move math constants to standard library (#9678)

# Description
we talked about this before in some meetings so i thought, why not?

the hope is that these constants do not require Rust code to be
implemented and that this move will make the Rust source base a bit
smaller 🤞

# User-Facing Changes
mathematical constants (e, pi, tau, phi and gamma) are now in `std math`
rather than `math`

## what can be done
```nushell
> use std; $std.math
> use std math; $math
> use std *; $math
```
will all give
```
╭───────┬────────────────────╮
│ GAMMA │ 0.5772156649015329 │
│ E     │ 2.718281828459045  │
│ PI    │ 3.141592653589793  │
│ TAU   │ 6.283185307179586  │
│ PHI   │ 1.618033988749895  │
╰───────┴────────────────────╯
```
and the following will work too
```nushell
> use std math E; $E
2.718281828459045
```
```nushell
> use std math *; $GAMMA
0.5772156649015329
```

## what can NOT be done
looks like every export works fine now 😌 

# Tests + Formatting
# After Submitting

crates/nu-cmd-extra/src/example_test.rs

@@ -15,8 +15,6 @@ mod test_examples {
         check_example_input_and_output_types_match_command_signature,
     };
 
-    use crate::MathEuler;
-    use crate::MathPi;
     use nu_protocol::{
         engine::{Command, EngineState, StateWorkingSet},
         Type,
@@ -64,9 +62,6 @@ mod test_examples {
 
             working_set.add_decl(Box::new(nu_command::Enumerate));
             working_set.add_decl(Box::new(nu_cmd_lang::If));
-            // math commands
-            working_set.add_decl(Box::new(MathEuler));
-            working_set.add_decl(Box::new(MathPi));
             working_set.add_decl(Box::new(nu_command::MathRound));
 
             // Adding the command that is being tested to the working set

crates/nu-cmd-extra/src/extra/math/cos.rs

@@ -54,7 +54,7 @@ impl Command for SubCommand {
         vec![
             Example {
                 description: "Apply the cosine to π",
-                example: "math pi | math cos",
+                example: "3.141592 | math cos | math round --precision 4",
                 result: Some(Value::test_float(-1f64)),
             },
             Example {

crates/nu-cmd-extra/src/extra/math/egamma.rs

@@ -1,64 +0,0 @@
-use nu_protocol::ast::Call;
-use nu_protocol::engine::{Command, EngineState, Stack};
-use nu_protocol::{
-    Category, Example, IntoPipelineData, PipelineData, ShellError, Signature, Type, Value,
-};
-
-#[allow(clippy::excessive_precision)]
-/// The Euler-Mascheroni constant (γ)
-pub const EGAMMA: f64 = 0.577215664901532860606512090082402431_f64;
-
-#[derive(Clone)]
-pub struct SubCommand;
-
-impl Command for SubCommand {
-    fn name(&self) -> &str {
-        "math egamma"
-    }
-
-    fn signature(&self) -> Signature {
-        Signature::build("math egamma")
-            .input_output_types(vec![(Type::Any, Type::Float)])
-            .category(Category::Math)
-    }
-
-    fn usage(&self) -> &str {
-        "Returns the Euler–Mascheroni constant γ. ( 1 | math egamma)."
-    }
-
-    fn search_terms(&self) -> Vec<&str> {
-        vec!["euler", "constant", "gamma"]
-    }
-
-    #[allow(clippy::approx_constant)]
-    fn examples(&self) -> Vec<Example> {
-        vec![Example {
-            example: "math egamma | math round --precision 3",
-            description: "Get the first three decimal digits of γ",
-            result: Some(Value::test_float(0.577)),
-        }]
-    }
-
-    fn run(
-        &self,
-        _engine_state: &EngineState,
-        _stack: &mut Stack,
-        call: &Call,
-        _input: PipelineData,
-    ) -> Result<PipelineData, ShellError> {
-        // TODO: replace with std::f64::consts::EGAMMA when available https://github.com/rust-lang/rust/issues/103883
-        Ok(Value::float(EGAMMA, call.head).into_pipeline_data())
-    }
-}
-
-#[cfg(test)]
-mod test {
-    use super::*;
-
-    #[test]
-    fn test_examples() {
-        use crate::test_examples;
-
-        test_examples(SubCommand {})
-    }
-}

