源代码出处：github blue-app-eth/src_common。
这个源代码包括两个文件，分别是uint256.h和uint256.c。
有关计算是基于类型uint128_t上实现的。
uint256.h代码如下：
/*******************************************************************************
* Ledger Blue
* (c) 2016 Ledger
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
********************************************************************************/
// Adapted from https://github.com/calccrypto/uint256_t
#include <stdint.h>
#include <stdbool.h>
typedef struct uint128_t { uint64_t elements[2]; } uint128_t;
typedef struct uint256_t { uint128_t elements[2]; } uint256_t;
#define UPPER_P(x) x->elements[0]
#define LOWER_P(x) x->elements[1]
#define UPPER(x) x.elements[0]
#define LOWER(x) x.elements[1]
void readu128BE(uint8_t *buffer, uint128_t *target);
void readu256BE(uint8_t *buffer, uint256_t *target);
bool zero128(uint128_t *number);
bool zero256(uint256_t *number);
void copy128(uint128_t *target, uint128_t *number);
void copy256(uint256_t *target, uint256_t *number);
void clear128(uint128_t *target);
void clear256(uint256_t *target);
void shiftl128(uint128_t *number, uint32_t value, uint128_t *target);
void shiftr128(uint128_t *number, uint32_t value, uint128_t *target);
void shiftl256(uint256_t *number, uint32_t value, uint256_t *target);
void shiftr256(uint256_t *number, uint32_t value, uint256_t *target);
uint32_t bits128(uint128_t *number);
uint32_t bits256(uint256_t *number);
bool equal128(uint128_t *number1, uint128_t *number2);
bool equal256(uint256_t *number1, uint256_t *number2);
bool gt128(uint128_t *number1, uint128_t *number2);
bool gt256(uint256_t *number1, uint256_t *number2);
bool gte128(uint128_t *number1, uint128_t *number2);
bool gte256(uint256_t *number1, uint256_t *number2);
void add128(uint128_t *number1, uint128_t *number2, uint128_t *target);
void add256(uint256_t *number1, uint256_t *number2, uint256_t *target);
void minus128(uint128_t *number1, uint128_t *number2, uint128_t *target);
void minus256(uint256_t *number1, uint256_t *number2, uint256_t *target);
void or128(uint128_t *number1, uint128_t *number2, uint128_t *target);
void or256(uint256_t *number1, uint256_t *number2, uint256_t *target);
void mul128(uint128_t *number1, uint128_t *number2, uint128_t *target);
void mul256(uint256_t *number1, uint256_t *number2, uint256_t *target);
void divmod128(uint128_t *l, uint128_t *r, uint128_t *div, uint128_t *mod);
void divmod256(uint256_t *l, uint256_t *r, uint256_t *div, uint256_t *mod);
bool tostring128(uint128_t *number, uint32_t base, char *out,
uint32_t outLength);
bool tostring256(uint256_t *number, uint32_t base, char *out,
uint32_t outLength);uint256.c代码如下：
/*******************************************************************************
* Ledger Blue
* (c) 2016 Ledger
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
********************************************************************************/
// Adapted from https://github.com/calccrypto/uint256_t
#include <stdio.h>
#include <stdlib.h>
#include "uint256.h"
static const char HEXDIGITS[] = "0123456789abcdef";
static uint64_t readUint64BE(uint8_t *buffer) {
return (((uint64_t)buffer[0]) << 56) | (((uint64_t)buffer[1]) << 48) |
(((uint64_t)buffer[2]) << 40) | (((uint64_t)buffer[3]) << 32) |
(((uint64_t)buffer[4]) << 24) | (((uint64_t)buffer[5]) << 16) |
(((uint64_t)buffer[6]) << 8) | (((uint64_t)buffer[7]));
