[bitint] Division

2 files changed, 243 insertions, 43 deletions

diff --git a/source/kit/bigint.h b/source/kit/bigint.h
index 2ad7514..26268a6 100644
--- a/source/kit/bigint.h
+++ b/source/kit/bigint.h
@@ -52,36 +52,6 @@ typedef uint_fast8_t  kit_bit_t;
 #  pragma GCC            optimize("O3")
 #endif
 
-static uint8_t kit_hex_digit(char const hex) {
-  if (hex >= '0' && hex <= '9')
-    return hex - '0';
-  if (hex >= 'a' && hex <= 'f')
-    return hex - 'a';
-  if (hex >= 'A' && hex <= 'F')
-    return hex - 'A';
-  return 0;
-}
-
-static uint8_t kit_base58_digit(char const c) {
-  static const uint8_t BASE58_DIGITS[] = {
-    ['1'] = 0,  ['2'] = 1,  ['3'] = 2,  ['4'] = 3,  ['5'] = 4,
-    ['6'] = 5,  ['7'] = 6,  ['8'] = 7,  ['9'] = 8,  ['A'] = 9,
-    ['B'] = 10, ['C'] = 11, ['D'] = 12, ['E'] = 13, ['F'] = 14,
-    ['G'] = 15, ['H'] = 16, ['J'] = 17, ['K'] = 18, ['L'] = 19,
-    ['M'] = 20, ['N'] = 21, ['P'] = 22, ['Q'] = 23, ['R'] = 24,
-    ['S'] = 25, ['T'] = 26, ['U'] = 27, ['V'] = 28, ['W'] = 29,
-    ['X'] = 30, ['Y'] = 31, ['Z'] = 32, ['a'] = 33, ['b'] = 34,
-    ['c'] = 35, ['d'] = 36, ['e'] = 37, ['f'] = 38, ['g'] = 39,
-    ['h'] = 40, ['i'] = 41, ['j'] = 42, ['k'] = 43, ['m'] = 44,
-    ['n'] = 45, ['o'] = 46, ['p'] = 47, ['q'] = 48, ['r'] = 49,
-    ['s'] = 50, ['t'] = 51, ['u'] = 52, ['v'] = 53, ['w'] = 54,
-    ['x'] = 55, ['y'] = 56, ['z'] = 57
-  };
-  return c >= '\0' && c < (sizeof BASE58_DIGITS)
-             ? BASE58_DIGITS[(size_t) (unsigned char) c]
-             : 0;
-}
-
 static kit_bigint_t kit_bi_uword(kit_uword_t const x) {
   kit_bigint_t z;
   memset(z.v8, 0, KIT_BIGINT_SIZE);
@@ -96,22 +66,109 @@ static kit_bigint_t kit_bi_uint64(uint64_t const x) {
   return z;
 }
 
