和荣笔记 - 中国农历二百年算法及年历 杨和荣, 第 3.01 版, 2006年
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 * 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<t.length; i++) System.out.println(t[i]); } else if (cmd.equalsIgnoreCase("month")) { String[] t = c.getMonthTable(); for (int i=0; i<t.length; i++) System.out.println(t[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<m; 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<gregorianYear; i++) { daysDiff += 365; if (isGregorianLeapYear(i)) daysDiff += 1; // leap year } for (int i=startMonth; i<gregorianMonth; 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)<Math.abs(chineseMonth)) chineseYear++; 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<bigLeapMonthYears.length; 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<mLeft.length; 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.length() && s+t.length()<str.length()) 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<dayOfWeek; 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.length; i++) { table[i] = blank; } for (int i=0; i<table.length; 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 小寒 腊月 8/ 2 9/ 3 10/ 4 11/ 5 12/ 6 13/ 7 14/ 8 15/ 916/10 17/11 18/12 19/13 20/14 大寒 22/1623/17 24/18 25/19 26/20 27/21 28/22 29/2330/24 31/25其中：
- "1/25" - 表示公历 1 号和农历 25 号。
- "小寒" - 表示节气。
- "腊月" - 表示农历 12 月第一天。