}
void readu128BE(uint8_t *buffer, uint128_t *target) {
UPPER_P(target) = readUint64BE(buffer);
LOWER_P(target) = readUint64BE(buffer + 8);
}
void readu256BE(uint8_t *buffer, uint256_t *target) {
readu128BE(buffer, &UPPER_P(target));
readu128BE(buffer + 16, &LOWER_P(target));
}
bool zero128(uint128_t *number) {
return ((LOWER_P(number) == 0) && (UPPER_P(number) == 0));
}
bool zero256(uint256_t *number) {
return (zero128(&LOWER_P(number)) && zero128(&UPPER_P(number)));
}
void copy128(uint128_t *target, uint128_t *number) {
UPPER_P(target) = UPPER_P(number);
LOWER_P(target) = LOWER_P(number);
}
void copy256(uint256_t *target, uint256_t *number) {
copy128(&UPPER_P(target), &UPPER_P(number));
copy128(&LOWER_P(target), &LOWER_P(number));
}
void clear128(uint128_t *target) {
UPPER_P(target) = 0;
LOWER_P(target) = 0;
}
void clear256(uint256_t *target) {
clear128(&UPPER_P(target));
clear128(&LOWER_P(target));
}
void shiftl128(uint128_t *number, uint32_t value, uint128_t *target) {
if (value >= 128) {
clear128(target);
} else if (value == 64) {
UPPER_P(target) = LOWER_P(number);
LOWER_P(target) = 0;
} else if (value == 0) {
copy128(target, number);
} else if (value < 64) {
UPPER_P(target) =
(UPPER_P(number) << value) + (LOWER_P(number) >> (64 - value));
LOWER_P(target) = (LOWER_P(number) << value);
} else if ((128 > value) && (value > 64)) {
UPPER_P(target) = LOWER_P(number) << (value - 64);
LOWER_P(target) = 0;
} else {
clear128(target);
}
}
void shiftl256(uint256_t *number, uint32_t value, uint256_t *target) {
if (value >= 256) {
clear256(target);
} else if (value == 128) {
copy128(&UPPER_P(target), &LOWER_P(number));
clear128(&LOWER_P(target));
} else if (value == 0) {
copy256(target, number);
} else if (value < 128) {
uint128_t tmp1;
uint128_t tmp2;
uint256_t result;
shiftl128(&UPPER_P(number), value, &tmp1);
shiftr128(&LOWER_P(number), (128 - value), &tmp2);
add128(&tmp1, &tmp2, &UPPER(result));
shiftl128(&LOWER_P(number), value, &LOWER(result));
copy256(target, &result);
} else if ((256 > value) && (value > 128)) {
shiftl128(&LOWER_P(number), (value - 128), &UPPER_P(target));
clear128(&LOWER_P(target));
} else {
clear256(target);
}
}
void shiftr128(uint128_t *number, uint32_t value, uint128_t *target) {
if (value >= 128) {
clear128(target);
} else if (value == 64) {
UPPER_P(target) = 0;
LOWER_P(target) = UPPER_P(number);
} else if (value == 0) {
copy128(target, number);
} else if (value < 64) {
uint128_t result;
UPPER(result) = UPPER_P(number) >> value;
LOWER(result) =
(UPPER_P(number) << (64 - value)) + (LOWER_P(number) >> value);
copy128(target, &result);
} else if ((128 > value) && (value > 64)) {
LOWER_P(target) = UPPER_P(number) >> (value - 64);
UPPER_P(target) = 0;
} else {
clear128(target);
}
}
void shiftr256(uint256_t *number, uint32_t value, uint256_t *target) {
if (value >= 256) {
clear256(target);
} else if (value == 128) {
copy128(&LOWER_P(target), &UPPER_P(number));
clear128(&UPPER_P(target));
} else if (value == 0) {
copy256(target, number);
} else if (value < 128) {
uint128_t tmp1;
uint128_t tmp2;
uint256_t result;
shiftr128(&UPPER_P(number), value, &UPPER(result));
shiftr128(&LOWER_P(number), value, &tmp1);
shiftl128(&UPPER_P(number), (128 - value), &tmp2);
add128(&tmp1, &tmp2, &LOWER(result));
copy256(target, &result);
