What are the 14 types of Jewish Years?

Question

As a way of explanation, I'm working on Objective-C code that calculates parashat hashavua. Initially, I ported the Javascript offered by YYDL as an answer to this question. I've found that my port doesn't hold up in production. I've gone back and began simplifying my code so that it's easier to read and, by extension, to debug. The bit of information that I'm missing is this: What exactly are the 14 year configurations of the Hebrew Calendar?

I've got it defined as such:

/*

 There are fourteen year configurations, as per
 Arthur Spier, 'The Comprehensive Hebrew Calendar,
 3rd ed' (Behrman House 1986, ISBN 0-87306-398-8).

 Each configuration composites the weekday of 1 Tishri,
 the number of days in the year, and if the year 
 contains Adar II.

 */

typedef enum
{
    kHebrewYearTypeA = 0, //  Monday,     353, regular
    kHebrewYearTypeB,     //  Shabbat,    353, regular
    kHebrewYearTypeC,     //  Tuesday,    354, regular
    kHebrewYearTypeD,     //  Thursday,   354, regular
    kHebrewYearTypeE,     //  Monday,     355, regular
    kHebrewYearTypeF,     //  Thursday,   355, regular
    kHebrewYearTypeG,     //  Shabbat,    355, regular    -----
    kHebrewYearTypeH,     //  Monday,     383, leap       ----- 
    kHebrewYearTypeI,     //  Thursday,   383, leap
    kHebrewYearTypeJ,     //  Shabbat,    383, leap
    kHebrewYearTypeK,     //  Tuesday,    384, leap
    kHebrewYearTypeL,     //  Monday,     385, leap
    kHebrewYearTypeM,     //  Thursday,   385, leap
    kHebrewYearTypeN,     //  Shabbat,    385, leap
} kHebrewYearType;

I've found an error in the sample years offered by Spier's book, so I'm referring to Rabbi David Feinstein's book, "The Jewish Calendar". (Dr. Spier lists 5782 twice, which can't be right, since a year can't satisfy two configurations at once.)

In the back of the Rosh Hayeshiva's book, there are charts, but the year listings seem to differ from ones in the Spier book. Specifically, Rabbi Feinstein has a year listed beginning on a Monday, and containing 354 days, and being a non-leap year. I don't have such a configuration in my list, based on Dr. Spier's book. Am I missing something? What exactly are the 14 year configurations of the Hebrew Calendar?

Answer 1

As it turns out, I was reading the book wrong. Rabbi Feinstein's chart is referring to "type E" of the Spier book. I realized this halfway through writing the question, so it seems that the year configurations posted in the question are correct.

Answer 2

According to the Tur (OC 428), the fourteen types are as follows. Full means both Cheshvan and Kislev are 30 days, deficient means they're both 29, and normal means Cheshvan is 29 and Kislev is 30. In a non-leap year, these correspond to 353, 355, and 354 days, respectively. In a leap year, it's 383-385. RH stands for Rosh HaShanah.

Monday RH, either deficient or full, whether leap or not.

Tuesday RH, always normal, whether leap or not.

Thursday RH, either deficient or full in a leap year, and either normal or full in a non-leap year.

Shabbos RH, either full or deficient, whether leap or not.