中国年历算法和程式
本文摘自“和荣笔记 - 中国农历二百年算法及年历”
中国公历算法
中国公历算法不是太难，关键是星期值的确定。这里给出了简单算法：
public static int dayOfWeek(int y, int m, int d)
{ int w = 1;
// 公历一年一月一日是星期一，所以起始值为星期日 y = (y-1)%400 + 1;
// 公历星期值分部 400 年循环一次 int ly = (y-1)/4;
// 闰年次数 ly = ly - (y-1)/100; ly = ly + (y-1)/400; int ry = y - 1 - ly;
// 常年次数 w = w + ry;
// 常年星期值增一 w = w + 2*ly;
// 闰年星期值增二 w = w + dayOfYear(y,m,d); w = (w-1)%7 + 1; return w; }
中国农历算法
根公历相比，中国农历的算法相当复杂。我在网上找的算法之中，eleworld.com 的算法是最好的一个。这个算法使用了大量的数据来确定农历月份和节气的分部，它仅实用于公历 1901 年到 2100 年之间的 200 年。
中国农历计算程式
跟据 eleworld.com 提供的算法，我写了下面这个程式：
/**
* ChineseCalendarGB.java
* Copyright (c) 1997-2002 by Dr. Herong Yang. http://www.herongyang.com/
* 中国农历算法 - 实用于公历 1901 年至 2100 年之间的 200 年
*/
import java.text.*;
import java.util.*;
class ChineseCalendarGB {
private int gregorianYear;
private int gregorianMonth;
private int gregorianDate;
private boolean isGregorianLeap;
private int dayOfYear;
private int dayOfWeek; // 周日一星期的第一天
private int chineseYear;
private int chineseMonth; // 负数表示闰月
private int chineseDate;
private int sectionalTerm;
private int principleTerm;
private static char[] daysInGregorianMonth =
{31,28,31,30,31,30,31,31,30,31,30,31};
private static String[] stemNames =
{"甲","乙","丙","丁","戊","己","庚","辛","壬","癸"};
private static String[] branchNames =
{"子","丑","寅","卯","辰","巳","午","未","申","酉","戌","亥"};
private static String[] animalNames =
{"鼠","牛","虎","兔","龙","蛇","马","羊","猴","鸡","狗","猪"};
public static void main(String[] arg) {
ChineseCalendarGB c = new ChineseCalendarGB();
String cmd = "day";
int y = 1901;
int m = 1;
int d = 1;
if (arg.length>0) cmd = arg[0];
if (arg.length>1) y = Integer.parseInt(arg[1]);
if (arg.length>2) m = Integer.parseInt(arg[2]);
if (arg.length>3) d = Integer.parseInt(arg[3]);
c.setGregorian(y,m,d);
c.computeChineseFields();
c.computeSolarTerms();
if (cmd.equalsIgnoreCase("year")) {
String[] t = c.getYearTable();
for (int i=0; i } else if (cmd.equalsIgnoreCase("month")) {
String[] t = c.getMonthTable();
for (int i=0; i } else {
System.out.println(c.toString());
}
}
public ChineseCalendarGB() {
setGregorian(1901,1,1);
}
public void setGregorian(int y, int m, int d) {
gregorianYear = y;
gregorianMonth = m;
gregorianDate = d;
isGregorianLeap = isGregorianLeapYear(y);
dayOfYear = dayOfYear(y,m,d);
dayOfWeek = dayOfWeek(y,m,d);
chineseYear = 0;
chineseMonth = 0;
chineseDate = 0;
sectionalTerm = 0;
principleTerm = 0;
}
public static boolean isGregorianLeapYear(int year) {
boolean isLeap = false;
if (year%4==0) isLeap = true;
if (year%100==0) isLeap = false;
if (year%400==0) isLeap = true;
return isLeap;
}
public static int daysInGregorianMonth(int y, int m) {
int d = daysInGregorianMonth[m-1];
if (m==2 && isGregorianLeapYear(y)) d++; // 公历闰年二月多一天
