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-rw-r--r--src/crypto/CMakeLists.txt1
-rw-r--r--src/crypto/chacha.h23
-rw-r--r--src/crypto/crypto-ops-data.c6
-rw-r--r--src/crypto/crypto-ops.c16
-rw-r--r--src/crypto/crypto-ops.h3
-rw-r--r--src/crypto/crypto.cpp17
-rw-r--r--src/crypto/crypto.h10
-rw-r--r--src/crypto/generic-ops.h28
-rw-r--r--src/crypto/keccak.c74
-rw-r--r--src/crypto/keccak.h14
-rw-r--r--src/crypto/slow-hash.c252
-rw-r--r--src/crypto/variant2_int_sqrt.h163
12 files changed, 531 insertions, 76 deletions
diff --git a/src/crypto/CMakeLists.txt b/src/crypto/CMakeLists.txt
index 71dcedcab..0c635e7cb 100644
--- a/src/crypto/CMakeLists.txt
+++ b/src/crypto/CMakeLists.txt
@@ -78,6 +78,7 @@ target_link_libraries(cncrypto
PUBLIC
epee
${Boost_SYSTEM_LIBRARY}
+ ${SODIUM_LIBRARY}
PRIVATE
${EXTRA_LIBRARIES})
diff --git a/src/crypto/chacha.h b/src/crypto/chacha.h
index 2b3ed8043..6e85ad0e9 100644
--- a/src/crypto/chacha.h
+++ b/src/crypto/chacha.h
@@ -40,6 +40,7 @@
#include <memory.h>
#include "memwipe.h"
+#include "mlocker.h"
#include "hash.h"
namespace crypto {
@@ -50,7 +51,7 @@ namespace crypto {
#if defined(__cplusplus)
}
- using chacha_key = tools::scrubbed_arr<uint8_t, CHACHA_KEY_SIZE>;
+ using chacha_key = epee::mlocked<tools::scrubbed_arr<uint8_t, CHACHA_KEY_SIZE>>;
#pragma pack(push, 1)
// MS VC 2012 doesn't interpret `class chacha_iv` as POD in spite of [9.0.10], so it is a struct
@@ -69,22 +70,26 @@ namespace crypto {
chacha20(data, length, key.data(), reinterpret_cast<const uint8_t*>(&iv), cipher);
}
- inline void generate_chacha_key(const void *data, size_t size, chacha_key& key) {
+ inline void generate_chacha_key(const void *data, size_t size, chacha_key& key, uint64_t kdf_rounds) {
static_assert(sizeof(chacha_key) <= sizeof(hash), "Size of hash must be at least that of chacha_key");
- tools::scrubbed_arr<char, HASH_SIZE> pwd_hash;
+ epee::mlocked<tools::scrubbed_arr<char, HASH_SIZE>> pwd_hash;
crypto::cn_slow_hash(data, size, pwd_hash.data(), 0/*variant*/, 0/*prehashed*/);
- memcpy(&unwrap(key), pwd_hash.data(), sizeof(key));
+ for (uint64_t n = 1; n < kdf_rounds; ++n)
+ crypto::cn_slow_hash(pwd_hash.data(), pwd_hash.size(), pwd_hash.data(), 0/*variant*/, 0/*prehashed*/);
+ memcpy(&unwrap(unwrap(key)), pwd_hash.data(), sizeof(key));
}
- inline void generate_chacha_key_prehashed(const void *data, size_t size, chacha_key& key) {
+ inline void generate_chacha_key_prehashed(const void *data, size_t size, chacha_key& key, uint64_t kdf_rounds) {
static_assert(sizeof(chacha_key) <= sizeof(hash), "Size of hash must be at least that of chacha_key");
- tools::scrubbed_arr<char, HASH_SIZE> pwd_hash;
+ epee::mlocked<tools::scrubbed_arr<char, HASH_SIZE>> pwd_hash;
crypto::cn_slow_hash(data, size, pwd_hash.data(), 0/*variant*/, 1/*prehashed*/);
- memcpy(&unwrap(key), pwd_hash.data(), sizeof(key));
+ for (uint64_t n = 1; n < kdf_rounds; ++n)
