pkg/math: add tests which show the API constants

consts.txtar shows the constant values exposed via the CUE std API,
and Example_constants shows the same ones exposed via the Go API.
Note that we're not particular about the precision used by the Go test;
we mainly aim to see whether the values look roughly correct or not.

This is in preparation for https://cuelang.org/cl/557322,
which will fix one of the constants to not truncate to an integer.

Note that Log2E and Log10E are truncated to the integers 1 and 0,
a bug which will be fixed in the next commit.

Signed-off-by: Daniel Martí <mvdan@mvdan.cc>
Change-Id: Ie737f7a7ff7a609cdb9fc74df64bddc2e423f00f
Reviewed-on: https://review.gerrithub.io/c/cue-lang/cue/+/557321
Reviewed-by: Paul Jolly <paul@myitcv.io>
Unity-Result: CUE porcuepine <cue.porcuepine@gmail.com>
TryBot-Result: CUEcueckoo <cueckoo@cuelang.org>

pkg/math/math_test.go

@@ -15,11 +15,46 @@
 package math_test
 
 import (
+	"fmt"
 	"testing"
 
 	"cuelang.org/go/pkg/internal/builtintest"
+	"cuelang.org/go/pkg/math"
 )
 
 func TestBuiltin(t *testing.T) {
 	builtintest.Run("math", t)
 }
+
+func Example_constants() {
+	show := func(name string, value any) {
+		fmt.Printf("% 7s: %v\n", name, value)
+	}
+
+	show("E", math.E)
+	show("Pi", math.Pi)
+	show("Phi", math.Phi)
+
+	show("Sqrt2", math.Sqrt2)
+	show("SqrtE", math.SqrtE)
+	show("SqrtPi", math.SqrtPi)
+	show("SqrtPhi", math.SqrtPhi)
+
+	show("Ln2", math.Ln2)
+	show("Log2E", math.Log2E)
+	show("Ln10", math.Ln10)
+	show("Log10E", math.Log10E)
+
+	// Output:
+	//       E: 2.718281828459045
+	//      Pi: 3.141592653589793
+	//     Phi: 1.618033988749895
+	//   Sqrt2: 1.4142135623730951
+	//   SqrtE: 1.6487212707001282
+	//  SqrtPi: 1.772453850905516
+	// SqrtPhi: 1.272019649514069
+	//     Ln2: 0.6931471805599453
+	//   Log2E: 1
+	//    Ln10: 2.302585092994046
+	//  Log10E: 0
+}

pkg/math/testdata/consts.txtar

@@ -0,0 +1,29 @@
+-- in.cue --
+import "math"
+
+E:   math.E
+Pi:  math.Pi
+Phi: math.Phi
+
+Sqrt2:   math.Sqrt2
+SqrtE:   math.SqrtE
+SqrtPi:  math.SqrtPi
+SqrtPhi: math.SqrtPhi
+
+Ln2:    math.Ln2
+Log2E:  math.Log2E
+Ln10:   math.Ln10
+Log10E: math.Log10E
+-- out/math --
+E:       2.71828182845904523536028747135266249775724709369995957496696763
+Pi:      3.14159265358979323846264338327950288419716939937510582097494459
+Phi:     1.61803398874989484820458683436563811772030917980576286213544861
+Sqrt2:   1.41421356237309504880168872420969807856967187537694807317667974
+SqrtE:   1.64872127070012814684865078781416357165377610071014801157507931
+SqrtPi:  1.77245385090551602729816748334114518279754945612238712821380779
+SqrtPhi: 1.27201964951406896425242246173749149171560804184009624861664038
+Ln2:     0.693147180559945309417232121458176568075500134360255254120680009
+Log2E:   1.442695040888963407359924681001892137426645954152985934135449408
+Ln10:    2.3025850929940456840179914546843642076011014886287729760333278
+Log10E:  0.43429448190325182765112891891660508229439700580366656611445378
+

pkg/math/testdata/gen.txtar

@@ -3,7 +3,6 @@
 -- in.cue --
 import "math"
 
-t1:  math.Pi
 t2:  math.Floor(math.Pi)
 t3:  math.Pi(3)
 t6:  math.Jacobi(1000, 2000)
@@ -26,15 +25,14 @@ t33: math.Dim(5, 7.2)
 -- out/math --
 Errors:
 t3: cannot call non-function math.Pi (type float):
-    ./in.cue:5:6
+    ./in.cue:4:6
 t6: error in call to math.Jacobi: big: invalid 2nd argument to Int.Jacobi: need odd integer but got 2000:
-    ./in.cue:6:6
+    ./in.cue:5:6
 t8: cannot use 2.0E+400 (type float) as float64 in argument 0 to math.Asin: value was rounded up:
-    ./in.cue:8:6
-    ./in.cue:8:16
+    ./in.cue:7:6
+    ./in.cue:7:16
 
 Result:
-t1:  3.14159265358979323846264338327950288419716939937510582097494459
 t2:  3
 t3:  _|_ // t3: cannot call non-function math.Pi (type float)
 t6:  _|_ // t6: error in call to math.Jacobi: big: invalid 2nd argument to Int.Jacobi: need odd integer but got 2000