return d;
}
public static int dayOfYear(int y, int m, int d) {
int c = 0;
for (int i=1; i c = c + daysInGregorianMonth(y,i);
}
c = c + d;
return c;
}
public static int dayOfWeek(int y, int m, int d) {
int w = 1; // 公历一年一月一日是星期一，所以起始值为星期日
y = (y-1)%400 + 1; // 公历星期值分部 400 年循环一次
int ly = (y-1)/4; // 闰年次数
ly = ly - (y-1)/100;
ly = ly + (y-1)/400;
int ry = y - 1 - ly; // 常年次数
w = w + ry; // 常年星期值增一
w = w + 2*ly; // 闰年星期值增二
w = w + dayOfYear(y,m,d);
w = (w-1)%7 + 1;
return w;
}
private static char[] chineseMonths = {
// 农历月份大小压缩表，两个字节表示一年。两个字节共十六个二进制位数，
// 前四个位数表示闰月月份，后十二个位数表示十二个农历月份的大小。
0x00,0x04,0xad,0x08,0x5a,0x01,0xd5,0x54,0xb4,0x09,0x64,0x05,0x59,0x45,
0x95,0x0a,0xa6,0x04,0x55,0x24,0xad,0x08,0x5a,0x62,0xda,0x04,0xb4,0x05,
0xb4,0x55,0x52,0x0d,0x94,0x0a,0x4a,0x2a,0x56,0x02,0x6d,0x71,0x6d,0x01,
0xda,0x02,0xd2,0x52,0xa9,0x05,0x49,0x0d,0x2a,0x45,0x2b,0x09,0x56,0x01,
0xb5,0x20,0x6d,0x01,0x59,0x69,0xd4,0x0a,0xa8,0x05,0xa9,0x56,0xa5,0x04,
0x2b,0x09,0x9e,0x38,0xb6,0x08,0xec,0x74,0x6c,0x05,0xd4,0x0a,0xe4,0x6a,
0x52,0x05,0x95,0x0a,0x5a,0x42,0x5b,0x04,0xb6,0x04,0xb4,0x22,0x6a,0x05,
0x52,0x75,0xc9,0x0a,0x52,0x05,0x35,0x55,0x4d,0x0a,0x5a,0x02,0x5d,0x31,
0xb5,0x02,0x6a,0x8a,0x68,0x05,0xa9,0x0a,0x8a,0x6a,0x2a,0x05,0x2d,0x09,
0xaa,0x48,0x5a,0x01,0xb5,0x09,0xb0,0x39,0x64,0x05,0x25,0x75,0x95,0x0a,
0x96,0x04,0x4d,0x54,0xad,0x04,0xda,0x04,0xd4,0x44,0xb4,0x05,0x54,0x85,
0x52,0x0d,0x92,0x0a,0x56,0x6a,0x56,0x02,0x6d,0x02,0x6a,0x41,0xda,0x02,
0xb2,0xa1,0xa9,0x05,0x49,0x0d,0x0a,0x6d,0x2a,0x09,0x56,0x01,0xad,0x50,
0x6d,0x01,0xd9,0x02,0xd1,0x3a,0xa8,0x05,0x29,0x85,0xa5,0x0c,0x2a,0x09,
0x96,0x54,0xb6,0x08,0x6c,0x09,0x64,0x45,0xd4,0x0a,0xa4,0x05,0x51,0x25,
0x95,0x0a,0x2a,0x72,0x5b,0x04,0xb6,0x04,0xac,0x52,0x6a,0x05,0xd2,0x0a,
0xa2,0x4a,0x4a,0x05,0x55,0x94,0x2d,0x0a,0x5a,0x02,0x75,0x61,0xb5,0x02,
0x6a,0x03,0x61,0x45,0xa9,0x0a,0x4a,0x05,0x25,0x25,0x2d,0x09,0x9a,0x68,
0xda,0x08,0xb4,0x09,0xa8,0x59,0x54,0x03,0xa5,0x0a,0x91,0x3a,0x96,0x04,
0xad,0xb0,0xad,0x04,0xda,0x04,0xf4,0x62,0xb4,0x05,0x54,0x0b,0x44,0x5d,
0x52,0x0a,0x95,0x04,0x55,0x22,0x6d,0x02,0x5a,0x71,0xda,0x02,0xaa,0x05,
0xb2,0x55,0x49,0x0b,0x4a,0x0a,0x2d,0x39,0x36,0x01,0x6d,0x80,0x6d,0x01,
0xd9,0x02,0xe9,0x6a,0xa8,0x05,0x29,0x0b,0x9a,0x4c,0xaa,0x08,0xb6,0x08,
0xb4,0x38,0x6c,0x09,0x54,0x75,0xd4,0x0a,0xa4,0x05,0x45,0x55,0x95,0x0a,
0x9a,0x04,0x55,0x44,0xb5,0x04,0x6a,0x82,0x6a,0x05,0xd2,0x0a,0x92,0x6a,
0x4a,0x05,0x55,0x0a,0x2a,0x4a,0x5a,0x02,0xb5,0x02,0xb2,0x31,0x69,0x03,
0x31,0x73,0xa9,0x0a,0x4a,0x05,0x2d,0x55,0x2d,0x09,0x5a,0x01,0xd5,0x48,
0xb4,0x09,0x68,0x89,0x54,0x0b,0xa4,0x0a,0xa5,0x6a,0x95,0x04,0xad,0x08,
0x6a,0x44,0xda,0x04,0x74,0x05,0xb0,0x25,0x54,0x03
};
// 初始日，公历农历对应日期：
// 公历 1901 年 1 月 1 日，对应农历 4598 年 11 月 11 日
private static int baseYear = 1901;
