# Background

At contract bridge, each player gets a hand of 13 cards from a deck of 52 cards. To evaluate the potential of a hand, we need to calculate what we called the High Card Points (HCP) of it. To do so, we give to each card a value:

• Ace: 4 points
• King: 3 points
• Queen: 2 points
• Jack: 1 point
• Any other card: 0 points

For instance, if I have a hand with one ace, two kings and one jack, the value of my hand is 11 HCP.

# Challenge

What I want to know is what is the probability to have a hand of n HCP. To do so, I need to count the number of possible hands with n HCP and divide it by the number of the total possible hands at bridge which is $$\\binom{52}{13}\$$ or 635 013 559 600.

Therefore, the goal of my code below is to give the number of possible hands for each HCP value. Running it gives me this results:

635013559600:
0: 2310789600
1: 5006710800
2: 8611542576
3: 15636342960
4: 24419055136
5: 32933031040
6: 41619399184
7: 50979441968
8: 56466608128
9: 59413313872
10: 59723754816
11: 56799933520
12: 50971682080
13: 43906944752
14: 36153374224
15: 28090962724
16: 21024781756
17: 14997082848
18: 10192504020
19: 6579838440
20: 4086538404
21: 2399507844
22: 1333800036
23: 710603628
24: 354993864
25: 167819892
26: 74095248
27: 31157940
28: 11790760
29: 4236588
30: 1396068
31: 388196
32: 109156
33: 22360
34: 4484
35: 624
36: 60
37: 4


It means, for instance, there is 4 different hands of 37 HCP.

# Issues with my code

There are a lot of possible combinations of hands (as I said before, more than 635 billions). Therefore, my code took more than 29 hours to give me the results above. My main concern about it is: how can I improve the performance of my program?

However, I'm open to every suggestions that not concern performance. For instance, I would like to know if I could use different library from the standard library. Also, I compile my code with C++17, maybe I could use some new features of it.

About the algorithm I used, my work is based on this article. I modify it to implement the multi-threading in my program but it produces duplicate code and I didn't find a way to refactor it.

# Code

#include <iostream>
#include <vector>
#include <array>
#include <atomic>

#define DECK_SIZE 52
#define HAND_SIZE 13

// Array which will contain my results
// The key corresponds to the number of HCP
// The value corresponds to the number of hands with this HCP
// The maximum HCP of a hand is 37, so an array of 38 cells is enough
std::array<std::atomic<long long>, 38> results;

// A loop counter just to verify all the combination of hands are taken into account
std::atomic<long long> loop(0);

// Print the results
void print(std::array<std::atomic<long long>, 38>& vec)
{
std::string content;
content = std::to_string(loop) + ":\n";

for(int i = 0; i < vec.size(); i++)
content += std::to_string(i) + ": " + std::to_string(vec[i]) + "\n";

std::cout << content << std::endl;
}

// Compute and store into results the number of HCP of the hand given in parameter
void compute(std::vector<int>& hand)
{
loop++;

int value = 0;

for(auto it = hand.begin(); it != hand.end(); it++)
{
// A card is a value between 0 and 51
// To get the number of the card, we use its value % 13
// It gives a number between 0 and 12:
//  - Ace: 12
//  - King: 11
//  - Queen: 10
//  - Jack: 9
//  - Every other cards: value-2
// Only cards with a value above 9 are useful
// We substract 8 to get the HCP of the cards
value += (*it) % 13 >= 9 ? (*it) % 13 - 8 : 0;
}

results[value]++;
}

// Deal a hand in the same thread
// The parameters are in reference and modified by the function
void deal(std::vector<int>& deck, std::vector<int>& hand, int idxDeck, int idxHand)
{
if(idxHand == HAND_SIZE)
{
// The hand vector contains the maximum number of cards
// We can now compute its value
compute(hand);
return;
}

// There are no more cards in the deck
if(idxDeck >= DECK_SIZE)
return;

// Deal the current card of the deck into the hand
hand[idxHand] = deck[idxDeck];

// Continue to deal the cards
deal(deck, hand, idxDeck+1, idxHand+1);
deal(deck, hand, idxDeck+1, idxHand);
}