crates/nu-cmd-extra/src/extra/math/euler.rs

@@ -1,59 +0,0 @@
-use nu_protocol::ast::Call;
-use nu_protocol::engine::{Command, EngineState, Stack};
-use nu_protocol::{
-    Category, Example, IntoPipelineData, PipelineData, ShellError, Signature, Type, Value,
-};
-
-#[derive(Clone)]
-pub struct SubCommand;
-
-impl Command for SubCommand {
-    fn name(&self) -> &str {
-        "math e"
-    }
-
-    fn signature(&self) -> Signature {
-        Signature::build("math e")
-            .input_output_types(vec![(Type::Any, Type::Float)])
-            .category(Category::Math)
-    }
-
-    fn usage(&self) -> &str {
-        "Returns the mathematical constant e (exp(1)/'1 | math exp')."
-    }
-
-    fn search_terms(&self) -> Vec<&str> {
-        vec!["euler", "number", "constant"]
-    }
-
-    #[allow(clippy::approx_constant)]
-    fn examples(&self) -> Vec<Example> {
-        vec![Example {
-            example: "math e | math round --precision 3",
-            description: "Get the first three decimal digits of e",
-            result: Some(Value::test_float(2.718)),
-        }]
-    }
-
-    fn run(
-        &self,
-        _engine_state: &EngineState,
-        _stack: &mut Stack,
-        call: &Call,
-        _input: PipelineData,
-    ) -> Result<PipelineData, ShellError> {
-        Ok(Value::float(std::f64::consts::E, call.head).into_pipeline_data())
-    }
-}
-
-#[cfg(test)]
-mod test {
-    use super::*;
-
-    #[test]
-    fn test_examples() {
-        use crate::test_examples;
-
-        test_examples(SubCommand {})
-    }
-}

crates/nu-cmd-extra/src/extra/math/ln.rs

@@ -52,7 +52,7 @@ impl Command for SubCommand {
     fn examples(&self) -> Vec<Example> {
         vec![Example {
             description: "Get the natural logarithm of e",
-            example: "math e | math ln",
+            example: "2.7182818 | math ln | math round --precision 4",
             result: Some(Value::test_float(1.0f64)),
         }]
     }

crates/nu-cmd-extra/src/extra/math/mod.rs

@@ -5,13 +5,8 @@ mod sinh;
 mod tan;
 mod tanh;
 
-mod egamma;
-mod euler;
 mod exp;
 mod ln;
-mod phi;
-mod pi;
-mod tau;
 
 mod arccos;
 mod arccosh;
@@ -27,13 +22,8 @@ pub use sinh::SubCommand as MathSinH;
 pub use tan::SubCommand as MathTan;
 pub use tanh::SubCommand as MathTanH;
 
-pub use egamma::SubCommand as MathEulerGamma;
-pub use euler::SubCommand as MathEuler;
 pub use exp::SubCommand as MathExp;
 pub use ln::SubCommand as MathLn;
-pub use phi::SubCommand as MathPhi;
-pub use pi::SubCommand as MathPi;
-pub use tau::SubCommand as MathTau;
 
 pub use arccos::SubCommand as MathArcCos;
 pub use arccosh::SubCommand as MathArcCosH;

