add outstanding changes

12 files changed, 2557 insertions, 381 deletions

diff --git a/Makefile b/Makefile
index d3e0254..6ddfbc0 100644
--- a/Makefile
+++ b/Makefile
@@ -1,10 +1,10 @@
 APP=km-test
 CFLAGS=-W -Wall -Wextra -pedantic -std=c11 -O2
-OBJS=km.o main.o
+OBJS=km.o km-draw.o km-load.o km-find.o km-rand-src.o km-solve.o main.o
 LIBS=-lm
 
 .PHONY=all clean
-app: $(APP)
+all: $(APP)
 
 $(APP): $(OBJS)
 	$(CC) -o $(APP) $(OBJS) $(LIBS)
diff --git a/gen-data.rb b/gen-data.rb
new file mode 100755
index 0000000..e010ed1
--- /dev/null
+++ b/gen-data.rb
@@ -0,0 +1,23 @@
+#!/usr/bin/env ruby
+
+# get number of rows 
+NUM_ROWS = (ARGV.shift || 100).to_i
+
+# data shape (num_floats, num_ints)
+SHAPE = [2, 0]
+
+# cluster centers
+Q = [[-1, -1], [-1, +1], [+1, -1], [+1, +1]].map { |c|
+  c.map { |v| 0.5 + 0.25 * v }
+}
+
+def noise(y, x, scale)
+  Q[y % Q.size][x] + scale * rand * Math.cos(Math::PI * rand)
+end
+
+# print output
+puts [SHAPE.join(' ')] + NUM_ROWS.times.map { |y|
+  SHAPE.first.times.map { |x|
+    '%1.5f' % [noise(y, x, 0.1)]
+  }.join(' ')
+}
diff --git a/km-draw.c b/km-draw.c
new file mode 100644
index 0000000..7f59df3
--- /dev/null
+++ b/km-draw.c
@@ -0,0 +1,30 @@
+#include <stdint.h> // size_t
+#include "util.h"
+#include "km.h"
+
+void
+km_set_draw(
+  const km_set_t * const set,
+  uint8_t * const rgb,
+  const size_t width,
+  const size_t height,
+  const uint32_t color
+) {
+  for (size_t i = 0; i < set->num_rows; i++) {
+    const float *row = km_set_get_row(set, i);
+    const size_t x = (width - 1) * row[0],
+                 y = (height - 1) * row[1],
+                 ofs = 3 * (width * y + x);
+
+    if (x >= width || y >= height) {
+      die(
+        "km_set_draw(): point out of bounds (row: %zu, point: [%0.2f, %0.2f], pixel: %zux%zu, bounds: %zux%zu)",
+        i, row[0], row[1], x, y, width, height
+      );
+    }
+                
+    rgb[ofs + 0] = (color & 0xff0000) >> 16;
+    rgb[ofs + 1] = (color & 0x00ff00) >> 8;
+    rgb[ofs + 2] = (color & 0x0000ff);
+  }
+}
diff --git a/km-find.c b/km-find.c
new file mode 100644
index 0000000..2dd1ba1
--- /dev/null
+++ b/km-find.c
@@ -0,0 +1,143 @@
+#include <stdbool.h> // bool
+#include <math.h> // fabsf()
+#include "util.h"
+#include "km.h"
+
+#define MIN_CLUSTER_DISTANCE 0.0001
+
+typedef struct {
+  float distance_sum,
+        variance_sum;
+  size_t num_empty_clusters;
+} find_solve_data_t;
+
+static float
+find_get_mean_distance(
+  const find_solve_data_t * const d,
+  const size_t num_clusters
+) {
+  const bool num_filled = num_clusters - d->num_empty_clusters;
+  return num_filled ? (d->distance_sum / num_filled) : 0;
+}
+
+static float
+find_get_mean_variance(
+  const find_solve_data_t * const d,
+  const size_t num_clusters
+) {
+  const bool num_filled = num_clusters - d->num_empty_clusters;
+  return num_filled ? (d->variance_sum / num_filled) : 0;
+}
+
+static float
+find_get_mean_cluster_size(
+  const km_set_t * const set
+) {
+  float sum = 0;
+  size_t num_filled = 0;
+
+  for (size_t i = 0; i < set->num_rows; i++) {
+    if (set->ints[i] > 0) {
+      sum += set->ints[i];
+      num_filled++;
+    }
+  }
+
+  return (num_filled > 0) ? sum / num_filled : 0;
+}
+
+static void
+find_solve_on_stats(
+  const km_set_t * const set,
+  const km_solve_stats_t * const stats,
+  void * const cb_data
+) {
+  find_solve_data_t * const solve_data = cb_data;
+  UNUSED(set);
+
+  // calculate numerator for the average distance across all clusters in
+  // this test
+  for (size_t i = 0; i < stats->num_clusters; i++) {
+    if (fabsf(stats->means[i]) > MIN_CLUSTER_DISTANCE) {
+      // increment mean count
+      solve_data->distance_sum += stats->means[i];
+      solve_data->variance_sum += stats->variances[i];
+    } else {
+      // increment empty cluster count
+      solve_data->num_empty_clusters++;
+    }
+  }
+}
+
+static const km_solve_cbs_t
+FIND_SOLVE_CBS = {
+  .on_stats = find_solve_on_stats,
+};
+
+bool
+km_find(
+  const km_set_t * const set,
+  const km_find_cbs_t * const cbs,
+  void * const cb_data
+) {
+  // check init callback
+  if (!cbs->on_init) {
+    return false;
+  }
+
+  // check fini callback
+  if (!cbs->on_fini) {
+    return false;
+  }
+
+  // check data callback
+  if (!cbs->on_data) {
+    return false;
+  }
+
+  for (size_t i = 2; i < cbs->max_clusters; i++) {
+    for (size_t j = 0; j < cbs->num_tests; j++) {
+      // init cluster set
+      km_set_t cs;
+      if (!cbs->on_init(&cs, set->shape.num_floats, i, cb_data)) {
+        // return failure
+        return false;
+      }
+
+      // init solve data
+      find_solve_data_t solve_data = {
+        .distance_sum       = 0,
+        .variance_sum       = 0,
+        .num_empty_clusters = 0,
+      };
+
+      // solve test
+      if (!km_solve(&cs, set, &FIND_SOLVE_CBS, &solve_data)) {
+        // return failure
+        return false;
+      }
+
+      // init result data
+      const km_find_data_t result = {
+        .cluster_set        = &cs,
+        .num_clusters       = i,
+        .mean_distance      = find_get_mean_distance(&solve_data, i),
+        .mean_variance      = find_get_mean_variance(&solve_data, i),
+        .mean_cluster_size  = find_get_mean_cluster_size(&cs),
+        .num_empty_clusters = solve_data.num_empty_clusters,
+      };
+
+      // emit result
+      cbs->on_data(&result, cb_data);
+
+      // finalize cluster set
+      if (!cbs->on_fini(&cs, cb_data)) {
+        // return failure
+        return false;
+      }
+    }
+  }
+
+  // return success
+  return true;
+}
diff --git a/km-load.c b/km-load.c
new file mode 100644
index 0000000..3615aa9
--- /dev/null
+++ b/km-load.c
@@ -0,0 +1,112 @@
+#include <stdbool.h> // bool
+#include <stdio.h> // fscanf()
+#include <string.h> // strerror()
+#include <errno.h> // errno
+#include "util.h"
+#include "km.h"
+
+#define FAIL(...) do { \
+  if (cbs && cbs->on_error) { \
+    char buf[1024]; \
+    snprintf(buf, sizeof(buf), __VA_ARGS__); \
+    cbs->on_error(buf, cb_data); \
+  } \
+  return false; \
+} while (0)
+
+_Bool
+km_load(
+  FILE * const fh,
+  const km_load_cbs_t * const cbs,
+  void * const cb_data
+) {
+  // read shape
+  km_shape_t shape = { 0, 0 };
+  if (fscanf(fh, "%zu %zu", &(shape.num_floats), &(shape.num_ints)) != 2) {
+    FAIL("shape fscanf() failed: %s", strerror(errno));
+  }
+
+  if (cbs && cbs->on_shape) {
+    // emit shape
+    if (!cbs->on_shape(&shape, cb_data)) {
+      // return failure
+      return false;
+    }
+  }
+
+  // alloc floats buffer
+  float *floats = NULL;
+  if (shape.num_floats > 0) {
+    floats = malloc(sizeof(float) * shape.num_floats);
+    if (!floats) {
+      FAIL("floats malloc() failed: %s", strerror(errno));
+    }
+  }
+
+  // alloc ints buffer
+  int *ints = NULL;
+  if (shape.num_ints > 0) {
+    ints = malloc(sizeof(int) * shape.num_ints);
+    if (!ints) {
+      FAIL("ints malloc() failed: %s", strerror(errno));
+    }
+  }
+
+  for (size_t row = 0; !feof(fh); row++) {
+    for (size_t i = 0; i < shape.num_floats; i++) {
+      if (fscanf(fh, " %f ", floats + i) != 1) {
+        FAIL("[%zu, %zu] float fscanf() failed: %s", row, i, strerror(errno));
+      }
+    }
+
+    // read ints
+    for (size_t i = 0; i < shape.num_ints; i++) {
+      if (fscanf(fh, " %d ", ints + i) != 1) {
+        FAIL("[%zu, %zu] int fscanf() failed: %s", row, i, strerror(errno));
+      }
+    }
+
+    if (cbs && cbs->on_row) {
+      // emit row
+      if (!cbs->on_row(floats, ints, cb_data)) {
+        // return failure
+        return false;
+      }
+    }
+  }
+
+  if (shape.num_floats > 0) {
+    // free float buffer
+    free(floats);
+  }
+
+  if (shape.num_ints > 0) {
+    // free int buffer
+    free(ints);
+  }
+
+  // return success
+  return true;
+}
+
+_Bool
+km_load_path(
+  const char * const path,
+  const km_load_cbs_t * const cbs,
+  void * const cb_data
+) {
+  // open file
+  FILE *fh = fopen(path, "rb");
+  if (!fh) {
+    FAIL("fopen(\"%s\") failed: %s", path, strerror(errno));
+  }
+
+  // load file, get result
+  const bool r = km_load(fh, cbs, cb_data);
+
+  // close file
+  fclose(fh);
+
+  // return result
+  return r;
+}
diff --git a/km-rand-src.c b/km-rand-src.c
new file mode 100644
index 0000000..0ddc1bb
--- /dev/null
+++ b/km-rand-src.c
@@ -0,0 +1,57 @@
+#include <stdbool.h>
+#include "util.h"
+#include "km.h"
+
+// fill buffer with N random floats
+bool
+km_rand_src_fill(
+  km_rand_src_t * const rs,
+  const size_t num_floats,
+  float * const floats
+) {
+  return rs->cbs->fill(rs, num_floats, floats);
+}
+
+// finalize random source
+void
+km_rand_src_fini(
+  km_rand_src_t * const rs
+) {
+  if (rs->cbs->fini) {
+    rs->cbs->fini(rs);
+  }
+}
+
+// fill callback for system random source
+static bool
+rand_src_system_on_fill(
+  km_rand_src_t * const rs,
+  const size_t num_floats,
+  float * const floats
+) {
+  UNUSED(rs);
+
+  // generate random cluster centers
+  for (size_t i = 0; i < num_floats; i++) {
+    floats[i] = 1.0 * rand() / RAND_MAX;
+  }
+
+  // return success
+  return true;
+}
+
+// system random source callbacks
+static const km_rand_src_cbs_t
+RAND_SRC_SYSTEM_CBS = {
+  .fill = rand_src_system_on_fill,
+  .fini = NULL,
+};
+
+// init system random source (uses system rand())
+void
+km_rand_src_system_init(
+  km_rand_src_t * const rs
+) {
+  rs->cbs = &RAND_SRC_SYSTEM_CBS;
+  rs->data = NULL;
+}
diff --git a/km-solve.c b/km-solve.c
new file mode 100644
index 0000000..4560c67
--- /dev/null
+++ b/km-solve.c
@@ -0,0 +1,193 @@
+#include <stdbool.h> // bool
+#include <string.h> // memset()
+#include <float.h> // FLT_MAX
+#include <math.h> // sqrt()
+#include "util.h"
+#include "km.h"
+
+// calculate squared euclidean distance between two points
+static float
+distance_squared(
+  const size_t num_floats,
+  const float * const a,
+  const float * const b
+) {
+  float r = 0.0;
+
+  for (size_t i = 0; i < num_floats; i++) {
+    r += (b[i] - a[i]) * (b[i] - a[i]);
+  }
+
+  // return squared distance
+  return r;
+}
+
+// alloc and initialize row map
+static km_row_map_t *
+km_row_map_init(
+  const size_t num_rows
+) {
+  // alloc row map
+  km_row_map_t * const row_map = malloc(sizeof(km_row_map_t) * num_rows);
+
+  // check for error
+  if (!row_map) {
+    // return failure
+    return false;
+  }
+
+  // init row map by setting the maximum distance
+  for (size_t i = 0; i < num_rows; i++) {
+    row_map[i].d2 = FLT_MAX;
+  }
+
+  // return row map
+  return row_map;
+}
+
+static void
+km_row_map_fini(
+  km_row_map_t * const row_map
+) {
+  free(row_map);
+}
+
+// use k-means to iteratively update the cluster centroids until there
+// are no more changes to the centroids
+bool
+km_solve(
+  km_set_t * const cs,
+  const km_set_t * const set,
+  const km_solve_cbs_t * const cbs,
+  void * const cb_data
+) {
+  const size_t num_clusters = cs->num_rows,
+               num_floats = set->shape.num_floats;
+
+  // row map: row => distance, cluster ID
+  km_row_map_t *row_map = km_row_map_init(set->num_rows);
+  if (!row_map) {
+    // return failure
+    return false;
+  }
+
+  // calculate clusters by doing the following:
+  //   * walk all clusters and all rows
+  //   * if we find a closer cluster, move row to cluster
+  //   * if there were changes to any cluster, then calculate a new
+  //     centroid for each cluster by averaging the cluster rows
+  //   * repeat until there are no more changes
+  bool changed = false;
+  do {
+    // no changes yet
+    changed = false;
+
+    for (size_t i = 0; i < num_clusters; i++) {
+      // get the floats for this cluster
+      const float * const floats = km_set_get_row(cs, i);
+
+      for (size_t j = 0; j < set->num_rows; j++) {
+        const float * const row_floats = km_set_get_row(set, j);
+
+        // calculate the distance squared between these clusters
+        const float d2 = distance_squared(num_floats, floats, row_floats);
+
+        if (d2 < row_map[j].d2) {
+          // row is closer to this cluster, update distance and cluster
+          row_map[j].d2 = d2;
+          row_map[j].cluster = i;
+
+          // flag change
+          changed = true;
+        }
+      }
+    }
+
+    if (changed) {
+      // if there were changes, then we need to calculate the new
+      // cluster centers
+
+      // calculate new center
+      for (size_t i = 0; i < num_clusters; i++) {
+        size_t num_rows = 0;
+        float * const floats = km_set_get_row(cs, i);
+        memset(floats, 0, sizeof(float) * num_floats);
+
+        for (size_t j = 0; j < set->num_rows; j++) {
+          const float * const row_floats = km_set_get_row(set, j);
+
+          if (row_map[j].cluster == i) {
+            // calculate numerator for average
+            for (size_t k = 0; k < num_floats; k++) {
+              floats[k] += row_floats[k];
+            }
+
+            // increment denominator for average
+            num_rows++;
+          }
+        }
+
+        // save number of rows in this cluster
+        cs->ints[i] = num_rows;
+
+        if (num_rows > 0) {
+          for (size_t k = 0; k < num_floats; k++) {
+            // divide by denominator to get average
+            floats[k] /= num_rows;
+          }
+        }
+      }
+    }
+
+    if (cbs && cbs->on_step) {
+      // pass clusters and row map to step callback
+      cbs->on_step(cs, row_map, cb_data);
+    }
+  } while (changed);
+
+  if (cbs && cbs->on_stats) {
+    float means[num_clusters],
+          variances[num_clusters];
+    memset(means, 0, sizeof(float) * num_clusters);
+    memset(variances, 0, sizeof(float) * num_clusters);
+
+    // calculate mean distances
+    for (size_t i = 0; i < set->num_rows; i++) {
+      means[row_map[i].cluster] += row_map[i].d2;
+    }
+
+    // finalize means
+    for (size_t i = 0; i < num_clusters; i++) {
+      means[i] = (cs->ints[i]) ? (sqrt(means[i]) / cs->ints[i]) : 0;
+    }
+
+    // calculate variances
+    for (size_t i = 0; i < set->num_rows; i++) {
+      const size_t cluster = row_map[i].cluster;
+      const float variance = (sqrt(row_map[i].d2) - means[cluster]) *
+                             (sqrt(row_map[i].d2) - means[cluster]);
+      variances[cluster] += variance;
+    }
+
+    // finalize variances
+    for (size_t i = 0; i < num_clusters; i++) {
+      variances[i] = (cs->ints[i]) ? (variances[i] / cs->ints[i]) : 0;
+    }
+
+    // build stats
+    const km_solve_stats_t stats = {
+      .means        = means,
+      .variances    = variances,
+      .num_clusters = num_clusters,
+    };
+
+    // emit means
+    cbs->on_stats(cs, &stats, cb_data);
+  }
+
+  // free row_map
+  km_row_map_fini(row_map);
+
+  // return success
+  return true;
+}
diff --git a/km.c b/km.c
index 135132b..5b9ae4c 100644
--- a/km.c
+++ b/km.c
@@ -2,85 +2,10 @@
 #include <stdint.h> // size_t
 #include <string.h> // memcpy()
 #include <stdlib.h> // rand()
-#include <float.h> // FLT_MAX
-#include <math.h> // sqrt()
+#include "util.h"
 #include "km.h"
 
