nevermind, the results are worse when an assign is free

.gitignore

@@ -1,5 +1,19 @@
 
+bin
+
+.simplifications.bin
+.~lock.stats.ods#
+stats.ods
+
+
 simplifications.bin
 
 .simplifier-*.bin
 
+.direnv/
+
+typescript
+
+vgcore.*
+
+*~

buildtypes/debug.txt

@@ -0,0 +1,18 @@
+
+-g
+
+-D _GNU_SOURCE
+
+-D ZDEBUG=1
+
+-D DEBUG_BUILD
+
+-I .
+
+-Werror -Wall -Wextra -Wstrict-prototypes -Wfatal-errors
+
+-Wno-unused
+
+-lreadline
+-lm
+

buildtypes/release.txt

@@ -0,0 +1,14 @@
+
+-D _GNU_SOURCE
+
+-D ZDEBUG=0
+
+-I .
+
+-O3
+
+-Werror -Wall -Wextra -Wstrict-prototypes -Wfatal-errors
+
+-lreadline
+-lm
+

buildtypes/test-multithreaded.txt

@@ -0,0 +1,18 @@
+
+-g
+
+-D _GNU_SOURCE
+
+-D TEST_BUILD
+
+-D MULTITHREADED_BUILD
+
+-I .
+
+-Werror -Wall -Wextra -Wstrict-prototypes -Wfatal-errors
+
+-Wno-unused
+
+-lreadline
+-lm
+

buildtypes/test.txt

@@ -0,0 +1,18 @@
+
+-g
+
+-D _GNU_SOURCE
+
+-D ZDEBUG=0
+
+-D TEST_BUILD
+
+-I .
+
+-Werror -Wall -Wextra -Wstrict-prototypes -Wfatal-errors
+
+-Wno-unused
+
+-lreadline
+-lm
+

calculate_assignment_simplifications.c

@@ -0,0 +1,41 @@
+
+#if 0
+#include <limits.h>
+#include <stdio.h>
+#include <assert.h>
+
+#include <debug.h>
+
+#include <defines.h>
+
+#include <cmdln.h>
+
+#include "simplifications.h"
+#include "calculate_simplifications.h"
+#include "calculate_assignment_simplifications.h"
+
+void calculate_assignment_simplifications(
+    const struct cmdln_flags* flags,
+    struct simplifications* simps)
+{
+    ENTER;
+    
+    struct cmdln_flags flag_no_assign = *flags;
+    
+    flag_no_assign.use_operators.assignment = false;
+    
+    for (int a = 0; a < N; a++)
+    {
+        simps->with_vars[a] = \
+            calculate_simplifications(
+                /* cmdln flags: */ &flag_no_assign,
+                /* have extra variable? */ true,
+                /* extra variable value: */ a);
+    }
+    
+    simps->main = calculate_simplifications(flags, false, 0);
+    
+    EXIT;
+}
+
+#endif

calculate_assignment_simplifications.h

@@ -0,0 +1,11 @@
+
+#if 0
+
+struct cmdln_flags;
+struct simplifications;
+
+void calculate_assignment_simplifications(
+    const struct cmdln_flags* flags,
+    struct simplifications* simps);
+
+#endif

calculate_simplifications.c

@@ -0,0 +1,637 @@
+
+#include <unistd.h>
+#include <stdio.h>
+#include <limits.h>
+#include <assert.h>
+#include <stdbool.h>
+
+#include <debug.h>
+
+#include <cmdln.h>
+
+#include <print.h>
+
+#ifdef MULTITHREADED_BUILD
+#include <pthread.h>
+#endif
+
+#include "calculate_simplifications.h"
+
+void helper(
+    const struct cmdln_flags* flags,
+    struct simplifications* simps,
+    bool have_extra_variable,
+    uint16_t A)
+{
+    ENTER;
+    
+    struct row* row = have_extra_variable ? &simps->with_vars[A] : &simps->main;
+    
+    // init 'row->data':
+    {
+        for (int i = 0; i < N; i++)
+        {
+            row->data[i].kind = ek_unreachable;
+            
+            row->data[i].cost = INT_MAX;
+        }
+    }
+    
+    // heap of truthtables; key = cost
+    struct {
+        uint16_t data[N];
+        int n;
+        
+        // truthtable -> index in 'todo'
+        int reverse[N];
+    } todo;
+    
+    // init 'todo':
+    {
+        todo.n = 0;
+        
+        for (int i = 0; i < N; i++)
+        {
+            todo.reverse[i] = -1;
+        }
+    }
+    
+    uint16_t pop(void)
+    {
+        assert(todo.n > 0);
+
+        uint16_t retval = todo.data[0];
+
+        todo.reverse[retval] = -1;
+
+        uint16_t moving = todo.data[todo.n-- - 1];
+
+        int cost = row->data[moving].cost;
+
+        int index = 0;
+
+        again:
+        {
+            int left = index * 2 + 1;
+            int right = index * 2 + 2;
+
+            uint16_t smallest = moving;
+
+            if (left < todo.n && row->data[todo.data[left]].cost < cost)
+                smallest = todo.data[left];
+
+            if (right < todo.n && row->data[todo.data[right]].cost < row->data[smallest].cost)
+                smallest = todo.data[right];
+
+            if (smallest == moving)
+            {
+                todo.data[index] = moving;
+
+                todo.reverse[moving] = index;
+            }
+            else
+            {
+                int new = todo.reverse[smallest];
+
+                todo.data[index] = smallest;
+
+                todo.reverse[smallest] = index;
+
+                index = new;
+
+                goto again;
+            }
+        }
+
+        return retval;
+    }
+
+    void append(uint16_t truthtable, int cost)
+    {
+        assert(todo.reverse[truthtable] == -1);
+
+        int index = todo.n++, new_index;
+
+        while (index > 0 && row->data[todo.data[new_index = (index - 1) / 2]].cost > cost)
+        {
+            todo.data[index] = todo.data[new_index];
+
+            todo.reverse[todo.data[new_index]] = index;
+
+            index = new_index;
+        }
+        
+        todo.data[index] = truthtable;
+        
+        todo.reverse[truthtable] = index;
+        
+        row->data[truthtable].cost = cost;
+    }
+
+    void update(uint16_t truthtable, int cost)
+    {
+        assert(todo.reverse[truthtable] != -1);
+
+        assert(cost < row->data[truthtable].cost);
+
+        int index =todo. reverse[truthtable], new_index;
+
+        while (index > 0 && row->data[todo.data[new_index = (index - 1) / 2]].cost > cost)
+        {
+            todo.data[index] = todo.data[new_index];
+
+            todo.reverse[todo.data[new_index]] = index;
+
+            index = new_index;
+        }
+
+        todo.data[index] = truthtable;
+        todo.reverse[truthtable] = index;
+
+        row->data[truthtable].cost = cost;
+    }
+    
+    // create a list of the "done" truthtables
+    struct {
+        int headtails[N], next[N], head;
+        
+        // for debugging:
+        #if ZDEBUG
+        bool in[N];
+        #endif
+    } done = {};
+    
+    // init 'done':
+    {
+        done.head = -1;
+        
+        for (int i = 0; i < N; i++)
+        {
+            done.headtails[i] = -1;
+            
+            #if ZDEBUG
+            done.in[i] = false;
+            #endif
+        }
+    }
+    
+    void insert(int index)
+    {
+        #if ZDEBUG
+        assert(!done.in[index]);
+        #endif
+        
+        int head = index & 1 ? index & ~(index & -index) : index, prevhead = -1;
+        
+        while (done.headtails[head] == -1 || index < done.headtails[head])
+        {
+            done.headtails[head] = index;
+            
+            prevhead = head, head = head & ~(head & -head);
+        }
+        
+        if (done.headtails[head] < index)
+        {
+            if (prevhead == -1)
+            {
+                assert(done.headtails[head] == head);
+                
+                done.next[head] = index;
+            }
+            else
+            {
+                int tophalftail = done.headtails[prevhead - 1];
+                
+                assert(tophalftail != -1);
+                
+                done.next[tophalftail] = index;
+            }
+        }
+        else
+        {
+            done.head = index;
+        }
+        
+        int n = ~index & M;
+        int tail = index & 1 ? index : index | (n & -n), prevtail = -1;
+        
+        while (done.headtails[tail] == -1 || done.headtails[tail] < index)
+        {
+            done.headtails[tail] = index;
+            
+            prevtail = tail, tail = tail | (n = ~tail & M, n & -n);
+        }
+        
+        if (index < done.headtails[tail])
+        {
+            if (prevtail == -1)
+            {
+                assert(done.headtails[tail] == tail);
+                
+                #if ZDEBUG
+                assert(done.in[tail]);
+                #endif
+                
+                done.next[index] = tail;
+            }
+            else
+            {
+                int bottomhalfhead = done.headtails[prevtail + 1];
+                
+                assert(bottomhalfhead != -1);
+                
+                done.next[index] = bottomhalfhead;
+            }
+        }
+        else
+        {
+            done.next[index] = -1;
+        }
+        
+        #if ZDEBUG
+        done.in[index] = true;
+        #endif
+    }
+    
+    append(W, 0), row->data[W].kind = ek_W;
+    append(X, 0), row->data[X].kind = ek_X;
+    append(Y, 0), row->data[Y].kind = ek_Y;
+    append(Z, 0), row->data[Z].kind = ek_Z;
+    
+    append(0, 1), row->data[0].kind = ek_0;
+    append(M, 1), row->data[M].kind = ek_1;
+    
+    if (have_extra_variable && todo.reverse[A] == -1)
+    {
+        append(A, 0), row->data[A].kind = ek_A;
+    }
+    
+    // disable terminal autowrap:
+    if (!ZDEBUG && flags->verbose && flags->print_with_color)
+    {
+        printf("\e[?7l");
+    }
+
+    for (int iterations = 1; todo.n && iterations <= N; iterations++)
+    {
+        uint16_t truthtable = pop();
+        
+        insert(truthtable);
+        
+        int cost = row->data[truthtable].cost;
+
+        if (flags->verbose)
+        {
+            if (!ZDEBUG && flags->print_with_color)
+            {
+                printf("\e[2K");
+            }
+
+            printf("%i of %i (%.2f%%): [%i] ",
+                iterations, N, (100.0 * iterations / N), cost);
+
+            if (have_extra_variable)
+            {
+                printf("a = 0b%016b, ", A);
+            }
+            
+            print(flags, simps, row, truthtable);
+            
+            puts("");
+
+            if (!ZDEBUG && flags->print_with_color)
+            {
+                printf("\e[1A");
+            }
+        }
+
+        // consider NOT:
+        if (flags->use_operators.not)
+        {
+            uint16_t not_truthtable = ~truthtable & M;
+
+            int not_cost = cost + 1;
+
+            if (not_cost < row->data[not_truthtable].cost)
+            {
+                if (todo.reverse[not_truthtable] == -1)
+                {
+                    append(not_truthtable, not_cost);
+                }
+                else
+                {
+                    update(not_truthtable, not_cost);
+                }
+
+                row->data[not_truthtable].kind = ek_not;
+                row->data[not_truthtable].left = truthtable;
+            }
+        }
+
+        #define BINARY_OPERATOR(ekind, function) \
+        { \
+            for (int i = done.head; i != -1; i = done.next[i]) \
+            { \
+                { \
+                    uint16_t bin_truthtable = function(truthtable, i) & M; \
+                     \
+                    int bin_cost = 1 + cost + row->data[i].cost; \
+                     \
+                    if (bin_cost < row->data[bin_truthtable].cost) \
+                    { \
+                        if (todo.reverse[bin_truthtable] == -1) \
+                            append(bin_truthtable, bin_cost); \
+                        else \
+                            update(bin_truthtable, bin_cost); \
+                         \
+                        row->data[bin_truthtable].kind = ekind; \
+                        row->data[bin_truthtable].left = truthtable; \
+                        row->data[bin_truthtable].right = i; \
+                    } \
+                } \
+                \
+                { \
+                    uint16_t bin_truthtable = function(i, truthtable) & M; \
+                     \
+                    int bin_cost = 1 + cost + row->data[i].cost; \
+                     \
+                    if (bin_cost < row->data[bin_truthtable].cost) \
+                    { \
+                        if (todo.reverse[bin_truthtable] == -1) \
+                            append(bin_truthtable, bin_cost); \
+                        else \
+                            update(bin_truthtable, bin_cost); \
+                         \
+                        row->data[bin_truthtable].kind = ekind; \
+                        row->data[bin_truthtable].left = i; \
+                        row->data[bin_truthtable].right = truthtable; \
+                    } \
+                } \
+            } \
+        }
+
+        #define  OR(a, b) ((a) | (b))
+        #define AND(a, b) ((a) & (b))
+
+        #define  ORN(a, b)  (~(a) |  (b))
+        #define  NOR(a, b) ~( (a) |  (b))
+        #define ANDN(a, b)  (~(a) &  (b))
+        #define NAND(a, b) ~( (a) &  (b))
+        #define  XOR(a, b)  (( a) ^  (b))
+        #define NXOR(a, b) ~( (a) ^  (b))
+
+        #define   LT(a, b)  ((~a) &  (b))
+        #define  LTE(a, b)  ((~a) |  (b))
+        #define   GT(a, b)  (( a) & ~(b))
+        #define  GTE(a, b)  (( a) | ~(b))
+
+        if (flags->use_operators.or)
+        {
+            BINARY_OPERATOR(ek_or, OR);
+        }
+
+        if (flags->use_operators.and)
+        {
+            BINARY_OPERATOR(ek_and, AND);
+        }
+
+        if (flags->use_operators.orn)
+        {
+            BINARY_OPERATOR(ek_orn, ORN);
+        }
+
+        if (flags->use_operators.nor)
+        {
+            BINARY_OPERATOR(ek_nor, NOR);
+        }
+
+        if (flags->use_operators.andn)
+        {
+            BINARY_OPERATOR(ek_andn, ANDN);
+        }
+
+        if (flags->use_operators.nand)
+        {
+            BINARY_OPERATOR(ek_nand, NAND);
+        }
+
+        if (flags->use_operators.xor)
+        {
+            BINARY_OPERATOR(ek_xor,   XOR);
+        }
+
+        if (flags->use_operators.nxor)
+        {
+            BINARY_OPERATOR(ek_nxor, NXOR);
+        }
+
+        if (flags->use_operators.lt)
+        {
+            BINARY_OPERATOR(ek_lt,  LT);
+        }
+
+        if (flags->use_operators.lte)
+        {
+            BINARY_OPERATOR(ek_lte, LTE);
+        }
+
+        if (flags->use_operators.gt)
+        {
+            BINARY_OPERATOR(ek_gt,  GT);
+        }
+
+        if (flags->use_operators.gte)
+        {
+            BINARY_OPERATOR(ek_gte, GTE);
+        }
+
+        if (flags->use_operators.ternary)
+        {
+            for (int i = done.head; i != -1; i = done.next[i])
+            {
+                for (int j = done.head; j != -1; j = done.next[j])
+                {
+                    int ternary_cost = 1 + cost + row->data[i].cost + row->data[j].cost;
+
+                    #define TERNARY(C, T, F) \
+                    { \
+                        uint16_t ternary_truthtable = \
+                            ((C) & (T)) | (~(C) & (F)); \
+                        \
+                        if (ternary_cost < row->data[ternary_truthtable].cost) \
+                        { \
+                            if (todo.reverse[ternary_truthtable] == -1) \
+                            { \
+                                append(ternary_truthtable, ternary_cost); \
+                            } \
+                            else \
+                            { \
+                                update(ternary_truthtable, ternary_cost); \
+                            } \
+                            \
+                            row->data[ternary_truthtable].kind = ek_ternary; \
+                            row->data[ternary_truthtable].cond = (C); \
+                            row->data[ternary_truthtable].left = (T); \
+                            row->data[ternary_truthtable].right = (F); \
+                        } \
+                    } \
+
+                    TERNARY(truthtable, i, j);
+                    TERNARY(i, truthtable, j);
+                    TERNARY(i, j, truthtable);
+                }
+            }
+        }
+        
+        if (flags->use_operators.assignment)
+        {
+            assert(row == &simps->main);
+            
+            for (int t = 0; t < N; t++)
+            {
+                int using_me_cost = simps->with_vars[truthtable].data[t].cost;
+                
+                if (using_me_cost < INT_MAX)
+                {
+                    int assign_cost = cost + 1 + using_me_cost;
+                    
+                    if (assign_cost < simps->main.data[t].cost)
+                    {
+                        if (todo.reverse[t] == -1)
+                        {
+                            append(t, assign_cost);
+                        }
+                        else
+                        {
+                            update(t, assign_cost);
+                        }
+
+                        row->data[t].kind = ek_assignment;
+                        row->data[t].left = truthtable;
+                        row->data[t].right = t;
+                    }
+                }
+            }
+        }
+    }
+
+    // clear progress line, enable terminal autowrap:
+    if (!ZDEBUG && flags->verbose && flags->print_with_color)
+    {
+        printf("\e[2K"), printf("\e[?7h");
+    }
+    
+    EXIT;
+}
+
+void calculate_simplifications(
+    const struct cmdln_flags* flags,
+    struct simplifications* simps)
+{
+    ENTER;
+    
+    if (flags->use_operators.assignment)
+    {
+        struct cmdln_flags flag_no_assign = *flags;
+        
+        flag_no_assign.use_operators.assignment = false;
+        
+        #ifdef MULTITHREADED_BUILD
+        {
+            int num_cores = sysconf(_SC_NPROCESSORS_ONLN);
+            
+            zprintf("num_cores = %i" "\n", num_cores);
+            
+            assert(0 < num_cores && num_cores < 100);
+            
+            struct cmdln_flags flag_no_verbose = flag_no_assign;
+            
+            if (!flags->quiet && flags->verbose)
+            {
+                printf(""
+                    "note: the usual verbosity is disabled in the "
+                    "multithreaded section" "\n"
+                "");
+                
+                flag_no_verbose.verbose = false;
+            }
+            
+            int starts[num_cores];
+            
+            void* runner(void* _start)
+            {
+                const int* start = _start;
+                
+                for (int a = *start; a < N; a += num_cores)
+                {
+                    if (flags->verbose)
+                    {
+                        printf("a = 0b%016b" "\n", a);
+                    }
+                    
+                    helper(
+                        /* cmdln flags: */ &flag_no_verbose,
+                        /* simplifications */ simps,
+                        /* have extra variable? */ true,
+                        /* extra variable value: */ a);
+                }
+                
+                return NULL;
+            }
+            
+            pthread_t handles[num_cores];
+            
+            for (int i = 0; i < num_cores; i++)
+            {
+                starts[i] = i;
+                
+                pthread_create(
+                    /* handle */ &handles[i],
+                    /* attributes: */ NULL,
+                    /* start_routine: */ runner,
+                    /* arg: */ &starts[i]);
+            }
+            
+            for (int i = 0; i < num_cores; i++)
+            {
+                pthread_join(
+                    /* handle: */ handles[i],
+                    /* return value: */ (void*[1]){});
+            }
+        }
+        #else
+        {
+            for (int a = 0; a < N; a++)
+            {
+                helper(
+                    /* cmdln flags: */ &flag_no_assign,
+                    /* simplifications */ simps,
+                    /* have extra variable? */ true,
+                    /* extra variable value: */ a);
+            }
+        }
+        #endif
+    }
+    
+    helper(
+        /* cmdln flags: */ flags,
+        /* simplifications */ simps,
+        /* have extra variable? */ false,
+        /* extra variable value: */ 0);
+    
+    EXIT;
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+