crates/nu-cmd-extra/src/extra/math/phi.rs

@@ -1,64 +0,0 @@
-use nu_protocol::ast::Call;
-use nu_protocol::engine::{Command, EngineState, Stack};
-use nu_protocol::{
-    Category, Example, IntoPipelineData, PipelineData, ShellError, Signature, Type, Value,
-};
-
-#[allow(clippy::excessive_precision)]
-/// The golden ratio (φ)
-pub const PHI: f64 = 1.618033988749894848204586834365638118_f64;
-
-#[derive(Clone)]
-pub struct SubCommand;
-
-impl Command for SubCommand {
-    fn name(&self) -> &str {
-        "math phi"
-    }
-
-    fn signature(&self) -> Signature {
-        Signature::build("math phi")
-            .input_output_types(vec![(Type::Any, Type::Float)])
-            .category(Category::Math)
-    }
-
-    fn usage(&self) -> &str {
-        "Returns the golden ratio φ. ( (1 + sqrt(5) ) / 2 )"
-    }
-
-    fn search_terms(&self) -> Vec<&str> {
-        vec!["golden", "ratio", "constant"]
-    }
-
-    #[allow(clippy::approx_constant)]
-    fn examples(&self) -> Vec<Example> {
-        vec![Example {
-            example: "math phi | math round --precision 3",
-            description: "Get the first two decimal digits of φ",
-            result: Some(Value::test_float(1.618)),
-        }]
-    }
-
-    fn run(
-        &self,
-        _engine_state: &EngineState,
-        _stack: &mut Stack,
-        call: &Call,
-        _input: PipelineData,
-    ) -> Result<PipelineData, ShellError> {
-        // TODO: replace with std::f64::consts::PHI when available https://github.com/rust-lang/rust/issues/103883
-        Ok(Value::float(PHI, call.head).into_pipeline_data())
-    }
-}
-
-#[cfg(test)]
-mod test {
-    use super::*;
-
-    #[test]
-    fn test_examples() {
-        use crate::test_examples;
-
-        test_examples(SubCommand {})
-    }
-}

crates/nu-cmd-extra/src/extra/math/pi.rs

@@ -1,59 +0,0 @@
-use nu_protocol::ast::Call;
-use nu_protocol::engine::{Command, EngineState, Stack};
-use nu_protocol::{
-    Category, Example, IntoPipelineData, PipelineData, ShellError, Signature, Type, Value,
-};
-
-#[derive(Clone)]
-pub struct SubCommand;
-
-impl Command for SubCommand {
-    fn name(&self) -> &str {
-        "math pi"
-    }
-
-    fn signature(&self) -> Signature {
-        Signature::build("math pi")
-            .input_output_types(vec![(Type::Any, Type::Float)])
-            .category(Category::Math)
-    }
-
-    fn usage(&self) -> &str {
-        "Returns the mathematical constant π."
-    }
-
-    fn search_terms(&self) -> Vec<&str> {
-        vec!["trigonometry", "constant"]
-    }
-
-    #[allow(clippy::approx_constant)]
-    fn examples(&self) -> Vec<Example> {
-        vec![Example {
-            example: "math pi | math round --precision 2",
-            description: "Get the first two decimal digits of π",
-            result: Some(Value::test_float(3.14)),
-        }]
-    }
-
-    fn run(
-        &self,
-        _engine_state: &EngineState,
-        _stack: &mut Stack,
-        call: &Call,
-        _input: PipelineData,
-    ) -> Result<PipelineData, ShellError> {
-        Ok(Value::float(std::f64::consts::PI, call.head).into_pipeline_data())
-    }
-}
-
-#[cfg(test)]
-mod test {
-    use super::*;
-
-    #[test]
-    fn test_examples() {
-        use crate::test_examples;
-
-        test_examples(SubCommand {})
-    }
-}

crates/nu-cmd-extra/src/extra/math/sin.rs

@@ -54,7 +54,7 @@ impl Command for SubCommand {
         vec![
             Example {
                 description: "Apply the sine to π/2",
-                example: "(math pi) / 2 | math sin",
+                example: "3.141592 / 2 | math sin | math round --precision 4",
                 result: Some(Value::test_float(1f64)),
             },
             Example {

