Move sqrt_3 from constants.h to accurate_norm_test.cc

sqrt_3_v and sqrt_3 are only used as test expectations in
accurate_norm_test.cc. Move them out of the public ceres::constants
namespace and into the test file.

Change-Id: I64fa1177cd6695838e10fc48b7cc736400de5241

include/ceres/constants.h

diff --git a/include/ceres/constants.h b/include/ceres/constants.h
index e3c0680..e4c96da 100644
--- a/include/ceres/constants.h
+++ b/include/ceres/constants.h
@@ -34,13 +34,12 @@
 // TODO(HSHelson): This header should no longer be necessary once C++20's
 // <numbers> (e.g. std::numbers::pi_v) becomes usable
 
-// The constants are computed using mpmath by the following shell command:
+// The constant is computed using mpmath by the following shell command:
 //
 // python3 - <<EOF
 // from mpmath import mp
 // mp.dps = 64
 // print(mp.pi)
-// print(mp.sqrt(3))
 // EOF
 namespace ceres::constants {
 // π
@@ -48,11 +47,6 @@
 inline constexpr T pi_v(
     3.141592653589793238462643383279502884197169399375105820974944592L);
 inline constexpr double pi = pi_v<double>;
-// √3
-template <typename T>
-inline constexpr T sqrt_3_v(
-    1.732050807568877293527446341505872366942805253810380628055806979L);
-inline constexpr double sqrt_3 = sqrt_3_v<double>;
 }  // namespace ceres::constants
 
 #endif  // CERES_PUBLIC_CONSTANTS_H_

internal/ceres/accurate_norm_test.cc

diff --git a/internal/ceres/accurate_norm_test.cc b/internal/ceres/accurate_norm_test.cc
index 102cd65..e5d0570 100644
--- a/internal/ceres/accurate_norm_test.cc
+++ b/internal/ceres/accurate_norm_test.cc
@@ -36,10 +36,21 @@
 #include <limits>
 #include <type_traits>
 
-#include "ceres/constants.h"
 #include "gmock/gmock.h"
 #include "gtest/gtest.h"
 
+// The constant is computed using mpmath by the following shell command:
+//
+// python3 - <<EOF
+// from mpmath import mp
+// mp.dps = 64
+// print(mp.sqrt(3))
+// EOF
+// √3
+template <typename T>
+inline constexpr T kSqrt3(
+    1.732050807568877293527446341505872366942805253810380628055806979L);
+
 // Matches if the argument is at most n floating-point values away from the
 // expected value.
 MATCHER_P2(MaxNumUlp, expected, n, "") {
@@ -180,10 +191,8 @@
               MaxNumUlp(1 / (std::sqrt(Scalar{2}) * this->kTiny), 1));
 
   const auto tiny3 = std::sqrt(this->kTiny) / Scalar{3};
-  EXPECT_THAT(
-      ceres::AccurateRNorm(tiny3, tiny3, tiny3),
-      MaxNumUlp(ceres::constants::sqrt_3_v<Scalar> / std::sqrt(this->kTiny),
-                1));
+  EXPECT_THAT(ceres::AccurateRNorm(tiny3, tiny3, tiny3),
+              MaxNumUlp(kSqrt3<Scalar> / std::sqrt(this->kTiny), 1));
 
   const auto tiny4 = std::sqrt(this->kTiny) / Scalar{4};
   EXPECT_THAT(ceres::AccurateRNorm(tiny4, tiny4, tiny4, tiny4),
@@ -335,7 +344,7 @@
 
 TEST(AccurateNorm, VariadicNormAccuracy) {
   EXPECT_THAT(ceres::AccurateNorm(1.0, 1.0, 1.0),
-              MaxNumUlp(ceres::constants::sqrt_3, 0));
+              MaxNumUlp(kSqrt3<double>, 0));
 
   // Combination exposing a difference of at least two ULPs in inaccurate
   // implementations found by random search.