// Deal a hand in a new thread if currentDepth <= threadMinDepth
// The parameters are in copy to let each thread working with its own copy
void deal_copy(std::vector<int> deck, std::vector<int> hand, int idxDeck, int idxHand, int currentDepth, int threadMinDepth)
{
if(idxHand == HAND_SIZE)
{
// The hand vector contains the maximum number of cards
// We can now compute its value
compute(hand);
return;
}

// There are no more cards in the deck
if(idxDeck >= DECK_SIZE)
return;

// Deal the current card of the deck into the hand
hand[idxHand] = deck[idxDeck];

// If we want to continue to create new thread for each new cards
{
// Creation of two new threads with their own copy of the deck and the hands

t1.join();
t2.join();
}
else
{
// No more thread, we continue with this version of the deal function
// The parameters are provided by reference to increase speed
deal(deck, hand, idxDeck+1, idxHand+1);
deal(deck, hand, idxDeck+1, idxHand);
}
}

int main() {
// This vector will contains all the possible cards
std::vector<int> deck;

// A card is represented by an integer with a value from 0 to 51
// To get the suit of a card, suit = value / 4:
// 0: clubs, 1: diamonds, 2: hearts, 3: spades (however, not relevant here)
// To get the number of a card, number = (value % 13) + 2
// Ace = 14, King = 13, Queen = 12, Jack = 11
for(int i = 0; i < DECK_SIZE; i++)
{
deck.push_back(i);
}

// The hand is empty at the beginning...
std::vector<int> hand(HAND_SIZE, 0);

// and it will be filled by recursive call to deal function
deal_copy(deck, hand, 0, 0, 0, 3);

print(results);

return 0;
}


To compile it: g++ -std=c++17 -pthread count.cpp -o count

• How many tasks do you perform per thread? – S.S. Anne Mar 11 at 19:44
• @S.S.Anne I'm not sure to exactly understand what you mean by task. However, the computational work is not correctly divided between the threads. Indeed, I used an arbitrary value for threadMinDepth(3 will create 8 threads) and each thread calls the deal function. But the recursion can be more or less longer depending of the arguments which are different for all the different threads. – Pierre Mar 11 at 19:53
• I assume that you treat hands as if they are rearranged as any bridge player would (regardless of the order of the deal to the hand): (e.g. for four cards) Dj,Sk,Hq,Sa is reordered to Sa,Sk,Hq,Dj and they are counted as one unique hand [not two]. Is that correct? – Craig Estey Mar 12 at 0:03
• @CraigEstey Yes, the algorithm I used to create all the combinations of hand always create ordered hands and doesn't create the same one twice. – Pierre Mar 12 at 9:18

how can I improve the performance of my program?

A standard answer is use a better algorithm.

Trying to improve performance by shaving cycles while enumerating a 635 013 559 600 strong set is futile.

Consider instead enumerating subsets of valuable cards. There are merely $$\2^{16} = 65536\$$ of them; a trillion time acceleration. Given a popcount function, you may do something along the lines of

for (int value_cards = 0; value_cards < (1 << 16); value_cards++) {
if (popcount(value_cards) <= 13) {
hand_value = compute_hand_value(value_cards);
hands[hand_value] += choose((52 - 16), 13 - popcount(value_cards));
}
}


52 - 16 above is a number of a non-value cards in the deck. 13 - popcount(value_cards) is a number of non-value cards which could be dealt to the hand with a given number of value cards.

And of course, the choose shall be a precomputed array.

• This is indeed the simplest solution. Also, I didn't create a popcount nor a compute_hand_value function and put all the instructions into the for loop because it avoids redundant computation. – Pierre Mar 29 at 8:32

# Redundant summing

    // The hand vector contains the maximum number of cards
// We can now compute its value


That is not completely true, the value could have been built up incrementally each time a card was added to the hand, which would remove some duplicated work: hands that share a common prefix would not each recompute the sum of the values of that prefix, as they do now. So it's not just redistributing the work that is done in that loop, duplicate work goes away by reusing the results.