+ crypto::cn_slow_hash(pwd_hash.data(), pwd_hash.size(), pwd_hash.data(), 0/*variant*/, 0/*prehashed*/);
+ memcpy(&unwrap(unwrap(key)), pwd_hash.data(), sizeof(key));
}
- inline void generate_chacha_key(std::string password, chacha_key& key) {
- return generate_chacha_key(password.data(), password.size(), key);
+ inline void generate_chacha_key(std::string password, chacha_key& key, uint64_t kdf_rounds) {
+ return generate_chacha_key(password.data(), password.size(), key, kdf_rounds);
}
}
diff --git a/src/crypto/crypto-ops-data.c b/src/crypto/crypto-ops-data.c
index 4ff4310de..1f77513ca 100644
--- a/src/crypto/crypto-ops-data.c
+++ b/src/crypto/crypto-ops-data.c
@@ -871,3 +871,9 @@ const fe fe_fffb2 = {8166131, -6741800, -17040804, 3154616, 21461005, 1466302, -
const fe fe_fffb3 = {-13620103, 14639558, 4532995, 7679154, 16815101, -15883539, -22863840, -14813421, 13716513, -6477756}; /* sqrt(-sqrt(-1) * A * (A + 2)) */
const fe fe_fffb4 = {-21786234, -12173074, 21573800, 4524538, -4645904, 16204591, 8012863, -8444712, 3212926, 6885324}; /* sqrt(sqrt(-1) * A * (A + 2)) */
const ge_p3 ge_p3_identity = { {0}, {1, 0}, {1, 0}, {0} };
+const ge_p3 ge_p3_H = {
+ {7329926, -15101362, 31411471, 7614783, 27996851, -3197071, -11157635, -6878293, 466949, -7986503},
+ {5858699, 5096796, 21321203, -7536921, -5553480, -11439507, -5627669, 15045946, 19977121, 5275251},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+ {23443568, -5110398, -8776029, -4345135, 6889568, -14710814, 7474843, 3279062, 14550766, -7453428}
+};
diff --git a/src/crypto/crypto-ops.c b/src/crypto/crypto-ops.c
index 45d412ac6..09296d6f9 100644
--- a/src/crypto/crypto-ops.c
+++ b/src/crypto/crypto-ops.c
@@ -3707,9 +3707,8 @@ void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b,
s[31] = s11 >> 17;
}
-/* Assumes that a != INT64_MIN */
static int64_t signum(int64_t a) {
- return (a >> 63) - ((-a) >> 63);
+ return a > 0 ? 1 : a < 0 ? -1 : 0;
}
int sc_check(const unsigned char *s) {
@@ -3730,3 +3729,16 @@ int sc_isnonzero(const unsigned char *s) {
s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] |
s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1;
}
+
+int ge_p3_is_point_at_infinity(const ge_p3 *p) {
+ // X = 0 and Y == Z
+ int n;
+ for (n = 0; n < 10; ++n)
+ {
+ if (p->X[n] | p->T[n])
+ return 0;
+ if (p->Y[n] != p->Z[n])
+ return 0;
+ }
+ return 1;
+}
diff --git a/src/crypto/crypto-ops.h b/src/crypto/crypto-ops.h
index dc3c60794..2910dafd4 100644
--- a/src/crypto/crypto-ops.h
+++ b/src/crypto/crypto-ops.h
@@ -140,6 +140,7 @@ extern const fe fe_fffb2;
extern const fe fe_fffb3;
extern const fe fe_fffb4;
extern const ge_p3 ge_p3_identity;
+extern const ge_p3 ge_p3_H;
void ge_fromfe_frombytes_vartime(ge_p2 *, const unsigned char *);
void sc_0(unsigned char *);
void sc_reduce32(unsigned char *);
@@ -158,3 +159,5 @@ void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
void fe_add(fe h, const fe f, const fe g);