private static int baseMonth = 1;
private static int baseDate = 1;
private static int baseIndex = 0;
private static int baseChineseYear = 4598-1;
private static int baseChineseMonth = 11;
private static int baseChineseDate = 11;
public int computeChineseFields() {
if (gregorianYear<1901 || gregorianYear>2100) return 1;
int startYear = baseYear;
int startMonth = baseMonth;
int startDate = baseDate;
chineseYear = baseChineseYear;
chineseMonth = baseChineseMonth;
chineseDate = baseChineseDate;
// 第二个对应日，用以提高计算效率
// 公历 2000 年 1 月 1 日，对应农历 4697 年 11 月 25 日
if (gregorianYear >= 2000) {
startYear = baseYear + 99;
startMonth = 1;
startDate = 1;
chineseYear = baseChineseYear + 99;
chineseMonth = 11;
chineseDate = 25;
}
int daysDiff = 0;
for (int i=startYear; i daysDiff += 365;
if (isGregorianLeapYear(i)) daysDiff += 1; // leap year
}
for (int i=startMonth; i daysDiff += daysInGregorianMonth(gregorianYear,i);
}
daysDiff += gregorianDate - startDate;
chineseDate += daysDiff;
int lastDate = daysInChineseMonth(chineseYear, chineseMonth);
int nextMonth = nextChineseMonth(chineseYear, chineseMonth);
while (chineseDate>lastDate) {
if (Math.abs(nextMonth) chineseMonth = nextMonth;
chineseDate -= lastDate;
lastDate = daysInChineseMonth(chineseYear, chineseMonth);
nextMonth = nextChineseMonth(chineseYear, chineseMonth);
}
return 0;
}
private static int[] bigLeapMonthYears = {
// 大闰月的闰年年份
6, 14, 19, 25, 33, 36, 38, 41, 44, 52,
55, 79,117,136,147,150,155,158,185,193
};
public static int daysInChineseMonth(int y, int m) {
// 注意：闰月 m < 0
int index = y - baseChineseYear + baseIndex;
int v = 0;
int l = 0;
int d = 30;
if (1<=m && m<=8) {
v = chineseMonths[2*index];
l = m - 1;
if ( ((v>>l)&0x01)==1 ) d = 29;
} else if (9<=m && m<=12) {
v = chineseMonths[2*index+1];
l = m - 9;
if ( ((v>>l)&0x01)==1 ) d = 29;
} else {
v = chineseMonths[2*index+1];
v = (v>>4)&0x0F;
if (v!=Math.abs(m)) {
d = 0;
} else {
d = 29;
for (int i=0; i if (bigLeapMonthYears[i]==index) {
d = 30;
break;
}
}
}
}
return d;
}
public static int nextChineseMonth(int y, int m) {
int n = Math.abs(m) + 1;
if (m>0) {
int index = y - baseChineseYear + baseIndex;
int v = chineseMonths[2*index+1];
v = (v>>4)&0x0F;
if (v==m) n = -m;
}
if (n==13) n = 1;
return n;
}
private static char[][] sectionalTermMap = {
{7,6,6,6,6,6,6,6,6,5,6,6,6,5,5,6,6,5,5,5,5,5,5,5,5,4,5,5},
{5,4,5,5,5,4,4,5,5,4,4,4,4,4,4,4,4,3,4,4,4,3,3,4,4,3,3,3},
{6,6,6,7,6,6,6,6,5,6,6,6,5,5,6,6,5,5,5,6,5,5,5,5,4,5,5,5,5},
{5,5,6,6,5,5,5,6,5,5,5,5,4,5,5,5,4,4,5,5,4,4,4,5,4,4,4,4,5},
{6,6,6,7,6,6,6,6,5,6,6,6,5,5,6,6,5,5,5,6,5,5,5,5,4,5,5,5,5},
{6,6,7,7,6,6,6,7,6,6,6,6,5,6,6,6,5,5,6,6,5,5,5,6,5,5,5,5,4,5,5,5,5},
{7,8,8,8,7,7,8,8,7,7,7,8,7,7,7,7,6,7,7,7,6,6,7,7,6,6,6,7,7},