# Contention

A performance trap here is that all threads are slamming the same results array, and even in the same places. Of course, the counters are atomic, so the result should come out fine. But there is heavy contention, and even atomic operations don't make contention fast. The contention can be solved by giving each thread its own array of local counts (sufficiently aligned and padded to also avoid false sharing), and summing them into the total at the end. As a bonus, only the additions at the end need to be atomic, not the individual increments - they can be the faster non-atomic increments now.

On my PC (4770K Haswell), compiled with MSVC and using DECK_SIZE 31 (to save time), and commenting out loop++ (which has a significant cost), the effect of that was:

original:    3.0 seconds
incremental: 2.6 seconds
local count: 0.6 seconds


Since the deck was smaller, the access pattern to results was different, so esspecially the result for using local counts is not necessarily representative of how much speedup the "full deck" version would have.

# Missing include

std::to_string is in <string> which was not included.

Here's a better algorithm:

It has been benchmarked and reduces the time from 29 hours to 1.1 seconds

This is approximately 95,000 times faster.

Edit: Faster version, described below, reduces the execution time to 0.68 seconds, which is 153,500 times faster.

We only need to consider the number of each type of honor and then combinations of remaining spot cards.

Using a state vector for the honors, we calculate all possible honor distributions [based on count]. The state vector is similar to a 4 digit base 5 number: nA|nK|nQ|nJ where each digit represents the number of the given card we are "dealing"

We reject any state that has more than 13 honors.

We reject any state that has a different HCP than we want (we loop on all desired HCP in the range 0-37).

Edit: Added an output vector, indexed by HCP, that accumulates all intermediate hand deal results, so that the honors state vector only needs to be cycled once, instead of a full pass for each given/desired HCP. (i.e. looping on the "desired" HCP is no longer required). The original behavior can be seen by adding a command line option of -v

We get the total number of combinations of honors:

honornCk = nCk(4,nJ) * nCk(4,nQ) * nCk(4,nK) * nCk(4,nA)


We calculate the number of slots left for spot cards:

nslot = 36 - (nJ + nQ + nK + nA)


We calculate the number of combinations of spots:

spotnCk = nCk(36,nslot)


We get the total number of combinations of cards for this hand:

curhand = spotnCk * honornCk


We accumulate the total number of hand combinations:

tothand += curhand


This is the final result

Here is the [working] code

It is written in C. Many combinations of caching/memoization and other [failed] attempts before coming up with this final version were tried. Side note: The primary criterion was on the algorithm vs. use of STL or style, so go easy on the niceties.

It used gmp for large integers, so it must be linked with -lgmp

The algorithm is primarily in the handinc and handhcp functions.

// bridgehcp/bridgehcp.c -- calculate HCP of bridge hand

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <gmp.h>

#define NHONOR              4               // number of different honor types
#define NSUIT               4               // number of suits
#define DECKSIZE            52
#define MAXHONOR            (NHONOR * NSUIT)
#define MAXSPOT             (DECKSIZE - MAXHONOR)
#define CARDS_PER_HAND      13
#define HCPMAX              38

#define SPT                 0

typedef unsigned long long u64;
typedef unsigned long ui_t;
typedef unsigned char byte;
typedef int inum_t;
typedef inum_t *inum_p;

typedef mpz_t qnum_t;
typedef mpz_t qnum_p;

int opt_d = 0;
int opt_b = 0;
int opt_t = 0;
int opt_v = 0;
int opt_commatst = 0;

#define OPTCMP(_str) \
if (optcmp(cp,#_str,&opt_##_str)) \
continue

// honor state/slot control
typedef struct {
int slot_ctype;                     // card type 0=J, 1=Q, 2=Q, 3=A
int slot_count;                     // number of cards of given type (0-4)
inum_t slot_nCk;                    // multiplier for slot_count
} slot_t;
typedef slot_t *slot_p;

slot_t honors[NHONOR];                  // honor counts in given dealt hand

typedef struct {
qnum_t hand_tot;                    // total for hand
} handvec_t;
typedef handvec_t *handvec_p;

handvec_t handvec[HCPMAX];              // vector of final values

#define HANDVEC(_hcp) \
handvec_p hand = &handvec[_hcp]