 #define MIN_ROWS (4096 / sizeof(float))
-#define MAX(a, b) ((a) > (b) ? (a) : (b))
-#define UNUSED(a) ((void) (a))
-#define MIN_CLUSTER_DISTANCE 0.0001
-
-// calculate squared euclidean distance between two points
-static float
-distance_squared(
-  const size_t num_floats,
-  const float * const a,
-  const float * const b
-) {
-  float r = 0.0;
-
-  for (size_t i = 0; i < num_floats; i++) {
-    r += (b[i] - a[i]) * (b[i] - a[i]);
-  }
-
-  // return squared distance
-  return r;
-}
-
-// fill buffer with N random floats
-bool
-km_rand_src_fill(
-  km_rand_src_t * const rs,
-  const size_t num_floats,
-  float * const floats
-) {
-  return rs->cbs->fill(rs, num_floats, floats);
-}
-
-// finalize random source
-void
-km_rand_src_fini(
-  km_rand_src_t * const rs
-) {
-  if (rs->cbs->fini) {
-    rs->cbs->fini(rs);
-  }
-}
-
-// fill callback for system random source
-static bool
-rand_src_system_on_fill(
-  km_rand_src_t * const rs,
-  const size_t num_floats,
-  float * const floats
-) {
-  UNUSED(rs);
-
-  // generate random cluster centers
-  for (size_t i = 0; i < num_floats; i++) {
-    floats[i] = 1.0 * rand() / RAND_MAX;
-  }
-
-  // return success
-  return true;
-}
-
-// system random source callbacks
-static const km_rand_src_cbs_t
-RAND_SRC_SYSTEM_CBS = {
-  .fill = rand_src_system_on_fill,
-  .fini = NULL,
-};
-
-// init system random source (uses system rand())
-void
-km_rand_src_system_init(
-  km_rand_src_t * const rs
-) {
-  rs->cbs = &RAND_SRC_SYSTEM_CBS;
-  rs->data = NULL;
-}
 
 // grow data set
 static bool
@@ -104,6 +29,7 @@ km_set_grow(
     return false;
   }
 
+  // update set
   set->floats = floats;
   set->ints = ints;
   set->capacity = capacity;
@@ -119,11 +45,20 @@ km_set_init(
   const km_shape_t * const shape,
   const size_t row_capacity
 ) {
+  // alloc bounds
+  float * const bounds = malloc(2 * sizeof(float) * shape->num_floats);
+  if (!bounds) {
+    // return error
+    return false;
+  }
+
+  set->state = KM_SET_STATE_INIT;
   set->floats = NULL;
   set->ints = NULL;
   set->shape = *shape;
   set->num_rows = 0;
   set->capacity = 0;
+  set->bounds = bounds;
 
   return km_set_grow(set, MAX(MIN_ROWS, row_capacity + 1));
 }
@@ -131,6 +66,16 @@ km_set_init(
 // finalize data set
 void
 km_set_fini(km_set_t * const set) {
+  if (set->state == KM_SET_STATE_FINI) {
+    return;
+  }
+
+  if (set->bounds) {
+    // free bounds
+    free(set->bounds);
+    set->bounds = NULL;
+  }
+
   if (set->floats) {
     // free floats
     free(set->floats);
@@ -145,16 +90,25 @@ km_set_fini(km_set_t * const set) {
 
   // shrink capacity
   set->capacity = 0;
+
+  // set state
+  set->state = KM_SET_STATE_FINI;
 }
 
 // append rows to data set, growing set if necessary
 bool
-km_set_push_rows(
+km_set_push(
   km_set_t * const set,
   const size_t num_rows,
   const float * const floats,
   const int * const ints
 ) {
+  // check state
+  if (set->state != KM_SET_STATE_INIT) {
+    // return failure
+    return false;
+  }
+
   const size_t capacity_needed = set->num_rows + num_rows;
   // FIXME: potential overflow here
   if (capacity_needed >= set->capacity) {
@@ -175,6 +129,28 @@ km_set_push_rows(
 
     // copy floats
     memcpy(dst, floats, stride * num_rows);
+
+    if (!set->num_rows) {
+      // there were no rows, so populate bounds with first row
+      memcpy(set->bounds, floats, stride);
+      memcpy(set->bounds + num_floats, floats, stride);
+    }
+
+    for (size_t i = 0; i < num_rows; i++) {
+      for (size_t j = 0; j < num_floats; j++) {
+        const float val = floats[i * num_floats + j];
+
+        if (val < set->bounds[j]) {
+          // update min bound
+          set->bounds[j] = val;
+        }
+
+        if (val > set->bounds[num_floats + j]) {
+          // update max bound
+          set->bounds[num_floats + j] = val;
+        }
+      }
+    }
   }
 
   // copy ints
@@ -194,6 +170,38 @@ km_set_push_rows(
   return true;
 }
 
+bool
+km_set_normalize(
+  km_set_t * const set
+) {
+  const size_t num_floats = set->shape.num_floats;
+
+  // check set state
+  if (set->state != KM_SET_STATE_INIT) {
+    // return failure
+    return false;
+  }
+
+  // normalize values
+  for (size_t i = 0; i < set->num_rows; i++) {
+    for (size_t j = 0; j < num_floats; j++) {
+      const size_t ofs = i * num_floats + j;
+      const float val = set->floats[ofs],
+                  min = set->bounds[j],
+                  max = set->bounds[num_floats + j];
+
+      // normalize and write value
+      set->floats[ofs] = (val - min) / (max - min);
+    }
+  }
+
+  // set state
+  set->state = KM_SET_STATE_NORMALIZED;
+
+  // return success
+  return true;
+}
+
 // get row from data set
 float *
 km_set_get_row(
@@ -204,15 +212,10 @@ km_set_get_row(
   return set->floats + i * num_floats;
 }
 
-typedef struct {
-  float d2;
-  size_t cluster;
-} row_map_item_t;
-
-// init a cluster set of size N from a data set by picking random
-// cluster centers
+// init a set with num_clusters clusters of shape num_floats by picking
+// random cluster centers
 bool
-km_clusters_rand_init(
+km_set_init_rand_clusters(
   km_set_t * const cs,
   const size_t num_floats,
   const size_t num_clusters,
@@ -242,217 +245,5 @@ km_clusters_rand_init(
   }
 
   // add data, return result
-  return km_set_push_rows(cs, num_clusters, floats, ints);
-}
-
-// use k-means to iteratively update the cluster centroids until there
-// are no more changes to the centroids
-bool
-km_clusters_solve(
-  km_set_t * const cs,
-  const km_set_t * const set,
-  const km_clusters_solve_cbs_t * const cbs,
-  void * const cb_data
-) {
-  const size_t num_clusters = cs->num_rows,
-               num_floats = set->shape.num_floats;
-
-  // row map: row => distance, cluster ID
-  row_map_item_t *row_map = malloc(sizeof(row_map_item_t) * set->num_rows);
-  if (!row_map) {
-    // return failure
-    return false;
-  }
-
-  // init row map by setting the maximum distance
-  for (size_t i = 0; i < set->num_rows; i++) {
-    row_map[i].d2 = FLT_MAX;
-  }
-
-  // calculate clusters by doing the following:
-  //   * walk all clusters and all rows
-  //   * if we find a closer cluster, move row to cluster
-  //   * if there were changes to any cluster, then calculate a new
-  //     centroid for each cluster by averaging the cluster rows
-  //   * repeat until there are no more changes
-  bool changed = false;
-  do {
-    // no changes yet
-    changed = false;
-
-    for (size_t i = 0; i < num_clusters; i++) {
-      // get the floats for this cluster
-      const float * const floats = km_set_get_row(cs, i);
-
-      for (size_t j = 0; j < set->num_rows; j++) {
-        const float * const row_floats = km_set_get_row(set, j);
-
-        // calculate the distance squared between these clusters
-        const float d2 = distance_squared(num_floats, floats, row_floats);
-
-        if (d2 < row_map[j].d2) {
-          // row is closer to this cluster, update distance and cluster
-          row_map[j].d2 = d2;
-          row_map[j].cluster = i;
-
-          // flag change
-          changed = true;
-        }
-      }
-    }
-
-    if (changed) {
-      // if there were changes, then we need to calculate the new
-      // cluster centers
-
-      // calculate new center
-      for (size_t i = 0; i < num_clusters; i++) {
-        size_t num_rows = 0;
-        float * const floats = km_set_get_row(cs, i);
-        memset(floats, 0, sizeof(float) * num_floats);
-
-        for (size_t j = 0; j < set->num_rows; j++) {
-          const float * const row_floats = km_set_get_row(set, j);
-
-          if (row_map[j].cluster == i) {
-            // calculate numerator for average
-            for (size_t k = 0; k < num_floats; k++) {
-              floats[k] += row_floats[k];
-            }
-
-            // increment denominator for average
-            num_rows++;
-          }
-        }
-
-        // save number of rows in this cluster
-        cs->ints[i] = num_rows;
-
-        if (num_rows > 0) {
-          for (size_t k = 0; k < num_floats; k++) {
-            // divide by denominator to get average
-            floats[k] /= num_rows;
-          }
-        }
-      }
-    }
-
-    if (cbs && cbs->on_step) {
-      // pass clusters to step callback
-      cbs->on_step(cs, cb_data);
-    }
-  } while (changed);
-
-  if (cbs && cbs->on_step) {
-    float means[num_clusters];
-    memset(means, 0, sizeof(float) * num_clusters);
-
-    // calculate mean distances
-    for (size_t i = 0; i < set->num_rows; i++) {
-      means[row_map[i].cluster] += row_map[i].d2;
-    }
-
-    // calculate mean distances
-    for (size_t i = 0; i < num_clusters; i++) {
-      means[i] = (cs->ints[i]) ? (sqrt(means[i]) / cs->ints[i]) : 0;
-    }
-
-    // emit means
-    cbs->on_means(cs, means, num_clusters, cb_data);
-  }
-
-  // free row_map
-  free(row_map);
-
-  // return success
-  return true;
-}
-
-typedef struct {
-  float sum;
-  size_t num_empty_clusters;
-} search_test_data_t;
-
-static void
-search_test_on_means(
-  const km_set_t * const set,
-  const float * const means,
-  const size_t num_clusters,
-  void * const cb_data
-) {
-  search_test_data_t *test_data = cb_data;
-  UNUSED(set);
-
-  // calculate numerator for the average distance across all clusters in
-  // this test
-  for (size_t i = 0; i < num_clusters; i++) {
-    if (fabsf(means[i]) > MIN_CLUSTER_DISTANCE) {
-      test_data->sum += means[i];
-    } else {
-      test_data->num_empty_clusters++;
-    }
-  }
-}
-
-static const km_clusters_solve_cbs_t
-SEARCH_TEST_CBS = {
-  .on_means = search_test_on_means,
-};
-
-bool
-km_search(
-  const km_set_t * const set,
-  const size_t max_clusters,
-  const size_t num_tests,
-  const km_search_row_cb_t on_row,
-  void *cb_data
-) {
-  // init random source
-  km_rand_src_t rs;
-  km_rand_src_system_init(&rs);
-
-  for (size_t i = 2; i < max_clusters; i++) {
-    for (size_t j = 0; j < num_tests; j++) {
-      // init cluster set
-      km_set_t cs;
-      if (!km_clusters_rand_init(&cs, set->shape.num_floats, i, &rs)) {
-        // return failure
-        return false;
-      }
-
-      // init test data
-      search_test_data_t data = {
-        .sum = 0,
-        .num_empty_clusters = 0,
-      };
-
-      // solve test
-      if (!km_clusters_solve(&cs, set, &SEARCH_TEST_CBS, &data)) {
-        // return failure
-        return false;
-      }
-
-      if (on_row) {
-        // calculate mean
-        const float mean = (data.num_empty_clusters < i) ? (data.sum / (i - data.num_empty_clusters)) : 0;
-
-        // init search result row
-        km_search_row_t row = {
-          .cluster_set        = &cs,
-          .num_clusters       = i,
-          .mean_distance      = mean,
-          .num_empty_clusters = data.num_empty_clusters,
-        };
-
-        // emit row
-        on_row(&row, cb_data);
-      }
-
-      // free cluster set
-      km_set_fini(&cs);
-    }
-  }
-
-  // return success
-  return true;
+  return km_set_push(cs, num_clusters, floats, ints);
 }
diff --git a/km.h b/km.h
index 0c49832..642560b 100644
--- a/km.h
+++ b/km.h
@@ -2,6 +2,8 @@
 #define KM_H
 
 #include <stddef.h> // size_t
+#include <stdint.h> // uint8_t
+#include <stdio.h> // FILE
 
 // forward typedef for callbacks
 typedef struct km_rand_src_t_ km_rand_src_t;
@@ -33,9 +35,19 @@ typedef struct {
          num_ints;
 } km_shape_t;
 
+typedef enum {
+  KM_SET_STATE_INIT,
+  KM_SET_STATE_NORMALIZED,
+  KM_SET_STATE_FINI,
+  KM_SET_STATE_LAST,
+} km_set_state_t;
+
 // data set
 typedef struct {
-  float *floats;
+  km_set_state_t state;
+
+  float *floats,
+        *bounds;
   int *ints;
 
   km_shape_t shape;
@@ -50,14 +62,28 @@ _Bool km_set_init(km_set_t * const, const km_shape_t *, const size_t);
 void km_set_fini(km_set_t * const);
 
 // append rows to data set, growing set if necessary
-_Bool km_set_push_rows(km_set_t *, const size_t, const float *, const int *);
+_Bool km_set_push(km_set_t *, const size_t, const float *, const int *);
 
-// get row from data set
+// normalize data set
+_Bool km_set_normalize(km_set_t * const);
+
+// get pointer to data set row
 float *km_set_get_row(const km_set_t *, const size_t);
 