calculate_simplifications.h

@@ -0,0 +1,13 @@
+
+#include <stdbool.h>
+
+#include <expr.h>
+
+#include <simplifications.h>
+
+struct cmdln_flags;
+
+    
+void calculate_simplifications(
+    const struct cmdln_flags* flags,
+    struct simplifications* simps);

cmdln.c

@@ -0,0 +1,214 @@
+
+#include <string.h>
+#include <unistd.h>
+#include <getopt.h>
+#include <assert.h>
+
+#include "cmdln.h"
+
+#include "debug.h"
+
+struct cmdln_flags parse_args(int argc, char* const* argv)
+{
+    struct cmdln_flags flags = {};
+    
+    flags.argv0 = argv[0];
+    
+    bool unset_operators = true;
+
+    bool unset_print_with_color = true;
+
+    for (int opt; (opt = getopt(argc, argv, "pyqmvc:eEo:C:B")) != -1; )
+    {
+        switch (opt)
+        {
+            case 'p':
+            {
+                flags.print_all_and_quit = true;
+                break;
+            }
+            
+            case 'y':
+            {
+                flags.assume_yes = true;
+                break;
+            }
+
+            case 'q':
+            {
+                flags.quiet = true;
+                break;
+            }
+
+            case 'm':
+            {
+                flags.print_max_operators_needed_and_quit = true;
+                break;
+            }
+            
+            case 'v':
+            {
+                flags.verbose = true;
+                break;
+            }
+
+            case 'c':
+            {
+                flags.command = optarg;
+                break;
+            }
+
+            case 'E':
+            {
+                flags.use_operators.ternary = true;
+            }
+            // fallthrough
+
+            case 'e':
+            {
+                flags.use_operators.not = true;
+                flags.use_operators.or = true;
+                flags.use_operators.and = true;
+
+                flags.use_operators.orn = true;
+                flags.use_operators.nor = true;
+
+                flags.use_operators.andn = true;
+                flags.use_operators.nand = true;
+
+                flags.use_operators. xor = true;
+                flags.use_operators.nxor = true;
+
+                unset_operators = false;
+                break;
+            }
+
+            case 'o':
+            {
+                unset_operators = false;
+
+                for (char* moving; (moving = strtok_r(NULL, ",", &optarg)); )
+                {
+                    if (!strcmp(moving, "not") || !strcmp(moving, "!"))
+                    {
+                        flags.use_operators.not = true;
+                    }
+                    else if (!strcmp(moving, "or") || !strcmp(moving, "||"))
+                    {
+                        flags.use_operators.or = true;
+                    }
+                    else if (!strcmp(moving, "orn") || !strcmp(moving, "|!"))
+                    {
+                        flags.use_operators.orn = true;
+                    }
+                    else if (!strcmp(moving, "nor") || !strcmp(moving, "!|"))
+                    {
+                        flags.use_operators.nor = true;
+                    }
+                    else if (!strcmp(moving, "and") || !strcmp(moving, "&&"))
+                    {
+                        flags.use_operators.and = true;
+                    }
+                    else if (!strcmp(moving, "andn") || !strcmp(moving, "&!"))
+                    {
+                        flags.use_operators.andn = true;
+                    }
+                    else if (!strcmp(moving, "nand") || !strcmp(moving, "!&"))
+                    {
+                        flags.use_operators.nand = true;
+                    }
+                    else if (!strcmp(moving, "xor") || !strcmp(moving, "!="))
+                    {
+                        flags.use_operators.xor = true;
+                    }
+                    else if (!strcmp(moving, "nxor") || !strcmp(moving, "=="))
+                    {
+                        flags.use_operators.nxor = true;
+                    }
+                    else if (!strcmp(moving, "lt") || !strcmp(moving, "<"))
+                    {
+                        flags.use_operators.lt = true;
+                    }
+                    else if (!strcmp(moving, "lte") || !strcmp(moving, "<="))
+                    {
+                        flags.use_operators.lte = true;
+                    }
+                    else if (!strcmp(moving, "gt") || !strcmp(moving, ">"))
+                    {
+                        flags.use_operators.gt = true;
+                    }
+                    else if (!strcmp(moving, "gte") || !strcmp(moving, ">="))
+                    {
+                        flags.use_operators.gte = true;
+                    }
+                    else if (!strcmp(moving, "ternary") || !strcmp(moving, "?:"))
+                    {
+                        flags.use_operators.ternary = true;
+                    }
+                    else if (!strcmp(moving, "assign") || !strcmp(moving, "="))
+                    {
+                        flags.use_operators.assignment = true;
+                    }
+                    else
+                    {
+                        assert(!"TODO");
+                    }
+                }
+                break;
+            }
+
+            case 'C':
+            {
+                unset_print_with_color = false;
+                
+                if (!strcmp(optarg, "yes") || !strcmp(optarg, "on"))
+                {
+                    flags.print_with_color = true;
+                }
+                else if (!strcmp(optarg, "no") || !strcmp(optarg, "off"))
+                {
+                    flags.print_with_color = false;
+                }
+                else if (!strcmp(optarg, "auto"))
+                {
+                    flags.print_with_color = isatty(1);
+                }
+                else
+                {
+                    assert(!"TODO");
+                }
+
+                break;
+            }
+            
+            case 'B':
+            {
+                flags.force_rebuild = true;
+                
+                break;
+            }
+            
+            default:
+            {
+                assert(!"TODO");
+                break;
+            }
+        }
+    }
+    
+    if (unset_operators)
+    {
+        flags.use_operators.not = true;
+        flags.use_operators.or = true;
+        flags.use_operators.and = true;
+    }
+    
+    if (unset_print_with_color)
+    {
+        flags.print_with_color = isatty(1);
+    }
+    
+    return flags;
+}
+
+

cmdln.h

@@ -0,0 +1,42 @@
+
+#include <stdbool.h>
+
+struct cmdln_flags
+{
+    const char* argv0;
+    
+    const char* command;
+
+    struct use_operators {
+        bool not;
+
+        bool or, orn, nor;
+
+        bool and, andn, nand;
+
+        bool xor, nxor;
+
+        bool lt, lte, gt, gte;
+
+        bool ternary;
+        
+        bool assignment;
+    } use_operators;
+
+    bool print_all_and_quit;
+    
+    bool print_max_operators_needed_and_quit;
+    
+    bool assume_yes;
+
+    bool verbose;
+
+    bool print_with_color;
+
+    bool force_rebuild;
+
+    bool quiet;
+};
+
+struct cmdln_flags parse_args(int argc, char* const* argv);
+

debug.c

@@ -0,0 +1,4 @@
+
+int debug_depth = 0;
+
+

debug.h

@@ -0,0 +1,35 @@
+
+#ifdef DEBUG_BUILD
+extern int debug_depth;
+#endif
+
+#ifdef DEBUG_BUILD
+    #define ZDEBUG 1
+#else
+    #define ZDEBUG 0
+#endif
+
+#ifdef DEBUG_BUILD
+    #define zprintf(fmt, ...) printf("%*s" fmt, debug_depth, "", ## __VA_ARGS__);
+#else
+    #define zprintf(...);
+#endif
+
+#ifdef DEBUG_BUILD
+    #define ENTER \
+        { zprintf("%s():" "\n", __PRETTY_FUNCTION__); debug_depth++; }
+
+    #define EXIT \
+        { zprintf("return" "\n");  debug_depth--; }
+#else
+    #define ENTER ;
+
+    #define EXIT ;
+#endif
+
+#define TODO \
+    assert(!"TODO");
+
+#define CHECK \
+    assert(!"CHECK");
+

defines.h

@@ -0,0 +1,9 @@
+
+#define W 0b0101010101010101
+#define X 0b0011001100110011
+#define Y 0b0000111100001111
+#define Z 0b0000000011111111
+#define M 0b1111111111111111
+
+#define N (65536)
+