const char *hcpstr[HCPMAX] = {
[0] = "2,310,789,600",
[1] = "5,006,710,800",
[2] = "8,611,542,576",
[3] = "15,636,342,960",
[4] = "24,419,055,136",
[5] = "32,933,031,040",
[6] = "41,619,399,184",
[7] = "50,979,441,968",
[8] = "56,466,608,128",
[9] = "59,413,313,872",
[10] = "59,723,754,816",
[11] = "56,799,933,520",
[12] = "50,971,682,080",
[13] = "43,906,944,752",
[14] = "36,153,374,224",
[15] = "28,090,962,724",
[16] = "21,024,781,756",
[17] = "14,997,082,848",
[18] = "10,192,504,020",
[19] = "6,579,838,440",
[20] = "4,086,538,404",
[21] = "2,399,507,844",
[22] = "1,333,800,036",
[23] = "710,603,628",
[24] = "354,993,864",
[25] = "167,819,892",
[26] = "74,095,248",
[27] = "31,157,940",
[28] = "11,790,760",
[29] = "4,236,588",
[30] = "1,396,068",
[31] = "388,196",
[32] = "109,156",
[33] = "22,360",
[34] = "4,484",
[35] = "624",
[36] = "60",
[37] = "4",
};

#define FOR_ALL_HONORS(_hon) \
_hon = &honors[0];  _hon < &honors[NHONOR];  ++_hon

#define MPZALL(_cmd) \
_cmd(qtmp,"temp variable") \
_cmd(kfac,"k!") \
_cmd(nkfac,"(n - k)!") \
_cmd(abstot,"absolute total number of hands (e.g. ~650G)") \
_cmd(spotnCk,"current number of combinations of spot cards") \
_cmd(curhand,"spotnCk * honornCk") \
_cmd(totspot,"total number of spot cards") \
_cmd(tothand,"totspot * honornCk") \
_cmd(expres,"expected result") \
_cmd(exptot,"expected total")

#define _MPXDEF(_sym,_reason) \
qnum_t _sym;
MPZALL(_MPXDEF)

#define _MPXINIT(_sym,_reason) \
mpz_init(_sym);
#define _MPXCLEAR(_sym,_reason) \
mpz_clear(_sym);

#define outf(_fmt...) \
do { \
if (! opt_t) \
printf(_fmt); \
} while (0)

#ifdef DEBUG
#define dbgprt(_lvl,_fmt...) \
do { \
if (opt_d >= _lvl) \
outf(_fmt); \
} while (0)
#else
#define dbgprt(_lvl,_fmt...) \
do { \
} while (0)
#endif

#define TLSMAX      10

char *
strtls(void)
{
static char bufpool[TLSMAX][1024];
static int bufidx = 0;
char *buf;

buf = bufpool[bufidx];
bufidx += 1;
bufidx %= TLSMAX;

*buf = 0;

return buf;
}

int
optcmp(char *cp,const char *str,int *opt)
{
int len;
int matchflg;

len = strlen(str);

do {
matchflg = (strncmp(cp,str,len) == 0);
if (! matchflg)
break;

cp += len;

if (*cp == 0) {
*opt = ! *opt;
break;
}

if (*cp == '=')
++cp;

*opt = atoi(cp);
} while (0);

return matchflg;
}

void
commaprt(char *dst,const char *src,int len)
{
const char *dot;
char *bp;
int sep;
int off;

if (len < 0)
len = strlen(src);

dot = strchr(src,'.');
if (dot == NULL)
dot = &src[len];

len = dot - src;

bp = dst;
off = 0;
sep = 0;

for (;  src < dot;  ++src, ++off) {
int chr = *src;

if (((len - off) % 3) == 0) {
if (sep)
*bp++ = ',';
}
sep = 1;

*bp++ = chr;
}

for (int chr = *src++;  chr != 0;  chr = *src++)
*bp++ = chr;