{8,8,8,9,8,8,8,8,7,8,8,8,7,7,8,8,7,7,7,8,7,7,7,7,6,7,7,7,6,6,7,7,7},
{8,8,8,9,8,8,8,8,7,8,8,8,7,7,8,8,7,7,7,8,7,7,7,7,6,7,7,7,7},
{9,9,9,9,8,9,9,9,8,8,9,9,8,8,8,9,8,8,8,8,7,8,8,8,7,7,8,8,8},
{8,8,8,8,7,8,8,8,7,7,8,8,7,7,7,8,7,7,7,7,6,7,7,7,6,6,7,7,7},
{7,8,8,8,7,7,8,8,7,7,7,8,7,7,7,7,6,7,7,7,6,6,7,7,6,6,6,7,7}
};
private static char[][] sectionalTermYear = {
{13,49,85,117,149,185,201,250,250},
{13,45,81,117,149,185,201,250,250},
{13,48,84,112,148,184,200,201,250},
{13,45,76,108,140,172,200,201,250},
{13,44,72,104,132,168,200,201,250},
{5 ,33,68,96 ,124,152,188,200,201},
{29,57,85,120,148,176,200,201,250},
{13,48,76,104,132,168,196,200,201},
{25,60,88,120,148,184,200,201,250},
{16,44,76,108,144,172,200,201,250},
{28,60,92,124,160,192,200,201,250},
{17,53,85,124,156,188,200,201,250}
};
private static char[][] principleTermMap = {
{21,21,21,21,21,20,21,21,21,20,20,21,21,20,20,20,20,20,20,20,20,19,
20,20,20,19,19,20},
{20,19,19,20,20,19,19,19,19,19,19,19,19,18,19,19,19,18,18,19,19,18,
18,18,18,18,18,18},
{21,21,21,22,21,21,21,21,20,21,21,21,20,20,21,21,20,20,20,21,20,20,
20,20,19,20,20,20,20},
{20,21,21,21,20,20,21,21,20,20,20,21,20,20,20,20,19,20,20,20,19,19,
20,20,19,19,19,20,20},
{21,22,22,22,21,21,22,22,21,21,21,22,21,21,21,21,20,21,21,21,20,20,
21,21,20,20,20,21,21},
{22,22,22,22,21,22,22,22,21,21,22,22,21,21,21,22,21,21,21,21,20,21,
21,21,20,20,21,21,21},
{23,23,24,24,23,23,23,24,23,23,23,23,22,23,23,23,22,22,23,23,22,22,
22,23,22,22,22,22,23},
{23,24,24,24,23,23,24,24,23,23,23,24,23,23,23,23,22,23,23,23,22,22,
23,23,22,22,22,23,23},
{23,24,24,24,23,23,24,24,23,23,23,24,23,23,23,23,22,23,23,23,22,22,
23,23,22,22,22,23,23},
{24,24,24,24,23,24,24,24,23,23,24,24,23,23,23,24,23,23,23,23,22,23,
23,23,22,22,23,23,23},
{23,23,23,23,22,23,23,23,22,22,23,23,22,22,22,23,22,22,22,22,21,22,
22,22,21,21,22,22,22},
{22,22,23,23,22,22,22,23,22,22,22,22,21,22,22,22,21,21,22,22,21,21,
21,22,21,21,21,21,22}
};
private static char[][] principleTermYear = {
{13,45,81,113,149,185,201},
{21,57,93,125,161,193,201},
{21,56,88,120,152,188,200,201},
{21,49,81,116,144,176,200,201},
{17,49,77,112,140,168,200,201},
{28,60,88,116,148,180,200,201},
{25,53,84,112,144,172,200,201},
{29,57,89,120,148,180,200,201},
{17,45,73,108,140,168,200,201},
{28,60,92,124,160,192,200,201},
{16,44,80,112,148,180,200,201},
{17,53,88,120,156,188,200,201}
};
public int computeSolarTerms() {
if (gregorianYear<1901 || gregorianYear>2100) return 1;
sectionalTerm = sectionalTerm(gregorianYear, gregorianMonth);
principleTerm = principleTerm(gregorianYear, gregorianMonth);
return 0;
}
public static int sectionalTerm(int y, int m) {
if (y<1901 || y>2100) return 0;
int index = 0;
int ry = y-baseYear+1;
while (ry>=sectionalTermYear[m-1][index]) index++;