evaluate.c

@@ -0,0 +1,500 @@
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <assert.h>
+
+#include <defines.h>
+
+#include "evaluate.h"
+
+uint16_t evaluate(const char* text)
+{
+    enum {
+        tk_uninitialized,
+
+        tk_0,
+        tk_1,
+
+        tk_w,
+        tk_x,
+        tk_y,
+        tk_z,
+
+        tk_oparen,
+        tk_cparen,
+
+        tk_emark,
+        tk_emarkequals,
+        tk_emarkvbar,
+        tk_emarkampersand,
+
+        tk_equalsequals,
+
+        tk_vbarvbar,
+        tk_vbaremark,
+
+        tk_qmark,
+
+        tk_less_than,
+        tk_less_than_eq,
+
+        tk_greater_than,
+        tk_greater_than_eq,
+
+        tk_ampersandemark,
+        tk_ampersandampersand,
+
+        tk_colon,
+
+        tk_EOF,
+    } tokenkind = tk_uninitialized;
+
+    const char* moving = text;
+
+    void next_token(void)
+    {
+        while (*moving && *moving == ' ')
+            moving++;
+
+        switch (*moving)
+        {
+            case 0:
+                tokenkind = tk_EOF;
+                break;
+
+            case '0':
+                tokenkind = tk_0, moving++;
+                break;
+
+            case '1':
+                tokenkind = tk_1, moving++;
+                break;
+
+            case 'w':
+                tokenkind = tk_w, moving++;
+                break;
+
+            case 'x':
+                tokenkind = tk_x, moving++;
+                break;
+
+            case 'y':
+                tokenkind = tk_y, moving++;
+                break;
+
+            case 'z':
+                tokenkind = tk_z, moving++;
+                break;
+
+            case '(':
+                tokenkind = tk_oparen, moving++;
+                break;
+
+            case ')':
+                tokenkind = tk_cparen, moving++;
+                break;
+
+            case '?':
+                tokenkind = tk_qmark, moving++;
+                break;
+
+            case ':':
+                tokenkind = tk_colon, moving++;
+                break;
+
+            // either '||' or '|!':
+            case '|':
+            {
+                moving++;
+
+                switch (*moving)
+                {
+                    case '|':
+                        tokenkind = tk_vbarvbar, moving++;
+                        break;
+
+                    case '!':
+                        tokenkind = tk_vbaremark, moving++;
+                        break;
+
+                    default:
+                    {
+                        puts("syntax error");
+                        exit(1);
+                        break;
+                    }
+                }
+
+                break;
+            }
+
+            // either '&&' or '&!':
+            case '&':
+            {
+                moving++;
+
+                switch (*moving)
+                {
+                    case '&':
+                        tokenkind = tk_ampersandampersand, moving++;
+                        break;
+
+                    case '!':
+                        tokenkind = tk_ampersandemark, moving++;
+                        break;
+
+                    default:
+                    {
+                        puts("syntax error");
+                        exit(1);
+                        break;
+                    }
+                }
+
+                break;
+            }
+
+            // either '!' or '!=' or '!&' or '!|'
+            case '!':
+            {
+                moving++;
+
+                switch (*moving)
+                {
+                    case '=':
+                        tokenkind = tk_emarkequals, moving++;
+                        break;
+
+                    case '|':
+                        tokenkind = tk_emarkvbar, moving++;
+                        break;
+
+                    case '&':
+                        tokenkind = tk_emarkampersand, moving++;
+                        break;
+
+                    default:
+                        tokenkind = tk_emark;
+                        break;
+                }
+
+                break;
+            }
+
+            case '<':
+            {
+                moving++;
+
+                switch (*moving)
+                {
+                    case '=':
+                        tokenkind = tk_less_than_eq, moving++;
+                        break;
+
+                    default:
+                    {
+                        tokenkind = tk_less_than;
+                        break;
+                    }
+                }
+
+                break;
+            }
+
+            case '>':
+            {
+                moving++;
+
+                switch (*moving)
+                {
+                    case '=':
+                        tokenkind = tk_greater_than_eq, moving++;
+                        break;
+
+                    default:
+                    {
+                        tokenkind = tk_greater_than;
+                        break;
+                    }
+                }
+
+                break;
+            }
+
+            // could only be '==':
+            case '=':
+            {
+                moving++;
+
+                switch (*moving)
+                {
+                    case '=':
+                        tokenkind = tk_equalsequals, moving++;
+                        break;
+
+                    default:
+                    {
+                        puts("syntax error");
+                        exit(1);
+                        break;
+                    }
+                }
+
+                break;
+            }
+
+            default:
+                assert(!"TODO");
+                break;
+        }
+    }
+
+    next_token();
+
+    uint16_t parse_root(void)
+    {
+        uint16_t parse_ternary(void)
+        {
+            uint16_t parse_ors(void)
+            {
+                uint16_t parse_ands(void)
+                {
+                    uint16_t parse_equals(void)
+                    {
+                        uint16_t parse_compares(void)
+                        {
+                            uint16_t parse_prefix(void)
+                            {
+                                uint16_t parse_primary(void)
+                                {
+                                    uint16_t retval;
+
+                                    switch (tokenkind)
+                                    {
+                                        case tk_0:
+                                            retval = 0, next_token();
+                                            break;
+
+                                        case tk_1:
+                                            retval = M, next_token();
+                                            break;
+
+                                        case tk_w:
+                                            retval = W, next_token();
+                                            break;
+
+                                        case tk_x:
+                                            retval = X, next_token();
+                                            break;
+
+                                        case tk_y:
+                                            retval = Y, next_token();
+                                            break;
+
+                                        case tk_z:
+                                            retval = Z, next_token();
+                                            break;
+
+                                        case tk_oparen:
+                                        {
+                                            next_token();
+
+                                            retval = parse_root();
+
+                                            if (tokenkind != tk_cparen)
+                                            {
+                                                assert(!"NOPE");
+                                            }
+
+                                            next_token();
+                                            break;
+                                        }
+
+                                        default:
+                                            assert(!"TODO");
+                                            break;
+                                    }
+
+                                    return retval;
+                                }
+
+                                if (tokenkind == tk_emark)
+                                {
+                                    next_token();
+
+                                    return ~parse_prefix();
+                                }
+                                else
+                                {
+                                    return parse_primary();
+                                }
+                            }
+
+                            uint16_t left = parse_prefix();
+
+                            again: switch (tokenkind)
+                            {
+                                case tk_less_than:
+                                {
+                                    next_token();
+                                    left = (~left &  parse_equals()) & M;
+                                    goto again;
+                                }
+
+                                case tk_less_than_eq:
+                                {
+                                    next_token();
+                                    left = (~left |  parse_equals()) & M;
+                                    goto again;
+                                }
+
+                                case tk_greater_than_eq:
+                                {
+                                    next_token();
+                                    left = ( left | ~parse_equals()) & M;
+                                    goto again;
+                                }
+
+                                case tk_greater_than:
+                                {
+                                    next_token();
+                                    left = ( left & ~parse_equals()) & M;
+                                    goto again;
+                                }
+
+                                default:
+                                    break;
+                            }
+
+                            return left;
+                        }
+
+                        uint16_t left = parse_compares();
+
+                        again: switch (tokenkind)
+                        {
+                            case tk_equalsequals:
+                            {
+                                next_token();
+                                left = ~(left ^ parse_equals()) & M;
+                                goto again;
+                            }
+
+                            case tk_emarkequals:
+                            {
+                                next_token();
+                                left = left ^ parse_equals();
+                                goto again;
+                            }
+
+                            default:
+                                break;
+                        }
+
+                        return left;
+                    }
+
+                    uint16_t left = parse_equals();
+
+                    again: switch (tokenkind)
+                    {
+                        case tk_ampersandampersand:
+                        {
+                            next_token();
+                            left = left & parse_equals();
+                            goto again;
+                        }
+
+                        case tk_ampersandemark:
+                        {
+                            next_token();
+                            left = ~left & parse_equals();
+                            goto again;
+                        }
+
+                        case tk_emarkampersand:
+                        {
+                            next_token();
+                            left = ~(left & parse_equals());
+                            goto again;
+                        }
+
+                        default:
+                            break;
+                    }
+
+                    return left;
+                }
+
+                uint16_t left = parse_ands();
+
+                again: switch (tokenkind)
+                {
+                    case tk_vbarvbar:
+                    {
+                        next_token();
+                        left = left | parse_ands();
+                        goto again;
+                    }
+
+                    case tk_vbaremark:
+                    {
+                        next_token();
+                        left = (~left | parse_ands()) & M;
+                        goto again;
+                    }
+
+                    case tk_emarkvbar:
+                    {
+                        next_token();
+                        left = ~(left | parse_ands()) & M;
+                        goto again;
+                    }
+
+                    default:
+                        break;
+                }
+
+                return left;
+            }
+
+            uint16_t cond = parse_ors();
+
+            if (tokenkind == tk_qmark)
+            {
+                next_token();
+
+                uint16_t left = parse_ors();
+
+                if (tokenkind != tk_colon)
+                {
+                    puts("syntax error!");
+                    exit(1);
+                }
+
+                next_token();
+
+                uint16_t right = parse_ternary();
+
+                return (cond & left) | (~cond & right);
+            }
+            else
+            {
+                return cond;
+            }
+        }
+
+        return parse_ternary();
+    }
+
+    uint16_t truthtable = parse_root();
+
+    if (tokenkind != tk_EOF)
+    {
+        puts("syntax error!");
+        exit(1);
+    }
+
+    return truthtable;
+}
+

evaluate.h

@@ -0,0 +1,5 @@
+
+#include <stdint.h>
+
+uint16_t evaluate(const char* text);
+

expr.h

@@ -0,0 +1,62 @@
+
+#ifndef STRUCT_EXPR
+#define STRUCT_EXPR
+
+#include <stdint.h>
+
+enum ekind
+{
+    ek_unreachable,
+    
+    ek_0,
+    ek_1,
+    ek_W,
+    ek_X,
+    ek_Y,
+    ek_Z,
+    
+    // very special:
+    ek_A,
+
+    ek_not,
+    ek_or,
+    ek_and,
+
+    ek_orn,
+    ek_nor,
+
+    ek_andn,
+    ek_nand,
+
+    ek_xor,
+    ek_nxor,
+
+    ek_lt,
+    ek_lte,
+    ek_gt,
+    ek_gte,
+
+    ek_ternary,
+    
+    // also very special.
+    // 'left' is the variable's truthtable
+    // to print the requested truthtable
+    // look a the relavent lookup.
+    ek_assignment,
+};
+
+struct expr
+{
+    enum ekind kind;
+
+    uint16_t cond, left, right;
+    
+    int cost;
+};
+
+
+
+
+
+
+#endif

flake.lock

@@ -36,15 +36,16 @@
     },
     "nixpkgs": {
       "locked": {
-        "lastModified": 1749664469,
+        "lastModified": 1750838302,
-        "narHash": "sha256-Ar3r6cmQVKVoEy/TWAKq8WuGqZibRjMt5oZRvkn+2Bk=",
+        "narHash": "sha256-aVkL3/yu50oQzi2YuKo0ceiCypVZpZXYd2P2p1FMJM4=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "3fa008da69980bd61324ad9e3a825022f0b736f1",
+        "rev": "7284e2decc982b81a296ab35aa46e804baaa1cfe",
         "type": "github"
       },
       "original": {
         "owner": "NixOS",
+        "ref": "nixos-25.05",
         "repo": "nixpkgs",
         "type": "github"
       }

flake.nix

@@ -2,10 +2,10 @@
 # vim: set sw=2 ts=2 et: #
 
 {
-  description = "An example project using flutter";
+  description = "description";
-
-  inputs.nixpkgs = { url = "github:NixOS/nixpkgs"; };
 
+  inputs.nixpkgs = { url = "github:NixOS/nixpkgs?ref=nixos-25.05"; };
+  
   inputs.flake-utils.url = "github:numtide/flake-utils";
 
   inputs.flake-compat = {
@@ -19,17 +19,42 @@
         inherit system;
 
         config.allowUnfree = true;
-      };
+      }; in {
-      in {
         devShells.default =
           pkgs.mkShell {
             buildInputs = with pkgs; [
               gcc
+              gcc.man
               gnumake
               readline.dev
               python3
+              valgrind
+              linux-manual
+              man-pages
+              man-pages-posix
+              
+              # for my sake:
+              gedit
+              libreoffice
             ];
           };
       });
 }
 