*bp = 0;
}

static inline void
qnum_init(qnum_p num)
{

mpz_init(num);
}

static inline void
qnum_set_ui(qnum_p num,ui_t val)
{

mpz_set_ui(num,val);
}

static inline void
qnum_mul_ui(qnum_p dst,qnum_p src,ui_t val)
{

mpz_mul_ui(dst,src,val);
}

static inline void
qnum_set(qnum_p num,qnum_p val)
{

mpz_set(num,val);
}

static inline void
{

}

static inline void
qnum_mul(qnum_p dst,qnum_p src,qnum_p val)
{

mpz_mul(dst,src,val);
}

static inline void
qnum_div(qnum_p dst,qnum_p src,qnum_p val)
{

mpz_div(dst,src,val);
}

void
_qnumprt(char *buf,qnum_p num)
{
char tmp[1000];
int len;

len = gmp_sprintf(tmp,"%Zd",num);

commaprt(buf,tmp,len);
}

char *
qnumprt(qnum_p num)
{
char *buf;

buf = strtls();
_qnumprt(buf,num);

return buf;
}

void
qnumset(qnum_p num,const char *str)
{
char *dst;
char tmp[1000];

dst = tmp;

for (int chr = *str++;  chr != 0;  chr = *str++) {
switch (chr) {
case ',':
break;
default:
*dst++ = chr;
break;
}
}

*dst = 0;

mpz_set_str(num,tmp,10);
}

void
commatst(const char *src)
{
char buf[1000];

if (opt_commatst) {
commaprt(buf,src,-1);
outf("\n");
outf("commatst: SRC '%s'\n",src);
outf("commatst: DST '%s'\n",buf);
}
}

// qnumfac -- get n!
void
qnumfac(qnum_p num,int n)
{

qnum_set_ui(num,1);
for (int idx = 2;  idx <= n;  ++idx)
qnum_mul_ui(num,num,idx);
}

// qnumnCk -- get nCk (combinations of n things taken k at a time)
void
qnumnCk(qnum_p rtn,int n,int k)
{

// rtn = n! / (k! (n - k)!)

// get n!
qnumfac(rtn,n);

// get k!
qnumfac(kfac,k);

// get (n - k)!
qnumfac(nkfac,n - k);

// get k! * (n - k)!
qnum_mul(kfac,kfac,nkfac);

// get n! / (k! * (n - k)!)
qnum_div(rtn,rtn,kfac);
}

// qnumnPk -- get nPk (permutations of n things taken k at a time)
void
qnumnPk(qnum_p rtn,int n,int k)
{

// rtn = n! / (n - k)!

// get n!
qnumfac(rtn,n);

// get (n - k)!
qnumfac(nkfac,n - k);

// get n! / (n - k)!
qnum_div(rtn,rtn,nkfac);
}

inum_t
inumfac(int n)
{
inum_t rtn;

rtn = 1;
for (int idx = 2;  idx <= n;  ++idx)
rtn *= idx;

return rtn;
}

inum_t
inumnCk(int n,int k)
{
inum_t kfac;
inum_t nkfac;
inum_t rtn;

// rtn = n! / (k! (n - k)!)

// get n!
rtn = inumfac(n);

// get k!
kfac = inumfac(k);

// get (n - k)!
nkfac = inumfac(n - k);

// get k! * (n - k)!
kfac *= nkfac;

// get n! / (k! * (n - k)!)
rtn /= kfac;

return rtn;
}

inum_t
inumnPk(int n,int k)
{
inum_t nkfac;
inum_t rtn;

// rtn = n! / (n - k)!

// get n!
rtn = inumfac(n);

// get (n - k)!
nkfac = inumfac(n - k);

// get n! / (n - k)!
rtn /= nkfac;

return rtn;
}

int
honortag(slot_p hon)
{
static char *tag = "JQKA";

return tag[hon->slot_ctype];
}

char *
honorshow(void)
{
slot_p hon;
static char buf[100];
char *bp = buf;
char *sep = "";

bp += sprintf(bp,"(");

for (FOR_ALL_HONORS(hon)) {
bp += sprintf(bp,"%s%c%d/%d",
sep,honortag(hon),
hon->slot_count,hon->slot_nCk);
sep = " ";
}

bp += sprintf(bp,")");

return buf;
}

// handhcp -- get HCP and number of hands for a given deal of honor cards
int
handhcp(int hcpneed)
{
slot_p hon;
int hcptot = 0;
int nslot = CARDS_PER_HAND;
int hontot = 0;
int slotnCk;
int honornCk = 1;

dbgprt(2,"handhcp: ENTER hcpneed=%d\n",hcpneed);

do {
// get number of honors in this hand
for (FOR_ALL_HONORS(hon)) {
// get number of slots that this honor needs
int honcnt = hon->slot_count;