} else if ((256 > value) && (value > 128)) {
shiftr128(&UPPER_P(number), (value - 128), &LOWER_P(target));
clear128(&UPPER_P(target));
} else {
clear256(target);
}
}
uint32_t bits128(uint128_t *number) {
uint32_t result = 0;
if (UPPER_P(number)) {
result = 64;
uint64_t up = UPPER_P(number);
while (up) {
up >>= 1;
result++;
}
} else {
uint64_t low = LOWER_P(number);
while (low) {
low >>= 1;
result++;
}
}
return result;
}
uint32_t bits256(uint256_t *number) {
uint32_t result = 0;
if (!zero128(&UPPER_P(number))) {
result = 128;
uint128_t up;
copy128(&up, &UPPER_P(number));
while (!zero128(&up)) {
shiftr128(&up, 1, &up);
result++;
}
} else {
uint128_t low;
copy128(&low, &LOWER_P(number));
while (!zero128(&low)) {
shiftr128(&low, 1, &low);
result++;
}
}
return result;
}
bool equal128(uint128_t *number1, uint128_t *number2) {
return (UPPER_P(number1) == UPPER_P(number2)) &&
(LOWER_P(number1) == LOWER_P(number2));
}
bool equal256(uint256_t *number1, uint256_t *number2) {
return (equal128(&UPPER_P(number1), &UPPER_P(number2)) &&
equal128(&LOWER_P(number1), &LOWER_P(number2)));
}
bool gt128(uint128_t *number1, uint128_t *number2) {
if (UPPER_P(number1) == UPPER_P(number2)) {
return (LOWER_P(number1) > LOWER_P(number2));
}
return (UPPER_P(number1) > UPPER_P(number2));
}
bool gt256(uint256_t *number1, uint256_t *number2) {
if (equal128(&UPPER_P(number1), &UPPER_P(number2))) {
return gt128(&LOWER_P(number1), &LOWER_P(number2));
}
return gt128(&UPPER_P(number1), &UPPER_P(number2));
}
bool gte128(uint128_t *number1, uint128_t *number2) {
return gt128(number1, number2) || equal128(number1, number2);
}
bool gte256(uint256_t *number1, uint256_t *number2) {
return gt256(number1, number2) || equal256(number1, number2);
}
void add128(uint128_t *number1, uint128_t *number2, uint128_t *target) {
UPPER_P(target) =
UPPER_P(number1) + UPPER_P(number2) +
((LOWER_P(number1) + LOWER_P(number2)) < LOWER_P(number1));
LOWER_P(target) = LOWER_P(number1) + LOWER_P(number2);
}
void add256(uint256_t *number1, uint256_t *number2, uint256_t *target) {
uint128_t tmp;
add128(&UPPER_P(number1), &UPPER_P(number2), &UPPER_P(target));
add128(&LOWER_P(number1), &LOWER_P(number2), &tmp);
if (gt128(&LOWER_P(number1), &tmp)) {
uint128_t one;
UPPER(one) = 0;
LOWER(one) = 1;
add128(&UPPER_P(target), &one, &UPPER_P(target));
}
add128(&LOWER_P(number1), &LOWER_P(number2), &LOWER_P(target));
}
void minus128(uint128_t *number1, uint128_t *number2, uint128_t *target) {
UPPER_P(target) =
UPPER_P(number1) - UPPER_P(number2) -
((LOWER_P(number1) - LOWER_P(number2)) > LOWER_P(number1));
LOWER_P(target) = LOWER_P(number1) - LOWER_P(number2);
}
void minus256(uint256_t *number1, uint256_t *number2, uint256_t *target) {
uint128_t tmp;
minus128(&UPPER_P(number1), &UPPER_P(number2), &UPPER_P(target));
minus128(&LOWER_P(number1), &LOWER_P(number2), &tmp);
if (gt128(&tmp, &LOWER_P(number1))) {
uint128_t one;
UPPER(one) = 0;
LOWER(one) = 1;
minus128(&UPPER_P(target), &one, &UPPER_P(target));
}
minus128(&LOWER_P(number1), &LOWER_P(number2), &LOWER_P(target));
}
void or128(uint128_t *number1, uint128_t *number2, uint128_t *target) {
UPPER_P(target) = UPPER_P(number1) | UPPER_P(number2);
LOWER_P(target) = LOWER_P(number1) | LOWER_P(number2);
}
void or256(uint256_t *number1, uint256_t *number2, uint256_t *target) {
or128(&UPPER_P(number1), &UPPER_P(number2), &UPPER_P(target));