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

get_cached_simplifications.c

@@ -0,0 +1,231 @@
+
+#include <sys/mman.h>
+
+#include <errno.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <unistd.h>
+#include <fcntl.h>
+#include <string.h>
+#include <limits.h>
+#include <assert.h>
+
+#include <defines.h>
+
+#include <debug.h>
+
+#include <cmdln.h>
+
+#include "calculate_assignment_simplifications.h"
+#include "get_cached_simplifications.h"
+#include "calculate_simplifications.h"
+
+static struct path { char data[PATH_MAX]; } get_path(
+    const struct cmdln_flags* flags)
+{
+    struct path path = {};
+    
+    strcat(path.data, ".simplifier-cache-64GB");
+
+    if (flags->use_operators.not)
+        strcat(path.data, "-not");
+
+    if (flags->use_operators.or)
+        strcat(path.data, "-or");
+
+    if (flags->use_operators.orn)
+        strcat(path.data, "-orn");
+
+    if (flags->use_operators.nor)
+        strcat(path.data, "-nor");
+
+    if (flags->use_operators.and)
+        strcat(path.data, "-and");
+
+    if (flags->use_operators.andn)
+        strcat(path.data, "-andn");
+
+    if (flags->use_operators.nand)
+        strcat(path.data, "-nand");
+
+    if (flags->use_operators.xor)
+        strcat(path.data, "-xor");
+
+    if (flags->use_operators.nxor)
+        strcat(path.data, "-nxor");
+
+    if (flags->use_operators.lt)
+        strcat(path.data, "-lt");
+
+    if (flags->use_operators.lte)
+        strcat(path.data, "-lte");
+
+    if (flags->use_operators.gt)
+        strcat(path.data, "-gt");
+
+    if (flags->use_operators.gte)
+        strcat(path.data, "-gte");
+
+    if (flags->use_operators.ternary)
+        strcat(path.data, "-ternary");
+
+    if (flags->use_operators.assignment)
+        strcat(path.data, "-assignment");
+
+    strcat(path.data, ".bin");
+    
+    return path;
+}
+
+struct simplifications* get_cached_simplifications(const struct cmdln_flags* flags)
+{
+    ENTER;
+    
+    struct path path = get_path(flags);
+    
+    bool rebuild = flags->force_rebuild;
+    
+    if (!rebuild)
+    {
+        int fd = open(path.data, O_RDONLY);
+        
+        if (fd > 0)
+        {
+            close(fd);
+        }
+        else if (errno == ENOENT)
+        {
+            rebuild = true;
+        }
+        else
+        {
+            TODO;
+            exit(1);
+        }
+    }
+    
+    if (rebuild)
+    {
+        #ifndef DEBUG_BUILD
+        if (!flags->quiet)
+        {
+            puts(""
+                "I'll have to build up my cache of simplifications" "\n"
+                "I'll only have to do this once." "\n"
+                "\n"
+                "This may take a while." "\n"
+            "");
+        }
+        
+        if (!flags->quiet && !flags->verbose)
+        {
+            puts("Re-run with '-v' to watch progress");
+        }
+
+        if (!flags->quiet && !flags->assume_yes)
+        {
+            puts("");
+            puts("Any input to start:"), getchar();
+            puts("Started.");
+        }
+        #endif
+
+        int fd = open(".", O_TMPFILE | O_RDWR, 0664);
+    
+        if (fd < 0)
+        {
+            TODO;
+            exit(1);
+        }
+        
+        if (ftruncate(fd, sizeof(struct simplifications)) < 0)
+        {
+            TODO;
+        }
+        
+        void* ptr = mmap(
+            /* addr: */ NULL,
+            /* len: */ sizeof(struct simplifications),
+            /* prot: */ PROT_WRITE | PROT_READ,
+            /* flags: */ MAP_SHARED,
+            /* fd: */ fd,
+            /* offset: */ 0);
+
+        if (ptr == MAP_FAILED)
+        {
+            TODO;
+        }
+        
+        calculate_simplifications(flags, ptr);
+        
+        // flush mmap:
+        if (munmap(ptr, sizeof(struct simplifications)) < 0)
+        {
+            TODO;
+            exit(1);
+        }
+        
+        {
+            char buffer[PATH_MAX];
+
+            snprintf(buffer, PATH_MAX,  "/proc/self/fd/%d", fd);
+            
+            if (unlink(path.data) < 0 && errno != ENOENT)
+            {
+                printf("unlink(%s): %m" "\n", path.data);
+                
+                exit(1);
+            }
+            
+            if (linkat(AT_FDCWD, buffer, AT_FDCWD, path.data, AT_SYMLINK_FOLLOW) < 0)
+            {
+                printf("linkat(%s): %m" "\n", path.data);
+                
+                exit(1);
+            }
+        }
+        
+        close(fd);
+    }
+
+    int fd = open(path.data, O_RDONLY);
+    
+    if (fd < 0)
+    {
+        TODO;
+    }
+    
+    void* ptr = mmap(
+        /* addr: */ NULL,
+        /* len: */ sizeof(struct simplifications),
+        /* prot: */ PROT_READ,
+        /* flags: */ MAP_PRIVATE,
+        /* fd: */ fd,
+        /* offset: */ 0);
+
+    if (ptr == MAP_FAILED)
+    {
+        TODO;
+    }
+
+    close(fd);
+    
+    EXIT;
+    return ptr;
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

get_cached_simplifications.h

@@ -0,0 +1,7 @@
+
+// #include <expr.h>
+
+struct cmdln_flags;
+
+struct simplifications* get_cached_simplifications(const struct cmdln_flags* flags);
+

makefile

@@ -1,27 +1,64 @@
 
 # vim: noexpandtab tabstop=4 :
 
+buildtype ?= release
+
+optionset = buildtypes/${buildtype}.txt
+
+prefix = bin/${buildtype}
+
+default: ${prefix}/bsimp
+
+.PRECIOUS: %/
+
+%/:
+	@mkdir -p $@
+
+srcs += calculate_simplifications.c calculate_assignment_simplifications.c
+srcs += cmdln.c evaluate.c debug.c
+srcs += get_cached_simplifications.c main.c print.c
+
+${prefix}/%.o ${prefix}/%.d: %.c ${optionset} | ${prefix}/%/
+	@echo "compiling (${buildtype}) ${*}.c ..."
+	@gcc -c @${optionset} $< -MD -MF ${prefix}/${*}.d -o ${prefix}/${*}.o
+
+objs = $(patsubst %.c,${prefix}/%.o,${srcs})
+
+${prefix}/bsimp: ${optionset} ${objs} | bin/
+	@echo "linking (${buildtype})"
+	@gcc @${optionset} ${objs} -o $@
+
 args =
 
-cc = gcc
+run: ${prefix}/bsimp
-
-cppflags += -D _GNU_SOURCE
-#cppflags += -D ZDEBUG
-
-cflags = -Werror -Wall -Wextra -Wstrict-prototypes -Wfatal-errors
-
-cflags += -O3
-
-cflags += -Wno-unused
-
-ldflags += -lreadline
-
-/tmp/4-variable-simplifier: main.c
-	$(cc) $(cppflags) $(cflags) $< -o $@ $(ldflags)
-
-run: /tmp/4-variable-simplifier
 	$< $(args)
 
+valrun: ${prefix}/bsimp
+	valgrind --max-stackframe=2031768 \
+		--exit-on-first-error=yes --error-exitcode=1 -- $< ${args}
+
+PREFIX ?= ${HOME}
+
+install: ${PREFIX}/bin/bsimp
+
+${PREFIX}/bin/bsimp: bin/release/bsimp | ${PREFIX}/bin/
+	cp -vau $< $@
+
+include $(patsubst %.c,${prefix}/%.d,${srcs})
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
 
-# nix --extra-experimental-features nix-command --extra-experimental-features flakes develop --command 'make'
 

nix-make.sh

@@ -0,0 +1,6 @@
+#!/bin/sh
+set -ev
+nix --extra-experimental-features nix-command \
+    --extra-experimental-features flakes \
+    develop \
+    --command "make" "$@"

print.c

@@ -0,0 +1,241 @@
+
+#include <stdio.h>
+#include <assert.h>
+
+#include <debug.h>
+
+#include <cmdln.h>
+
+#include <expr.h>
+
+#include "simplifications.h"
+
+#include "print.h"
+
+static void helper(
+    const struct simplifications* simps,
+    const struct row* row,
+    uint16_t truthtable,
+    bool print_with_color,
+    int depth)
+{
+    #define LITERAL_ESCAPE "\e[38;2;200;200;100m"
+    #define VARIABLE_ESCAPE "\e[38;2;100;100;200m"
+    #define RESET_ESCAPE "\e[0m"
+
+    static const char* const operator_colors[10] = {
+        "\e[38;2;204;0;0m",
+        "\e[38;2;204;122;0m",
+        "\e[38;2;163;204;0m",
+        "\e[38;2;40;204;0m",
+        "\e[38;2;0;204;81m",
+        "\e[38;2;0;204;204m",
+        "\e[38;2;0;81;204m",
+        "\e[38;2;40;0;204m",
+        "\e[38;2;163;0;204m",
+        "\e[38;2;204;0;122m",
+    };
+
+    const struct expr* e = &row->data[truthtable];
+
+    switch (e->kind)
+    {
+        case ek_unreachable:
+        {
+            assert(!"NOPE");
+            break;
+        }
+        
+        case ek_0:
+        {
+            printf(print_with_color ? LITERAL_ESCAPE "0" RESET_ESCAPE : "0");
+            break;
+        }
+
+        case ek_1:
+        {
+            printf(print_with_color ? LITERAL_ESCAPE "1" RESET_ESCAPE : "1");
+            break;
+        }
+
+        case ek_W:
+        {
+            printf(print_with_color ? VARIABLE_ESCAPE "w" RESET_ESCAPE : "w");
+            break;
+        }
+
+        case ek_X:
+        {
+            printf(print_with_color ? VARIABLE_ESCAPE "x" RESET_ESCAPE : "x");
+            break;
+        }
+
+        case ek_Y:
+        {
+            printf(print_with_color ? VARIABLE_ESCAPE "y" RESET_ESCAPE : "y");
+            break;
+        }
+
+        case ek_Z:
+        {
+            printf(print_with_color ? VARIABLE_ESCAPE "z" RESET_ESCAPE : "z");
+            break;
+        }
+
+        case ek_A:
+        {
+            printf(print_with_color ? VARIABLE_ESCAPE "a" RESET_ESCAPE : "a");
+            break;
+        }
+
+        case ek_not:
+        {
+            const char* start = print_with_color ? operator_colors[depth % 10] : "";
+            const char* end = print_with_color ? RESET_ESCAPE : "";
+
+            printf("%s(!%s", start, end);
+
+            helper(simps, row, e->left, print_with_color, depth + 1);
+
+            printf("%s)%s", start, end);
+            break;
+        }
+
+        #define BINARY_OPERATOR(kind, operatorstring) \
+            case kind: \
+            { \
+                const char *start = "", *end = ""; \
+                \
+                if (print_with_color) \
+                { \
+                    start = operator_colors[depth % 10]; \
+                    \
+                    end = RESET_ESCAPE; \
+                } \
+                \
+                printf("%s(%s", start, end); \
+                \
+                helper(simps, row, e->left, print_with_color, depth + 1); \
+                \
+                printf("%s%s%s", start, operatorstring, end); \
+                \
+                helper(simps, row, e->right, print_with_color, depth + 1); \
+                \
+                printf("%s)%s", start, end); \
+                break; \
+            }
+
+        BINARY_OPERATOR(ek_or, " || ");
+        BINARY_OPERATOR(ek_orn, " |! ");
+        BINARY_OPERATOR(ek_nor, " !| ");
+
+        BINARY_OPERATOR(ek_and, " && ");
+        BINARY_OPERATOR(ek_andn, " &! ");
+        BINARY_OPERATOR(ek_nand, " !& ");
+
+        BINARY_OPERATOR(ek_xor, " != ");
+        BINARY_OPERATOR(ek_nxor, " == ");
+
+        BINARY_OPERATOR(ek_lt, " < ");
+        BINARY_OPERATOR(ek_lte, " <= ");
+        BINARY_OPERATOR(ek_gt, " > ");
+        BINARY_OPERATOR(ek_gte, " >= ");
+
+        #undef BINARY_OPERATOR
+
+        case ek_ternary:
+        {
+            const char *start = "", *end = "";
+
+            if (print_with_color)
+            {
+                start = operator_colors[depth % 10];
+
+                end = RESET_ESCAPE;
+            }
+
+            printf("%s(%s", start, end);
+            helper(simps, row, e->cond, print_with_color, depth + 1);
+            printf(" %s?%s ", start, end);
+            helper(simps, row, e->left, print_with_color, depth + 1);
+            printf(" %s:%s ", start, end);
+            helper(simps, row, e->right, print_with_color, depth + 1);
+            printf("%s)%s", start, end);
+
+            break;
+        }
+        
+        case ek_assignment:
+        {
+            assert(row == &simps->main);
+            
+            const char *start = "", *end = "";
+
+            if (print_with_color)
+            {
+                start = operator_colors[depth % 10];
+
+                end = RESET_ESCAPE;
+            }
+
+            printf("%s(%s", start, end);
+            
+            printf("%s", print_with_color ? VARIABLE_ESCAPE "a" RESET_ESCAPE : "a");
+            
+            printf(" ");
+            
+            printf("%s=%s", start, end);
+            
+            printf(" ");
+            
+            helper(simps, row, e->left, print_with_color, depth + 1);
+            
+            printf("%s, %s", start, end);
+            
+            helper(simps, &simps->with_vars[e->left], e->right,
+                print_with_color, depth + 1);
+            
+            printf("%s)%s", start, end);
+            break;
+        };
+    }
+}
+
+void print(
+    const struct cmdln_flags* flags,
+    const struct simplifications* simps,
+    const struct row* row,
+    uint16_t truthtable)
+{
+    helper(simps, row, truthtable, flags->print_with_color, 0);
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

print.h

@@ -0,0 +1,18 @@
+
+#include <stdint.h>
+
+#include <defines.h>
+
+#include <expr.h>
+
+struct cmdln_flags;
+struct simplifications;
+struct row;
+
+void print(
+    const struct cmdln_flags* flags,
+    const struct simplifications* simps,
+    const struct row* row,
+    uint16_t truthtable);
+
+

simplifications.h

@@ -0,0 +1,17 @@
+
+#ifndef STRUCT_SIMPLIFICATIONS
+#define STRUCT_SIMPLIFICATIONS
+
+#include "defines.h"
+
+#include "expr.h"
+
+struct simplifications
+{
+    struct row {
+        struct expr data[N];
+    } main, with_vars[N];
+};
+
+#endif
+