-// init a cluster set of size N from a data set by picking random
-// cluster centers
-_Bool km_clusters_rand_init(
+typedef struct {
+  float d2;
+  size_t cluster;
+} km_row_map_t;
+
+typedef struct {
+  const float *means;
+  const float *variances;
+  const size_t num_clusters;
+} km_solve_stats_t;
+
+// init a set with num_clusters clusters of shape num_floats by picking
+// random cluster centers
+_Bool km_set_init_rand_clusters(
   km_set_t *,
   const size_t,
   const size_t,
@@ -65,40 +91,96 @@ _Bool km_clusters_rand_init(
 );
 
 typedef struct {
-  void (*on_step)(const km_set_t *, void *);
-  void (*on_means)(const km_set_t *, const float *, const size_t, void *);
-} km_clusters_solve_cbs_t;
+  void (*on_step)(const km_set_t *, const km_row_map_t *, void *);
+  void (*on_stats)(const km_set_t *, const km_solve_stats_t *, void *);
+} km_solve_cbs_t;
 
 // use k-means to iteratively update the cluster centroids until there
 // are no more changes to the centroids
 _Bool
-km_clusters_solve(
+km_solve(
   km_set_t * const,
   const km_set_t * const,
-  const km_clusters_solve_cbs_t * const,
+  const km_solve_cbs_t * const,
   void * const
 );
 
 typedef struct {
   const km_set_t * const cluster_set;
-  const size_t num_clusters;
-  const float mean_distance;
-  const size_t num_empty_clusters;
-} km_search_row_t;
 
-typedef void (*km_search_row_cb_t)(
-  const km_search_row_t * const,
+  const float mean_distance,
+              mean_variance,
+              mean_cluster_size;
+
+  const size_t num_clusters,
+               num_empty_clusters;
+} km_find_data_t;
+
+typedef _Bool (*km_find_init_cb_t)(
+  km_set_t * const cluster_set,
+  const size_t num_floats,
+  const size_t num_clusters,
+  void *cb_data
+);
+
+typedef _Bool (*km_find_fini_cb_t)(
+  km_set_t * const cluster_set,
+  void *cb_data
+);
+
+typedef void (*km_find_data_cb_t)(
+  const km_find_data_t * const,
   void *
 );
 
+typedef struct {
+  size_t max_clusters;
+  size_t num_tests;
+  km_rand_src_t *rand_src;
+
+  km_find_init_cb_t on_init;
+  km_find_fini_cb_t on_fini;
+  km_find_data_cb_t on_data;
+} km_find_cbs_t;
+
 // repeatedly test different cluster sizes and report results
 _Bool
-km_search(
+km_find(
   const km_set_t * const set,
-  const size_t max_clusters,
-  const size_t num_tests,
-  const km_search_row_cb_t on_row,
-  void *cb_data
+  const km_find_cbs_t * const cbs,
+  void * const cb_data
+);
+
+// render set to rgb buffer
+void
+km_set_draw(
+  const km_set_t * const set,
+  uint8_t * const rgb,
+  const size_t width,
+  const size_t height,
+  const uint32_t color
+);
+
+// load callbacks
+typedef struct {
+  _Bool (*on_shape)(const km_shape_t * const, void *);
+  _Bool (*on_row)(const float *, const int *, void *);
+  void (*on_error)(const char * const, void *);
+} km_load_cbs_t;
+
+// load set from file
+_Bool
+km_load(
+  FILE * const fh,
+  const km_load_cbs_t * const cbs,
+  void * const cb_data
+);
+
+_Bool
+km_load_path(
+  const char * const path,
+  const km_load_cbs_t * const cbs,
+  void * const cb_data
 );
 
 #endif /* KM_H */
diff --git a/main.c b/main.c
index 143c14a..bd4192f 100644
--- a/main.c
+++ b/main.c
@@ -1,88 +1,248 @@
+#include <stdbool.h> // bool
 #include <stdio.h> // fprintf()
 #include <unistd.h> // EXIT_{FAILURE,SUCCESS}
 #include <stdlib.h> // exit()
-#include "km.h"
+#include <string.h> // memset()
+#include <math.h>  // fabsf()
 
-#define UNUSED(a) ((void) (a))
-
-// >> puts [[-1, -1], [-1, 1], [1, 1], [1, -1]].reduce([]) { |r, c| 5.times { r << [0.5 + 0.25 * c[0] + 0.4 * rand - 0.2, 0.5 + 0.25 * c[1] + 0.4 * rand - 0.2] }; r }.map { |row| '%1.3f, %1.3f,' % row }
-static const float
-DATA[] = {
-	0.132, 0.190,
-	0.313, 0.187,
-	0.076, 0.276,
-	0.443, 0.414,
-	0.136, 0.060,
-	0.344, 0.815,
-	0.259, 0.760,
-	0.211, 0.949,
-	0.103, 0.903,
-	0.173, 0.818,
-	0.873, 0.735,
-	0.783, 0.593,
-	0.845, 0.674,
-	0.808, 0.868,
-	0.871, 0.947,
-	0.917, 0.090,
-	0.691, 0.058,
-	0.840, 0.357,
-	0.783, 0.275,
-	0.807, 0.336,
-};
+#define STB_IMAGE_WRITE_IMPLEMENTATION
+#define STB_ONLY_PNG
+#include "stb_image_write.h"
 
-#define die(...) do { \
-  fputs("FATAL: ", stderr); \
-  fprintf(stderr, __VA_ARGS__); \
-  fputs("\n", stderr); \
-  exit(EXIT_FAILURE); \
-} while (0)
+#include "util.h"
+#include "km.h"
 
 #define MAX_CLUSTERS 10
-#define NUM_TESTS 10
+#define NUM_TESTS 100
 
-static const km_shape_t
-SHAPE = {
-  .num_floats = 2,
-  .num_ints = 0,
-};
+typedef struct {
+  km_rand_src_t rs;
+
+  struct {
+    float distance,
+          variance,
+          cluster_size;
+    size_t num_empty_clusters;
+  } rows[MAX_CLUSTERS - 2];
+} find_t;
+
+static bool
+load_on_shape(
+  const km_shape_t * const shape,
+  void * const cb_data
+) {
+  km_set_t * const set = cb_data;
+
+  fprintf(stderr, "DEBUG: shape = { %zu, %zu }\n", shape->num_floats, shape->num_ints);
+
+  // init set
+  if (!km_set_init(set, shape, 100)) {
+    die("km_set_init() failed");
+  }
+
+  // return success
+  return true;
+}
+
+static bool
+load_on_row(
+  const float * const floats,
+  const int * const ints,
+  void * const cb_data
+) {
+  km_set_t * const set = cb_data;
+
+  // push row
+  if (!km_set_push(set, 1, floats, ints)) {
+    die("km_set_push_rows() failed");
+  }
+
+  // return success
+  return true;
+}
 
 static void
-on_search_row(
-  const km_search_row_t * const row,
+load_on_error(
+  const char * const err,
+  void * const cb_data
+) {
+  UNUSED(cb_data);
+  die(err);
+}
+
+static const km_load_cbs_t
+LOAD_CBS = {
+  .on_shape = load_on_shape,
+  .on_row   = load_on_row,
+  .on_error = load_on_error,
+};
+
+static bool
+find_on_init(
+  km_set_t * const cs,
+  const size_t num_floats,
+  const size_t num_clusters,
+  void *cb_data
+) {
+  find_t *data = cb_data;
+  return km_set_init_rand_clusters(cs, num_floats, num_clusters, &(data->rs));
+}
+
+static bool
+find_on_fini(
+  km_set_t * const cs,
   void *cb_data
 ) {
   UNUSED(cb_data);
+  km_set_fini(cs);
+  return true;
+}
+
+static void
+find_on_data(
+  const km_find_data_t * const data,
+  void *cb_data
+) {
+  find_t * const find_data = cb_data;
+  const size_t ofs = data->num_clusters - 2;
+
+  find_data->rows[ofs].distance += data->mean_distance;
+  find_data->rows[ofs].variance += data->mean_variance;
+  find_data->rows[ofs].cluster_size += data->mean_cluster_size;
+  find_data->rows[ofs].num_empty_clusters += data->num_empty_clusters;
+}
 
-  printf("%zu,%0.5f,%zu\n",
-    row->num_clusters,
-    row->mean_distance,
-    row->num_empty_clusters
+// init find config
+static const km_find_cbs_t
+FIND_CBS = {
+  .max_clusters = MAX_CLUSTERS,
+  .num_tests    = NUM_TESTS,
+  .on_init      = find_on_init,
+  .on_fini      = find_on_fini,
+  .on_data      = find_on_data,
+};
+
+static float
+get_score(
+  const size_t ofs,
+  const find_t * const find_data
+) {
+  if (!ofs || ofs == MAX_CLUSTERS - 3) {
+    return 0;
+  }
+  // const size_t num_clusters = ofs + 2;
+  const float mean_empty_clusters = 1.0 * find_data->rows[ofs].num_empty_clusters / NUM_TESTS;
+
+  const float ds[3] = {
+    find_data->rows[ofs - 1].distance / NUM_TESTS,
+    find_data->rows[ofs + 0].distance / NUM_TESTS,
+    find_data->rows[ofs + 1].distance / NUM_TESTS,
+  };
+
+  return (
+    (fabsf(ds[0] - ds[1]) / fabsf(ds[1] - ds[2])) +
+    -2.0 * mean_empty_clusters
+  );
+}
+
+static void
+print_csv_row(
+  const size_t i,
+  const find_t * const find_data
+) {
+  const size_t num_clusters = i + 2;
+  const float mean_distance = find_data->rows[i].distance / NUM_TESTS,
+              mean_variance = find_data->rows[i].variance / NUM_TESTS,
+              mean_cluster_size = find_data->rows[i].cluster_size / NUM_TESTS,
+              mean_empty_clusters = 1.0 * find_data->rows[i].num_empty_clusters / NUM_TESTS;
+
+  // print result
+  printf("%zu,%0.3f,%0.3f,%0.3f,%0.3f,%0.3f\n",
+    num_clusters,
+    get_score(i, find_data),
+    mean_distance,
+    mean_variance,
+    mean_cluster_size,
+    mean_empty_clusters
+  );
+}
+
+static void
+print_csv(
+  const find_t * const find_data
+) {
+  // print headers
+  printf(
+    "#,"
+    "score,"
+    "distance,"
+    "variance,"
+    "cluster_size,"
+    "empty_clusters\n"
   );
+
+  for (size_t i = 0; i < MAX_CLUSTERS - 2; i++) {
+    print_csv_row(i, find_data);
+  }
+}
+
+#define IM_WIDTH 128
+#define IM_HEIGHT 128
+#define IM_STRIDE (3 * IM_WIDTH)
+
+static uint8_t im_data[3 * IM_WIDTH * IM_HEIGHT];
+
+static void
+save_png(
+  const char * const png_path,
+  const km_set_t * const set
+) {
+  // clear image data to white
+  memset(im_data, 0xff, sizeof(im_data));
+
+  // draw red points
+  km_set_draw(set, im_data, IM_WIDTH, IM_HEIGHT, 0xff0000);
+  if (!stbi_write_png(png_path, IM_WIDTH, IM_HEIGHT, 3, im_data, IM_STRIDE)) {
+    die("stbi_write_png(\"%s\")", png_path);
+  }
 }
 
 int main(int argc, char *argv[]) {
-  km_set_t set;
-  UNUSED(argc);
-  UNUSED(argv);
+  // check command-line
+  if (argc < 2) {
+    fprintf(stderr, "Usage: %s <data>\n", argv[0]);
+    return EXIT_FAILURE;
+  }
+
+  // init random seed
+  srand(getpid());
+
+  // init find data
+  find_t find_data;
+  memset(find_data.rows, 0, sizeof(find_data.rows));
+  km_rand_src_system_init(&(find_data.rs));
 
   // init data set
-  if (!km_set_init(&set, &SHAPE, 20)) {
-    die("km_set_init() failed");
+  km_set_t set;
+  if (!km_load_path(argv[1], &LOAD_CBS, &set)) {
+    die("km_load_path() failed");
   }
 
-  // push rows
-  if (!km_set_push_rows(&set, 20, DATA, NULL)) {
-    die("km_set_push_rows() failed");
+  if (!km_set_normalize(&set)) {
+    die("km_set_normalize() failed");
   }
 
-  // print headers
-  printf("num_clusters,mean_distance,num_empty_clusters\n");
-
-  // search for best solution
-  if (!km_search(&set, MAX_CLUSTERS, NUM_TESTS, on_search_row, NULL)) {
-    die("km_search()");
+  // find best solution
+  if (!km_find(&set, &FIND_CBS, &find_data)) {
+    die("km_find()");
   }
 
+  // print csv
+  print_csv(&find_data);
+
+  // save png of data set
+  save_png("data.png", &set);
+
   // finalize data set
   km_set_fini(&set);
 