or128(&LOWER_P(number1), &LOWER_P(number2), &LOWER_P(target));
}
void mul128(uint128_t *number1, uint128_t *number2, uint128_t *target) {
uint64_t top[4] = {UPPER_P(number1) >> 32, UPPER_P(number1) & 0xffffffff,
LOWER_P(number1) >> 32, LOWER_P(number1) & 0xffffffff};
uint64_t bottom[4] = {UPPER_P(number2) >> 32, UPPER_P(number2) & 0xffffffff,
LOWER_P(number2) >> 32,
LOWER_P(number2) & 0xffffffff};
uint64_t products[4][4];
uint128_t tmp, tmp2;
for (int y = 3; y > -1; y--) {
for (int x = 3; x > -1; x--) {
products[3 - x][y] = top[x] * bottom[y];
}
}
uint64_t fourth32 = products[0][3] & 0xffffffff;
uint64_t third32 = (products[0][2] & 0xffffffff) + (products[0][3] >> 32);
uint64_t second32 = (products[0][1] & 0xffffffff) + (products[0][2] >> 32);
uint64_t first32 = (products[0][0] & 0xffffffff) + (products[0][1] >> 32);
third32 += products[1][3] & 0xffffffff;
second32 += (products[1][2] & 0xffffffff) + (products[1][3] >> 32);
first32 += (products[1][1] & 0xffffffff) + (products[1][2] >> 32);
second32 += products[2][3] & 0xffffffff;
first32 += (products[2][2] & 0xffffffff) + (products[2][3] >> 32);
first32 += products[3][3] & 0xffffffff;
UPPER(tmp) = first32 << 32;
LOWER(tmp) = 0;
UPPER(tmp2) = third32 >> 32;
LOWER(tmp2) = third32 << 32;
add128(&tmp, &tmp2, target);
UPPER(tmp) = second32;
LOWER(tmp) = 0;
add128(&tmp, target, &tmp2);
UPPER(tmp) = 0;
LOWER(tmp) = fourth32;
add128(&tmp, &tmp2, target);
}
void mul256(uint256_t *number1, uint256_t *number2, uint256_t *target) {
uint128_t top[4];
uint128_t bottom[4];
uint128_t products[4][4];
uint128_t tmp, tmp2, fourth64, third64, second64, first64;
uint256_t target1, target2;
UPPER(top[0]) = 0;
LOWER(top[0]) = UPPER(UPPER_P(number1));
UPPER(top[1]) = 0;
LOWER(top[1]) = LOWER(UPPER_P(number1));
UPPER(top[2]) = 0;
LOWER(top[2]) = UPPER(LOWER_P(number1));
UPPER(top[3]) = 0;
LOWER(top[3]) = LOWER(LOWER_P(number1));
UPPER(bottom[0]) = 0;
LOWER(bottom[0]) = UPPER(UPPER_P(number2));
UPPER(bottom[1]) = 0;
LOWER(bottom[1]) = LOWER(UPPER_P(number2));
UPPER(bottom[2]) = 0;
LOWER(bottom[2]) = UPPER(LOWER_P(number2));
UPPER(bottom[3]) = 0;
LOWER(bottom[3]) = LOWER(LOWER_P(number2));
for (int y = 3; y > -1; y--) {
for (int x = 3; x > -1; x--) {
mul128(&top[x], &bottom[y], &products[3 - x][y]);
}
}
UPPER(fourth64) = 0;
LOWER(fourth64) = LOWER(products[0][3]);
UPPER(tmp) = 0;
LOWER(tmp) = LOWER(products[0][2]);
UPPER(tmp2) = 0;
LOWER(tmp2) = UPPER(products[0][3]);
add128(&tmp, &tmp2, &third64);
UPPER(tmp) = 0;
LOWER(tmp) = LOWER(products[0][1]);
UPPER(tmp2) = 0;
LOWER(tmp2) = UPPER(products[0][2]);
add128(&tmp, &tmp2, &second64);
UPPER(tmp) = 0;
LOWER(tmp) = LOWER(products[0][0]);
UPPER(tmp2) = 0;
LOWER(tmp2) = UPPER(products[0][1]);
add128(&tmp, &tmp2, &first64);
UPPER(tmp) = 0;
LOWER(tmp) = LOWER(products[1][3]);
add128(&tmp, &third64, &tmp2);
copy128(&third64, &tmp2);
UPPER(tmp) = 0;
LOWER(tmp) = LOWER(products[1][2]);
add128(&tmp, &second64, &tmp2);
UPPER(tmp) = 0;
LOWER(tmp) = UPPER(products[1][3]);
add128(&tmp, &tmp2, &second64);
UPPER(tmp) = 0;
LOWER(tmp) = LOWER(products[1][1]);
add128(&tmp, &first64, &tmp2);
UPPER(tmp) = 0;
LOWER(tmp) = UPPER(products[1][2]);
add128(&tmp, &tmp2, &first64);
UPPER(tmp) = 0;
LOWER(tmp) = LOWER(products[2][3]);
add128(&tmp, &second64, &tmp2);
copy128(&second64, &tmp2);
UPPER(tmp) = 0;