// accumulate number of honors for this dealt hand
hontot += honcnt;
}

// impossible hand -- there are more honors dealt than the number of
// cards in a hand (e.g. 14 honors dealt)
if (hontot > CARDS_PER_HAND) {
hcptot = -1;
break;
}

// get HCP for this hand
for (FOR_ALL_HONORS(hon)) {
int honcnt = hon->slot_count;

// get number of HCP for this honor
int hcpcur = honcnt * (hon->slot_ctype + 1);

// accumulate total number of HCP for all honors in this hand
hcptot += hcpcur;
}

// insufficient/incorrect HCP -- doesn't match the _desired_ HCP
if (hcpneed >= 0) {
if (hcptot != hcpneed)
break;
}

// get number of combinations of honor cards
for (FOR_ALL_HONORS(hon)) {
int honcnt = hon->slot_count;

// number of combinations of honors of the given type
slotnCk = inumnCk(NSUIT,honcnt);

// accumulate number of combinations of all honors
honornCk *= slotnCk;
}

// reduce number of available slots for spot cards in this hand by
// number of honors in this hand
nslot -= hontot;

// get number of combinations of remaining spot cards
qnumnCk(spotnCk,MAXSPOT,nslot);

// accumlate total for this
// FIXME -- really not needed anymore

// get number of hands that have the given distribution of honors and
// spots [for the desired HCP]
qnum_mul_ui(curhand,spotnCk,honornCk);

// accumulate total for all hands for the given HCP

// save in vector
HANDVEC(hcptot);

// brief output
if (opt_b)
break;

outf("handhcp: STATE honors=%s",honorshow());

outf(" hcptot=%d",hcptot);
outf(" hontot=%d",hontot);
outf(" honornCk=%d",honornCk);

outf(" nspot=%d",MAXSPOT);
outf(" nslot=%d",nslot);
outf(" spotnCk=%s",qnumprt(spotnCk));

#if SPT
outf(" totspot=%s",qnumprt(totspot));
#endif
outf(" curhand=%s",qnumprt(curhand));
outf(" tothand=%s",qnumprt(tothand));

outf("\n");
} while (0);

dbgprt(2,"handhcp: EXIT hcptot=%d\n",hcptot);

return hcptot;
}

// handinit -- initialize honors state vector
void
handinit(void)
{
slot_p hon;
int idx;

// set initial state of all honors (e.g. all honor counts are zero
// J=0, Q=0, K=0, A=0)
idx = 0;
for (FOR_ALL_HONORS(hon), ++idx) {
hon->slot_ctype = idx;
hon->slot_count = 0;
}

qnum_set_ui(totspot,0);
qnum_set_ui(tothand,0);

qnum_set_ui(exptot,0);
}

// _handinc -- increment single digit in honors state vector
int
_handinc(slot_p hon)
{
int cout;

// NOTE: we only care about the _number_ of honors of a given type
int val = hon->slot_count;

dbgprt(3,"_handinc: ctype=%d val=%d",hon->slot_ctype,val);

val += 1;

cout = (val > NSUIT);
if (cout)
val = 0;

hon->slot_count = val;

dbgprt(3," val=%d cout=%d\n",val,cout);

return cout;
}

// handinc -- increment honors state vector
int
handinc(void)
{
slot_p hon;
int cout = 0;

for (FOR_ALL_HONORS(hon)) {
cout = _handinc(hon);
if (! cout)
break;
}

return cout;
}

// prettyprt -- define result output
void
prettyprt(const char *tag,qnum_p num)
{

outf("%s: %s\n",tag,qnumprt(num));
}

// dotest -- perform algorithm for given HCP
void
dotest(int hcpneed,const char *str)
// hcpneed -- desired HCP
// str -- expected result
{

handinit();

int handgud = 0;
int handtot = 0;

outf("\n");
outf("HCP: %d\n",hcpneed);

while (1) {
int hcpcur = handhcp(hcpneed);

if (hcpcur == hcpneed)
handgud += 1;

handtot += 1;

