diff --git a/src/hb-buffer.cc b/src/hb-buffer.cc
index 7b95aea..d04e1e8 100644
--- a/src/hb-buffer.cc
+++ b/src/hb-buffer.cc
@@ -124,14 +124,14 @@
   hb_glyph_info_t *new_info = nullptr;
   bool separate_out = out_info != info;
 
-  if (unlikely (_hb_unsigned_int_mul_overflows (size, sizeof (info[0]))))
+  if (unlikely (hb_unsigned_mul_overflows (size, sizeof (info[0]))))
     goto done;
 
   while (size >= new_allocated)
     new_allocated += (new_allocated >> 1) + 32;
 
   static_assert ((sizeof (info[0]) == sizeof (pos[0])), "");
-  if (unlikely (_hb_unsigned_int_mul_overflows (new_allocated, sizeof (info[0]))))
+  if (unlikely (hb_unsigned_mul_overflows (new_allocated, sizeof (info[0]))))
     goto done;
 
   new_pos = (hb_glyph_position_t *) realloc (pos, new_allocated * sizeof (pos[0]));
diff --git a/src/hb-dsalgs.hh b/src/hb-dsalgs.hh
index 0e44d7c..ef48fb0 100644
--- a/src/hb-dsalgs.hh
+++ b/src/hb-dsalgs.hh
@@ -278,7 +278,7 @@
     }
     else
     {
-      bool overflows = (new_allocated < allocated) || _hb_unsigned_int_mul_overflows (new_allocated, sizeof (Type));
+      bool overflows = (new_allocated < allocated) || hb_unsigned_mul_overflows (new_allocated, sizeof (Type));
       if (likely (!overflows))
         new_array = (Type *) realloc (arrayZ, new_allocated * sizeof (Type));
     }
diff --git a/src/hb-map-private.hh b/src/hb-map-private.hh
index d3d4dde..c4f2fc7 100644
--- a/src/hb-map-private.hh
+++ b/src/hb-map-private.hh
@@ -89,7 +89,7 @@
   {
     if (unlikely (!successful)) return false;
 
-    unsigned int power = _hb_bit_storage (population * 2 + 8);
+    unsigned int power = hb_bit_storage (population * 2 + 8);
     unsigned int new_size = 1u << power;
     item_t *new_items = (item_t *) malloc ((size_t) new_size * sizeof (item_t));
     if (unlikely (!new_items))
diff --git a/src/hb-open-type-private.hh b/src/hb-open-type-private.hh
index 9a4835b..59b8cc0 100644
--- a/src/hb-open-type-private.hh
+++ b/src/hb-open-type-private.hh
@@ -230,7 +230,7 @@
   inline bool check_array (const void *base, unsigned int record_size, unsigned int len) const
   {
     const char *p = (const char *) base;
-    bool overflows = _hb_unsigned_int_mul_overflows (len, record_size);
+    bool overflows = hb_unsigned_mul_overflows (len, record_size);
     unsigned int array_size = record_size * len;
     bool ok = !overflows && this->check_range (base, array_size);
 
@@ -1178,7 +1178,7 @@
   {
     len.set (v);
     assert (len == v);
-    entrySelector.set (MAX (1u, _hb_bit_storage (v)) - 1);
+    entrySelector.set (MAX (1u, hb_bit_storage (v)) - 1);
     searchRange.set (16 * (1u << entrySelector));
     rangeShift.set (v * 16 > searchRange
 		    ? 16 * v - searchRange
diff --git a/src/hb-ot-cmap-table.hh b/src/hb-ot-cmap-table.hh
index c1903f6..0ea3720 100644
--- a/src/hb-ot-cmap-table.hh
+++ b/src/hb-ot-cmap-table.hh
@@ -89,7 +89,7 @@
     this->length.set (get_sub_table_size (segments));
 
     this->segCountX2.set (segments.len * 2);
-    this->entrySelector.set (MAX (1u, _hb_bit_storage (segments.len)) - 1);
+    this->entrySelector.set (MAX (1u, hb_bit_storage (segments.len)) - 1);
     this->searchRange.set (2 * (1u << this->entrySelector));
     this->rangeShift.set (segments.len * 2 > this->searchRange
                           ? 2 * segments.len - this->searchRange
diff --git a/src/hb-ot-hdmx-table.hh b/src/hb-ot-hdmx-table.hh
index d406e3e..0951871 100644
--- a/src/hb-ot-hdmx-table.hh
+++ b/src/hb-ot-hdmx-table.hh
@@ -199,7 +199,7 @@
   {
     TRACE_SANITIZE (this);
     return_trace (c->check_struct (this) && version == 0 &&
-		  !_hb_unsigned_int_mul_overflows (num_records, size_device_record) &&
+		  !hb_unsigned_mul_overflows (num_records, size_device_record) &&
 		  size_device_record >= DeviceRecord::min_size &&
 		  c->check_range (this, get_size()));
   }
diff --git a/src/hb-ot-layout-gpos-table.hh b/src/hb-ot-layout-gpos-table.hh
index 182c8d9..b52c014 100644
--- a/src/hb-ot-layout-gpos-table.hh
+++ b/src/hb-ot-layout-gpos-table.hh
@@ -99,7 +99,7 @@
 #endif
 
   inline unsigned int get_len (void) const
-  { return _hb_popcount ((unsigned int) *this); }
+  { return hb_popcount ((unsigned int) *this); }
   inline unsigned int get_size (void) const
   { return get_len () * Value::static_size; }
 