LOWER(tmp) = LOWER(products[2][2]);
add128(&tmp, &first64, &tmp2);
UPPER(tmp) = 0;
LOWER(tmp) = UPPER(products[2][3]);
add128(&tmp, &tmp2, &first64);
UPPER(tmp) = 0;
LOWER(tmp) = LOWER(products[3][3]);
add128(&tmp, &first64, &tmp2);
copy128(&first64, &tmp2);
clear256(&target1);
shiftl128(&first64, 64, &UPPER(target1));
clear256(&target2);
UPPER(UPPER(target2)) = UPPER(third64);
shiftl128(&third64, 64, &LOWER(target2));
add256(&target1, &target2, target);
clear256(&target1);
copy128(&UPPER(target1), &second64);
add256(&target1, target, &target2);
clear256(&target1);
copy128(&LOWER(target1), &fourth64);
add256(&target1, &target2, target);
}
void divmod128(uint128_t *l, uint128_t *r, uint128_t *retDiv,
uint128_t *retMod) {
uint128_t copyd, adder, resDiv, resMod;
uint128_t one;
UPPER(one) = 0;
LOWER(one) = 1;
uint32_t diffBits = bits128(l) - bits128(r);
clear128(&resDiv);
copy128(&resMod, l);
if (gt128(r, l)) {
copy128(retMod, l);
clear128(retDiv);
} else {
shiftl128(r, diffBits, ©d);
shiftl128(&one, diffBits, &adder);
if (gt128(©d, &resMod)) {
shiftr128(©d, 1, ©d);
shiftr128(&adder, 1, &adder);
}
while (gte128(&resMod, r)) {
if (gte128(&resMod, ©d)) {
minus128(&resMod, ©d, &resMod);
or128(&resDiv, &adder, &resDiv);
}
shiftr128(©d, 1, ©d);
shiftr128(&adder, 1, &adder);
}
copy128(retDiv, &resDiv);
copy128(retMod, &resMod);
}
}
void divmod256(uint256_t *l, uint256_t *r, uint256_t *retDiv,
uint256_t *retMod) {
uint256_t copyd, adder, resDiv, resMod;
uint256_t one;
clear256(&one);
UPPER(LOWER(one)) = 0;
LOWER(LOWER(one)) = 1;
uint32_t diffBits = bits256(l) - bits256(r);
clear256(&resDiv);
copy256(&resMod, l);
if (gt256(r, l)) {
copy256(retMod, l);
clear256(retDiv);
} else {
shiftl256(r, diffBits, ©d);
shiftl256(&one, diffBits, &adder);
if (gt256(©d, &resMod)) {
shiftr256(©d, 1, ©d);
shiftr256(&adder, 1, &adder);
}
while (gte256(&resMod, r)) {
if (gte256(&resMod, ©d)) {
minus256(&resMod, ©d, &resMod);
or256(&resDiv, &adder, &resDiv);
}
shiftr256(©d, 1, ©d);
shiftr256(&adder, 1, &adder);
}
copy256(retDiv, &resDiv);
copy256(retMod, &resMod);
}
}
static void reverseString(char *str, uint32_t length) {
uint32_t i, j;
for (i = 0, j = length - 1; i < j; i++, j--) {
uint8_t c;
c = str[i];
str[i] = str[j];
str[j] = c;
}
}
bool tostring128(uint128_t *number, uint32_t baseParam, char *out,
uint32_t outLength) {
uint128_t rDiv;
uint128_t rMod;
uint128_t base;
copy128(&rDiv, number);
clear128(&rMod);
clear128(&base);
LOWER(base) = baseParam;
uint32_t offset = 0;
if ((baseParam < 2) || (baseParam > 16)) {
return false;
}
do {
if (offset > (outLength - 1)) {
return false;
}
divmod128(&rDiv, &base, &rDiv, &rMod);
out[offset++] = HEXDIGITS[(uint8_t)LOWER(rMod)];
} while (!zero128(&rDiv));
out[offset] = ' ';
reverseString(out, offset);
return true;
}
bool tostring256(uint256_t *number, uint32_t baseParam, char *out,
uint32_t outLength) {
uint256_t rDiv;
uint256_t rMod;
uint256_t base;
copy256(&rDiv, number);
clear256(&rMod);
clear256(&base);
UPPER(LOWER(base)) = 0;
LOWER(LOWER(base)) = baseParam;
uint32_t offset = 0;
if ((baseParam < 2) || (baseParam > 16)) {
return false;
}
do {
if (offset > (outLength - 1)) {
return false;
}
divmod256(&rDiv, &base, &rDiv, &rMod);
out[offset++] = HEXDIGITS[(uint8_t)LOWER(LOWER(rMod))];
} while (!zero256(&rDiv));
out[offset] = ' ';
reverseString(out, offset);
return true;
}