-static kit_bigint_t kit_bi_hex(kit_str_t const hex) {
+static int kit_bi_equal(kit_bigint_t const x, kit_bigint_t const y) {
+  return kit_ar_equal_bytes(1, KIT_BIGINT_SIZE, x.v8, 1,
+                            KIT_BIGINT_SIZE, y.v8);
+}
+
+static int kit_bi_compare(kit_bigint_t const x,
+                          kit_bigint_t const y) {
+  for (ptrdiff_t i = KIT_BIGINT_SIZE / KIT_UWORD_SIZE - 1; i >= 0;
+       i--)
+    if (x.v[i] < y.v[i])
+      return -1;
+    else if (x.v[i] > y.v[i])
+      return 1;
+  return 0;
+}
+
+static ptrdiff_t kit_bi_significant_bit_count(kit_bigint_t const x) {
+  ptrdiff_t bytes = KIT_BIGINT_SIZE - 1;
+
+  while (bytes > 0 && x.v8[bytes] == 0) bytes--;
+
+  uint8_t const byte = x.v8[bytes];
+
+  if (byte == 0)
+    return 0;
+
+  ptrdiff_t const bits = (byte & 0x80) != 0   ? 8
+                         : (byte & 0x40) != 0 ? 7
+                         : (byte & 0x20) != 0 ? 6
+                         : (byte & 0x10) != 0 ? 5
+                         : (byte & 0x08) != 0 ? 4
+                         : (byte & 0x04) != 0 ? 3
+                         : (byte & 0x02) != 0 ? 2
+                         : (byte & 0x01) != 0 ? 1
+                                              : 0;
+
+  return bytes * 8 + bits;
+}
+
+static kit_bigint_t kit_bi_and(kit_bigint_t const x,
+                               kit_bigint_t const y) {
+  kit_bigint_t z;
+
+  for (ptrdiff_t i = 0; i < KIT_BIGINT_SIZE / KIT_UWORD_SIZE; i++)
+    z.v[i] = x.v[i] & y.v[i];
+
+  return z;
+}
+
+static kit_bigint_t kit_bi_or(kit_bigint_t const x,
+                              kit_bigint_t const y) {
+  kit_bigint_t z;
+
+  for (ptrdiff_t i = 0; i < KIT_BIGINT_SIZE / KIT_UWORD_SIZE; i++)
+    z.v[i] = x.v[i] | y.v[i];
+
+  return z;
+}
+
+static kit_bigint_t kit_bi_xor(kit_bigint_t const x,
+                               kit_bigint_t const y) {
+  kit_bigint_t z;
+
+  for (ptrdiff_t i = 0; i < KIT_BIGINT_SIZE / KIT_UWORD_SIZE; i++)
+    z.v[i] = x.v[i] ^ y.v[i];
+
+  return z;
+}
+
+static kit_bigint_t kit_bi_shl_uword(kit_bigint_t const x,
+                                     kit_uword_t        y) {
   kit_bigint_t z;
   memset(z.v8, 0, KIT_BIGINT_SIZE);
 
-  for (ptrdiff_t i = 0; i < hex.size && i / 2 < KIT_BIGINT_SIZE;
+  ptrdiff_t const words = (ptrdiff_t) (y / (8 * KIT_UWORD_SIZE));
+  ptrdiff_t const bits  = (ptrdiff_t) (y % (8 * KIT_UWORD_SIZE));
+
+  for (ptrdiff_t i = words; i < KIT_BIGINT_SIZE / KIT_UWORD_SIZE;
        i++) {
-    uint8_t const digit = kit_hex_digit(hex.values[hex.size - i - 1]);
-    z.v8[i / 2] |= ((i % 2) == 0) ? digit : (digit << 4);
+    z.v[i] |= x.v[i - words] << bits;
+    if (bits != 0 && i + 1 < KIT_BIGINT_SIZE / KIT_UWORD_SIZE)
+      z.v[i + 1] = x.v[i - words] >> (8 * KIT_UWORD_SIZE - bits);
   }
 
   return z;
 }
 
-static int kit_bi_equal(kit_bigint_t const x, kit_bigint_t const y) {
-  return kit_ar_equal_bytes(1, KIT_BIGINT_SIZE, x.v8, 1,
-                            KIT_BIGINT_SIZE, y.v8);
+static kit_bigint_t kit_bi_shr_uword(kit_bigint_t const x,
+                                     kit_uword_t        y) {
+  kit_bigint_t z;
+  memset(z.v8, 0, KIT_BIGINT_SIZE);
+
+  ptrdiff_t const words = (ptrdiff_t) (y / (8 * KIT_UWORD_SIZE));
+  ptrdiff_t const bits  = (ptrdiff_t) (y % (8 * KIT_UWORD_SIZE));
+
+  for (ptrdiff_t i = KIT_BIGINT_SIZE / KIT_UWORD_SIZE - words - 1;
+       i >= 0; i--) {
+    z.v[i] |= x.v[i + words] >> bits;
+    if (bits != 0 && i > 0)
+      z.v[i - 1] = x.v[i + words] << (8 * KIT_UWORD_SIZE - bits);
+  }
+
+  return z;
 }
 
 static kit_bit_t kit_bi_carry(kit_uword_t const x,
@@ -210,6 +267,152 @@ static kit_bigint_t kit_bi_mul(kit_bigint_t const x,
   return z;
 }
 