spikes/assignment.py

@@ -0,0 +1,199 @@
+#!/usr/bin/env python3
+
+from heapq import heappush, heappop
+
+X = 0b01010101
+Y = 0b00110011
+Z = 0b00001111
+M = 0b11111111
+
+B = 1 << 3
+N = 1 << B
+
+def calc_simps(A = None):
+    # truthtable -> ('var', name)
+    # truthtable -> ('not', inner truthtable)
+    # truthtable -> (binary op, left truthtable, right truthtable)
+    lookup = dict();
+
+    # truthtable -> cost
+    costs = dict();
+
+    todo = set();
+
+    def initial(exp, truthtable):
+        lookup[truthtable] = exp;
+        costs[truthtable] = 0;
+        todo.add(truthtable);
+
+    initial(('var', 'x'), X);
+    initial(('var', 'y'), Y);
+    initial(('var', 'z'), Z);
+    initial(('lit', '0'), 0);
+    initial(('lit', '1'), M);
+    
+    if (A is not None):
+        initial(('var', 'a'), A);
+    
+    done = list();
+
+    for iteration in range(1, N + 1):
+        mytruthtable = min(todo, key = lambda x: (costs[x], x));
+        
+        mycost = costs[mytruthtable];
+        
+        todo.remove(mytruthtable);
+        
+        # consider NOT:
+        not_cost = mycost + 1
+        not_truthtable = ~mytruthtable & M;
+        if (not_truthtable not in costs) or (not_cost < costs[not_truthtable]):
+            todo.add(not_truthtable);
+            
+            lookup[not_truthtable] = ("not", mytruthtable);
+            
+            costs[not_truthtable] = not_cost;
+        
+        # consider OR:
+        for othertruthtable in done:
+            or_cost = 1 + mycost + costs[othertruthtable];
+            
+            or_truthtable = mytruthtable | othertruthtable;
+            
+            if (or_truthtable not in costs) or (or_cost < costs[or_truthtable]):
+                todo.add(or_truthtable);
+                
+                lookup[or_truthtable] = ("or", mytruthtable, othertruthtable);
+                
+                costs[or_truthtable] = or_cost;
+        
+        # consider AND:
+        for othertruthtable in done:
+            and_cost = 1 + mycost + costs[othertruthtable];
+            
+            and_truthtable = mytruthtable & othertruthtable;
+            
+            if (and_truthtable not in costs) or (and_cost < costs[and_truthtable]):
+                todo.add(and_truthtable);
+                
+                lookup[and_truthtable] = ("and", mytruthtable, othertruthtable);
+                
+                costs[and_truthtable] = and_cost;
+        
+        # consider XOR:
+        if 0:
+            for othertruthtable in done:
+                xor_cost = 1 + mycost + costs[othertruthtable];
+                
+                xor_truthtable = mytruthtable ^ othertruthtable;
+                
+                if (xor_truthtable not in costs) or (xor_cost < costs[xor_truthtable]):
+                    todo.add(xor_truthtable);
+                    
+                    lookup[xor_truthtable] = ("xor", mytruthtable, othertruthtable);
+                    
+                    costs[xor_truthtable] = xor_cost;
+        
+        done.append(mytruthtable);
+
+    assert(sorted(done) == sorted(costs));
+    
+    return costs, lookup;
+
+def etostr(lookup, expr):
+    match expr:
+        case ('lit', x):
+            return x;
+        case ('var', x):
+            return x;
+        case ('not', inner):
+            return "(!" + tostr(lookup, inner) + ")";
+        case ('or', left, right):
+            return "(" + tostr(lookup, left) + " || " + tostr(lookup, right) + ")";
+        case ('and', left, right):
+            return "(" + tostr(lookup, left) + " && " + tostr(lookup, right) + ")";
+        case ('xor', left, right):
+            return "(" + tostr(lookup, left) + " != " + tostr(lookup, right) + ")";
+        case _:
+            assert(not "TODO");
+
+def tostr(lookup, truthtable):
+    return etostr(lookup, lookup[truthtable]);
+
+zdcosts, zdlookup = calc_simps();
+
+# now that we've figured out the zero-depth trees, we need to figure out which
+# trees could be done faster with a variable. We need to go through every
+# possible truthtable, considering them the new variable, building up a new
+# table of what expressions are the cheapiest with that variable.
+# Then, if that figured out for all of them, we could read down the columns
+# figuring out the best answers for anything the user gives.
+
+# truthtable -> cost
+costs = zdcosts;
+
+# truthtable -> variable truthtable
+varlookup = {x: None for x in range(1 << B)};
+
+all_costs = dict(); # variable truthtable -> truthtable -> cost
+all_lookups = dict(); # variable truthtable -> truthtable -> expr
+
+for A in range(0, 1 << B):
+    print(f"what if the variable was 0b{A:08b}?");
+    
+    var_costs, var_lookup = calc_simps(A);
+    
+    for t in range(0, 1 << B):
+        mycost = var_costs[t] + 1 + zdcosts[A];
+        
+        if mycost < costs[t]:
+            varlookup[t] = A;
+            
+            costs[t] = mycost;
+    
+    all_costs[A] = var_costs;
+    
+    all_lookups[A] = var_lookup;
+    
+for t in range(0, 1 << B):
+    line = f"0b{t:08b}: ";
+    
+    line += f"[{costs[t]}] ";
+    
+    if varlookup[t] is None:
+        line += tostr(zdlookup, t);
+    else:
+        line += "("
+        
+        a = varlookup[t];
+        
+        line += "a = " + tostr(zdlookup, a);
+        
+        line += ", "
+        
+        line += tostr(all_lookups[a], t);
+        
+        line += ")"
+        
+        line += " [before: " + tostr(zdlookup, t) + "]";
+    
+    print(line);
+
+print();
+print(f"we can do anything in {max(costs.values())} operations");
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

spikes/boolean-array-or-2.c

@@ -0,0 +1,148 @@
+
+#include <stdio.h>
+#include <assert.h>
+#include <string.h>
+
+#ifdef ZDEBUG
+    #define zprintf(fmt, ...) printf(fmt, ## __VA_ARGS__);
+#else
+    #define zprintf(...) ;
+#endif
+
+#define N (256)
+
+#define M (255)
+
+struct boolist
+{
+    int data[8][256];
+};
+
+void init(struct boolist* this)
+{
+    memset(this, 0, sizeof(*this));
+}
+
+void add(struct boolist* this, int e)
+{
+    zprintf("insert(e = %i);\n", e);
+
+    if (!this->data[0][e])
+    {
+        for (int k = 0; k < 8 && !this->data[k][e >> k]++; k++);
+    }
+}
+
+void search(
+    struct boolist* alist,
+    struct boolist* blist,
+    int k,
+    int ai, int bi,
+    int findme,
+    int calldepth)
+{
+    zprintf("%*s" "search(k = %i, ai = %#b, bi = %#b, findme = %#b):" "\n", calldepth++, "", k, ai, bi, findme);
+    
+    if (k >= 0)
+    {
+        // x | y | z
+        //-----------
+        // 0 | 0 | 0
+        // 0 | 1 | 1
+        // 1 | 0 | 1
+        // 1 | 1 | 1
+        
+        if (findme & (1 << k))
+        {
+            // there are three cases that would make 'z' one:
+            zprintf("%*s" "one case" "\n", calldepth, "");
+            
+            // x is 0 and y is 1:
+            if (alist->data[k][(ai >> k) + 0] && blist->data[k][(bi >> k) + 1])
+            {
+                search(alist, blist, k - 1, ai, bi + (1 << k), findme, calldepth);
+            }
+            
+            // x is 1 and y is 0:
+            if (alist->data[k][(ai >> k) + 1] && blist->data[k][(bi >> k) + 0])
+            {
+                search(alist, blist, k - 1, ai + (1 << k), bi, findme, calldepth);
+            }
+            
+            // x is 1 and y is 1:
+            if (alist->data[k][(ai >> k) + 1] && blist->data[k][(bi >> k) + 1])
+            {
+                search(alist, blist, k - 1, ai + (1 << k), bi + (1 << k), findme, calldepth);
+            }
+        }
+        else
+        {
+            zprintf("%*s" "zero case" "\n", calldepth, "");
+            
+            // there's only one case when 'z' is zero: 'x' and 'y' both
+            // must be zero.
+            
+            // check that both corrasponding quadrants are not empty first.
+            if (alist->data[k][(ai >> k) + 0] && blist->data[k][(bi >> k) + 0])
+            {
+                search(alist, blist, k - 1, ai, bi, findme, calldepth);
+            }
+        }
+    }
+    else
+    {
+        assert((ai | bi) == findme);
+        
+        printf("%2i (0b%05b) | %2i (0b%05b) == %2i (0b%05b)" "\n",
+            ai, ai, bi, bi, findme, findme);
+    }
+}
+
+//            0   1   2   3   4   5   6   7   8   9
+int a[10] = { 2,  4,  5,  7,  9, 11, 15, 17, 17, 19};
+int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
+
+//          [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
+//            2    4    5    7    9   11   15   17   17   19
+//          --------------------------------------------------
+// [ 0] 10 | 10   14   15   15   11   11   15   27   27   27
+
+// [ 1] 11 | 11   15   15   15   11   11   15   27   27   27
+
+// [ 2] 11 | 11   15   15   15   11   11   15   27   27   27
+
+// [ 3] 14 | 14   14   15   15   15   15   15   31   31   31
+
+// [ 4] 14 | 14   14   15   15   15   15   15   31   31   31
+
+// [ 5] 19 | 19  (23) (23) (23)  27   27   31   19   19   19
+
+// [ 6] 20 | 22   20   21  (23)  29   31   31   21   21  (23)
+
+// [ 7](23)|(23) (23) (23) (23)  31   31   31  (23) (23) (23)
+
+// [ 8] 26 | 26   30   31   31   27   27   31   27   27   27
+
+// [ 9] 29 | 31   29   29   31   29   31   31   29   29   31
+
+int main()
+{
+    struct boolist alist, blist;
+
+    init(&alist), init(&blist);
+
+    for (int i = 0; i < 10; i++)
+    {
+        add(&alist, a[i]);
+    }
+
+    for (int i = 0; i < 10; i++)
+    {
+        add(&blist, b[i]);
+    }
+
+    search(&alist, &blist, 7, 0, 0, 23, 0);
+
+    return 0;
+}
+

spikes/boolean-array-reverse-or.c

@@ -0,0 +1,189 @@
+
+#include <stdio.h>
+#include <assert.h>
+#include <string.h>
+#include <stdbool.h>
+
+#ifdef ZDEBUG
+    #define zprintf(fmt, ...) printf(fmt, ## __VA_ARGS__);
+#else
+    #define zprintf(...) ;
+#endif
+
+#define TODO \
+    assert(!"TODO");
+
+#define N (256)
+
+#define M (255)
+
+struct boolist
+{
+    int data[8][256];
+};
+
+void init(struct boolist* this)
+{
+    memset(this, 0, sizeof(*this));
+}
+
+void add(struct boolist* this, int e)
+{
+    zprintf("insert(e = %i);\n", e);
+
+    if (!this->data[0][e])
+    {
+        for (int k = 0; k < 8 && !this->data[k][e >> k]++; k++);
+    }
+}
+
+void search(
+    int a,
+    struct boolist* blist,
+    struct boolist* clist,
+    int k,
+    int bi, int ci,
+    int calldepth)
+{
+    zprintf("%*s" "search(k = %i, bi = %#b, ci = %#b):" "\n",
+        calldepth++, "", k, bi, ci);
+    
+    if (k >= 0)
+    {
+        // a | b | c
+        //-----------
+        // 0 | 0 | 0
+        // 0 | 1 | 1
+        // 1 | 0 | 1
+        // 1 | 1 | 1
+        
+        if (a & (1 << k))
+        {
+            // there are three cases that would make 'z' one:
+            zprintf("%*s" "one case" "\n", calldepth, "");
+            
+            // if the left operand is providing the one-ness, then the right
+            // operand can be whatever it wants, and the resultant must be one
+            
+            // b == 0 and c == 1
+            if (blist->data[k][(bi >> k) + 0] && clist->data[k][(ci >> k) + 1])
+            {
+                search(a, blist, clist, k - 1, bi, ci + (1 << k), calldepth);
+            }
+            
+            // b == 1 and c == 1
+            if (blist->data[k][(bi >> k) + 1] && clist->data[k][(ci >> k) + 1])
+            {
+                search(a, blist, clist, k - 1, bi + (1 << k), ci + (1 << k), calldepth);
+            }
+        }
+        else
+        {
+            zprintf("%*s" "zero case" "\n", calldepth, "");
+            
+            // there two cases to consider then. If the left operand
+            // is not providing the one-ness, then it's up to the right operand
+            // to provide it if it's needed.
+            
+            // b == 0 and c == 0
+            if (blist->data[k][(bi >> k) + 0] && clist->data[k][(ci >> k) + 0])
+            {
+                search(a, blist, clist, k - 1, bi, ci, calldepth);
+            }
+            
+            // b == 1 and c == 1
+            if (blist->data[k][(bi >> k) + 1] && clist->data[k][(ci >> k) + 1])
+            {
+                search(a, blist, clist, k - 1, bi + (1 << k), ci + (1 << k), calldepth);
+            }
+        }
+    }
+    else
+    {
+        printf("%2i (0b%05b) | %2i (0b%05b) == %2i (0b%05b)" "\n",
+            a, a, bi, bi, ci, ci);
+            
+        assert((a | bi) == ci);
+    }
+}
+
+
+int a = 17;
+
+//            0   1   2   3   4   5   6   7   8   9
+int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
+
+int c[20] = {
+//   0   1   2   3   4   5   6   7   8   9
+    15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
+    
+//  10  11  12  13  14  15  16  17  18  19
+    33, 33, 36, 39, 42, 44, 48, 49, 49, 49
+};
+
+//          [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
+//           10   11   11   14   14   19   20   23   26   29
+//          --------------------------------------------------
+// [ 0] 15 |  5    4    4    1    1   12   11    8    5    2
+
+// [ 1] 17 | 17   16   16   17   17    0    1    0    1    0
+
+// [ 2] 19 | 17   16   16   17   17   (0)   3    0    1    2
+
+// [ 3] 21 | 21   20   20   17   17    4   (1)   0    5    0
+
+// [ 4] 22 | 20   20   20   16   16    4    2    0    4    2
+
+// [ 5] 25 | 17   16   16   17   17    8    9    8    1    0
+
+// [ 6] 26 | 16   16   16   16   16    8   10    8    0    2
+
+// [ 7] 26 | 16   16   16   16   16    8   10    8    0    2
+
+// [ 8] 27 |(17) (16) (16)  17   17    8   11    8  ( 1)   2
+
+// [ 9] 32 | 32   32   32   32   32   32   32   32   32   32
+
+// [10] 33 | 33   32   32   33   33   32   33   32   33   32
+
+// [11] 33 | 33   32   32   33   33   32   33   32   33   32
+
+// [12] 36 | 36   36   36   32   32   36   32   32   36   32
+
+// [13] 39 | 37   36   36   33   33   36   35   32   37   34
+
+// [14] 42 | 32   32   32   32   32   40   42   40   32   34
+
+// [15] 44 | 36   36   36   32   32   44   40   40   36   32
+
+// [16] 48 | 48   48   48   48   48   32   32   32   32   32
+
+// [17] 49 | 49   48   48   49   49   32   33   32   33   32
+
+// [18] 49 | 49   48   48   49   49   32   33   32   33   32
+
+// [19] 49 | 49   48   48   49   49   32   33   32   33   32
+
+
+
+int main()
+{
+    struct boolist blist, clist;
+
+    init(&blist), init(&clist);
+
+    for (int i = 0; i < 10; i++)
+    {
+        add(&blist, b[i]);
+    }
+
+    for (int i = 0; i < 20; i++)
+    {
+        add(&clist, c[i]);
+    }
+
+    search(a, &blist, &clist, 7, 0, 0, 0);
+
+    return 0;
+}
+