@@ -374,7 +374,7 @@
   {
     TRACE_SANITIZE (this);
     if (!c->check_struct (this)) return_trace (false);
-    if (unlikely (_hb_unsigned_int_mul_overflows (rows, cols))) return_trace (false);
+    if (unlikely (hb_unsigned_mul_overflows (rows, cols))) return_trace (false);
     unsigned int count = rows * cols;
     if (!c->check_array (matrixZ, matrixZ[0].static_size, count)) return_trace (false);
     for (unsigned int i = 0; i < count; i++)
diff --git a/src/hb-ot-layout-gsub-table.hh b/src/hb-ot-layout-gsub-table.hh
index bd72fe6..91b898b 100644
--- a/src/hb-ot-layout-gsub-table.hh
+++ b/src/hb-ot-layout-gsub-table.hh
@@ -511,7 +511,7 @@
     hb_mask_t lookup_mask = c->lookup_mask;
 
     /* Note: This breaks badly if two features enabled this lookup together. */
-    unsigned int shift = _hb_ctz (lookup_mask);
+    unsigned int shift = hb_ctz (lookup_mask);
     unsigned int alt_index = ((lookup_mask & glyph_mask) >> shift);
 
     if (unlikely (alt_index > alt_set.len || alt_index == 0)) return_trace (false);
diff --git a/src/hb-ot-map.cc b/src/hb-ot-map.cc
index 46bf2db..f26cac9 100644
--- a/src/hb-ot-map.cc
+++ b/src/hb-ot-map.cc
@@ -145,7 +145,7 @@
 {
   static_assert ((!(HB_GLYPH_FLAG_DEFINED & (HB_GLYPH_FLAG_DEFINED + 1))), "");
   unsigned int global_bit_mask = HB_GLYPH_FLAG_DEFINED + 1;
-  unsigned int global_bit_shift = _hb_popcount (HB_GLYPH_FLAG_DEFINED);
+  unsigned int global_bit_shift = hb_popcount (HB_GLYPH_FLAG_DEFINED);
 
   m.global_mask = global_bit_mask;
 
@@ -209,7 +209,7 @@
       bits_needed = 0;
     else
       /* Limit to 8 bits per feature. */
-      bits_needed = MIN(8u, _hb_bit_storage (info->max_value));
+      bits_needed = MIN(8u, hb_bit_storage (info->max_value));
 
     if (!info->max_value || next_bit + bits_needed > 8 * sizeof (hb_mask_t))
       continue; /* Feature disabled, or not enough bits. */
diff --git a/src/hb-ot-shape.cc b/src/hb-ot-shape.cc
index 36e0bf9..1189b20 100644
--- a/src/hb-ot-shape.cc
+++ b/src/hb-ot-shape.cc
@@ -829,12 +829,12 @@
 {
   c->buffer->deallocate_var_all ();
   c->buffer->scratch_flags = HB_BUFFER_SCRATCH_FLAG_DEFAULT;
-  if (likely (!_hb_unsigned_int_mul_overflows (c->buffer->len, HB_BUFFER_MAX_LEN_FACTOR)))
+  if (likely (!hb_unsigned_mul_overflows (c->buffer->len, HB_BUFFER_MAX_LEN_FACTOR)))
   {
     c->buffer->max_len = MAX (c->buffer->len * HB_BUFFER_MAX_LEN_FACTOR,
 			      (unsigned) HB_BUFFER_MAX_LEN_MIN);
   }
-  if (likely (!_hb_unsigned_int_mul_overflows (c->buffer->len, HB_BUFFER_MAX_OPS_FACTOR)))
+  if (likely (!hb_unsigned_mul_overflows (c->buffer->len, HB_BUFFER_MAX_OPS_FACTOR)))
   {
     c->buffer->max_ops = MAX (c->buffer->len * HB_BUFFER_MAX_OPS_FACTOR,
 			      (unsigned) HB_BUFFER_MAX_OPS_MIN);
diff --git a/src/hb-private.hh b/src/hb-private.hh
index 65d4bae..fa9a1ae 100644
--- a/src/hb-private.hh
+++ b/src/hb-private.hh
@@ -362,7 +362,7 @@
 /* Return the number of 1 bits in v. */
 template <typename T>
 static inline HB_CONST_FUNC unsigned int
-_hb_popcount (T v)
+hb_popcount (T v)
 {
 #if (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4)) && defined(__OPTIMIZE__)
   if (sizeof (T) <= sizeof (unsigned int))
@@ -387,13 +387,13 @@
   if (sizeof (T) == 8)
   {
     unsigned int shift = 32;
-    return _hb_popcount<uint32_t> ((uint32_t) v) + _hb_popcount ((uint32_t) (v >> shift));
+    return hb_popcount<uint32_t> ((uint32_t) v) + hb_popcount ((uint32_t) (v >> shift));
   }
 