+typedef struct {
+  kit_bit_t    undefined;
+  kit_bigint_t quotient;
+  kit_bigint_t remainder;
+} kit_bi_division_t;
+
+static kit_bi_division_t kit_bi_div(kit_bigint_t const x,
+                                    kit_bigint_t       y) {
+  kit_bi_division_t result;
+  memset(&result, 0, sizeof result);
+
+  ptrdiff_t const y_bits = kit_bi_significant_bit_count(y);
+
+  if (y_bits == 0) {
+    result.undefined = 1;
+    return result;
+  }
+
+  ptrdiff_t const x_bits = kit_bi_significant_bit_count(x);
+  ptrdiff_t       shift  = x_bits - y_bits;
+
+  result.remainder = x;
+  result.quotient  = kit_bi_uword(0);
+
+  y = kit_bi_shl_uword(y, (kit_uword_t) shift);
+
+  while (shift >= 0) {
+    if (kit_bi_compare(result.remainder, y) > 0) {
+      result.remainder = kit_bi_sub(result.remainder, y);
+      result.quotient.v8[shift / 8] |= (1u << (shift % 8));
+    }
+
+    y = kit_bi_shr_uword(y, 1);
+    shift--;
+  }
+
+  return result;
+}
+
+static uint8_t kit_bin_digit(char const hex) {
+  return hex == '1' ? 1 : 0;
+}
+
+static kit_bigint_t kit_bi_bin(kit_str_t const bin) {
+  kit_bigint_t z;
+  memset(z.v8, 0, KIT_BIGINT_SIZE);
+
+  for (ptrdiff_t i = 0; i < bin.size && i / 8 < KIT_BIGINT_SIZE;
+       i++) {
+    uint8_t const digit = kit_bin_digit(bin.values[bin.size - i - 1]);
+    z.v8[i / 8] |= digit << (i % 8);
+  }
+
+  return z;
+}
+
+static uint8_t kit_dec_digit(char const c) {
+  return c >= '0' && c <= '9' ? (uint8_t) (c - '0') : 0;
+}
+
+static kit_bigint_t kit_bi_dec(kit_str_t const dec) {
+  kit_bigint_t z      = kit_bi_uword(0);
+  kit_bigint_t factor = kit_bi_uword(1);
+
+  for (ptrdiff_t i = 0; i < dec.size; i++) {
+    uint32_t const digit = kit_dec_digit(
+        dec.values[dec.size - i - 1]);
+    z      = kit_bi_add(z, kit_bi_mul_uint32(factor, digit));
+    factor = kit_bi_mul_uint32(factor, 10);
+  }
+
+  return z;
+}
+
+static uint8_t kit_hex_digit(char const hex) {
+  if (hex >= '0' && hex <= '9')
+    return hex - '0';
+  if (hex >= 'a' && hex <= 'f')
+    return hex - 'a';
+  if (hex >= 'A' && hex <= 'F')
+    return hex - 'A';
+  return 0;
+}
+
+static kit_bigint_t kit_bi_hex(kit_str_t const hex) {
+  kit_bigint_t z;
+  memset(z.v8, 0, KIT_BIGINT_SIZE);
+
+  for (ptrdiff_t i = 0; i < hex.size && i / 2 < KIT_BIGINT_SIZE;
+       i++) {
+    uint8_t const digit = kit_hex_digit(hex.values[hex.size - i - 1]);
+    z.v8[i / 2] |= ((i % 2) == 0) ? digit : (digit << 4);
+  }
+
+  return z;
+}
+
+static const uint8_t KIT_BASE32_DIGITS[] = {
+  ['1'] = 0,  ['2'] = 1,  ['3'] = 2,  ['4'] = 3,  ['5'] = 4,
+  ['6'] = 5,  ['7'] = 6,  ['8'] = 7,  ['9'] = 8,  ['a'] = 9,
+  ['b'] = 10, ['c'] = 11, ['d'] = 12, ['e'] = 13, ['f'] = 14,
+  ['g'] = 15, ['h'] = 16, ['j'] = 17, ['k'] = 18, ['m'] = 19,
+  ['n'] = 20, ['p'] = 21, ['q'] = 22, ['r'] = 23, ['s'] = 24,
+  ['t'] = 25, ['u'] = 26, ['v'] = 27, ['w'] = 28, ['x'] = 29,
+  ['y'] = 30, ['z'] = 31
+};
+
+static uint8_t kit_base32_digit(char const c) {
+  return c >= '\0' && c < (sizeof KIT_BASE32_DIGITS)
+             ? KIT_BASE32_DIGITS[(size_t) (unsigned char) c]
+             : 0;
+}
+
+static kit_bigint_t kit_bi_base32(kit_str_t const base32) {
+  kit_bigint_t z;
+  memset(z.v8, 0, KIT_BIGINT_SIZE);
+
+  for (ptrdiff_t i = 0; i < base32.size; i++) {
+    z = kit_bi_shl_uword(z, 5 * i);
+    z.v8[i] |= kit_base32_digit(base32.values[i]);
+  }
+
+  return z;
+}
+
+static const uint8_t KIT_BASE58_DIGITS[] = {
+  ['1'] = 0,  ['2'] = 1,  ['3'] = 2,  ['4'] = 3,  ['5'] = 4,
+  ['6'] = 5,  ['7'] = 6,  ['8'] = 7,  ['9'] = 8,  ['A'] = 9,
+  ['B'] = 10, ['C'] = 11, ['D'] = 12, ['E'] = 13, ['F'] = 14,
+  ['G'] = 15, ['H'] = 16, ['J'] = 17, ['K'] = 18, ['L'] = 19,
+  ['M'] = 20, ['N'] = 21, ['P'] = 22, ['Q'] = 23, ['R'] = 24,
+  ['S'] = 25, ['T'] = 26, ['U'] = 27, ['V'] = 28, ['W'] = 29,
+  ['X'] = 30, ['Y'] = 31, ['Z'] = 32, ['a'] = 33, ['b'] = 34,
+  ['c'] = 35, ['d'] = 36, ['e'] = 37, ['f'] = 38, ['g'] = 39,
+  ['h'] = 40, ['i'] = 41, ['j'] = 42, ['k'] = 43, ['m'] = 44,
+  ['n'] = 45, ['o'] = 46, ['p'] = 47, ['q'] = 48, ['r'] = 49,
+  ['s'] = 50, ['t'] = 51, ['u'] = 52, ['v'] = 53, ['w'] = 54,
+  ['x'] = 55, ['y'] = 56, ['z'] = 57
+};
+
+static uint8_t kit_base58_digit(char const c) {
+  return c >= '\0' && c < (sizeof KIT_BASE58_DIGITS)
+             ? KIT_BASE58_DIGITS[(size_t) (unsigned char) c]
+             : 0;
+}
+
 static kit_bigint_t kit_bi_base58(kit_str_t const base58) {
   kit_bigint_t z      = kit_bi_uword(0);
   kit_bigint_t factor = kit_bi_uword(1);
@@ -231,18 +434,17 @@ static kit_bigint_t kit_bi_base58(kit_str_t const base58) {
 