void fe_tobytes(unsigned char *, const fe);
void fe_invert(fe out, const fe z);
+
+int ge_p3_is_point_at_infinity(const ge_p3 *p);
diff --git a/src/crypto/crypto.cpp b/src/crypto/crypto.cpp
index 0c019938d..ad7721cf0 100644
--- a/src/crypto/crypto.cpp
+++ b/src/crypto/crypto.cpp
@@ -70,6 +70,9 @@ namespace crypto {
#include "random.h"
}
+ const crypto::public_key null_pkey = crypto::public_key{};
+ const crypto::secret_key null_skey = crypto::secret_key{};
+
static inline unsigned char *operator &(ec_point &point) {
return &reinterpret_cast<unsigned char &>(point);
}
@@ -113,7 +116,7 @@ namespace crypto {
do
{
generate_random_bytes_thread_safe(32, bytes);
- } while (!less32(bytes, limit)); // should be good about 15/16 of the time
+ } while (!sc_isnonzero(bytes) && !less32(bytes, limit)); // should be good about 15/16 of the time
sc_reduce32(bytes);
}
/* generate a random 32-byte (256-bit) integer and copy it to res */
@@ -271,11 +274,18 @@ namespace crypto {
#endif
buf.h = prefix_hash;
buf.key = pub;
+ try_again:
random_scalar(k);
+ if (((const uint32_t*)(&k))[7] == 0) // we don't want tiny numbers here
+ goto try_again;
ge_scalarmult_base(&tmp3, &k);
ge_p3_tobytes(&buf.comm, &tmp3);
hash_to_scalar(&buf, sizeof(s_comm), sig.c);
+ if (!sc_isnonzero((const unsigned char*)sig.c.data))
+ goto try_again;
sc_mulsub(&sig.r, &sig.c, &unwrap(sec), &k);
+ if (!sc_isnonzero((const unsigned char*)sig.r.data))
+ goto try_again;
}
bool crypto_ops::check_signature(const hash &prefix_hash, const public_key &pub, const signature &sig) {
@@ -289,11 +299,14 @@ namespace crypto {
if (ge_frombytes_vartime(&tmp3, &pub) != 0) {
return false;
}
- if (sc_check(&sig.c) != 0 || sc_check(&sig.r) != 0) {
+ if (sc_check(&sig.c) != 0 || sc_check(&sig.r) != 0 || !sc_isnonzero(&sig.c)) {
return false;
}
ge_double_scalarmult_base_vartime(&tmp2, &sig.c, &tmp3, &sig.r);
ge_tobytes(&buf.comm, &tmp2);
+ static const ec_point infinity = {{ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
+ if (memcmp(&buf.comm, &infinity, 32) == 0)
+ return false;
hash_to_scalar(&buf, sizeof(s_comm), c);
sc_sub(&c, &c, &sig.c);
return sc_isnonzero(&c) == 0;
diff --git a/src/crypto/crypto.h b/src/crypto/crypto.h
index 449af8f6d..33cc0a25a 100644
--- a/src/crypto/crypto.h
+++ b/src/crypto/crypto.h
@@ -34,7 +34,6 @@
#include <iostream>
#include <boost/thread/mutex.hpp>
#include <boost/thread/lock_guard.hpp>
-#include <boost/utility/value_init.hpp>
#include <boost/optional.hpp>
#include <type_traits>
#include <vector>
@@ -42,6 +41,7 @@
#include "common/pod-class.h"
#include "common/util.h"
#include "memwipe.h"
+#include "mlocker.h"
#include "generic-ops.h"
#include "hex.h"
#include "span.h"
@@ -66,7 +66,7 @@ namespace crypto {
friend class crypto_ops;
};
- using secret_key = tools::scrubbed<ec_scalar>;
+ using secret_key = epee::mlocked<tools::scrubbed<ec_scalar>>;
POD_CLASS public_keyV {
std::vector<public_key> keys;
@@ -278,11 +278,11 @@ namespace crypto {