int term = sectionalTermMap[m-1][4*index+ry%4];
if ((ry == 121)&&(m == 4)) term = 5;
if ((ry == 132)&&(m == 4)) term = 5;
if ((ry == 194)&&(m == 6)) term = 6;
return term;
}
public static int principleTerm(int y, int m) {
if (y<1901 || y>2100) return 0;
int index = 0;
int ry = y-baseYear+1;
while (ry>=principleTermYear[m-1][index]) index++;
int term = principleTermMap[m-1][4*index+ry%4];
if ((ry == 171)&&(m == 3)) term = 21;
if ((ry == 181)&&(m == 5)) term = 21;
return term;
}
public String toString() {
StringBuffer buf = new StringBuffer();
buf.append("Gregorian Year: "+gregorianYear+"\n");
buf.append("Gregorian Month: "+gregorianMonth+"\n");
buf.append("Gregorian Date: "+gregorianDate+"\n");
buf.append("Is Leap Year: "+isGregorianLeap+"\n");
buf.append("Day of Year: "+dayOfYear+"\n");
buf.append("Day of Week: "+dayOfWeek+"\n");
buf.append("Chinese Year: "+chineseYear+"\n");
buf.append("Heavenly Stem: "+((chineseYear-1)%10)+"\n");
buf.append("Earthly Branch: "+((chineseYear-1)%12)+"\n");
buf.append("Chinese Month: "+chineseMonth+"\n");
buf.append("Chinese Date: "+chineseDate+"\n");
buf.append("Sectional Term: "+sectionalTerm+"\n");
buf.append("Principle Term: "+principleTerm+"\n");
return buf.toString();
}
public String[] getYearTable() {
setGregorian(gregorianYear,1,1);
computeChineseFields();
computeSolarTerms();
String[] table = new String[58]; // 6*9 + 4
table[0] = getTextLine(27, "公历年历："+gregorianYear);
table[1] = getTextLine(27, "农历年历："+(chineseYear+1)
+ " ("+stemNames[(chineseYear+1-1)%10]
+ branchNames[(chineseYear+1-1)%12]
+ " - "+animalNames[(chineseYear+1-1)%12]+"年)");
int ln = 2;
String blank = " "
+" " + " ";
String[] mLeft = null;
String[] mRight = null;
for (int i=1; i<=6; i++) {
table[ln] = blank;
ln++;
mLeft = getMonthTable();
mRight = getMonthTable();
for (int j=0; j String line = mLeft[j] + " " + mRight[j];
table[ln] = line;
ln++;
}
}
table[ln] = blank;
ln++;
table[ln] = getTextLine(0,
"##/## - 公历日期/农历日期，(*)#月 - (闰)农历月第一天");
ln++;
return table;
}
public static String getTextLine(int s, String t) {
String str = " "
+" " + " ";
if (t!=null && s str = str.substring(0,s) + t + str.substring(s+t.length());
return str;
}
private static String[] monthNames =
{"一","二","三","四","五","六","七","八","九","十","十一","十二"};
public String[] getMonthTable() {
setGregorian(gregorianYear,gregorianMonth,1);
computeChineseFields();
computeSolarTerms();
String[] table = new String[8];
String title = null;
if (gregorianMonth<11) title = " ";
else title = " ";
title = title + monthNames[gregorianMonth-1] + "月"
+ " ";
String header = " 日 一 二 三 四 五 六 ";
String blank = " ";
table[0] = title;
table[1] = header;
int wk = 2;
String line = "";
for (int i=1; i line += " " + ' ';