 #ifndef KIT_DISABLE_SHORT_NAMES
 #  define bigint_t kit_bigint_t
-#  define hex_digit kit_hex_digit
-#  define base58_digit kit_base58_digit
 #  define bi_uword kit_bi_uword
 #  define bi_uint64 kit_bi_uint64
-#  define bi_hex kit_bi_hex
-#  define bi_base58 kit_bi_base58
 #  define bi_equal kit_bi_equal
 #  define bi_carry kit_bi_carry
 #  define bi_add kit_bi_add
 #  define bi_neg kit_bi_neg
 #  define bi_sub kit_bi_sub
 #  define bi_mul kit_bi_mul
+#  define hex_digit kit_hex_digit
+#  define bi_hex kit_bi_hex
+#  define bi_base58 kit_bi_base58
 #endif
 
 #ifdef __cplusplus
diff --git a/source/test/unittests/bigint.test.c b/source/test/unittests/bigint.test.c
index 7df2fcc..87bbc60 100644
--- a/source/test/unittests/bigint.test.c
+++ b/source/test/unittests/bigint.test.c
@@ -3,8 +3,6 @@
 #define KIT_TEST_FILE bigint
 #include "../../kit_test/test.h"
 
-#include <stdio.h>
-
 TEST("bigint hex add") {
   SZ(foo, "4242424242424242424242424242424242424242");
   SZ(bar, "1111111111111111111111111111111111111111");