feat(utils): 新增快速平方根算法实现，包含卡马克算法及性能测试

common/utils/sqrt_test.go

@@ -0,0 +1,91 @@
+package utils
+
+import (
+	"fmt"
+	"math"
+	"testing"
+)
+
+func Test_fastSqrt(t *testing.T) {
+	// 测试用例
+	testCases := []float64{2, 4, 10, 16, 25, 100, 1000, 0.5, 0.01, 1e-20}
+
+	fmt.Println("测试卡马克快速平方根算法与标准库的对比：")
+	fmt.Println("数值\t快速算法结果\t标准库结果\t绝对误差")
+	fmt.Println("--------------------------------------------------------------")
+
+	for _, x := range testCases {
+		fastResult := fastSqrt(x)
+		stdResult := math.Sqrt(x)
+		error := math.Abs(fastResult - stdResult)
+
+		fmt.Printf("%.10g\t%.10g\t\t%.10g\t\t%.2e\n",
+			x, fastResult, stdResult, error)
+	}
+
+	// 测试整数版本
+	fmt.Println("\n测试整数快速平方根算法：")
+	fmt.Println("数值\t快速算法结果\t标准库转换结果")
+	fmt.Println("--------------------------------------")
+
+	for _, x := range []int{2, 4, 10, 16, 25, 100, 1000} {
+		fastResult := fastSqrtInt(x)
+		stdResult := int(math.Sqrt(float64(x)))
+
+		fmt.Printf("%d\t%d\t\t%d\n", x, fastResult, stdResult)
+	}
+}
+func BenchmarkMathSqrt(b *testing.B) {
+	testValues := []float64{2, 4, 10, 16, 25, 100, 1000, 0.5, 0.01, 1e-20}
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		for _, x := range testValues {
+			_ = math.Sqrt(x)
+		}
+	}
+}
+
+func BenchmarkFastSqrt(b *testing.B) {
+	testValues := []float64{2, 4, 10, 16, 25, 100, 1000, 0.5, 0.01, 1e-20}
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		for _, x := range testValues {
+			_ = fastSqrt(x)
+		}
+	}
+}
+
+func BenchmarkFastSqrtCarmack(b *testing.B) {
+	testValues := []float64{2, 4, 10, 16, 25, 100, 1000, 0.5, 0.01, 1e-20}
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		for _, x := range testValues {
+			_ = fastSqrtCarmack(x)
+		}
+	}
+}
+
+func BenchmarkMathSqrtInt(b *testing.B) {
+	testValues := []int{2, 4, 10, 16, 25, 100, 1000, 10000, 100000}
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		for _, x := range testValues {
+			_ = int(math.Sqrt(float64(x)))
+		}
+	}
+}
+
+func BenchmarkFastSqrtInt(b *testing.B) {
+	testValues := []int{2, 4, 10, 16, 25, 100, 1000, 10000, 100000}
+	b.ResetTimer()
+
+	for i := 0; i < b.N; i++ {
+		for _, x := range testValues {
+			_ = fastSqrtInt(x)
+		}
+	}
+}