
242            }
243        }
244    }
245
246    #[test]
247    fn test_cot_scalar_f64() {
248        let arg_fields = vec![Field::new("a", DataType::Float64, false).into()];
249        let args = ScalarFunctionArgs {
250            args: vec![ColumnarValue::Scalar(ScalarValue::Float64(Some(1.0)))],
251            arg_fields,
252            number_rows: 1,
253            return_field: Field::new("f", DataType::Float64, false).into(),
254            config_options: Arc::new(ConfigOptions::default()),
255        };
256        let result = CotFunc::new()
257            .invoke_with_args(args)
258            .expect("cot scalar should succeed");
259
260        match result {
261            ColumnarValue::Scalar(ScalarValue::Float64(Some(v))) => {
262                // cot(1.0) = 1/tan(1.0) ≈ 0.6420926159343306
263                let expected = 1.0_f64 / 1.0_f64.tan();
264                assert!((v - expected).abs() < 1e-12);
265            }
266            _ => panic!("Expected Float64 scalar"),
267        }
268    }
269
270    #[test]
271    fn test_cot_scalar_f32() {
272        let arg_fields = vec![Field::new("a", DataType::Float32, false).into()];
273        let args = ScalarFunctionArgs {
274            args: vec![ColumnarValue::Scalar(ScalarValue::Float32(Some(1.0)))],
275            arg_fields,
276            number_rows: 1,
277            return_field: Field::new("f", DataType::Float32, false).into(),
278            config_options: Arc::new(ConfigOptions::default()),
279        };
280        let result = CotFunc::new()
281            .invoke_with_args(args)
282            .expect("cot scalar should succeed");
283
284        match result {
285            ColumnarValue::Scalar(ScalarValue::Float32(Some(v))) => {
286                let expected = 1.0_f32 / 1.0_f32.tan();
287                assert!((v - expected).abs() < 1e-6);
288            }
289            _ => panic!("Expected Float32 scalar"),
290        }
291    }
292
293    #[test]
294    fn test_cot_scalar_null() {
295        let arg_fields = vec![Field::new("a", DataType::Float64, true).into()];
296        let args = ScalarFunctionArgs {
297            args: vec![ColumnarValue::Scalar(ScalarValue::Float64(None))],
298            arg_fields,
299            number_rows: 1,
300            return_field: Field::new("f", DataType::Float64, true).into(),
301            config_options: Arc::new(ConfigOptions::default()),
302        };
303        let result = CotFunc::new()
304            .invoke_with_args(args)
305            .expect("cot null should succeed");
306
307        match result {
308            ColumnarValue::Scalar(scalar) => {
309                assert!(scalar.is_null());
310            }
311            _ => panic!("Expected scalar result"),
312        }
313    }
314
315    #[test]
316    fn test_cot_scalar_zero() {
317        let arg_fields = vec![Field::new("a", DataType::Float64, false).into()];
318        let args = ScalarFunctionArgs {
319            args: vec![ColumnarValue::Scalar(ScalarValue::Float64(Some(0.0)))],
320            arg_fields,
321            number_rows: 1,
322            return_field: Field::new("f", DataType::Float64, false).into(),
323            config_options: Arc::new(ConfigOptions::default()),
324        };
325        let result = CotFunc::new()
326            .invoke_with_args(args)
327            .expect("cot zero should succeed");
328
329        match result {
330            ColumnarValue::Scalar(ScalarValue::Float64(Some(v))) => {
331                // cot(0) = 1/tan(0) = infinity
332                assert!(v.is_infinite());
333            }
334            _ => panic!("Expected Float64 scalar"),
335        }
336    }
337
338    #[test]
339    fn test_cot_scalar_pi() {
340        let arg_fields = vec![Field::new("a", DataType::Float64, false).into()];
341        let args = ScalarFunctionArgs {
342            args: vec![ColumnarValue::Scalar(ScalarValue::Float64(Some(
343                std::f64::consts::PI,
344            )))],
345            arg_fields,
346            number_rows: 1,
347            return_field: Field::new("f", DataType::Float64, false).into(),
348            config_options: Arc::new(ConfigOptions::default()),
349        };
350        let result = CotFunc::new()
351            .invoke_with_args(args)
352            .expect("cot pi should succeed");
353
354        match result {
355            ColumnarValue::Scalar(ScalarValue::Float64(Some(v))) => {
356                // cot(PI) = 1/tan(PI) - very large negative number due to floating point
357                let expected = 1.0_f64 / std::f64::consts::PI.tan();
358                assert!((v - expected).abs() < 1e-6);
359            }
360            _ => panic!("Expected Float64 scalar"),
361        }
362    }
363}
datafusion_functions/math/cot.rs

datafusion_functions/math/
cot.rs
