程序由Golang实现，代码如下：

1.使用递归实现二分查找

//使用递归进行二分查找
func binarySearchTest() {
	//二分查找的数组必须是已经排好序的
	nums := []int{1, 3, 5, 6, 7, 10, 12, 15, 17, 18, 19, 20, 21}
	value := 2
	var index int = searchIndex(nums, value)
	fmt.Println("index:", index)
}

//在nums中查找元素value，返回index
func searchIndex(nums []int, value int) int {
	return searchIndexInArea(nums, value, 0, len(nums)-1)
}

//在nums中查找元素value，返回index. 其中index位于[left,right]之间
func searchIndexInArea(nums []int, value int, left int, right int) int {
	if left > right {
		return -1
	}

	mid := left + (right-left)/2
	if nums[mid] < value {
		return searchIndexInArea(nums, value, mid+1, right)
	} else if nums[mid] > value {
		return searchIndexInArea(nums, value, left, mid-1)
	}

	return mid
}

2.使用循环实现二分查找

func searchIndex2(nums []int, value int) int {
	left, right := 0, len(nums)-1
	for left <= right {
		mid := left + (right-left)/2
		if nums[mid] < value {
			left = mid + 1
		} else if nums[mid] > value {
			right = mid - 1
		} else {
			return mid
		}
	}

	return -1
}