diff --git a/stb_image_write.h b/stb_image_write.h
new file mode 100644
index 0000000..c05e958
--- /dev/null
+++ b/stb_image_write.h
@@ -0,0 +1,1568 @@
+/* stb_image_write - v1.09 - public domain - http://nothings.org/stb/stb_image_write.h
+   writes out PNG/BMP/TGA/JPEG/HDR images to C stdio - Sean Barrett 2010-2015
+                                     no warranty implied; use at your own risk
+
+   Before #including,
+
+       #define STB_IMAGE_WRITE_IMPLEMENTATION
+
+   in the file that you want to have the implementation.
+
+   Will probably not work correctly with strict-aliasing optimizations.
+
+   If using a modern Microsoft Compiler, non-safe versions of CRT calls may cause 
+   compilation warnings or even errors. To avoid this, also before #including,
+
+       #define STBI_MSC_SECURE_CRT
+
+ABOUT:
+
+   This header file is a library for writing images to C stdio. It could be
+   adapted to write to memory or a general streaming interface; let me know.
+
+   The PNG output is not optimal; it is 20-50% larger than the file
+   written by a decent optimizing implementation; though providing a custom
+   zlib compress function (see STBIW_ZLIB_COMPRESS) can mitigate that.
+   This library is designed for source code compactness and simplicity,
+   not optimal image file size or run-time performance.
+
+BUILDING:
+
+   You can #define STBIW_ASSERT(x) before the #include to avoid using assert.h.
+   You can #define STBIW_MALLOC(), STBIW_REALLOC(), and STBIW_FREE() to replace
+   malloc,realloc,free.
+   You can #define STBIW_MEMMOVE() to replace memmove()
+   You can #define STBIW_ZLIB_COMPRESS to use a custom zlib-style compress function
+   for PNG compression (instead of the builtin one), it must have the following signature:
+   unsigned char * my_compress(unsigned char *data, int data_len, int *out_len, int quality);
+   The returned data will be freed with STBIW_FREE() (free() by default),
+   so it must be heap allocated with STBIW_MALLOC() (malloc() by default),
+
+USAGE:
+
+   There are five functions, one for each image file format:
+
+     int stbi_write_png(char const *filename, int w, int h, int comp, const void *data, int stride_in_bytes);
+     int stbi_write_bmp(char const *filename, int w, int h, int comp, const void *data);
+     int stbi_write_tga(char const *filename, int w, int h, int comp, const void *data);
+     int stbi_write_jpg(char const *filename, int w, int h, int comp, const void *data, int quality);
+     int stbi_write_hdr(char const *filename, int w, int h, int comp, const float *data);
+
+     void stbi_flip_vertically_on_write(int flag); // flag is non-zero to flip data vertically
+
+   There are also five equivalent functions that use an arbitrary write function. You are
+   expected to open/close your file-equivalent before and after calling these:
+
+     int stbi_write_png_to_func(stbi_write_func *func, void *context, int w, int h, int comp, const void  *data, int stride_in_bytes);
+     int stbi_write_bmp_to_func(stbi_write_func *func, void *context, int w, int h, int comp, const void  *data);
+     int stbi_write_tga_to_func(stbi_write_func *func, void *context, int w, int h, int comp, const void  *data);
+     int stbi_write_hdr_to_func(stbi_write_func *func, void *context, int w, int h, int comp, const float *data);
+     int stbi_write_jpg_to_func(stbi_write_func *func, void *context, int x, int y, int comp, const void *data, int quality);
+
+   where the callback is:
+      void stbi_write_func(void *context, void *data, int size);
+
+   You can configure it with these global variables:
+      int stbi_write_tga_with_rle;             // defaults to true; set to 0 to disable RLE
+      int stbi_write_png_compression_level;    // defaults to 8; set to higher for more compression
+      int stbi_write_force_png_filter;         // defaults to -1; set to 0..5 to force a filter mode
+
+
+   You can define STBI_WRITE_NO_STDIO to disable the file variant of these
+   functions, so the library will not use stdio.h at all. However, this will
+   also disable HDR writing, because it requires stdio for formatted output.
+
+   Each function returns 0 on failure and non-0 on success.
+
+   The functions create an image file defined by the parameters. The image
+   is a rectangle of pixels stored from left-to-right, top-to-bottom.
+   Each pixel contains 'comp' channels of data stored interleaved with 8-bits
+   per channel, in the following order: 1=Y, 2=YA, 3=RGB, 4=RGBA. (Y is
+   monochrome color.) The rectangle is 'w' pixels wide and 'h' pixels tall.
+   The *data pointer points to the first byte of the top-left-most pixel.
+   For PNG, "stride_in_bytes" is the distance in bytes from the first byte of
+   a row of pixels to the first byte of the next row of pixels.
+
+   PNG creates output files with the same number of components as the input.
+   The BMP format expands Y to RGB in the file format and does not
+   output alpha.
+
+   PNG supports writing rectangles of data even when the bytes storing rows of
+   data are not consecutive in memory (e.g. sub-rectangles of a larger image),
+   by supplying the stride between the beginning of adjacent rows. The other
+   formats do not. (Thus you cannot write a native-format BMP through the BMP
+   writer, both because it is in BGR order and because it may have padding
+   at the end of the line.)
+
+   PNG allows you to set the deflate compression level by setting the global
+   variable 'stbi_write_png_compression_level' (it defaults to 8).
+
+   HDR expects linear float data. Since the format is always 32-bit rgb(e)
+   data, alpha (if provided) is discarded, and for monochrome data it is
+   replicated across all three channels.
+
+   TGA supports RLE or non-RLE compressed data. To use non-RLE-compressed
+   data, set the global variable 'stbi_write_tga_with_rle' to 0.
+   
+   JPEG does ignore alpha channels in input data; quality is between 1 and 100.
+   Higher quality looks better but results in a bigger image.
+   JPEG baseline (no JPEG progressive).
+
+CREDITS:
+
+
+   Sean Barrett           -    PNG/BMP/TGA 
+   Baldur Karlsson        -    HDR
+   Jean-Sebastien Guay    -    TGA monochrome
+   Tim Kelsey             -    misc enhancements
+   Alan Hickman           -    TGA RLE
+   Emmanuel Julien        -    initial file IO callback implementation
+   Jon Olick              -    original jo_jpeg.cpp code
+   Daniel Gibson          -    integrate JPEG, allow external zlib
+   Aarni Koskela          -    allow choosing PNG filter
+
+   bugfixes:
+      github:Chribba
+      Guillaume Chereau
+      github:jry2
+      github:romigrou
+      Sergio Gonzalez
+      Jonas Karlsson
+      Filip Wasil
+      Thatcher Ulrich
+      github:poppolopoppo
+      Patrick Boettcher
+      github:xeekworx
+      Cap Petschulat
+      Simon Rodriguez
+      Ivan Tikhonov
+      github:ignotion
+      Adam Schackart
+
+LICENSE
+
+  See end of file for license information.
+
+*/
+
+#ifndef INCLUDE_STB_IMAGE_WRITE_H
+#define INCLUDE_STB_IMAGE_WRITE_H
+
+// if STB_IMAGE_WRITE_STATIC causes problems, try defining STBIWDEF to 'inline' or 'static inline'
+#ifndef STBIWDEF
+#ifdef STB_IMAGE_WRITE_STATIC
+#define STBIWDEF  static
+#else
+#ifdef __cplusplus
+#define STBIWDEF  extern "C"
+#else
+#define STBIWDEF  extern
+#endif
+#endif
+#endif
+
+#ifndef STB_IMAGE_WRITE_STATIC  // C++ forbids static forward declarations
+extern int stbi_write_tga_with_rle;
+extern int stbi_write_png_compression_level;
+extern int stbi_write_force_png_filter;
+#endif
+
+#ifndef STBI_WRITE_NO_STDIO
+STBIWDEF int stbi_write_png(char const *filename, int w, int h, int comp, const void  *data, int stride_in_bytes);
+STBIWDEF int stbi_write_bmp(char const *filename, int w, int h, int comp, const void  *data);
+STBIWDEF int stbi_write_tga(char const *filename, int w, int h, int comp, const void  *data);
+STBIWDEF int stbi_write_hdr(char const *filename, int w, int h, int comp, const float *data);
+STBIWDEF int stbi_write_jpg(char const *filename, int x, int y, int comp, const void  *data, int quality);
+#endif
+
+typedef void stbi_write_func(void *context, void *data, int size);
+
+STBIWDEF int stbi_write_png_to_func(stbi_write_func *func, void *context, int w, int h, int comp, const void  *data, int stride_in_bytes);
+STBIWDEF int stbi_write_bmp_to_func(stbi_write_func *func, void *context, int w, int h, int comp, const void  *data);
+STBIWDEF int stbi_write_tga_to_func(stbi_write_func *func, void *context, int w, int h, int comp, const void  *data);
+STBIWDEF int stbi_write_hdr_to_func(stbi_write_func *func, void *context, int w, int h, int comp, const float *data);
+STBIWDEF int stbi_write_jpg_to_func(stbi_write_func *func, void *context, int x, int y, int comp, const void  *data, int quality);
+
+STBIWDEF void stbi_flip_vertically_on_write(int flip_boolean);
+
+#endif//INCLUDE_STB_IMAGE_WRITE_H
+
+#ifdef STB_IMAGE_WRITE_IMPLEMENTATION
+
+#ifdef _WIN32
+   #ifndef _CRT_SECURE_NO_WARNINGS
+   #define _CRT_SECURE_NO_WARNINGS
+   #endif
+   #ifndef _CRT_NONSTDC_NO_DEPRECATE
+   #define _CRT_NONSTDC_NO_DEPRECATE
+   #endif
+#endif
+
+#ifndef STBI_WRITE_NO_STDIO
+#include <stdio.h>
+#endif // STBI_WRITE_NO_STDIO
+
+#include <stdarg.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+
+#if defined(STBIW_MALLOC) && defined(STBIW_FREE) && (defined(STBIW_REALLOC) || defined(STBIW_REALLOC_SIZED))
+// ok
+#elif !defined(STBIW_MALLOC) && !defined(STBIW_FREE) && !defined(STBIW_REALLOC) && !defined(STBIW_REALLOC_SIZED)
+// ok
+#else
+#error "Must define all or none of STBIW_MALLOC, STBIW_FREE, and STBIW_REALLOC (or STBIW_REALLOC_SIZED)."
+#endif
+
+#ifndef STBIW_MALLOC
+#define STBIW_MALLOC(sz)        malloc(sz)
+#define STBIW_REALLOC(p,newsz)  realloc(p,newsz)
+#define STBIW_FREE(p)           free(p)
+#endif
+
+#ifndef STBIW_REALLOC_SIZED
+#define STBIW_REALLOC_SIZED(p,oldsz,newsz) STBIW_REALLOC(p,newsz)
+#endif
+
+
+#ifndef STBIW_MEMMOVE
+#define STBIW_MEMMOVE(a,b,sz) memmove(a,b,sz)
+#endif
+
+
+#ifndef STBIW_ASSERT
+#include <assert.h>
+#define STBIW_ASSERT(x) assert(x)
+#endif
+
+#define STBIW_UCHAR(x) (unsigned char) ((x) & 0xff)
+
+#ifdef STB_IMAGE_WRITE_STATIC
+static int stbi__flip_vertically_on_write=0;
+static int stbi_write_png_compression_level = 8;
+static int stbi_write_tga_with_rle = 1;
+static int stbi_write_force_png_filter = -1;
+#else
+int stbi_write_png_compression_level = 8;
+int stbi__flip_vertically_on_write=0;
+int stbi_write_tga_with_rle = 1;
+int stbi_write_force_png_filter = -1;
+#endif
+
+STBIWDEF void stbi_flip_vertically_on_write(int flag)
+{
+   stbi__flip_vertically_on_write = flag;
+}
+
+typedef struct
+{
+   stbi_write_func *func;
+   void *context;
+} stbi__write_context;
+
+// initialize a callback-based context
+static void stbi__start_write_callbacks(stbi__write_context *s, stbi_write_func *c, void *context)
+{
+   s->func    = c;
+   s->context = context;
+}
+
+#ifndef STBI_WRITE_NO_STDIO
+
+static void stbi__stdio_write(void *context, void *data, int size)
+{
+   fwrite(data,1,size,(FILE*) context);
+}
+
+static int stbi__start_write_file(stbi__write_context *s, const char *filename)
+{
+   FILE *f;
+#ifdef STBI_MSC_SECURE_CRT
+   if (fopen_s(&f, filename, "wb"))
+      f = NULL;
+#else
+   f = fopen(filename, "wb");
+#endif
+   stbi__start_write_callbacks(s, stbi__stdio_write, (void *) f);
+   return f != NULL;
+}
+
+static void stbi__end_write_file(stbi__write_context *s)
+{
+   fclose((FILE *)s->context);
+}
+
+#endif // !STBI_WRITE_NO_STDIO
+
+typedef unsigned int stbiw_uint32;
+typedef int stb_image_write_test[sizeof(stbiw_uint32)==4 ? 1 : -1];
+
+static void stbiw__writefv(stbi__write_context *s, const char *fmt, va_list v)
+{
+   while (*fmt) {
+      switch (*fmt++) {
+         case ' ': break;
+         case '1': { unsigned char x = STBIW_UCHAR(va_arg(v, int));
+                     s->func(s->context,&x,1);
+                     break; }
+         case '2': { int x = va_arg(v,int);
+                     unsigned char b[2];
+                     b[0] = STBIW_UCHAR(x);
+                     b[1] = STBIW_UCHAR(x>>8);
+                     s->func(s->context,b,2);
+                     break; }
+         case '4': { stbiw_uint32 x = va_arg(v,int);
+                     unsigned char b[4];
+                     b[0]=STBIW_UCHAR(x);
+                     b[1]=STBIW_UCHAR(x>>8);
+                     b[2]=STBIW_UCHAR(x>>16);
+                     b[3]=STBIW_UCHAR(x>>24);
+                     s->func(s->context,b,4);
+                     break; }
+         default:
+            STBIW_ASSERT(0);
+            return;
+      }
+   }
+}
+
+static void stbiw__writef(stbi__write_context *s, const char *fmt, ...)
+{
+   va_list v;
+   va_start(v, fmt);
+   stbiw__writefv(s, fmt, v);
+   va_end(v);
+}
+
+static void stbiw__putc(stbi__write_context *s, unsigned char c)
+{
+   s->func(s->context, &c, 1);
+}
+
+static void stbiw__write3(stbi__write_context *s, unsigned char a, unsigned char b, unsigned char c)
+{
+   unsigned char arr[3];
+   arr[0] = a, arr[1] = b, arr[2] = c;
+   s->func(s->context, arr, 3);
+}
+
+static void stbiw__write_pixel(stbi__write_context *s, int rgb_dir, int comp, int write_alpha, int expand_mono, unsigned char *d)