}
int days = daysInGregorianMonth(gregorianYear,gregorianMonth);
for (int i=gregorianDate; i<=days; i++) {
line += getDateString() + ' ';
rollUpOneDay();
if (dayOfWeek==1) {
table[wk] = line;
line = "";
wk++;
}
}
for (int i=dayOfWeek; i<=7; i++) {
line += " " + ' ';
}
table[wk] = line;
for (int i=wk+1; i
table[i] = blank;
}
for (int i=0; i
table[i] = table[i].substring(0,table[i].length()-1);
}
return table;
}
private static String[] chineseMonthNames =
{"正","二","三","四","五","六","七","八","九","十","冬","腊"};
private static String[] principleTermNames =
{"大寒","雨水","春分","谷雨","夏满","夏至","大暑","处暑","秋分",
"霜降","小雪","冬至"};
private static String[] sectionalTermNames =
{"小寒","立春","惊蛰","清明","立夏","芒种","小暑","立秋","白露",
"寒露","立冬","大雪"};
public String getDateString() {
String str = "* / ";
String gm = String.valueOf(gregorianMonth);
if (gm.length()==1) gm = ' ' + gm;
String cm = String.valueOf(Math.abs(chineseMonth));
if (cm.length()==1) cm = ' ' + cm;
String gd = String.valueOf(gregorianDate);
if (gd.length()==1) gd = ' ' + gd;
String cd = String.valueOf(chineseDate);
if (cd.length()==1) cd = ' ' + cd;
if (gregorianDate==sectionalTerm) {
str = " "+sectionalTermNames[gregorianMonth-1];
} else if (gregorianDate==principleTerm) {
str = " "+principleTermNames[gregorianMonth-1];
} else if (chineseDate==1 && chineseMonth>0) {
str = " "+chineseMonthNames[chineseMonth-1]+"月";
} else if (chineseDate==1 && chineseMonth<0) {
str = "*"+chineseMonthNames[-chineseMonth-1]+"月";
} else {
str = gd+'/'+cd;
}
return str;
}
public int rollUpOneDay() {
dayOfWeek = dayOfWeek%7 + 1;
dayOfYear++;
gregorianDate++;
int days = daysInGregorianMonth(gregorianYear,gregorianMonth);
if (gregorianDate>days) {
gregorianDate = 1;
gregorianMonth++;
if (gregorianMonth>12) {
gregorianMonth = 1;
gregorianYear++;
dayOfYear = 1;
isGregorianLeap = isGregorianLeapYear(gregorianYear);
}
sectionalTerm = sectionalTerm(gregorianYear,gregorianMonth);
principleTerm = principleTerm(gregorianYear,gregorianMonth);
}
chineseDate++;
days = daysInChineseMonth(chineseYear,chineseMonth);
if (chineseDate>days) {
chineseDate = 1;
chineseMonth = nextChineseMonth(chineseYear,chineseMonth);
if (chineseMonth==1) chineseYear++;
}
return 0;
}
}
中国二百年年历 1901 年至 2100 年
我用上面这个程式制作了二百年年历，1901 年至 2100 年，全部收录在这本书中。
年历格式说明：
农历日期列在公历日期后面。
节气用节气名称标明。
农历每月第一天用月份名称标明。
例如，2000 年一月的表达格式如下：
一月
日 一 二 三 四 五 六
1/25
2/26 3/27 4/28 5/29 立春 腊月 8/ 2
9/ 3 10/ 4 11/ 5 12/ 6 13/ 7 14/ 8 15/ 9
16/10 17/11 18/12 19/13 20/14 雨水 22/16
23/17 24/18 25/19 26/20 27/21 28/22 29/23
30/24 31/25
其中：
"1/25" - 表示公历 1 号和农历 25 号。
"立春" - 表示节气。
"腊月" - 表示农历 12 月第一天。
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有关中国年历算法和程式的详细注解和二百年年历，请参考
“和荣笔记 - 中国农历二百年算法及年历”
- http://www.herongyang.com/year_gb/
