From 2a673a8cb44fe34e1a0feed7fb40d7fc9e0203cd Mon Sep 17 00:00:00 2001
From: Mitya Selivanov <automainint@guattari.tech>
Date: Fri, 9 Dec 2022 20:08:07 +0100
Subject: [bitint] Division
---
source/kit/bigint.h | 284 ++++++++++++++++++++++++++++++------
source/test/unittests/bigint.test.c | 2 -
2 files changed, 243 insertions(+), 43 deletions(-)
(limited to 'source')
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");
--
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