+{
+   unsigned char bg[3] = { 255, 0, 255}, px[3];
+   int k;
+
+   if (write_alpha < 0)
+      s->func(s->context, &d[comp - 1], 1);
+
+   switch (comp) {
+      case 2: // 2 pixels = mono + alpha, alpha is written separately, so same as 1-channel case
+      case 1:
+         if (expand_mono)
+            stbiw__write3(s, d[0], d[0], d[0]); // monochrome bmp
+         else
+            s->func(s->context, d, 1);  // monochrome TGA
+         break;
+      case 4:
+         if (!write_alpha) {
+            // composite against pink background
+            for (k = 0; k < 3; ++k)
+               px[k] = bg[k] + ((d[k] - bg[k]) * d[3]) / 255;
+            stbiw__write3(s, px[1 - rgb_dir], px[1], px[1 + rgb_dir]);
+            break;
+         }
+         /* FALLTHROUGH */
+      case 3:
+         stbiw__write3(s, d[1 - rgb_dir], d[1], d[1 + rgb_dir]);
+         break;
+   }
+   if (write_alpha > 0)
+      s->func(s->context, &d[comp - 1], 1);
+}
+
+static void stbiw__write_pixels(stbi__write_context *s, int rgb_dir, int vdir, int x, int y, int comp, void *data, int write_alpha, int scanline_pad, int expand_mono)
+{
+   stbiw_uint32 zero = 0;
+   int i,j, j_end;
+
+   if (y <= 0)
+      return;
+
+   if (stbi__flip_vertically_on_write)
+      vdir *= -1;
+
+   if (vdir < 0)
+      j_end = -1, j = y-1;
+   else
+      j_end =  y, j = 0;
+
+   for (; j != j_end; j += vdir) {
+      for (i=0; i < x; ++i) {
+         unsigned char *d = (unsigned char *) data + (j*x+i)*comp;
+         stbiw__write_pixel(s, rgb_dir, comp, write_alpha, expand_mono, d);
+      }
+      s->func(s->context, &zero, scanline_pad);
+   }
+}
+
+static int stbiw__outfile(stbi__write_context *s, int rgb_dir, int vdir, int x, int y, int comp, int expand_mono, void *data, int alpha, int pad, const char *fmt, ...)
+{
+   if (y < 0 || x < 0) {
+      return 0;
+   } else {
+      va_list v;
+      va_start(v, fmt);
+      stbiw__writefv(s, fmt, v);
+      va_end(v);
+      stbiw__write_pixels(s,rgb_dir,vdir,x,y,comp,data,alpha,pad, expand_mono);
+      return 1;
+   }
+}
+
+static int stbi_write_bmp_core(stbi__write_context *s, int x, int y, int comp, const void *data)
+{
+   int pad = (-x*3) & 3;
+   return stbiw__outfile(s,-1,-1,x,y,comp,1,(void *) data,0,pad,
+           "11 4 22 4" "4 44 22 444444",
+           'B', 'M', 14+40+(x*3+pad)*y, 0,0, 14+40,  // file header
+            40, x,y, 1,24, 0,0,0,0,0,0);             // bitmap header
+}
+
+STBIWDEF int stbi_write_bmp_to_func(stbi_write_func *func, void *context, int x, int y, int comp, const void *data)
+{
+   stbi__write_context s;
+   stbi__start_write_callbacks(&s, func, context);
+   return stbi_write_bmp_core(&s, x, y, comp, data);
+}
+
+#ifndef STBI_WRITE_NO_STDIO
+STBIWDEF int stbi_write_bmp(char const *filename, int x, int y, int comp, const void *data)
+{
+   stbi__write_context s;
+   if (stbi__start_write_file(&s,filename)) {
+      int r = stbi_write_bmp_core(&s, x, y, comp, data);
+      stbi__end_write_file(&s);
+      return r;
+   } else
+      return 0;
+}
+#endif //!STBI_WRITE_NO_STDIO
+
+static int stbi_write_tga_core(stbi__write_context *s, int x, int y, int comp, void *data)
+{
+   int has_alpha = (comp == 2 || comp == 4);
+   int colorbytes = has_alpha ? comp-1 : comp;
+   int format = colorbytes < 2 ? 3 : 2; // 3 color channels (RGB/RGBA) = 2, 1 color channel (Y/YA) = 3
+
+   if (y < 0 || x < 0)
+      return 0;
+
+   if (!stbi_write_tga_with_rle) {
+      return stbiw__outfile(s, -1, -1, x, y, comp, 0, (void *) data, has_alpha, 0,
+         "111 221 2222 11", 0, 0, format, 0, 0, 0, 0, 0, x, y, (colorbytes + has_alpha) * 8, has_alpha * 8);
+   } else {
+      int i,j,k;
+      int jend, jdir;
+
+      stbiw__writef(s, "111 221 2222 11", 0,0,format+8, 0,0,0, 0,0,x,y, (colorbytes + has_alpha) * 8, has_alpha * 8);
+
+      if (stbi__flip_vertically_on_write) {
+         j = 0;
+         jend = y;
+         jdir = 1;
+      } else {
+         j = y-1;
+         jend = -1;
+         jdir = -1;
+      }
+      for (; j != jend; j += jdir) {
+         unsigned char *row = (unsigned char *) data + j * x * comp;
+         int len;
+
+         for (i = 0; i < x; i += len) {
+            unsigned char *begin = row + i * comp;
+            int diff = 1;
+            len = 1;
+
+            if (i < x - 1) {
+               ++len;
+               diff = memcmp(begin, row + (i + 1) * comp, comp);
+               if (diff) {
+                  const unsigned char *prev = begin;
+                  for (k = i + 2; k < x && len < 128; ++k) {
+                     if (memcmp(prev, row + k * comp, comp)) {
+                        prev += comp;
+                        ++len;
+                     } else {
+                        --len;
+                        break;
+                     }
+                  }
+               } else {
+                  for (k = i + 2; k < x && len < 128; ++k) {
+                     if (!memcmp(begin, row + k * comp, comp)) {
+                        ++len;
+                     } else {
+                        break;
+                     }
+                  }
+               }
+            }
+
+            if (diff) {
+               unsigned char header = STBIW_UCHAR(len - 1);
+               s->func(s->context, &header, 1);
+               for (k = 0; k < len; ++k) {
+                  stbiw__write_pixel(s, -1, comp, has_alpha, 0, begin + k * comp);
+               }
+            } else {
+               unsigned char header = STBIW_UCHAR(len - 129);
+               s->func(s->context, &header, 1);
+               stbiw__write_pixel(s, -1, comp, has_alpha, 0, begin);
+            }
+         }
+      }
+   }
+   return 1;
+}
+
+STBIWDEF int stbi_write_tga_to_func(stbi_write_func *func, void *context, int x, int y, int comp, const void *data)
+{
+   stbi__write_context s;
+   stbi__start_write_callbacks(&s, func, context);
+   return stbi_write_tga_core(&s, x, y, comp, (void *) data);
+}
+
+#ifndef STBI_WRITE_NO_STDIO
+STBIWDEF int stbi_write_tga(char const *filename, int x, int y, int comp, const void *data)
+{
+   stbi__write_context s;
+   if (stbi__start_write_file(&s,filename)) {
+      int r = stbi_write_tga_core(&s, x, y, comp, (void *) data);
+      stbi__end_write_file(&s);
+      return r;
+   } else
+      return 0;
+}
+#endif
+
+// *************************************************************************************************
+// Radiance RGBE HDR writer
+// by Baldur Karlsson
+
+#define stbiw__max(a, b)  ((a) > (b) ? (a) : (b))
+
+void stbiw__linear_to_rgbe(unsigned char *rgbe, float *linear)
+{
+   int exponent;
+   float maxcomp = stbiw__max(linear[0], stbiw__max(linear[1], linear[2]));
+
+   if (maxcomp < 1e-32f) {
+      rgbe[0] = rgbe[1] = rgbe[2] = rgbe[3] = 0;
+   } else {
+      float normalize = (float) frexp(maxcomp, &exponent) * 256.0f/maxcomp;
+
+      rgbe[0] = (unsigned char)(linear[0] * normalize);
+      rgbe[1] = (unsigned char)(linear[1] * normalize);
+      rgbe[2] = (unsigned char)(linear[2] * normalize);
+      rgbe[3] = (unsigned char)(exponent + 128);
+   }
+}
+
+void stbiw__write_run_data(stbi__write_context *s, int length, unsigned char databyte)
+{
+   unsigned char lengthbyte = STBIW_UCHAR(length+128);
+   STBIW_ASSERT(length+128 <= 255);
+   s->func(s->context, &lengthbyte, 1);
+   s->func(s->context, &databyte, 1);
+}
+
+void stbiw__write_dump_data(stbi__write_context *s, int length, unsigned char *data)
+{
+   unsigned char lengthbyte = STBIW_UCHAR(length);
+   STBIW_ASSERT(length <= 128); // inconsistent with spec but consistent with official code
+   s->func(s->context, &lengthbyte, 1);
+   s->func(s->context, data, length);
+}
+
+void stbiw__write_hdr_scanline(stbi__write_context *s, int width, int ncomp, unsigned char *scratch, float *scanline)
+{
+   unsigned char scanlineheader[4] = { 2, 2, 0, 0 };
+   unsigned char rgbe[4];
+   float linear[3];
+   int x;
+
+   scanlineheader[2] = (width&0xff00)>>8;
+   scanlineheader[3] = (width&0x00ff);
+
+   /* skip RLE for images too small or large */
+   if (width < 8 || width >= 32768) {
+      for (x=0; x < width; x++) {
+         switch (ncomp) {
+            case 4: /* fallthrough */
+            case 3: linear[2] = scanline[x*ncomp + 2];
+                    linear[1] = scanline[x*ncomp + 1];
+                    linear[0] = scanline[x*ncomp + 0];
+                    break;
+            default:
+                    linear[0] = linear[1] = linear[2] = scanline[x*ncomp + 0];
+                    break;
+         }
+         stbiw__linear_to_rgbe(rgbe, linear);
+         s->func(s->context, rgbe, 4);
+      }
+   } else {
+      int c,r;
+      /* encode into scratch buffer */
+      for (x=0; x < width; x++) {
+         switch(ncomp) {
+            case 4: /* fallthrough */
+            case 3: linear[2] = scanline[x*ncomp + 2];
+                    linear[1] = scanline[x*ncomp + 1];
+                    linear[0] = scanline[x*ncomp + 0];
+                    break;
+            default:
+                    linear[0] = linear[1] = linear[2] = scanline[x*ncomp + 0];
+                    break;
+         }
+         stbiw__linear_to_rgbe(rgbe, linear);
+         scratch[x + width*0] = rgbe[0];
+         scratch[x + width*1] = rgbe[1];
+         scratch[x + width*2] = rgbe[2];
+         scratch[x + width*3] = rgbe[3];
+      }
+
+      s->func(s->context, scanlineheader, 4);
+
+      /* RLE each component separately */
+      for (c=0; c < 4; c++) {
+         unsigned char *comp = &scratch[width*c];
+
+         x = 0;
+         while (x < width) {
+            // find first run
+            r = x;
+            while (r+2 < width) {
+               if (comp[r] == comp[r+1] && comp[r] == comp[r+2])
+                  break;
+               ++r;
+            }
+            if (r+2 >= width)
+               r = width;
+            // dump up to first run
+            while (x < r) {
+               int len = r-x;
+               if (len > 128) len = 128;
+               stbiw__write_dump_data(s, len, &comp[x]);
+               x += len;
+            }
+            // if there's a run, output it
+            if (r+2 < width) { // same test as what we break out of in search loop, so only true if we break'd
+               // find next byte after run
+               while (r < width && comp[r] == comp[x])
+                  ++r;
+               // output run up to r
+               while (x < r) {
+                  int len = r-x;
+                  if (len > 127) len = 127;
+                  stbiw__write_run_data(s, len, comp[x]);
+                  x += len;
+               }
+            }
+         }
+      }
+   }
+}
+
+static int stbi_write_hdr_core(stbi__write_context *s, int x, int y, int comp, float *data)
+{
+   if (y <= 0 || x <= 0 || data == NULL)
+      return 0;
+   else {
+      // Each component is stored separately. Allocate scratch space for full output scanline.
+      unsigned char *scratch = (unsigned char *) STBIW_MALLOC(x*4);
+      int i, len;
+      char buffer[128];
+      char header[] = "#?RADIANCE\n# Written by stb_image_write.h\nFORMAT=32-bit_rle_rgbe\n";
+      s->func(s->context, header, sizeof(header)-1);
+
+#ifdef STBI_MSC_SECURE_CRT
+      len = sprintf_s(buffer, "EXPOSURE=          1.0000000000000\n\n-Y %d +X %d\n", y, x);
+#else
+      len = sprintf(buffer, "EXPOSURE=          1.0000000000000\n\n-Y %d +X %d\n", y, x);
+#endif
+      s->func(s->context, buffer, len);
+
+      for(i=0; i < y; i++)
+         stbiw__write_hdr_scanline(s, x, comp, scratch, data + comp*x*(stbi__flip_vertically_on_write ? y-1-i : i)*x);
+      STBIW_FREE(scratch);
+      return 1;
+   }
+}
+
+STBIWDEF int stbi_write_hdr_to_func(stbi_write_func *func, void *context, int x, int y, int comp, const float *data)
+{
+   stbi__write_context s;
+   stbi__start_write_callbacks(&s, func, context);
+   return stbi_write_hdr_core(&s, x, y, comp, (float *) data);
+}
+
+#ifndef STBI_WRITE_NO_STDIO
+STBIWDEF int stbi_write_hdr(char const *filename, int x, int y, int comp, const float *data)
+{
+   stbi__write_context s;
+   if (stbi__start_write_file(&s,filename)) {
+      int r = stbi_write_hdr_core(&s, x, y, comp, (float *) data);
+      stbi__end_write_file(&s);
+      return r;
+   } else
+      return 0;
+}
+#endif // STBI_WRITE_NO_STDIO
+
+
+//////////////////////////////////////////////////////////////////////////////
+//
+// PNG writer
+//
+
+#ifndef STBIW_ZLIB_COMPRESS
+// stretchy buffer; stbiw__sbpush() == vector<>::push_back() -- stbiw__sbcount() == vector<>::size()
+#define stbiw__sbraw(a) ((int *) (a) - 2)
+#define stbiw__sbm(a)   stbiw__sbraw(a)[0]
+#define stbiw__sbn(a)   stbiw__sbraw(a)[1]
+
+#define stbiw__sbneedgrow(a,n)  ((a)==0 || stbiw__sbn(a)+n >= stbiw__sbm(a))
+#define stbiw__sbmaybegrow(a,n) (stbiw__sbneedgrow(a,(n)) ? stbiw__sbgrow(a,n) : 0)
+#define stbiw__sbgrow(a,n)  stbiw__sbgrowf((void **) &(a), (n), sizeof(*(a)))
+
+#define stbiw__sbpush(a, v)      (stbiw__sbmaybegrow(a,1), (a)[stbiw__sbn(a)++] = (v))
+#define stbiw__sbcount(a)        ((a) ? stbiw__sbn(a) : 0)
+#define stbiw__sbfree(a)         ((a) ? STBIW_FREE(stbiw__sbraw(a)),0 : 0)
+
+static void *stbiw__sbgrowf(void **arr, int increment, int itemsize)