// increment to next state for number of honors of each type
int cout = handinc();

// stop after the _last_ state (i.e. we just did: J=4, Q=4, K=4, A=4
// and we incremented back to the start (J=0, Q=0, K=0, A=0)
if (cout)
break;
}

outf("HANDS: %d of %d\n",handgud,handtot);

// pretty print the numbers
prettyprt("EXP",expres);
#if SPT
prettyprt("SPT",totspot);
#endif
prettyprt("ACT",tothand);
}

void
doall(void)
{

handinit();

while (1) {
handhcp(-1);

// increment to next state for number of honors of each type
int cout = handinc();

// stop after the _last_ state (i.e. we just did: J=4, Q=4, K=4, A=4
// and we incremented back to the start (J=0, Q=0, K=0, A=0)
if (cout)
break;
}
}

void
doany(int hcpneed,const char *str)
{

do {
qnumset(expres,str);

// accumulate expected results -- check OP's result, when done,
// this should be 52C13

if (opt_v) {
dotest(hcpneed,str);
break;
}

outf("\n");
outf("HCP: %d\n",hcpneed);

// pretty print the numbers
prettyprt("EXP",expres);
#if SPT
prettyprt("SPT",totspot);
#endif
HANDVEC(hcpneed);
prettyprt("ACT",hand->hand_tot);
} while (0);
}

int
main(int argc,char **argv)
{
char *cp;

--argc;
++argv;

for (;  argc > 0;  --argc, ++argv) {
cp = *argv;
if (*cp != '-')
break;

++cp;

OPTCMP(commatst);
OPTCMP(d);
OPTCMP(b);
OPTCMP(t);
OPTCMP(v);

printf("bridgehcp: unknown option -- '%s'\n",cp);
exit(1);
}

// test the commaprt routine
const char *digits = "1234567890";
for (const char *lhs = digits;  *lhs != 0;  ++lhs)
commatst(lhs);
for (const char *lhs = digits;  *lhs != 0;  ++lhs) {
for (const char *rhs = digits;  *rhs != 0;  ++rhs) {
char buf[100];
sprintf(buf,"%s.%s",lhs,rhs);
commatst(buf);
}
}

MPZALL(_MPXINIT)

// show all factorials
for (int n = 1;  n <= 52;  ++n) {
qnumfac(qtmp,n);
dbgprt(1,"qnumfac: n=%d %s\n",n,qnumprt(qtmp));
}

// total number of possible hands
qnumnCk(abstot,DECKSIZE,CARDS_PER_HAND);
outf("qnumnCk: %s\n",qnumprt(abstot));

// show nCk 4C0-4C4
for (int n = 1;  n <= 4;  ++n) {
for (int k = 0;  k <= 4;  ++k) {
qnumnCk(qtmp,n,k);
dbgprt(1,"%dC%d: %s\n",n,k,qnumprt(qtmp));
}
}

// when we're done this will match the number of possible hands
qnum_set_ui(exptot,0);

// initialize hand total vector
for (int hcpneed = 0;  hcpneed < HCPMAX;  ++hcpneed) {
HANDVEC(hcpneed);
memset(hand,0,sizeof(handvec_t));
qnum_init(hand->hand_tot);
qnum_set_ui(hand->hand_tot,0);
}

// precalc all
if (! opt_v)
doall();

for (int hcpneed = 0;  hcpneed < HCPMAX;  ++hcpneed)
doany(hcpneed,hcpstr[hcpneed]);

// NOTE: these should match
outf("\n");
outf("abstot: %s\n",qnumprt(abstot));
outf("exptot: %s\n",qnumprt(exptot));

MPZALL(_MPXCLEAR)

return 0;
}