/******************************************************************************* * Ledger Ethereum App * (c) 2016-2019 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 #include #include "uint128.h" #include "uint_common.h" #include "ethUtils.h" // HEXDIGITS void readu128BE(const uint8_t *const buffer, uint128_t *const target) { UPPER_P(target) = readUint64BE(buffer); LOWER_P(target) = readUint64BE(buffer + 8); } bool zero128(const uint128_t *const number) { return ((LOWER_P(number) == 0) && (UPPER_P(number) == 0)); } void copy128(uint128_t *const target, const uint128_t *const number) { UPPER_P(target) = UPPER_P(number); LOWER_P(target) = LOWER_P(number); } void clear128(uint128_t *const target) { UPPER_P(target) = 0; LOWER_P(target) = 0; } void shiftl128(const uint128_t *const number, uint32_t value, uint128_t *const 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 shiftr128(const uint128_t *const number, uint32_t value, uint128_t *const 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); } } uint32_t bits128(const uint128_t *const 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; } bool equal128(const uint128_t *const number1, const uint128_t *const number2) { return (UPPER_P(number1) == UPPER_P(number2)) && (LOWER_P(number1) == LOWER_P(number2)); } bool gt128(const uint128_t *const number1, const uint128_t *const number2) { if (UPPER_P(number1) == UPPER_P(number2)) { return (LOWER_P(number1) > LOWER_P(number2)); } return (UPPER_P(number1) > UPPER_P(number2)); } bool gte128(const uint128_t *const number1, const uint128_t *const number2) { return gt128(number1, number2) || equal128(number1, number2); } void add128(const uint128_t *const number1, const uint128_t *const number2, uint128_t *const 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 sub128(const uint128_t *const number1, const uint128_t *const number2, uint128_t *const 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 or128(const uint128_t *const number1, const uint128_t *const number2, uint128_t *const target) { UPPER_P(target) = UPPER_P(number1) | UPPER_P(number2); LOWER_P(target) = LOWER_P(number1) | LOWER_P(number2); } void mul128(const uint128_t *const number1, const uint128_t *const number2, uint128_t *const 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 divmod128(const uint128_t *const l, const uint128_t *const r, uint128_t *const retDiv, uint128_t *const 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)) { sub128(&resMod, ©d, &resMod); or128(&resDiv, &adder, &resDiv); } shiftr128(©d, 1, ©d); shiftr128(&adder, 1, &adder); } copy128(retDiv, &resDiv); copy128(retMod, &resMod); } } bool tostring128(const uint128_t *const number, uint32_t baseParam, char *const 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)); if (offset > (outLength - 1)) { return false; } out[offset] = '\0'; reverseString(out, offset); return true; } /** * Format a uint128_t into a string as a signed integer * * @param[in] number the number to format * @param[in] base the radix used in formatting * @param[out] out the output buffer * @param[in] out_length the length of the output buffer * @return whether the formatting was successful or not */ bool tostring128_signed(const uint128_t *const number, uint32_t base, char *const out, uint32_t out_length) { uint128_t max_unsigned_val; uint128_t max_signed_val; uint128_t one_val; uint128_t two_val; uint128_t tmp; // showing negative numbers only really makes sense in base 10 if (base == 10) { explicit_bzero(&one_val, sizeof(one_val)); LOWER(one_val) = 1; explicit_bzero(&two_val, sizeof(two_val)); LOWER(two_val) = 2; memset(&max_unsigned_val, 0xFF, sizeof(max_unsigned_val)); divmod128(&max_unsigned_val, &two_val, &max_signed_val, &tmp); if (gt128(number, &max_signed_val)) // negative value { sub128(&max_unsigned_val, number, &tmp); add128(&tmp, &one_val, &tmp); out[0] = '-'; return tostring128(&tmp, base, out + 1, out_length - 1); } } return tostring128(number, base, out, out_length); // positive value }