+{
+   int m = *arr ? 2*stbiw__sbm(*arr)+increment : increment+1;
+   void *p = STBIW_REALLOC_SIZED(*arr ? stbiw__sbraw(*arr) : 0, *arr ? (stbiw__sbm(*arr)*itemsize + sizeof(int)*2) : 0, itemsize * m + sizeof(int)*2);
+   STBIW_ASSERT(p);
+   if (p) {
+      if (!*arr) ((int *) p)[1] = 0;
+      *arr = (void *) ((int *) p + 2);
+      stbiw__sbm(*arr) = m;
+   }
+   return *arr;
+}
+
+static unsigned char *stbiw__zlib_flushf(unsigned char *data, unsigned int *bitbuffer, int *bitcount)
+{
+   while (*bitcount >= 8) {
+      stbiw__sbpush(data, STBIW_UCHAR(*bitbuffer));
+      *bitbuffer >>= 8;
+      *bitcount -= 8;
+   }
+   return data;
+}
+
+static int stbiw__zlib_bitrev(int code, int codebits)
+{
+   int res=0;
+   while (codebits--) {
+      res = (res << 1) | (code & 1);
+      code >>= 1;
+   }
+   return res;
+}
+
+static unsigned int stbiw__zlib_countm(unsigned char *a, unsigned char *b, int limit)
+{
+   int i;
+   for (i=0; i < limit && i < 258; ++i)
+      if (a[i] != b[i]) break;
+   return i;
+}
+
+static unsigned int stbiw__zhash(unsigned char *data)
+{
+   stbiw_uint32 hash = data[0] + (data[1] << 8) + (data[2] << 16);
+   hash ^= hash << 3;
+   hash += hash >> 5;
+   hash ^= hash << 4;
+   hash += hash >> 17;
+   hash ^= hash << 25;
+   hash += hash >> 6;
+   return hash;
+}
+
+#define stbiw__zlib_flush() (out = stbiw__zlib_flushf(out, &bitbuf, &bitcount))
+#define stbiw__zlib_add(code,codebits) \
+      (bitbuf |= (code) << bitcount, bitcount += (codebits), stbiw__zlib_flush())
+#define stbiw__zlib_huffa(b,c)  stbiw__zlib_add(stbiw__zlib_bitrev(b,c),c)
+// default huffman tables
+#define stbiw__zlib_huff1(n)  stbiw__zlib_huffa(0x30 + (n), 8)
+#define stbiw__zlib_huff2(n)  stbiw__zlib_huffa(0x190 + (n)-144, 9)
+#define stbiw__zlib_huff3(n)  stbiw__zlib_huffa(0 + (n)-256,7)
+#define stbiw__zlib_huff4(n)  stbiw__zlib_huffa(0xc0 + (n)-280,8)
+#define stbiw__zlib_huff(n)  ((n) <= 143 ? stbiw__zlib_huff1(n) : (n) <= 255 ? stbiw__zlib_huff2(n) : (n) <= 279 ? stbiw__zlib_huff3(n) : stbiw__zlib_huff4(n))
+#define stbiw__zlib_huffb(n) ((n) <= 143 ? stbiw__zlib_huff1(n) : stbiw__zlib_huff2(n))
+
+#define stbiw__ZHASH   16384
+
+#endif // STBIW_ZLIB_COMPRESS
+
+unsigned char * stbi_zlib_compress(unsigned char *data, int data_len, int *out_len, int quality)
+{
+#ifdef STBIW_ZLIB_COMPRESS
+   // user provided a zlib compress implementation, use that
+   return STBIW_ZLIB_COMPRESS(data, data_len, out_len, quality);
+#else // use builtin
+   static unsigned short lengthc[] = { 3,4,5,6,7,8,9,10,11,13,15,17,19,23,27,31,35,43,51,59,67,83,99,115,131,163,195,227,258, 259 };
+   static unsigned char  lengtheb[]= { 0,0,0,0,0,0,0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4,  4,  5,  5,  5,  5,  0 };
+   static unsigned short distc[]   = { 1,2,3,4,5,7,9,13,17,25,33,49,65,97,129,193,257,385,513,769,1025,1537,2049,3073,4097,6145,8193,12289,16385,24577, 32768 };
+   static unsigned char  disteb[]  = { 0,0,0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13 };
+   unsigned int bitbuf=0;
+   int i,j, bitcount=0;
+   unsigned char *out = NULL;
+   unsigned char ***hash_table = (unsigned char***) STBIW_MALLOC(stbiw__ZHASH * sizeof(char**));
+   if (hash_table == NULL)
+      return NULL;
+   if (quality < 5) quality = 5;
+
+   stbiw__sbpush(out, 0x78);   // DEFLATE 32K window
+   stbiw__sbpush(out, 0x5e);   // FLEVEL = 1
+   stbiw__zlib_add(1,1);  // BFINAL = 1
+   stbiw__zlib_add(1,2);  // BTYPE = 1 -- fixed huffman
+
+   for (i=0; i < stbiw__ZHASH; ++i)
+      hash_table[i] = NULL;
+
+   i=0;
+   while (i < data_len-3) {
+      // hash next 3 bytes of data to be compressed
+      int h = stbiw__zhash(data+i)&(stbiw__ZHASH-1), best=3;
+      unsigned char *bestloc = 0;
+      unsigned char **hlist = hash_table[h];
+      int n = stbiw__sbcount(hlist);
+      for (j=0; j < n; ++j) {
+         if (hlist[j]-data > i-32768) { // if entry lies within window
+            int d = stbiw__zlib_countm(hlist[j], data+i, data_len-i);
+            if (d >= best) best=d,bestloc=hlist[j];
+         }
+      }
+      // when hash table entry is too long, delete half the entries
+      if (hash_table[h] && stbiw__sbn(hash_table[h]) == 2*quality) {
+         STBIW_MEMMOVE(hash_table[h], hash_table[h]+quality, sizeof(hash_table[h][0])*quality);
+         stbiw__sbn(hash_table[h]) = quality;
+      }
+      stbiw__sbpush(hash_table[h],data+i);
+
+      if (bestloc) {
+         // "lazy matching" - check match at *next* byte, and if it's better, do cur byte as literal
+         h = stbiw__zhash(data+i+1)&(stbiw__ZHASH-1);
+         hlist = hash_table[h];
+         n = stbiw__sbcount(hlist);
+         for (j=0; j < n; ++j) {
+            if (hlist[j]-data > i-32767) {
+               int e = stbiw__zlib_countm(hlist[j], data+i+1, data_len-i-1);
+               if (e > best) { // if next match is better, bail on current match
+                  bestloc = NULL;
+                  break;
+               }
+            }
+         }
+      }
+
+      if (bestloc) {
+         int d = (int) (data+i - bestloc); // distance back
+         STBIW_ASSERT(d <= 32767 && best <= 258);
+         for (j=0; best > lengthc[j+1]-1; ++j);
+         stbiw__zlib_huff(j+257);
+         if (lengtheb[j]) stbiw__zlib_add(best - lengthc[j], lengtheb[j]);
+         for (j=0; d > distc[j+1]-1; ++j);
+         stbiw__zlib_add(stbiw__zlib_bitrev(j,5),5);
+         if (disteb[j]) stbiw__zlib_add(d - distc[j], disteb[j]);
+         i += best;
+      } else {
+         stbiw__zlib_huffb(data[i]);
+         ++i;
+      }
+   }
+   // write out final bytes
+   for (;i < data_len; ++i)
+      stbiw__zlib_huffb(data[i]);
+   stbiw__zlib_huff(256); // end of block
+   // pad with 0 bits to byte boundary
+   while (bitcount)
+      stbiw__zlib_add(0,1);
+
+   for (i=0; i < stbiw__ZHASH; ++i)
+      (void) stbiw__sbfree(hash_table[i]);
+   STBIW_FREE(hash_table);
+
+   {
+      // compute adler32 on input
+      unsigned int s1=1, s2=0;
+      int blocklen = (int) (data_len % 5552);
+      j=0;
+      while (j < data_len) {
+         for (i=0; i < blocklen; ++i) s1 += data[j+i], s2 += s1;
+         s1 %= 65521, s2 %= 65521;
+         j += blocklen;
+         blocklen = 5552;
+      }
+      stbiw__sbpush(out, STBIW_UCHAR(s2 >> 8));
+      stbiw__sbpush(out, STBIW_UCHAR(s2));
+      stbiw__sbpush(out, STBIW_UCHAR(s1 >> 8));
+      stbiw__sbpush(out, STBIW_UCHAR(s1));
+   }
+   *out_len = stbiw__sbn(out);
+   // make returned pointer freeable
+   STBIW_MEMMOVE(stbiw__sbraw(out), out, *out_len);
+   return (unsigned char *) stbiw__sbraw(out);
+#endif // STBIW_ZLIB_COMPRESS
+}
+
+static unsigned int stbiw__crc32(unsigned char *buffer, int len)
+{
+   static unsigned int crc_table[256] =
+   {
+      0x00000000, 0x77073096, 0xEE0E612C, 0x990951BA, 0x076DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3,
+      0x0eDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988, 0x09B64C2B, 0x7EB17CBD, 0xE7B82D07, 0x90BF1D91,
+      0x1DB71064, 0x6AB020F2, 0xF3B97148, 0x84BE41DE, 0x1ADAD47D, 0x6DDDE4EB, 0xF4D4B551, 0x83D385C7,
+      0x136C9856, 0x646BA8C0, 0xFD62F97A, 0x8A65C9EC, 0x14015C4F, 0x63066CD9, 0xFA0F3D63, 0x8D080DF5,
+      0x3B6E20C8, 0x4C69105E, 0xD56041E4, 0xA2677172, 0x3C03E4D1, 0x4B04D447, 0xD20D85FD, 0xA50AB56B,
+      0x35B5A8FA, 0x42B2986C, 0xDBBBC9D6, 0xACBCF940, 0x32D86CE3, 0x45DF5C75, 0xDCD60DCF, 0xABD13D59,
+      0x26D930AC, 0x51DE003A, 0xC8D75180, 0xBFD06116, 0x21B4F4B5, 0x56B3C423, 0xCFBA9599, 0xB8BDA50F,
+      0x2802B89E, 0x5F058808, 0xC60CD9B2, 0xB10BE924, 0x2F6F7C87, 0x58684C11, 0xC1611DAB, 0xB6662D3D,
+      0x76DC4190, 0x01DB7106, 0x98D220BC, 0xEFD5102A, 0x71B18589, 0x06B6B51F, 0x9FBFE4A5, 0xE8B8D433,
+      0x7807C9A2, 0x0F00F934, 0x9609A88E, 0xE10E9818, 0x7F6A0DBB, 0x086D3D2D, 0x91646C97, 0xE6635C01,
+      0x6B6B51F4, 0x1C6C6162, 0x856530D8, 0xF262004E, 0x6C0695ED, 0x1B01A57B, 0x8208F4C1, 0xF50FC457,
+      0x65B0D9C6, 0x12B7E950, 0x8BBEB8EA, 0xFCB9887C, 0x62DD1DDF, 0x15DA2D49, 0x8CD37CF3, 0xFBD44C65,
+      0x4DB26158, 0x3AB551CE, 0xA3BC0074, 0xD4BB30E2, 0x4ADFA541, 0x3DD895D7, 0xA4D1C46D, 0xD3D6F4FB,
+      0x4369E96A, 0x346ED9FC, 0xAD678846, 0xDA60B8D0, 0x44042D73, 0x33031DE5, 0xAA0A4C5F, 0xDD0D7CC9,
+      0x5005713C, 0x270241AA, 0xBE0B1010, 0xC90C2086, 0x5768B525, 0x206F85B3, 0xB966D409, 0xCE61E49F,
+      0x5EDEF90E, 0x29D9C998, 0xB0D09822, 0xC7D7A8B4, 0x59B33D17, 0x2EB40D81, 0xB7BD5C3B, 0xC0BA6CAD,
+      0xEDB88320, 0x9ABFB3B6, 0x03B6E20C, 0x74B1D29A, 0xEAD54739, 0x9DD277AF, 0x04DB2615, 0x73DC1683,
+      0xE3630B12, 0x94643B84, 0x0D6D6A3E, 0x7A6A5AA8, 0xE40ECF0B, 0x9309FF9D, 0x0A00AE27, 0x7D079EB1,
+      0xF00F9344, 0x8708A3D2, 0x1E01F268, 0x6906C2FE, 0xF762575D, 0x806567CB, 0x196C3671, 0x6E6B06E7,
+      0xFED41B76, 0x89D32BE0, 0x10DA7A5A, 0x67DD4ACC, 0xF9B9DF6F, 0x8EBEEFF9, 0x17B7BE43, 0x60B08ED5,
+      0xD6D6A3E8, 0xA1D1937E, 0x38D8C2C4, 0x4FDFF252, 0xD1BB67F1, 0xA6BC5767, 0x3FB506DD, 0x48B2364B,
+      0xD80D2BDA, 0xAF0A1B4C, 0x36034AF6, 0x41047A60, 0xDF60EFC3, 0xA867DF55, 0x316E8EEF, 0x4669BE79,
+      0xCB61B38C, 0xBC66831A, 0x256FD2A0, 0x5268E236, 0xCC0C7795, 0xBB0B4703, 0x220216B9, 0x5505262F,
+      0xC5BA3BBE, 0xB2BD0B28, 0x2BB45A92, 0x5CB36A04, 0xC2D7FFA7, 0xB5D0CF31, 0x2CD99E8B, 0x5BDEAE1D,
+      0x9B64C2B0, 0xEC63F226, 0x756AA39C, 0x026D930A, 0x9C0906A9, 0xEB0E363F, 0x72076785, 0x05005713,
+      0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0x0CB61B38, 0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0x0BDBDF21,
+      0x86D3D2D4, 0xF1D4E242, 0x68DDB3F8, 0x1FDA836E, 0x81BE16CD, 0xF6B9265B, 0x6FB077E1, 0x18B74777,
+      0x88085AE6, 0xFF0F6A70, 0x66063BCA, 0x11010B5C, 0x8F659EFF, 0xF862AE69, 0x616BFFD3, 0x166CCF45,
+      0xA00AE278, 0xD70DD2EE, 0x4E048354, 0x3903B3C2, 0xA7672661, 0xD06016F7, 0x4969474D, 0x3E6E77DB,
+      0xAED16A4A, 0xD9D65ADC, 0x40DF0B66, 0x37D83BF0, 0xA9BCAE53, 0xDEBB9EC5, 0x47B2CF7F, 0x30B5FFE9,
+      0xBDBDF21C, 0xCABAC28A, 0x53B39330, 0x24B4A3A6, 0xBAD03605, 0xCDD70693, 0x54DE5729, 0x23D967BF,
+      0xB3667A2E, 0xC4614AB8, 0x5D681B02, 0x2A6F2B94, 0xB40BBE37, 0xC30C8EA1, 0x5A05DF1B, 0x2D02EF8D
+   };
+
+   unsigned int crc = ~0u;
+   int i;
+   for (i=0; i < len; ++i)
+      crc = (crc >> 8) ^ crc_table[buffer[i] ^ (crc & 0xff)];
+   return ~crc;
+}
+
+#define stbiw__wpng4(o,a,b,c,d) ((o)[0]=STBIW_UCHAR(a),(o)[1]=STBIW_UCHAR(b),(o)[2]=STBIW_UCHAR(c),(o)[3]=STBIW_UCHAR(d),(o)+=4)
+#define stbiw__wp32(data,v) stbiw__wpng4(data, (v)>>24,(v)>>16,(v)>>8,(v));
+#define stbiw__wptag(data,s) stbiw__wpng4(data, s[0],s[1],s[2],s[3])
+
+static void stbiw__wpcrc(unsigned char **data, int len)
+{
+   unsigned int crc = stbiw__crc32(*data - len - 4, len+4);
+   stbiw__wp32(*data, crc);
+}
+
+static unsigned char stbiw__paeth(int a, int b, int c)
+{
+   int p = a + b - c, pa = abs(p-a), pb = abs(p-b), pc = abs(p-c);
+   if (pa <= pb && pa <= pc) return STBIW_UCHAR(a);
+   if (pb <= pc) return STBIW_UCHAR(b);
+   return STBIW_UCHAR(c);
+}
+
+// @OPTIMIZE: provide an option that always forces left-predict or paeth predict
+static void stbiw__encode_png_line(unsigned char *pixels, int stride_bytes, int width, int height, int y, int n, int filter_type, signed char *line_buffer)
+{
+   static int mapping[] = { 0,1,2,3,4 };
+   static int firstmap[] = { 0,1,0,5,6 };
+   int *mymap = (y != 0) ? mapping : firstmap;
+   int i;
+   int type = mymap[filter_type];
+   unsigned char *z = pixels + stride_bytes * (stbi__flip_vertically_on_write ? height-1-y : y);
+   int signed_stride = stbi__flip_vertically_on_write ? -stride_bytes : stride_bytes;
+   for (i = 0; i < n; ++i) {
+      switch (type) {
+         case 0: line_buffer[i] = z[i]; break;
+         case 1: line_buffer[i] = z[i]; break;
+         case 2: line_buffer[i] = z[i] - z[i-signed_stride]; break;
+         case 3: line_buffer[i] = z[i] - (z[i-signed_stride]>>1); break;
+         case 4: line_buffer[i] = (signed char) (z[i] - stbiw__paeth(0,z[i-signed_stride],0)); break;
+         case 5: line_buffer[i] = z[i]; break;
+         case 6: line_buffer[i] = z[i]; break;
+      }
+   }
+   for (i=n; i < width*n; ++i) {
+      switch (type) {
+         case 0: line_buffer[i] = z[i]; break;
+         case 1: line_buffer[i] = z[i] - z[i-n]; break;
+         case 2: line_buffer[i] = z[i] - z[i-signed_stride]; break;
+         case 3: line_buffer[i] = z[i] - ((z[i-n] + z[i-signed_stride])>>1); break;
+         case 4: line_buffer[i] = z[i] - stbiw__paeth(z[i-n], z[i-signed_stride], z[i-signed_stride-n]); break;
+         case 5: line_buffer[i] = z[i] - (z[i-n]>>1); break;
+         case 6: line_buffer[i] = z[i] - stbiw__paeth(z[i-n], 0,0); break;
+      }
+   }
+}
+
+unsigned char *stbi_write_png_to_mem(unsigned char *pixels, int stride_bytes, int x, int y, int n, int *out_len)
+{
+   int force_filter = stbi_write_force_png_filter;
+   int ctype[5] = { -1, 0, 4, 2, 6 };
+   unsigned char sig[8] = { 137,80,78,71,13,10,26,10 };
+   unsigned char *out,*o, *filt, *zlib;
+   signed char *line_buffer;
+   int j,zlen;
+
+   if (stride_bytes == 0)
+      stride_bytes = x * n;
+
+   if (force_filter >= 5) {
+      force_filter = -1;
+   }
+
+   filt = (unsigned char *) STBIW_MALLOC((x*n+1) * y); if (!filt) return 0;