crates/nu-cmd-extra/src/extra/math/tan.rs

@@ -54,7 +54,7 @@ impl Command for SubCommand {
         vec![
             Example {
                 description: "Apply the tangent to π/4",
-                example: "(math pi) / 4 | math tan",
+                example: "3.141592 / 4 | math tan | math round --precision 4",
                 result: Some(Value::test_float(1f64)),
             },
             Example {

crates/nu-cmd-extra/src/extra/math/tanh.rs

@@ -52,7 +52,7 @@ impl Command for SubCommand {
     fn examples(&self) -> Vec<Example> {
         vec![Example {
             description: "Apply the hyperbolic tangent to 10*π",
-            example: "(math pi) * 10 | math tanh",
+            example: "3.141592 * 10 | math tanh | math round --precision 4",
             result: Some(Value::test_float(1f64)),
         }]
     }

crates/nu-cmd-extra/src/extra/math/tau.rs

@@ -1,59 +0,0 @@
-use nu_protocol::ast::Call;
-use nu_protocol::engine::{Command, EngineState, Stack};
-use nu_protocol::{
-    Category, Example, IntoPipelineData, PipelineData, ShellError, Signature, Type, Value,
-};
-
-#[derive(Clone)]
-pub struct SubCommand;
-
-impl Command for SubCommand {
-    fn name(&self) -> &str {
-        "math tau"
-    }
-
-    fn signature(&self) -> Signature {
-        Signature::build("math tau")
-            .input_output_types(vec![(Type::Any, Type::Float)])
-            .category(Category::Math)
-    }
-
-    fn usage(&self) -> &str {
-        "Returns the mathematical constant τ."
-    }
-
-    fn search_terms(&self) -> Vec<&str> {
-        vec!["trigonometry", "constant"]
-    }
-
-    #[allow(clippy::approx_constant)]
-    fn examples(&self) -> Vec<Example> {
-        vec![Example {
-            example: "math tau | math round --precision 2",
-            description: "Get the first two decimal digits of τ",
-            result: Some(Value::test_float(6.28)),
-        }]
-    }
-
-    fn run(
-        &self,
-        _engine_state: &EngineState,
-        _stack: &mut Stack,
-        call: &Call,
-        _input: PipelineData,
-    ) -> Result<PipelineData, ShellError> {
-        Ok(Value::float(std::f64::consts::TAU, call.head).into_pipeline_data())
-    }
-}
-
-#[cfg(test)]
-mod test {
-    use super::*;
-
-    #[test]
-    fn test_examples() {
-        use crate::test_examples;
-
-        test_examples(SubCommand {})
-    }
-}

crates/nu-cmd-extra/src/extra/mod.rs

@@ -24,13 +24,8 @@ pub use math::MathSinH;
 pub use math::MathTan;
 pub use math::MathTanH;
 
-pub use math::MathEuler;
-pub use math::MathEulerGamma;
 pub use math::MathExp;
 pub use math::MathLn;
-pub use math::MathPhi;
-pub use math::MathPi;
-pub use math::MathTau;
 
 pub use math::MathArcCos;
 pub use math::MathArcCosH;
@@ -111,9 +106,6 @@ pub fn add_extra_command_context(mut engine_state: EngineState) -> EngineState {
             MathSinH,
             MathCosH,
             MathTanH,
-            MathPi,
-            MathTau,
-            MathEuler,
             MathExp,
             MathLn
         };

crates/nu-std/src/lib.rs

@@ -27,6 +27,7 @@ pub fn load_standard_library(
             ("assert.nu", include_str!("../std/assert.nu")),
             ("xml.nu", include_str!("../std/xml.nu")),
             ("input.nu", include_str!("../std/input.nu")),
+            ("math.nu", include_str!("../std/math.nu")),
         ];
 
         let mut working_set = StateWorkingSet::new(engine_state);

crates/nu-std/std/math.nu

@@ -0,0 +1,5 @@
+export const GAMMA = 0.5772156649015329
+export const E = 2.718281828459045
+export const PI = 3.141592653589793
+export const TAU = 6.283185307179586
+export const PHI = 1.618033988749895