spikes/boolean-array.c

@@ -0,0 +1,97 @@
+
+#include <stdbool.h>
+#include <assert.h>
+#include <stdio.h>
+
+#define N (256)
+
+#define M (255)
+
+struct boolist {
+    int data[8][256];
+} list = {};
+
+void add(int e)
+{
+    printf("insert(e = %i);\n", e);
+
+    assert(!list.data[0][e]);
+
+    for (int k = 0; k < 8 && !list.data[k][e >> k]++; k++);
+}
+
+void discard(int e)
+{
+    printf("discard(e = %i);\n", e);
+
+    assert(list.data[0][e]);
+
+    for (int k = 0; k < 8 && !--list.data[k][e >> k]; k++);
+}
+
+void print()
+{
+    puts("print():");
+
+    void walk(int k, int i)
+    {
+        if (k >= 0)
+        {
+            int* a = &list.data[k][i >> k];
+
+            if (a[0]) walk(k - 1, i);
+
+            if (a[1]) walk(k - 1, i + (1 << k));
+        }
+        else
+        {
+            printf("  " "%i\n", i);
+        }
+    }
+
+    walk(7, 0);
+}
+
+int main()
+{
+    print();
+
+    add(42);
+
+    print();
+
+    add(101);
+
+    print();
+
+    discard(42);
+
+    print();
+
+    add(34);
+
+    print();
+
+    add(35);
+
+    print();
+
+    add(36);
+
+    print();
+
+    discard(35);
+
+    print();
+
+    return 0;
+}
+
+
+
+
+
+
+
+
+

spikes/kattis-add-find-all.c

@@ -0,0 +1,100 @@
+
+#include <stdbool.h>
+#include <assert.h>
+#include <assert.h>
+#include <stdio.h>
+
+#define N(array) (sizeof(array) / sizeof(*array))
+
+//            0   1   2   3   4   5   6   7   8   9
+int a[10] = { 2,  4,  5,  7,  9, 11, 15, 17, 17, 19};
+int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
+
+int c[20] = {
+    15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
+    33, 33, 36, 39, 42, 44, 48, 49, 49, 49
+};
+
+//          [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
+//            2    4    5    7    9   11   15   17   17   19
+//          --------------------------------------------------
+// [ 0] 10 | 12   14  (15) (17) (19) (21) (25) (27) (27)  29
+
+// [ 1] 11 | 13  (15)  16   28   20  (22) (26)  28   28   30
+
+// [ 2] 11 | 13  (15)  16   18   20  (22) (26)  28   28   30
+
+// [ 3] 14 | 16   18  (19) (21)  23  (25)  29   31   31  (33)
+
+// [ 4] 14 | 16   18  (19) (21)  23  (25)  29   31   31  (33)
+
+// [ 5] 19 |(21)  23   24  (26)  28   30   34  (36) (36)  38
+
+// [ 6] 20 |(22)  24  (25) (27)  29   31   38   40   40  (42)
+
+// [ 7] 23 |(25) (27)  28   30  (32)  34   38   40   40  (42)
+
+// [ 8] 26 | 28   30   31  (33)  35   37   41   43   43   45
+
+// [ 9] 29 | 31  (33)  34  (36)  38   40  (44)  46   46  (48)
+
+int main()
+{
+    puts("hello, world!");
+    
+    for (int ci = 0; ci < 20; ci++)
+    {
+        bool found[10][10] = {};
+        
+        int goal = c[ci];
+        
+        bool again = true;
+        
+        while (again)
+        {
+            again = false;
+            
+            int ai = 0, bi = 9;
+            
+            while (ai < 10 && bi >= 0)
+            {
+                int sum = found[ai][bi] ? 0 : a[ai] + b[bi];
+                
+                if (sum < goal)
+                {
+                    ai++;
+                }
+                else if (sum > goal)
+                {
+                    bi--;
+                }
+                else
+                {
+                    assert(a[ai] + b[bi] == c[ci]);
+                    
+                    printf("a[%2i] + b[%2i] == c[%2i] "
+                        "(%2i + %2i == %2i)\n",
+                        ai, bi, ci, a[ai], b[bi], c[ci]);
+                    
+                    found[ai][bi] = true;
+                    again = true;
+                    
+                    bi--;
+                }
+            }
+        }
+    }
+    
+    return 0;
+}
+
+
+
+
+
+
+
+
+
+
+

spikes/kattis-add.c

@@ -0,0 +1,94 @@
+
+#include <stdbool.h>
+#include <assert.h>
+#include <assert.h>
+#include <stdio.h>
+
+#define N(array) (sizeof(array) / sizeof(*array))
+
+//            0   1   2   3   4   5   6   7   8   9
+int a[10] = { 2,  4,  5,  7,  9, 11, 15, 17, 17, 19};
+int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
+
+int c[20] = {
+    15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
+    33, 33, 36, 39, 42, 44, 48, 49, 49, 49
+};
+
+//          [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
+//            2    4    5    7    9   11   15   17   17   19
+//          --------------------------------------------------
+// [ 0] 10 | 12   14   15  (17)  19   21   25   27   27   29
+
+// [ 1] 11 | 13   15   16   28   20   22   26   28   28   30
+
+// [ 2] 11 | 13  (15)  16   18   20   22   26   28   28   30
+
+// [ 3] 14 | 16   18   19   21   23   25   29   31   31   33 
+
+// [ 4] 14 | 16   18  (19)  21   23   25   29   31   31   33 
+
+// [ 5] 19 |(21)  23   24  (26)  28   30   34   36   36   38
+
+// [ 6] 20 |(22)  24   25   27   29   31   38   40   40  (42)
+
+// [ 7] 23 |(25) (27)  28   30   32   34   38   40   40  (42)
+
+// [ 8] 26 | 28   30   31   33   35   37   41   43   43   45
+
+// [ 9] 29 | 31  (33)  34  (36)  38   40  (44)  46   46  (48)
+
+int main()
+{
+    puts("hello, world!");
+    
+    for (int ci = 0; ci < 20; ci++)
+    {
+        int goal = c[ci];
+        
+        int ai = 0, bi = 9;
+        
+        while (1)
+        {
+            int sum = a[ai] + b[bi];
+            
+            if (sum < goal)
+            {
+                ai++;
+                
+                if (ai == 10)
+                    break;
+            }
+            else if (sum > goal)
+            {
+                if (bi == 0)
+                    break;
+                    
+                bi--;
+            }
+            else
+            {
+                assert(a[ai] + b[bi] == c[ci]);
+                
+                printf("a[%2i] + b[%2i] == c[%2i] "
+                    "(%2i + %2i == %2i)\n",
+                    ai, bi, ci, a[ai], b[bi], c[ci]);
+                
+                break;
+            }
+        }
+    }
+    
+    return 0;
+}
+
+
+
+
+
+
+
+
+
+
+

spikes/kattis-subtract.c

@@ -0,0 +1,85 @@
+
+#include <limits.h>
+#include <stdio.h>
+#include <stdbool.h>
+#include <assert.h>
+
+// in this one, 'a' is fixed and we're trying to find a 'b' and 'c' to
+// satisify the equation: `a + b = c`
+
+// which we're re-writing as:
+    // `a = c - b`
+
+int a = 7;
+/*int a = 11;*/
+
+//            0   1   2   3   4   5   6   7   8   9
+int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
+
+int c[20] = {
+    15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
+    33, 33, 36, 39, 42, 44, 48, 49, 49, 49
+};
+
+int main()
+{
+    puts("hello, world!");
+    
+    bool found[10][20] = {};
+    
+    int passes = 0;
+    
+    bool again = true;
+    
+    while (again)
+    {
+        passes++;
+        again = false;
+        
+        int bi = 0, ci = 0;
+        
+        while (bi < 10 && ci < 20)
+        {
+            int diff = found[bi][ci] ? INT_MIN : c[ci] - b[bi];
+            
+            if (a < diff)
+            {
+                bi++;
+            }
+            else if (diff < a)
+            {
+                ci++;
+            }
+            else
+            {
+                assert(a + b[bi] == c[ci]);
+                
+                printf("a + b[%2i] == c[%2i] "
+                    "(%2i + %2i == %2i)\n",
+                    bi, ci, a, b[bi], c[ci]);
+                
+                found[bi][ci] = true;
+                again = true;
+                
+                // From now on, this cell will be seen as "too low"
+                // so we'll take that path like it's too high.
+                bi++;
+            }
+        }
+    }
+    
+    printf("passes = %i\n", passes);
+    
+    return 0;
+}
+
+
+
+
+
+
+
+
+
+
+

spikes/linear-add.c

@@ -0,0 +1,172 @@
+
+#include <stdbool.h>
+#include <assert.h>
+#include <assert.h>
+#include <stdio.h>
+
+#define N(array) (sizeof(array) / sizeof(*array))
+
+//            0   1   2   3   4   5   6   7   8   9
+int a[10] = { 2,  4,  5,  7,  9, 11, 15, 17, 17, 19};
+int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
+
+int c[20] = {
+    15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
+    33, 33, 36, 39, 42, 44, 48, 49, 49, 49
+};
+
+//          [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
+//            2    4    5    7    9   11   15   17   17   19
+//          --------------------------------------------------
+// [ 0] 10 | 12   14  (15) (17) (19) (21) (25) (27) (27)  29
+
+// [ 1] 11 | 13  (15)  16   28   20  (22) (26)  28   28   30
+
+// [ 2] 11 | 13  (15)  16   18   20  (22) (26)  28   28   30
+
+// [ 3] 14 | 16   18  (19) (21)  23  (25)  29   31   31  (33)
+
+// [ 4] 14 | 16   18  (19) (21)  23  (25)  29   31   31  (33)
+
+// [ 5] 19 |(21)  23   24  (26)  28   30   34  (36) (36)  38
+
+// [ 6] 20 |(22)  24  (25) (27)  29   31   38   40   40  (42)
+
+// [ 7] 23 |(25) (27)  28   30  (32)  34   38   40   40  (42)
+
+// [ 8] 26 | 28   30   31  (33)  35   37   41   43   43   45
+
+// [ 9] 29 | 31  (33)  34  (36)  38   40  (44)  46   46  (48)
+
+int sums[10 * 10];
+
+bool queued[10 * 10];
+
+struct {
+    int data[10 * 10];
+    int n;
+} heap;
+
+void append(int e)
+{
+    int index = heap.n++, new_index;
+
+    while (index > 0 && sums[heap.data[new_index = (index - 1) / 2]] > sums[e])
+    {
+        heap.data[index] = heap.data[new_index];
+
+        index = new_index;
+    }
+
+    heap.data[index] = e;
+}
+
+int pop(void)
+{
+    assert(heap.n > 0);
+
+    int retval = heap.data[0];
+
+    heap.data[0] = heap.data[heap.n-- - 1];
+
+    int index = 0;
+
+    again:
+    {
+        int left = index * 2 + 1;
+        int right = index * 2 + 2;
+
+        int smallest = index;
+
+        if (left < heap.n && sums[heap.data[left]] < sums[heap.data[index]])
+            smallest = left;
+
+        if (right < heap.n && sums[heap.data[right]] < sums[heap.data[smallest]])
+            smallest = right;
+
+        if (smallest != index)
+        {
+            int tmp = heap.data[index];
+            heap.data[index] = heap.data[smallest];
+            heap.data[smallest] = tmp;
+
+            index = smallest;
+
+            goto again;
+        }
+    }
+
+    return retval;
+}
+
+
+int main()
+{
+    puts("hello, world!");
+    
+    int ci = 0;
+    
+    sums[0] = a[0] + b[0];
+    queued[0] = true;
+    append(0);
+    
+    while (heap.n && ci < 20)
+    {
+        int sum = sums[heap.data[0]], ce = c[ci];
+        
+        // printf("sum = %i, ce = %i\n", sum, ce);
+        
+        if (sum < ce)
+        {
+            next_sum: ;
+            
+            int xy = pop();
+            
+            if (xy % 10 + 1 < 10 && !queued[xy + 1])
+            {
+                int nxy = xy + 1;
+                sums[nxy] = a[nxy % 10] + b[nxy / 10];
+                queued[nxy] = true;
+                append(nxy);
+            }
+            
+            if (xy + 10 < 100 && !queued[xy + 10])
+            {
+                int nxy = xy + 10;
+                sums[nxy] = a[nxy % 10] + b[nxy / 10];
+                queued[nxy] = true;
+                append(nxy);
+            }
+        }
+        else if (sum > ce)
+        {
+            ci++;
+        }
+        else
+        {
+            int xy = heap.data[0];
+            
+            int ai = xy % 10, bi = xy / 10;
+            
+            assert(a[ai] + b[bi] == c[ci]);
+            
+            printf("a[%2i] + b[%2i] == c[%2i] (%2i + %2i == %2i)\n",
+                ai, bi, ci, a[ai], b[bi], c[ci]);
+            
+            goto next_sum;
+        }
+    }
+    
+    return 0;
+}
+
+
+
+
+
+
+
+
+
+
+

spikes/proof-of-concept.py

@@ -369,7 +369,7 @@ def calculate_simplifications(args, available_operators):
 
     return costs, lookup
 
-pathname = "simplifications.bin"
+pathname = ".simplifications.bin"
 
 def get_simplifications(args, available_operators):
     available_operators = tuple(sorted(available_operators));

spikes/quadrant-or-1.c

@@ -0,0 +1,37 @@
+
+#include <stdio.h>
+#include <assert.h>
+
+void search(
+    int mask,
+    int ai, int bi,
+    int findme)
+{
+    if (mask)
+    {
+        if (findme & mask)
+        {
+            search(mask >> 1, ai,        bi | mask, findme);
+            search(mask >> 1, ai | mask, bi,        findme);
+            search(mask >> 1, ai | mask, bi | mask, findme);
+        }
+        else
+        {
+            search(mask >> 1, ai, bi, findme);
+        }
+    }
+    else
+    {
+        assert((ai | bi) == findme);
+
+        printf("0b%04b | 0b%04b == 0b%04b "
+            "(%2i | %2i == %2i)\n", ai, bi, findme, ai, bi, findme);
+    }
+}
+
+int main()
+{
+    search(0b1000, 0, 0, 11);
+
+    return 0;
+}