+   line_buffer = (signed char *) STBIW_MALLOC(x * n); if (!line_buffer) { STBIW_FREE(filt); return 0; }
+   for (j=0; j < y; ++j) {
+      int filter_type;
+      if (force_filter > -1) {
+         filter_type = force_filter;
+         stbiw__encode_png_line(pixels, stride_bytes, x, y, j, n, force_filter, line_buffer);
+      } else { // Estimate the best filter by running through all of them:
+         int best_filter = 0, best_filter_val = 0x7fffffff, est, i;
+         for (filter_type = 0; filter_type < 5; filter_type++) {
+            stbiw__encode_png_line(pixels, stride_bytes, x, y, j, n, filter_type, line_buffer);
+
+            // Estimate the entropy of the line using this filter; the less, the better.
+            est = 0;
+            for (i = 0; i < x*n; ++i) {
+               est += abs((signed char) line_buffer[i]);
+            }
+            if (est < best_filter_val) {
+               best_filter_val = est;
+               best_filter = filter_type;
+            }
+         }
+         if (filter_type != best_filter) {  // If the last iteration already got us the best filter, don't redo it
+            stbiw__encode_png_line(pixels, stride_bytes, x, y, j, n, best_filter, line_buffer);
+            filter_type = best_filter;
+         }
+      }
+      // when we get here, filter_type contains the filter type, and line_buffer contains the data
+      filt[j*(x*n+1)] = (unsigned char) filter_type;
+      STBIW_MEMMOVE(filt+j*(x*n+1)+1, line_buffer, x*n);
+   }
+   STBIW_FREE(line_buffer);
+   zlib = stbi_zlib_compress(filt, y*( x*n+1), &zlen, stbi_write_png_compression_level);
+   STBIW_FREE(filt);
+   if (!zlib) return 0;
+
+   // each tag requires 12 bytes of overhead
+   out = (unsigned char *) STBIW_MALLOC(8 + 12+13 + 12+zlen + 12);
+   if (!out) return 0;
+   *out_len = 8 + 12+13 + 12+zlen + 12;
+
+   o=out;
+   STBIW_MEMMOVE(o,sig,8); o+= 8;
+   stbiw__wp32(o, 13); // header length
+   stbiw__wptag(o, "IHDR");
+   stbiw__wp32(o, x);
+   stbiw__wp32(o, y);
+   *o++ = 8;
+   *o++ = STBIW_UCHAR(ctype[n]);
+   *o++ = 0;
+   *o++ = 0;
+   *o++ = 0;
+   stbiw__wpcrc(&o,13);
+
+   stbiw__wp32(o, zlen);
+   stbiw__wptag(o, "IDAT");
+   STBIW_MEMMOVE(o, zlib, zlen);
+   o += zlen;
+   STBIW_FREE(zlib);
+   stbiw__wpcrc(&o, zlen);
+
+   stbiw__wp32(o,0);
+   stbiw__wptag(o, "IEND");
+   stbiw__wpcrc(&o,0);
+
+   STBIW_ASSERT(o == out + *out_len);
+
+   return out;
+}
+
+#ifndef STBI_WRITE_NO_STDIO
+STBIWDEF int stbi_write_png(char const *filename, int x, int y, int comp, const void *data, int stride_bytes)
+{
+   FILE *f;
+   int len;
+   unsigned char *png = stbi_write_png_to_mem((unsigned char *) data, stride_bytes, x, y, comp, &len);
+   if (png == NULL) return 0;
+#ifdef STBI_MSC_SECURE_CRT
+   if (fopen_s(&f, filename, "wb"))
+      f = NULL;
+#else
+   f = fopen(filename, "wb");
+#endif
+   if (!f) { STBIW_FREE(png); return 0; }
+   fwrite(png, 1, len, f);
+   fclose(f);
+   STBIW_FREE(png);
+   return 1;
+}
+#endif
+
+STBIWDEF int stbi_write_png_to_func(stbi_write_func *func, void *context, int x, int y, int comp, const void *data, int stride_bytes)
+{
+   int len;
+   unsigned char *png = stbi_write_png_to_mem((unsigned char *) data, stride_bytes, x, y, comp, &len);
+   if (png == NULL) return 0;
+   func(context, png, len);
+   STBIW_FREE(png);
+   return 1;
+}
+
+
+/* ***************************************************************************
+ *
+ * JPEG writer
+ *
+ * This is based on Jon Olick's jo_jpeg.cpp:
+ * public domain Simple, Minimalistic JPEG writer - http://www.jonolick.com/code.html
+ */
+
+static const unsigned char stbiw__jpg_ZigZag[] = { 0,1,5,6,14,15,27,28,2,4,7,13,16,26,29,42,3,8,12,17,25,30,41,43,9,11,18,
+      24,31,40,44,53,10,19,23,32,39,45,52,54,20,22,33,38,46,51,55,60,21,34,37,47,50,56,59,61,35,36,48,49,57,58,62,63 };
+
+static void stbiw__jpg_writeBits(stbi__write_context *s, int *bitBufP, int *bitCntP, const unsigned short *bs) {
+   int bitBuf = *bitBufP, bitCnt = *bitCntP;
+   bitCnt += bs[1];
+   bitBuf |= bs[0] << (24 - bitCnt);
+   while(bitCnt >= 8) {
+      unsigned char c = (bitBuf >> 16) & 255;
+      stbiw__putc(s, c);
+      if(c == 255) {
+         stbiw__putc(s, 0);
+      }
+      bitBuf <<= 8;
+      bitCnt -= 8;
+   }
+   *bitBufP = bitBuf;
+   *bitCntP = bitCnt;
+}
+
+static void stbiw__jpg_DCT(float *d0p, float *d1p, float *d2p, float *d3p, float *d4p, float *d5p, float *d6p, float *d7p) {
+   float d0 = *d0p, d1 = *d1p, d2 = *d2p, d3 = *d3p, d4 = *d4p, d5 = *d5p, d6 = *d6p, d7 = *d7p;
+   float z1, z2, z3, z4, z5, z11, z13;
+
+   float tmp0 = d0 + d7;
+   float tmp7 = d0 - d7;
+   float tmp1 = d1 + d6;
+   float tmp6 = d1 - d6;
+   float tmp2 = d2 + d5;
+   float tmp5 = d2 - d5;
+   float tmp3 = d3 + d4;
+   float tmp4 = d3 - d4;
+
+   // Even part
+   float tmp10 = tmp0 + tmp3;   // phase 2
+   float tmp13 = tmp0 - tmp3;
+   float tmp11 = tmp1 + tmp2;
+   float tmp12 = tmp1 - tmp2;
+
+   d0 = tmp10 + tmp11;       // phase 3
+   d4 = tmp10 - tmp11;
+
+   z1 = (tmp12 + tmp13) * 0.707106781f; // c4
+   d2 = tmp13 + z1;       // phase 5
+   d6 = tmp13 - z1;
+
+   // Odd part
+   tmp10 = tmp4 + tmp5;       // phase 2
+   tmp11 = tmp5 + tmp6;
+   tmp12 = tmp6 + tmp7;
+
+   // The rotator is modified from fig 4-8 to avoid extra negations.
+   z5 = (tmp10 - tmp12) * 0.382683433f; // c6
+   z2 = tmp10 * 0.541196100f + z5; // c2-c6
+   z4 = tmp12 * 1.306562965f + z5; // c2+c6
+   z3 = tmp11 * 0.707106781f; // c4
+
+   z11 = tmp7 + z3;      // phase 5
+   z13 = tmp7 - z3;
+
+   *d5p = z13 + z2;         // phase 6
+   *d3p = z13 - z2;
+   *d1p = z11 + z4;
+   *d7p = z11 - z4;
+
+   *d0p = d0;  *d2p = d2;  *d4p = d4;  *d6p = d6;
+}
+
+static void stbiw__jpg_calcBits(int val, unsigned short bits[2]) {
+   int tmp1 = val < 0 ? -val : val;
+   val = val < 0 ? val-1 : val;
+   bits[1] = 1;
+   while(tmp1 >>= 1) {
+      ++bits[1];
+   }
+   bits[0] = val & ((1<<bits[1])-1);
+}
+
+static int stbiw__jpg_processDU(stbi__write_context *s, int *bitBuf, int *bitCnt, float *CDU, float *fdtbl, int DC, const unsigned short HTDC[256][2], const unsigned short HTAC[256][2]) {
+   const unsigned short EOB[2] = { HTAC[0x00][0], HTAC[0x00][1] };
+   const unsigned short M16zeroes[2] = { HTAC[0xF0][0], HTAC[0xF0][1] };
+   int dataOff, i, diff, end0pos;
+   int DU[64];
+
+   // DCT rows
+   for(dataOff=0; dataOff<64; dataOff+=8) {
+      stbiw__jpg_DCT(&CDU[dataOff], &CDU[dataOff+1], &CDU[dataOff+2], &CDU[dataOff+3], &CDU[dataOff+4], &CDU[dataOff+5], &CDU[dataOff+6], &CDU[dataOff+7]);
+   }
+   // DCT columns
+   for(dataOff=0; dataOff<8; ++dataOff) {
+      stbiw__jpg_DCT(&CDU[dataOff], &CDU[dataOff+8], &CDU[dataOff+16], &CDU[dataOff+24], &CDU[dataOff+32], &CDU[dataOff+40], &CDU[dataOff+48], &CDU[dataOff+56]);
+   }
+   // Quantize/descale/zigzag the coefficients
+   for(i=0; i<64; ++i) {
+      float v = CDU[i]*fdtbl[i];
+      // DU[stbiw__jpg_ZigZag[i]] = (int)(v < 0 ? ceilf(v - 0.5f) : floorf(v + 0.5f));
+      // ceilf() and floorf() are C99, not C89, but I /think/ they're not needed here anyway?
+      DU[stbiw__jpg_ZigZag[i]] = (int)(v < 0 ? v - 0.5f : v + 0.5f);
+   }
+
+   // Encode DC
+   diff = DU[0] - DC;
+   if (diff == 0) {
+      stbiw__jpg_writeBits(s, bitBuf, bitCnt, HTDC[0]);
+   } else {
+      unsigned short bits[2];
+      stbiw__jpg_calcBits(diff, bits);
+      stbiw__jpg_writeBits(s, bitBuf, bitCnt, HTDC[bits[1]]);
+      stbiw__jpg_writeBits(s, bitBuf, bitCnt, bits);
+   }
+   // Encode ACs
+   end0pos = 63;
+   for(; (end0pos>0)&&(DU[end0pos]==0); --end0pos) {
+   }
+   // end0pos = first element in reverse order !=0
+   if(end0pos == 0) {
+      stbiw__jpg_writeBits(s, bitBuf, bitCnt, EOB);
+      return DU[0];
+   }
+   for(i = 1; i <= end0pos; ++i) {
+      int startpos = i;
+      int nrzeroes;
+      unsigned short bits[2];
+      for (; DU[i]==0 && i<=end0pos; ++i) {
+      }
+      nrzeroes = i-startpos;
+      if ( nrzeroes >= 16 ) {
+         int lng = nrzeroes>>4;
+         int nrmarker;
+         for (nrmarker=1; nrmarker <= lng; ++nrmarker)
+            stbiw__jpg_writeBits(s, bitBuf, bitCnt, M16zeroes);
+         nrzeroes &= 15;
+      }
+      stbiw__jpg_calcBits(DU[i], bits);
+      stbiw__jpg_writeBits(s, bitBuf, bitCnt, HTAC[(nrzeroes<<4)+bits[1]]);
+      stbiw__jpg_writeBits(s, bitBuf, bitCnt, bits);
+   }
+   if(end0pos != 63) {
+      stbiw__jpg_writeBits(s, bitBuf, bitCnt, EOB);
+   }
+   return DU[0];
+}
+
+static int stbi_write_jpg_core(stbi__write_context *s, int width, int height, int comp, const void* data, int quality) {
+   // Constants that don't pollute global namespace
+   static const unsigned char std_dc_luminance_nrcodes[] = {0,0,1,5,1,1,1,1,1,1,0,0,0,0,0,0,0};
+   static const unsigned char std_dc_luminance_values[] = {0,1,2,3,4,5,6,7,8,9,10,11};
+   static const unsigned char std_ac_luminance_nrcodes[] = {0,0,2,1,3,3,2,4,3,5,5,4,4,0,0,1,0x7d};
+   static const unsigned char std_ac_luminance_values[] = {
+      0x01,0x02,0x03,0x00,0x04,0x11,0x05,0x12,0x21,0x31,0x41,0x06,0x13,0x51,0x61,0x07,0x22,0x71,0x14,0x32,0x81,0x91,0xa1,0x08,
+      0x23,0x42,0xb1,0xc1,0x15,0x52,0xd1,0xf0,0x24,0x33,0x62,0x72,0x82,0x09,0x0a,0x16,0x17,0x18,0x19,0x1a,0x25,0x26,0x27,0x28,
+      0x29,0x2a,0x34,0x35,0x36,0x37,0x38,0x39,0x3a,0x43,0x44,0x45,0x46,0x47,0x48,0x49,0x4a,0x53,0x54,0x55,0x56,0x57,0x58,0x59,
+      0x5a,0x63,0x64,0x65,0x66,0x67,0x68,0x69,0x6a,0x73,0x74,0x75,0x76,0x77,0x78,0x79,0x7a,0x83,0x84,0x85,0x86,0x87,0x88,0x89,
+      0x8a,0x92,0x93,0x94,0x95,0x96,0x97,0x98,0x99,0x9a,0xa2,0xa3,0xa4,0xa5,0xa6,0xa7,0xa8,0xa9,0xaa,0xb2,0xb3,0xb4,0xb5,0xb6,
+      0xb7,0xb8,0xb9,0xba,0xc2,0xc3,0xc4,0xc5,0xc6,0xc7,0xc8,0xc9,0xca,0xd2,0xd3,0xd4,0xd5,0xd6,0xd7,0xd8,0xd9,0xda,0xe1,0xe2,
+      0xe3,0xe4,0xe5,0xe6,0xe7,0xe8,0xe9,0xea,0xf1,0xf2,0xf3,0xf4,0xf5,0xf6,0xf7,0xf8,0xf9,0xfa
+   };
+   static const unsigned char std_dc_chrominance_nrcodes[] = {0,0,3,1,1,1,1,1,1,1,1,1,0,0,0,0,0};
+   static const unsigned char std_dc_chrominance_values[] = {0,1,2,3,4,5,6,7,8,9,10,11};
+   static const unsigned char std_ac_chrominance_nrcodes[] = {0,0,2,1,2,4,4,3,4,7,5,4,4,0,1,2,0x77};
+   static const unsigned char std_ac_chrominance_values[] = {
+      0x00,0x01,0x02,0x03,0x11,0x04,0x05,0x21,0x31,0x06,0x12,0x41,0x51,0x07,0x61,0x71,0x13,0x22,0x32,0x81,0x08,0x14,0x42,0x91,
+      0xa1,0xb1,0xc1,0x09,0x23,0x33,0x52,0xf0,0x15,0x62,0x72,0xd1,0x0a,0x16,0x24,0x34,0xe1,0x25,0xf1,0x17,0x18,0x19,0x1a,0x26,
+      0x27,0x28,0x29,0x2a,0x35,0x36,0x37,0x38,0x39,0x3a,0x43,0x44,0x45,0x46,0x47,0x48,0x49,0x4a,0x53,0x54,0x55,0x56,0x57,0x58,
+      0x59,0x5a,0x63,0x64,0x65,0x66,0x67,0x68,0x69,0x6a,0x73,0x74,0x75,0x76,0x77,0x78,0x79,0x7a,0x82,0x83,0x84,0x85,0x86,0x87,
+      0x88,0x89,0x8a,0x92,0x93,0x94,0x95,0x96,0x97,0x98,0x99,0x9a,0xa2,0xa3,0xa4,0xa5,0xa6,0xa7,0xa8,0xa9,0xaa,0xb2,0xb3,0xb4,
+      0xb5,0xb6,0xb7,0xb8,0xb9,0xba,0xc2,0xc3,0xc4,0xc5,0xc6,0xc7,0xc8,0xc9,0xca,0xd2,0xd3,0xd4,0xd5,0xd6,0xd7,0xd8,0xd9,0xda,
+      0xe2,0xe3,0xe4,0xe5,0xe6,0xe7,0xe8,0xe9,0xea,0xf2,0xf3,0xf4,0xf5,0xf6,0xf7,0xf8,0xf9,0xfa
+   };
+   // Huffman tables
+   static const unsigned short YDC_HT[256][2] = { {0,2},{2,3},{3,3},{4,3},{5,3},{6,3},{14,4},{30,5},{62,6},{126,7},{254,8},{510,9}};
+   static const unsigned short UVDC_HT[256][2] = { {0,2},{1,2},{2,2},{6,3},{14,4},{30,5},{62,6},{126,7},{254,8},{510,9},{1022,10},{2046,11}};
+   static const unsigned short YAC_HT[256][2] = {
+      {10,4},{0,2},{1,2},{4,3},{11,4},{26,5},{120,7},{248,8},{1014,10},{65410,16},{65411,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {12,4},{27,5},{121,7},{502,9},{2038,11},{65412,16},{65413,16},{65414,16},{65415,16},{65416,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {28,5},{249,8},{1015,10},{4084,12},{65417,16},{65418,16},{65419,16},{65420,16},{65421,16},{65422,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {58,6},{503,9},{4085,12},{65423,16},{65424,16},{65425,16},{65426,16},{65427,16},{65428,16},{65429,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {59,6},{1016,10},{65430,16},{65431,16},{65432,16},{65433,16},{65434,16},{65435,16},{65436,16},{65437,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {122,7},{2039,11},{65438,16},{65439,16},{65440,16},{65441,16},{65442,16},{65443,16},{65444,16},{65445,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {123,7},{4086,12},{65446,16},{65447,16},{65448,16},{65449,16},{65450,16},{65451,16},{65452,16},{65453,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {250,8},{4087,12},{65454,16},{65455,16},{65456,16},{65457,16},{65458,16},{65459,16},{65460,16},{65461,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {504,9},{32704,15},{65462,16},{65463,16},{65464,16},{65465,16},{65466,16},{65467,16},{65468,16},{65469,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {505,9},{65470,16},{65471,16},{65472,16},{65473,16},{65474,16},{65475,16},{65476,16},{65477,16},{65478,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {506,9},{65479,16},{65480,16},{65481,16},{65482,16},{65483,16},{65484,16},{65485,16},{65486,16},{65487,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {1017,10},{65488,16},{65489,16},{65490,16},{65491,16},{65492,16},{65493,16},{65494,16},{65495,16},{65496,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {1018,10},{65497,16},{65498,16},{65499,16},{65500,16},{65501,16},{65502,16},{65503,16},{65504,16},{65505,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {2040,11},{65506,16},{65507,16},{65508,16},{65509,16},{65510,16},{65511,16},{65512,16},{65513,16},{65514,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {65515,16},{65516,16},{65517,16},{65518,16},{65519,16},{65520,16},{65521,16},{65522,16},{65523,16},{65524,16},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {2041,11},{65525,16},{65526,16},{65527,16},{65528,16},{65529,16},{65530,16},{65531,16},{65532,16},{65533,16},{65534,16},{0,0},{0,0},{0,0},{0,0},{0,0}