   if (sizeof (T) == 16)
   {
     unsigned int shift = 64;
-    return _hb_popcount<uint64_t> ((uint64_t) v) + _hb_popcount ((uint64_t) (v >> shift));
+    return hb_popcount<uint64_t> ((uint64_t) v) + hb_popcount ((uint64_t) (v >> shift));
   }
 
   assert (0);
@@ -403,7 +403,7 @@
 /* Returns the number of bits needed to store number */
 template <typename T>
 static inline HB_CONST_FUNC unsigned int
-_hb_bit_storage (T v)
+hb_bit_storage (T v)
 {
   if (unlikely (!v)) return 0;
 
@@ -466,8 +466,8 @@
   if (sizeof (T) == 16)
   {
     unsigned int shift = 64;
-    return (v >> shift) ? _hb_bit_storage<uint64_t> ((uint64_t) (v >> shift)) + shift :
-			  _hb_bit_storage<uint64_t> ((uint64_t) v);
+    return (v >> shift) ? hb_bit_storage<uint64_t> ((uint64_t) (v >> shift)) + shift :
+			  hb_bit_storage<uint64_t> ((uint64_t) v);
   }
 
   assert (0);
@@ -477,7 +477,7 @@
 /* Returns the number of zero bits in the least significant side of v */
 template <typename T>
 static inline HB_CONST_FUNC unsigned int
-_hb_ctz (T v)
+hb_ctz (T v)
 {
   if (unlikely (!v)) return 0;
 
@@ -539,8 +539,8 @@
   if (sizeof (T) == 16)
   {
     unsigned int shift = 64;
-    return (uint64_t) v ? _hb_bit_storage<uint64_t> ((uint64_t) v) :
-			  _hb_bit_storage<uint64_t> ((uint64_t) v >> shift) + shift;
+    return (uint64_t) v ? hb_bit_storage<uint64_t> ((uint64_t) v) :
+			  hb_bit_storage<uint64_t> ((uint64_t) v >> shift) + shift;
   }
 
   assert (0);
@@ -548,18 +548,19 @@
 }
 
 static inline bool
-_hb_unsigned_int_mul_overflows (unsigned int count, unsigned int size)
+hb_unsigned_mul_overflows (unsigned int count, unsigned int size)
 {
   return (size > 0) && (count >= ((unsigned int) -1) / size);
 }
 
 static inline unsigned int
-_hb_ceil_to_4 (unsigned int v)
+hb_ceil_to_4 (unsigned int v)
 {
   return ((v - 1) | 3) + 1;
 }
 
-static inline bool _hb_ispow2 (unsigned int v)
+static inline bool
+hb_ispow2 (unsigned int v)
 {
   return 0 == (v & (v - 1));
 }
@@ -925,7 +926,7 @@
 static inline int
 _hb_memalign(void **memptr, size_t alignment, size_t size)
 {
-  if (unlikely (!_hb_ispow2 (alignment) ||
+  if (unlikely (!hb_ispow2 (alignment) ||
 		!alignment ||
 		0 != (alignment & (sizeof (void *) - 1))))
     return EINVAL;
diff --git a/src/hb-set-private.hh b/src/hb-set-private.hh
index 6841189..bdaf3f1a 100644
--- a/src/hb-set-private.hh
+++ b/src/hb-set-private.hh
@@ -94,7 +94,7 @@
     {
       unsigned int pop = 0;
       for (unsigned int i = 0; i < len (); i++)
-        pop += _hb_popcount (v[i]);
+        pop += hb_popcount (v[i]);
       return pop;
     }
 
@@ -161,8 +161,8 @@
     static const unsigned int PAGE_BITS = 512;
     static_assert ((PAGE_BITS & ((PAGE_BITS) - 1)) == 0, "");
 
-    static inline unsigned int elt_get_min (const elt_t &elt) { return _hb_ctz (elt); }
-    static inline unsigned int elt_get_max (const elt_t &elt) { return _hb_bit_storage (elt) - 1; }
+    static inline unsigned int elt_get_min (const elt_t &elt) { return hb_ctz (elt); }
+    static inline unsigned int elt_get_max (const elt_t &elt) { return hb_bit_storage (elt) - 1; }
 
     typedef hb_vector_size_t<elt_t, PAGE_BITS / 8> vector_t;
 
diff --git a/src/hb-subset.cc b/src/hb-subset.cc
index b97c763..e860634 100644
--- a/src/hb-subset.cc
+++ b/src/hb-subset.cc
@@ -154,7 +154,7 @@
   unsigned int face_length = table_count * 16 + 12;
 
   for (unsigned int i = 0; i < table_count; i++)
-    face_length += _hb_ceil_to_4 (hb_blob_get_length (data->tables.arrayZ[i].blob));
+    face_length += hb_ceil_to_4 (hb_blob_get_length (data->tables.arrayZ[i].blob));
 
   char *buf = (char *) malloc (face_length);
   if (unlikely (!buf))