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，要害是星期值的确定。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

* 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) {

// 注重：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具体注解和二百年年历，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/