+   };
+   static const unsigned short UVAC_HT[256][2] = {
+      {0,2},{1,2},{4,3},{10,4},{24,5},{25,5},{56,6},{120,7},{500,9},{1014,10},{4084,12},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {11,4},{57,6},{246,8},{501,9},{2038,11},{4085,12},{65416,16},{65417,16},{65418,16},{65419,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {26,5},{247,8},{1015,10},{4086,12},{32706,15},{65420,16},{65421,16},{65422,16},{65423,16},{65424,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {27,5},{248,8},{1016,10},{4087,12},{65425,16},{65426,16},{65427,16},{65428,16},{65429,16},{65430,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {58,6},{502,9},{65431,16},{65432,16},{65433,16},{65434,16},{65435,16},{65436,16},{65437,16},{65438,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {59,6},{1017,10},{65439,16},{65440,16},{65441,16},{65442,16},{65443,16},{65444,16},{65445,16},{65446,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {121,7},{2039,11},{65447,16},{65448,16},{65449,16},{65450,16},{65451,16},{65452,16},{65453,16},{65454,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {122,7},{2040,11},{65455,16},{65456,16},{65457,16},{65458,16},{65459,16},{65460,16},{65461,16},{65462,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {249,8},{65463,16},{65464,16},{65465,16},{65466,16},{65467,16},{65468,16},{65469,16},{65470,16},{65471,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {503,9},{65472,16},{65473,16},{65474,16},{65475,16},{65476,16},{65477,16},{65478,16},{65479,16},{65480,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {504,9},{65481,16},{65482,16},{65483,16},{65484,16},{65485,16},{65486,16},{65487,16},{65488,16},{65489,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {505,9},{65490,16},{65491,16},{65492,16},{65493,16},{65494,16},{65495,16},{65496,16},{65497,16},{65498,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {506,9},{65499,16},{65500,16},{65501,16},{65502,16},{65503,16},{65504,16},{65505,16},{65506,16},{65507,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {2041,11},{65508,16},{65509,16},{65510,16},{65511,16},{65512,16},{65513,16},{65514,16},{65515,16},{65516,16},{0,0},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {16352,14},{65517,16},{65518,16},{65519,16},{65520,16},{65521,16},{65522,16},{65523,16},{65524,16},{65525,16},{0,0},{0,0},{0,0},{0,0},{0,0},
+      {1018,10},{32707,15},{65526,16},{65527,16},{65528,16},{65529,16},{65530,16},{65531,16},{65532,16},{65533,16},{65534,16},{0,0},{0,0},{0,0},{0,0},{0,0}
+   };
+   static const int YQT[] = {16,11,10,16,24,40,51,61,12,12,14,19,26,58,60,55,14,13,16,24,40,57,69,56,14,17,22,29,51,87,80,62,18,22,
+                             37,56,68,109,103,77,24,35,55,64,81,104,113,92,49,64,78,87,103,121,120,101,72,92,95,98,112,100,103,99};
+   static const int UVQT[] = {17,18,24,47,99,99,99,99,18,21,26,66,99,99,99,99,24,26,56,99,99,99,99,99,47,66,99,99,99,99,99,99,
+                              99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99};
+   static const float aasf[] = { 1.0f * 2.828427125f, 1.387039845f * 2.828427125f, 1.306562965f * 2.828427125f, 1.175875602f * 2.828427125f, 
+                                 1.0f * 2.828427125f, 0.785694958f * 2.828427125f, 0.541196100f * 2.828427125f, 0.275899379f * 2.828427125f };
+
+   int row, col, i, k;
+   float fdtbl_Y[64], fdtbl_UV[64];
+   unsigned char YTable[64], UVTable[64];
+
+   if(!data || !width || !height || comp > 4 || comp < 1) {
+      return 0;
+   }
+
+   quality = quality ? quality : 90;
+   quality = quality < 1 ? 1 : quality > 100 ? 100 : quality;
+   quality = quality < 50 ? 5000 / quality : 200 - quality * 2;
+
+   for(i = 0; i < 64; ++i) {
+      int uvti, yti = (YQT[i]*quality+50)/100;
+      YTable[stbiw__jpg_ZigZag[i]] = (unsigned char) (yti < 1 ? 1 : yti > 255 ? 255 : yti);
+      uvti = (UVQT[i]*quality+50)/100;
+      UVTable[stbiw__jpg_ZigZag[i]] = (unsigned char) (uvti < 1 ? 1 : uvti > 255 ? 255 : uvti);
+   }
+
+   for(row = 0, k = 0; row < 8; ++row) {
+      for(col = 0; col < 8; ++col, ++k) {
+         fdtbl_Y[k]  = 1 / (YTable [stbiw__jpg_ZigZag[k]] * aasf[row] * aasf[col]);
+         fdtbl_UV[k] = 1 / (UVTable[stbiw__jpg_ZigZag[k]] * aasf[row] * aasf[col]);
+      }
+   }
+
+   // Write Headers
+   {
+      static const unsigned char head0[] = { 0xFF,0xD8,0xFF,0xE0,0,0x10,'J','F','I','F',0,1,1,0,0,1,0,1,0,0,0xFF,0xDB,0,0x84,0 };
+      static const unsigned char head2[] = { 0xFF,0xDA,0,0xC,3,1,0,2,0x11,3,0x11,0,0x3F,0 };
+      const unsigned char head1[] = { 0xFF,0xC0,0,0x11,8,(unsigned char)(height>>8),STBIW_UCHAR(height),(unsigned char)(width>>8),STBIW_UCHAR(width),
+                                      3,1,0x11,0,2,0x11,1,3,0x11,1,0xFF,0xC4,0x01,0xA2,0 };
+      s->func(s->context, (void*)head0, sizeof(head0));
+      s->func(s->context, (void*)YTable, sizeof(YTable));
+      stbiw__putc(s, 1);
+      s->func(s->context, UVTable, sizeof(UVTable));
+      s->func(s->context, (void*)head1, sizeof(head1));
+      s->func(s->context, (void*)(std_dc_luminance_nrcodes+1), sizeof(std_dc_luminance_nrcodes)-1);
+      s->func(s->context, (void*)std_dc_luminance_values, sizeof(std_dc_luminance_values));
+      stbiw__putc(s, 0x10); // HTYACinfo
+      s->func(s->context, (void*)(std_ac_luminance_nrcodes+1), sizeof(std_ac_luminance_nrcodes)-1);
+      s->func(s->context, (void*)std_ac_luminance_values, sizeof(std_ac_luminance_values));
+      stbiw__putc(s, 1); // HTUDCinfo
+      s->func(s->context, (void*)(std_dc_chrominance_nrcodes+1), sizeof(std_dc_chrominance_nrcodes)-1);
+      s->func(s->context, (void*)std_dc_chrominance_values, sizeof(std_dc_chrominance_values));
+      stbiw__putc(s, 0x11); // HTUACinfo
+      s->func(s->context, (void*)(std_ac_chrominance_nrcodes+1), sizeof(std_ac_chrominance_nrcodes)-1);
+      s->func(s->context, (void*)std_ac_chrominance_values, sizeof(std_ac_chrominance_values));
+      s->func(s->context, (void*)head2, sizeof(head2));
+   }
+
+   // Encode 8x8 macroblocks
+   {
+      static const unsigned short fillBits[] = {0x7F, 7};
+      const unsigned char *imageData = (const unsigned char *)data;
+      int DCY=0, DCU=0, DCV=0;
+      int bitBuf=0, bitCnt=0;
+      // comp == 2 is grey+alpha (alpha is ignored)
+      int ofsG = comp > 2 ? 1 : 0, ofsB = comp > 2 ? 2 : 0;
+      int x, y, pos;
+      for(y = 0; y < height; y += 8) {
+         for(x = 0; x < width; x += 8) {
+            float YDU[64], UDU[64], VDU[64];
+            for(row = y, pos = 0; row < y+8; ++row) {
+               for(col = x; col < x+8; ++col, ++pos) {
+                  int p = (stbi__flip_vertically_on_write ? height-1-row : row)*width*comp + col*comp;
+                  float r, g, b;
+                  if(row >= height) {
+                     p -= width*comp*(row+1 - height);
+                  }
+                  if(col >= width) {
+                     p -= comp*(col+1 - width);
+                  }
+
+                  r = imageData[p+0];
+                  g = imageData[p+ofsG];
+                  b = imageData[p+ofsB];
+                  YDU[pos]=+0.29900f*r+0.58700f*g+0.11400f*b-128;
+                  UDU[pos]=-0.16874f*r-0.33126f*g+0.50000f*b;
+                  VDU[pos]=+0.50000f*r-0.41869f*g-0.08131f*b;
+               }
+            }
+
+            DCY = stbiw__jpg_processDU(s, &bitBuf, &bitCnt, YDU, fdtbl_Y, DCY, YDC_HT, YAC_HT);
+            DCU = stbiw__jpg_processDU(s, &bitBuf, &bitCnt, UDU, fdtbl_UV, DCU, UVDC_HT, UVAC_HT);
+            DCV = stbiw__jpg_processDU(s, &bitBuf, &bitCnt, VDU, fdtbl_UV, DCV, UVDC_HT, UVAC_HT);
+         }
+      }
+
+      // Do the bit alignment of the EOI marker
+      stbiw__jpg_writeBits(s, &bitBuf, &bitCnt, fillBits);
+   }
+
+   // EOI
+   stbiw__putc(s, 0xFF);
+   stbiw__putc(s, 0xD9);
+
+   return 1;
+}
+
+STBIWDEF int stbi_write_jpg_to_func(stbi_write_func *func, void *context, int x, int y, int comp, const void *data, int quality)
+{
+   stbi__write_context s;
+   stbi__start_write_callbacks(&s, func, context);
+   return stbi_write_jpg_core(&s, x, y, comp, (void *) data, quality);
+}
+
+
+#ifndef STBI_WRITE_NO_STDIO
+STBIWDEF int stbi_write_jpg(char const *filename, int x, int y, int comp, const void *data, int quality)
+{
+   stbi__write_context s;
+   if (stbi__start_write_file(&s,filename)) {
+      int r = stbi_write_jpg_core(&s, x, y, comp, data, quality);
+      stbi__end_write_file(&s);
+      return r;
+   } else
+      return 0;
+}
+#endif
+
+#endif // STB_IMAGE_WRITE_IMPLEMENTATION
+
+/* Revision history
+      1.09  (2018-02-11)
+             fix typo in zlib quality API, improve STB_I_W_STATIC in C++
+      1.08  (2018-01-29)
+             add stbi__flip_vertically_on_write, external zlib, zlib quality, choose PNG filter
+      1.07  (2017-07-24)
+             doc fix
+      1.06 (2017-07-23)
+             writing JPEG (using Jon Olick's code)
+      1.05   ???
+      1.04 (2017-03-03)
+             monochrome BMP expansion
+      1.03   ???
+      1.02 (2016-04-02)
+             avoid allocating large structures on the stack
+      1.01 (2016-01-16)
+             STBIW_REALLOC_SIZED: support allocators with no realloc support
+             avoid race-condition in crc initialization
+             minor compile issues
+      1.00 (2015-09-14)
+             installable file IO function
+      0.99 (2015-09-13)
+             warning fixes; TGA rle support
+      0.98 (2015-04-08)
+             added STBIW_MALLOC, STBIW_ASSERT etc
+      0.97 (2015-01-18)
+             fixed HDR asserts, rewrote HDR rle logic
+      0.96 (2015-01-17)
+             add HDR output
+             fix monochrome BMP
+      0.95 (2014-08-17)
+		       add monochrome TGA output
+      0.94 (2014-05-31)
+             rename private functions to avoid conflicts with stb_image.h
+      0.93 (2014-05-27)
+             warning fixes
+      0.92 (2010-08-01)
+             casts to unsigned char to fix warnings
+      0.91 (2010-07-17)
+             first public release
+      0.90   first internal release
+*/
+
+/*
+------------------------------------------------------------------------------
+This software is available under 2 licenses -- choose whichever you prefer.
+------------------------------------------------------------------------------
+ALTERNATIVE A - MIT License
+Copyright (c) 2017 Sean Barrett
+Permission is hereby granted, free of charge, to any person obtaining a copy of 
+this software and associated documentation files (the "Software"), to deal in 
+the Software without restriction, including without limitation the rights to 
+use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies 
+of the Software, and to permit persons to whom the Software is furnished to do 
+so, subject to the following conditions:
+The above copyright notice and this permission notice shall be included in all 
+copies or substantial portions of the Software.
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 
+SOFTWARE.
+------------------------------------------------------------------------------
+ALTERNATIVE B - Public Domain (www.unlicense.org)
+This is free and unencumbered software released into the public domain.
+Anyone is free to copy, modify, publish, use, compile, sell, or distribute this 
+software, either in source code form or as a compiled binary, for any purpose, 
+commercial or non-commercial, and by any means.
+In jurisdictions that recognize copyright laws, the author or authors of this 
+software dedicate any and all copyright interest in the software to the public 
+domain. We make this dedication for the benefit of the public at large and to 
+the detriment of our heirs and successors. We intend this dedication to be an 
+overt act of relinquishment in perpetuity of all present and future rights to 
+this software under copyright law.
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 
+AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN 
+ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION 
+WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+------------------------------------------------------------------------------
+*/
diff --git a/util.h b/util.h
new file mode 100644
index 0000000..d13dfae
--- /dev/null
+++ b/util.h
@@ -0,0 +1,17 @@
+#ifndef UTIL_H
+#define UTIL_H
+
+#include <stdio.h> // fprintf()
+#include <stdlib.h> // exit()
+
+#define MAX(a, b) ((a) > (b) ? (a) : (b))
+#define UNUSED(a) ((void) (a))
+
+#define die(...) do { \
+  fputs("FATAL: ", stderr); \
+  fprintf(stderr, __VA_ARGS__); \
+  fputs("\n", stderr); \
+  exit(EXIT_FAILURE); \
+} while (0)
+
+#endif /* UTIL_H */