spikes/quadrant-or-2.c

@@ -0,0 +1,220 @@
+
+#include <stdio.h>
+#include <assert.h>
+
+#ifdef ZDEBUG
+    #define zprintf(fmt, ...) printf(fmt, ## __VA_ARGS__);
+#else
+    #define zprintf(...) ;
+#endif
+
+//            0   1   2   3   4   5   6   7   8   9
+int a[10] = { 2,  4,  5,  7,  9, 11, 15, 17, 17, 19};
+int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
+
+//          [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
+//            2    4    5    7    9   11   15   17   17   19
+//          --------------------------------------------------
+// [ 0] 10 | 10   14   15   15   11   11   15   27   27   27
+
+// [ 1] 11 | 11   15   15   15   11   11   15   27   27   27
+
+// [ 2] 11 | 11   15   15   15   11   11   15   27   27   27
+
+// [ 3] 14 | 14   14   15   15   15   15   15   31   31   31
+
+// [ 4] 14 | 14   14   15   15   15   15   15   31   31   31
+
+// [ 5] 19 | 19  (23) (23) (23)  27   27   31   19   19   19
+
+// [ 6] 20 | 22   20   21  (23)  29   31   31   21   21  (23)
+
+// [ 7](23)|(23) (23) (23) (23)  31   31   31  (23) (23) (23)
+
+// [ 8] 26 | 26   30   31   31   27   27   31   27   27   27
+
+// [ 9] 29 | 31   29   29   31   29   31   31   29   29   31
+
+int binary(
+    int mask,
+    int *array,
+    int i, int n)
+{
+    while (n > 1)
+    {
+        int m = n / 2;
+
+        if (array[i + m] & mask)
+            n = m;
+        else
+            i += m, n = n - m;
+    }
+
+    return (array[i] & mask) ? i : i + 1;
+}
+
+void search(
+    int mask,
+    int ai, int an,
+    int bi, int bn,
+    int findme,
+    int calldepth)
+{
+    zprintf("%*s" "search():" "\n", calldepth++, "");
+
+    zprintf("%*s" "mask = 0b%05b" "\n", calldepth, "", mask);
+
+    zprintf("%*s" "findme = 0b%05b" "\n", calldepth, "", findme);
+
+    zprintf("%*s" "ai = %i" "\n", calldepth, "", ai);
+    zprintf("%*s" "an = %i" "\n", calldepth, "", an);
+
+    zprintf("%*s" "bi = %i" "\n", calldepth, "", bi);
+    zprintf("%*s" "bn = %i" "\n", calldepth, "", bn);
+
+    if (mask)
+    {
+        int asplit = binary(mask, a + ai, 0, an);
+        int bsplit = binary(mask, b + bi, 0, bn);
+
+        zprintf("%*s" "asplit = %i" "\n", calldepth, "", asplit);
+        zprintf("%*s" "bsplit = %i" "\n", calldepth, "", bsplit);
+
+        assert((asplit == an) || (a[ai + asplit] & mask));
+        assert((bsplit == bn) || (b[bi + bsplit] & mask));
+
+        if (mask & findme)
+        {
+            zprintf("%*s" "one path" "\n", calldepth, "");
+
+            //                  0 ... (asplit - 1) | asplit ... (an - 1)
+            //                --------------------- -------------------
+            //            0 |                      |                   |
+            //          ... |   first quadrant.    | second quadrant   |
+            // (bsplit - 1) |                      |                   |
+            //          ---  ---------------------- -------------------
+            //       bsplit |                      |                   |
+            //          ... |    third quadrant    |   fourth quadrant |
+            //     (bn - 1) |                      |                   |
+            //          --- |                      |                   |
+            //               ---------------------- -------------------
+
+            // second quadrant.
+            if (asplit < an && 0 < bsplit)
+            {
+                zprintf("%*s" "entering second quadrant." "\n", calldepth, "");
+
+                search(
+                    mask >> 1,
+                    ai + asplit, an - asplit,
+                    bi, bsplit,
+                    findme,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty second quadrant." "\n", calldepth, "");
+            }
+
+            // third quadrant.
+            if (0 < asplit && bsplit < bn)
+            {
+                zprintf("%*s" "entering third quadrant." "\n", calldepth, "");
+
+                search(
+                    mask >> 1,
+                    ai, asplit,
+                    bi + bsplit, bn - bsplit,
+                    findme,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty third quadrant." "\n", calldepth, "");
+            }
+
+            // fourth quadrant.
+            if (asplit < an && bsplit < bn)
+            {
+                zprintf("%*s" "entering fourth quadrant." "\n", calldepth, "");
+
+                search(
+                    mask >> 1,
+                    ai + asplit, an - asplit,
+                    bi + bsplit, bn - bsplit,
+                    findme,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty fourth quadrant." "\n", calldepth, "");
+            }
+        }
+        else
+        {
+            zprintf("%*s" "zero path" "\n", calldepth, "");
+
+            // first quadrant.
+            if (0 < asplit && 0 < bsplit)
+            {
+                zprintf("%*s" "entering first quadrant." "\n", calldepth, "");
+
+                search(
+                    mask >> 1,
+                    ai, asplit,
+                    bi, bsplit,
+                    findme,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty first quadrant." "\n", calldepth, "");
+            }
+        }
+    }
+    else for (int i = 0; i < an; i++)
+    {
+        for (int j = 0; j < bn; j++)
+        {
+            assert((a[ai + i] | b[bi + j]) == findme);
+
+            printf("%2i [%2i] (0b%05b) | %2i [%2i] "
+                    "(0b%05b) == %2i (0b%05b)" "\n",
+                a[ai + i], ai + i, a[ai + i],
+                b[bi + j], bi + j, b[bi + j],
+                findme, findme);
+        }
+    }
+
+    calldepth--;
+}
+
+int main()
+{
+    search(
+        16,
+        0, 10,
+        0, 10,
+        23,
+        0);
+
+    return 0;
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

spikes/quadrant-reverse-or-with-lists.c

@@ -0,0 +1,341 @@
+
+#include <stdbool.h>
+#include <stdio.h>
+#include <assert.h>
+
+#ifdef ZDEBUG
+    #define zprintf(fmt, ...) printf(fmt, ## __VA_ARGS__);
+#else
+    #define zprintf(...) ;
+#endif
+
+#define N (256)
+
+#define M (255)
+
+struct sparselist {
+    int headtails[N], next[N], head;
+
+    bool in[N];
+} b, c;
+
+void init(struct sparselist* this)
+{
+    this->head = -1;
+    
+    for (int i = 0; i < N; i++)
+    {
+        this->headtails[i] = -1;
+        
+        this->next[i] = -1;
+        
+        this->in[i] = false;
+    }
+}
+
+void print(struct sparselist* this)
+{
+    puts("print():");
+    
+    for (int i = 0; i < N; i++)
+    {
+        if (this->headtails[i] != -1)
+        {
+            printf("  " "headtails[%3i (0b%08b)] = %i" "\n", i, i, this->headtails[i]);
+        }
+    }
+    
+    printf("head = %i\n", this->head);
+    
+    for (int index = this->head; index != -1; index = this->next[index])
+    {
+        printf("  " "index = %i\n", index);
+    }
+}
+
+void insert(struct sparselist* this, int index)
+{
+    assert(!this->in[index]);
+    
+    int head = index & 1 ? index & ~(index & -index) : index, prevhead = -1;
+    
+    while (this->headtails[head] == -1 || index < this->headtails[head])
+    {
+        this->headtails[head] = index;
+        prevhead = head, head = head & ~(head & -head);
+    }
+    
+    if (this->headtails[head] < index)
+    {
+        if (prevhead == -1)
+        {
+            assert(this->headtails[head] == head);
+            
+            assert(this->in[head]);
+            
+            this->next[head] = index;
+        }
+        else
+        {
+            int tophalftail = this->headtails[prevhead - 1];
+            
+            assert(tophalftail != -1);
+            
+            this->next[tophalftail] = index;
+        }
+    }
+    else
+    {
+        this->head = index;
+    }
+    
+    int n = ~index & M;
+    int tail = index & 1 ? index : index | (n & -n), prevtail = -1;
+    
+    while (this->headtails[tail] == -1 || this->headtails[tail] < index)
+    {
+        this->headtails[tail] = index;
+        prevtail = tail, tail = tail | (n = ~tail & M, n & -n);
+    }
+    
+    if (index < this->headtails[tail])
+    {
+        if (prevtail == -1)
+        {
+            assert(this->headtails[tail] == tail);
+            
+            assert(this->in[tail]);
+            
+            this->next[index] = tail;
+        }
+        else
+        {
+            int bottomhalfhead = this->headtails[prevtail + 1];
+            
+            assert(bottomhalfhead != -1);
+            
+            this->next[index] = bottomhalfhead;
+        }
+    }
+    else
+    {
+        this->next[index] = -1;
+    }
+    
+    this->in[index] = true;
+}
+
+int a = 17;
+
+void search(
+    int mask,
+    int bheadindex, int btailindex,
+    int cheadindex, int ctailindex,
+    int calldepth)
+{
+    zprintf("%*s" "quadrant_search():" "\n", calldepth++, "");
+    
+    zprintf("%*s" "mask = 0b%05b" "\n", calldepth, "", mask);
+    
+    zprintf("%*s" "bheadindex = %i" "\n", calldepth, "", bheadindex);
+    zprintf("%*s" "btailindex = %i" "\n", calldepth, "", btailindex);
+    
+    zprintf("%*s" "cheadindex = %i" "\n", calldepth, "", cheadindex);
+    zprintf("%*s" "ctailindex = %i" "\n", calldepth, "", ctailindex);
+    
+    if (mask)
+    {
+        //                  0 ... (bsplit - 1) | bsplit ... (an - 1)
+        //                --------------------- -------------------
+        //            0 |                      |                   |
+        //          ... |   first quadrant.    | second quadrant   |
+        // (csplit - 1) |                      |                   |
+        //          ---  ---------------------- -------------------
+        //       csplit |                      |                   |
+        //          ... |    third quadrant    |   fourth quadrant |
+        //     (cn - 1) |                      |                   |
+        //          --- |                      |                   |
+        //               ---------------------- -------------------
+            
+        if (mask & a)
+        {
+            zprintf("%*s" "one case" "\n", calldepth, "");
+            
+            // third quadrant
+            int q3_btailindex = btailindex & ~mask;
+            int q3_cheadindex = cheadindex |  mask;
+            
+            zprintf("%*s" "q3_btailindex = %i" "\n", calldepth, "", q3_btailindex);
+            zprintf("%*s" "q3_cheadindex = %i" "\n", calldepth, "", q3_cheadindex);
+            
+            if (true
+                && b.headtails[q3_btailindex] != -1
+                && c.headtails[q3_cheadindex] != -1)
+            {
+                zprintf("%*s" "entering third quadrant." "\n", calldepth, "");
+                
+                search(
+                    mask >> 1,
+                    bheadindex, q3_btailindex,
+                    q3_cheadindex, ctailindex,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty third quadrant." "\n", calldepth, "");
+            }
+            
+            // fourth quadrant
+            int q4_bheadindex = bheadindex |  mask;
+            int q4_cheadindex = cheadindex |  mask;
+            
+            if (true
+                && b.headtails[q4_bheadindex] != -1
+                && c.headtails[q4_cheadindex] != -1)
+            {
+                zprintf("%*s" "entering fourth quadrant." "\n", calldepth, "");
+                
+                search(
+                    mask >> 1,
+                    q4_bheadindex, btailindex,
+                    q4_cheadindex, ctailindex,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty fourth quadrant." "\n", calldepth, "");
+            }
+        }
+        else
+        {
+            zprintf("%*s" "zero case" "\n", calldepth, "");
+            
+            // first quadrant
+            int q1_btailindex = btailindex & ~mask;
+            int q1_ctailindex = ctailindex & ~mask;
+            
+            zprintf("%*s" "q1_btailindex = %i" "\n", calldepth, "", q1_btailindex);
+            zprintf("%*s" "q1_ctailindex = %i" "\n", calldepth, "", q1_ctailindex);
+            
+            if (true
+                && b.headtails[q1_btailindex] != -1
+                && c.headtails[q1_ctailindex] != -1)
+            {
+                zprintf("%*s" "entering first quadrant." "\n", calldepth, "");
+                
+                search(
+                    mask >> 1,
+                    bheadindex, q1_btailindex,
+                    cheadindex, q1_ctailindex,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty first quadrant." "\n", calldepth, "");
+            }
+            
+            // fourth quadrant
+            int q4_bheadindex = bheadindex |  mask;
+            int q4_cheadindex = cheadindex |  mask;
+            
+            if (true
+                && b.headtails[q4_bheadindex] != -1
+                && c.headtails[q4_cheadindex] != -1)
+            {
+                zprintf("%*s" "entering fourth quadrant." "\n", calldepth, "");
+                
+                search(
+                    mask >> 1,
+                    q4_bheadindex, btailindex,
+                    q4_cheadindex, ctailindex,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty fourth quadrant." "\n", calldepth, "");
+            }
+        }
+    }
+    else
+    {
+        assert(bheadindex == btailindex);
+        assert(cheadindex == ctailindex);
+        
+        int be = b.headtails[bheadindex];
+        
+        int ce = c.headtails[cheadindex];
+        
+        if (be == bheadindex && ce == cheadindex && (a | be) == ce)
+        {
+            assert(b.in[be]);
+            assert(c.in[ce]);
+            
+            printf("%2i (0b%05b) | %2i (0b%05b) == %2i (0b%05b)" "\n",
+                a, a, be, be, ce, ce);
+        }
+    }
+    
+    calldepth--;
+}
+
+int main()
+{
+    puts("hello, world!");
+    
+    init(&b);
+    insert(&b, 10);
+    insert(&b, 11);
+    insert(&b, 14);
+    insert(&b, 19);
+    insert(&b, 20);
+    insert(&b, 23);
+    insert(&b, 26);
+    insert(&b, 29);
+    
+    #ifdef ZDEBUG
+    print(&b);
+    #endif
+    
+    init(&c);
+    insert(&c, 15);
+    insert(&c, 17);
+    insert(&c, 19);
+    insert(&c, 21);
+    insert(&c, 22);
+    insert(&c, 25);
+    insert(&c, 26);
+    insert(&c, 27);
+    insert(&c, 32);
+    insert(&c, 33);
+    insert(&c, 36);
+    insert(&c, 39);
+    insert(&c, 42);
+    insert(&c, 44);
+    insert(&c, 48);
+    insert(&c, 49);
+    
+    #ifdef ZDEBUG
+    print(&c);
+    #endif
+    
+    search(128, 0, 255, 0, 255, 0);
+    
+    return 0;
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

spikes/quadrant-reverse-or.c

@@ -0,0 +1,271 @@
+
+#include <stdio.h>
+#include <assert.h>
+
+#ifdef ZDEBUG
+    #define zprintf(fmt, ...) printf(fmt, ## __VA_ARGS__);
+#else
+    #define zprintf(...) ;
+#endif
+
+int a = 17;
+
+//            0   1   2   3   4   5   6   7   8   9
+int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
+
+int c[20] = {
+//   0   1   2   3   4   5   6   7   8   9
+    15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
+    
+//  10  11  12  13  14  15  16  17  18  19
+    33, 33, 36, 39, 42, 44, 48, 49, 49, 49
+};
+
+//          [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
+//           10   11   11   14   14   19   20   23   26   29
+//          --------------------------------------------------
+// [ 0] 15 |  5    4    4    1    1   12   11    8    5    2
+
+// [ 1] 17 | 17   16   16   17   17    0    1    0    1    0
+
+// [ 2] 19 | 17   16   16   17   17   (0)   3    0    1    2
+
+// [ 3] 21 | 21   20   20   17   17    4   (1)   0    5    0
+
+// [ 4] 22 | 20   20   20   16   16    4    2    0    4    2
+
+// [ 5] 25 | 17   16   16   17   17    8    9    8    1    0
+
+// [ 6] 26 | 16   16   16   16   16    8   10    8    0    2
+
+// [ 7] 26 | 16   16   16   16   16    8   10    8    0    2
+
+// [ 8] 27 |(17) (16) (16)  17   17    8   11    8  ( 1)   2
+
+// [ 9] 32 | 32   32   32   32   32   32   32   32   32   32
+
+// [10] 33 | 33   32   32   33   33   32   33   32   33   32
+
+// [11] 33 | 33   32   32   33   33   32   33   32   33   32
+
+// [12] 36 | 36   36   36   32   32   36   32   32   36   32
+
+// [13] 39 | 37   36   36   33   33   36   35   32   37   34
+
+// [14] 42 | 32   32   32   32   32   40   42   40   32   34
+
+// [15] 44 | 36   36   36   32   32   44   40   40   36   32
+
+// [16] 48 | 48   48   48   48   48   32   32   32   32   32
+
+// [17] 49 | 49   48   48   49   49   32   33   32   33   32
+
+// [18] 49 | 49   48   48   49   49   32   33   32   33   32
+
+// [19] 49 | 49   48   48   49   49   32   33   32   33   32
+
+int binary(
+    int mask,
+    int *array,
+    int i, int n)
+{
+    while (n > 1)
+    {
+        int m = n / 2;
+        
+        if (array[i + m] & mask)
+            n = m;
+        else
+            i += m, n = n - m;
+    }
+    
+    return (array[i] & mask) ? i : i + 1;
+}
+
+void quadrant_search(
+    int mask,
+    int bi, int bn,
+    int ci, int cn,
+    int calldepth)
+{
+    zprintf("%*s" "quadrant_search():" "\n", calldepth++, "");
+    
+    zprintf("%*s" "mask = 0b%05b" "\n", calldepth, "", mask);
+    
+    zprintf("%*s" "bi = %i" "\n", calldepth, "", bi);
+    zprintf("%*s" "bn = %i" "\n", calldepth, "", bn);
+    
+    zprintf("%*s" "ci = %i" "\n", calldepth, "", ci);
+    zprintf("%*s" "cn = %i" "\n", calldepth, "", cn);
+    
+    if (mask)
+    {
+        int bsplit = binary(mask, b + bi, 0, bn);
+        int csplit = binary(mask, c + ci, 0, cn);
+        
+        zprintf("%*s" "bsplit = %i" "\n", calldepth, "", bsplit);
+        zprintf("%*s" "csplit = %i" "\n", calldepth, "", csplit);
+        
+        assert((bsplit == bn) || (b[bi + bsplit] & mask));
+        assert((csplit == cn) || (c[ci + csplit] & mask));
+        
+        //                  0 ... (bsplit - 1) | bsplit ... (an - 1)
+        //                --------------------- -------------------
+        //            0 |                      |                   |
+        //          ... |   first quadrant.    | second quadrant   |
+        // (csplit - 1) |                      |                   |
+        //          ---  ---------------------- -------------------
+        //       csplit |                      |                   |
+        //          ... |    third quadrant    |   fourth quadrant |
+        //     (cn - 1) |                      |                   |
+        //          --- |                      |                   |
+        //               ---------------------- -------------------
+            
+        if (mask & a)
+        {
+            zprintf("%*s" "one case" "\n", calldepth, "");
+            
+            // third quadrant
+            if (0 <  bsplit && csplit < cn)
+            {
+                zprintf("%*s" "entering third quadrant." "\n", calldepth, "");
+                
+                quadrant_search(
+                    mask >> 1,
+                    bi, bsplit,
+                    ci + csplit, cn - csplit,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty third quadrant." "\n", calldepth, "");
+            }
+            
+            // fourth quadrant
+            if (bsplit < bn && csplit < cn)
+            {
+                zprintf("%*s" "entering fourth quadrant." "\n", calldepth, "");
+                
+                quadrant_search(
+                    mask >> 1,
+                    bi + bsplit, bn - bsplit,
+                    ci + csplit, cn - csplit,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty fourth quadrant." "\n", calldepth, "");
+            }
+        }
+        else
+        {
+            zprintf("%*s" "zero case" "\n", calldepth, "");
+            
+            // first quadrant
+            if (0 < bsplit && 0 < csplit)
+            {
+                zprintf("%*s" "entering first quadrant." "\n", calldepth, "");
+                
+                quadrant_search(
+                    mask >> 1,
+                    bi, bsplit,
+                    ci, csplit,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty first quadrant." "\n", calldepth, "");
+            }
+            
+            // fourth quadrant
+            if (bsplit < bn && csplit < cn)
+            {
+                zprintf("%*s" "entering fourth quadrant." "\n", calldepth, "");
+                
+                quadrant_search(
+                    mask >> 1,
+                    bi + bsplit, bn - bsplit,
+                    ci + csplit, cn - csplit,
+                    calldepth);
+            }
+            else
+            {
+                zprintf("%*s" "empty fourth quadrant." "\n", calldepth, "");
+            }
+        }
+    }
+    else for (int i = 0; i < bn; i++)
+    {
+        for (int j = 0; j < cn; j++)
+        {
+            assert((a | b[bi + i]) == c[ci + j]);
+            
+            printf("%2i (0b%05b) | %2i [%2i] "
+                    "(0b%05b) == %2i [%2i] (0b%05b)" "\n",
+                a, a,
+                b[bi + i], bi + i, b[bi + i],
+                c[ci + j], ci + j, c[ci + j]);
+        }
+    }
+    
+    calldepth--;
+}
+
+void brute_force_search(int bn, int cn)
+{
+    for (int bi = 0; bi < bn; bi++)
+    {
+        for (int ci = 0; ci < cn; ci++)
+        {
+            if ((a | b[bi]) == c[ci])
+            {
+                printf("%2i (0b%05b) | %2i [%2i] "
+                        "(0b%05b) == %2i [%2i] (0b%05b)" "\n",
+                    a, a,
+                    b[bi], bi, b[bi],
+                    c[ci], ci, c[ci]);
+            }
+        }
+    }
+}
+
+int main()
+{
+    puts("divide-and-conquer:");
+    
+    quadrant_search(32, 0, 10, 0, 20, 0);
+    
+    puts("");
+    
+    puts("brute-force:");
+    brute_force_search(10, 20);
+    
+    return 0;
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

spikes/sorted-sparse-list-insert.c

@@ -0,0 +1,242 @@
+
+#include <stdbool.h>
+#include <assert.h>
+#include <stdio.h>
+
+#define N (256)
+
+#define M (255)
+
+int headtails[N], next[N], globalhead = -1;
+
+bool in[N];
+
+void init()
+{
+    for (int i = 0; i < N; i++)
+    {
+        headtails[i] = -1;
+        
+        next[i] = -1;
+        
+        in[i] = false;
+    }
+}
+
+void print()
+{
+    puts("print():");
+    
+    for (int i = 0; i < N; i++)
+    {
+        if (headtails[i] != -1)
+        {
+            printf("  " "headtails[%3i (0b%08b)] = %i" "\n", i, i, headtails[i]);
+        }
+    }
+    
+    printf("globalhead = %i\n", globalhead);
+    
+    for (int index = globalhead; index != -1; index = next[index])
+    {
+        printf("  " "index = %i\n", index);
+    }
+}
+
+void insert(int index)
+{
+    printf("insert():" "\n");
+    
+    assert(!in[index]);
+    
+    printf("  " "index = %i (0b%08b)" "\n", index, index);
+    
+    int head = index & 1 ? index & ~(index & -index) : index, prevhead = -1;
+    
+    printf("  " "head = %i (0b%08b)" "\n", head, head);
+    
+    // while they're blank or we beat them:
+    while (headtails[head] == -1 || index < headtails[head])
+    {
+        headtails[head] = index;
+        
+        printf("  " "headtails[%i] = %i" "\n", head, index);
+        
+        prevhead = head, head = head & ~(head & -head);
+        
+        printf("  " "head = %i (0b%08b)" "\n", head, head);
+    }
+    
+    // there should be only two reasons why we're stopped:
+    // - because we hit the limits of the list
+    // - because we found someone who beat us.
+    
+    if (headtails[head] < index)
+    {
+        printf("  " "hit someone with a better head" "\n");
+        
+        printf("  " "prevhead = %i (0b%08b)" "\n", prevhead, prevhead);
+        
+        if (prevhead == -1)
+        {
+            // if we got beat imeedately, connect to them.
+            
+            assert(headtails[head] == head);
+            
+            assert(in[head]);
+            
+            next[head] = index;
+            
+            printf("  " "next[%i] = %i" "\n", head, next[head]);
+        }
+        else
+        {
+            // we must be coming out of the bottom half
+            
+            // and if we lost, then we know there must be elements in the
+            // first half that should come before us.
+            
+            // and that we should connect to their tail.
+            
+            // so the top-half's tail's "next" should point to us.
+            
+            // and we also know that the top-half's tail comes right before
+            // our previous's head.
+            
+            int tophalftail = headtails[prevhead - 1];
+            
+            printf("  " "tophalftail = %i" "\n", tophalftail);
+            
+            assert(tophalftail != -1);
+            
+            next[tophalftail] = index;
+            
+            printf("  " "next[%i] = %i" "\n", tophalftail, next[tophalftail]);
+        }
+    }
+    else
+    {
+        printf("  " "hit the lower limit of the list" "\n");
+        
+        globalhead = index;
+        
+        printf("  " "globalhead = %i" "\n", globalhead);
+    }
+    
+    int n = ~index & M;
+    int tail = index & 1 ? index : index | (n & -n), prevtail = -1;
+    
+    printf("  " "tail = %i (0b%08b)" "\n", tail, tail);
+    
+    // while they're blank:
+    while (headtails[tail] == -1 || headtails[tail] < index)
+    {
+        headtails[tail] = index;
+        
+        printf("  " "headtails[%i] = %i" "\n", tail, index);
+        
+        prevtail = tail, tail = tail | (n = ~tail & M, n & -n);
+        
+        printf("  " "tail = %i (0b%08b)" "\n", tail, tail);
+    }
+    
+    // there should be only two reasons why we're stopped:
+    // - because we hit the limits of the list
+    // - because we found someone who beat us.
+    
+    if (index < headtails[tail])
+    {
+        printf("  " "hit someone with a better tail" "\n");
+        
+        printf("  " "prevtail = %i (0b%08b)" "\n", prevtail, prevtail);
+        
+        if (prevtail == -1)
+        {
+            // if we got beat imeedately, connect to them.
+            
+            assert(headtails[tail] == tail);
+            
+            assert(in[tail]);
+            
+            next[index] = tail;
+            
+            printf("  " "next[%i] = %i" "\n", index, next[index]);
+        }
+        else
+        {
+            // we must be coming out of the top half
+            
+            // and if we lost, then we know there must be elements in the
+            // second half that should come after us.
+            
+            // and that we should connect to their head.
+            
+            // so we should point to the bottom half's "head"
+            
+            // and we also know that the bottom half's haed comes right before
+            // our previous's tail.
+            
+            int bottomhalfhead = headtails[prevtail + 1];
+            
+            printf("  " "bottomhalfhead = %i" "\n", bottomhalfhead);
+            
+            assert(bottomhalfhead != -1);
+            
+            next[index] = bottomhalfhead;
+            
+            printf("  " "next[%i] = %i" "\n", index, next[index]);
+        }
+    }
+    else
+    {
+        printf("  " "hit the lower limit of the list" "\n");
+        
+        next[index] = -1;
+        
+        printf("  " "next[%i] = %i" "\n", index, next[index]);
+    }
+    
+    in[index] = true;
+}
+
+int main()
+{
+    puts("hello, world!");
+    
+    init();
+    
+    print();
+    
+    insert(42); print();
+    
+/*    insert(200); print();*/
+    
+/*    insert(128); print();*/
+    
+    insert(224); print();
+    
+/*    insert(1); print();*/
+/*    */
+/*    insert(255); print();*/
+
+    insert(96); print();
+    
+    insert(97); print();
+    
+    insert(98); print();
+    
+    insert(99); print();
+    
+    return 0;
+}
+
+
+
+
+
+
+
+
+
+
+

spikes/sorted-sparse-list-remove.c

@@ -0,0 +1,5 @@
+
+// we need to implement this one
+
+// should be fairly easy
+