epee::to_hex::formatted(o, epee::as_byte_span(v)); return o;
}
- const static crypto::public_key null_pkey = boost::value_initialized<crypto::public_key>();
- const static crypto::secret_key null_skey = boost::value_initialized<crypto::secret_key>();
+ const extern crypto::public_key null_pkey;
+ const extern crypto::secret_key null_skey;
}
CRYPTO_MAKE_HASHABLE(public_key)
-CRYPTO_MAKE_HASHABLE(secret_key)
+CRYPTO_MAKE_HASHABLE_CONSTANT_TIME(secret_key)
CRYPTO_MAKE_HASHABLE(key_image)
CRYPTO_MAKE_COMPARABLE(signature)
diff --git a/src/crypto/generic-ops.h b/src/crypto/generic-ops.h
index 62bc758c9..42b98706e 100644
--- a/src/crypto/generic-ops.h
+++ b/src/crypto/generic-ops.h
@@ -33,19 +33,30 @@
#include <cstddef>
#include <cstring>
#include <functional>
+#include <sodium/crypto_verify_32.h>
#define CRYPTO_MAKE_COMPARABLE(type) \
namespace crypto { \
inline bool operator==(const type &_v1, const type &_v2) { \
- return std::memcmp(&_v1, &_v2, sizeof(type)) == 0; \
+ return !memcmp(&_v1, &_v2, sizeof(_v1)); \
} \
inline bool operator!=(const type &_v1, const type &_v2) { \
- return std::memcmp(&_v1, &_v2, sizeof(type)) != 0; \
+ return !operator==(_v1, _v2); \
} \
}
-#define CRYPTO_MAKE_HASHABLE(type) \
-CRYPTO_MAKE_COMPARABLE(type) \
+#define CRYPTO_MAKE_COMPARABLE_CONSTANT_TIME(type) \
+namespace crypto { \
+ inline bool operator==(const type &_v1, const type &_v2) { \
+ static_assert(sizeof(_v1) == 32, "constant time comparison is only implenmted for 32 bytes"); \
+ return crypto_verify_32((const unsigned char*)&_v1, (const unsigned char*)&_v2) == 0; \
+ } \
+ inline bool operator!=(const type &_v1, const type &_v2) { \
+ return !operator==(_v1, _v2); \
+ } \
+}
+
+#define CRYPTO_DEFINE_HASH_FUNCTIONS(type) \
namespace crypto { \
static_assert(sizeof(std::size_t) <= sizeof(type), "Size of " #type " must be at least that of size_t"); \
inline std::size_t hash_value(const type &_v) { \
@@ -60,3 +71,12 @@ namespace std { \
} \
}; \
}
+
+#define CRYPTO_MAKE_HASHABLE(type) \
+CRYPTO_MAKE_COMPARABLE(type) \
+CRYPTO_DEFINE_HASH_FUNCTIONS(type)
+
+#define CRYPTO_MAKE_HASHABLE_CONSTANT_TIME(type) \
+CRYPTO_MAKE_COMPARABLE_CONSTANT_TIME(type) \
+CRYPTO_DEFINE_HASH_FUNCTIONS(type)
+
diff --git a/src/crypto/keccak.c b/src/crypto/keccak.c
index de8e2a5b3..8fcd2138e 100644
--- a/src/crypto/keccak.c
+++ b/src/crypto/keccak.c
@@ -132,3 +132,77 @@ void keccak1600(const uint8_t *in, size_t inlen, uint8_t *md)
{
keccak(in, inlen, md, sizeof(state_t));
}
+
+#define KECCAK_FINALIZED 0x80000000
+#define KECCAK_BLOCKLEN 136
+#define KECCAK_WORDS 17
+#define KECCAK_DIGESTSIZE 32
+#define IS_ALIGNED_64(p) (0 == (7 & ((const char*)(p) - (const char*)0)))
+#define KECCAK_PROCESS_BLOCK(st, block) { \
+ for (int i_ = 0; i_ < KECCAK_WORDS; i_++){ \
+ ((st))[i_] ^= ((block))[i_]; \
+ }; \
+ keccakf(st, KECCAK_ROUNDS); }
+
+
+void keccak_init(KECCAK_CTX * ctx){
+ memset(ctx, 0, sizeof(KECCAK_CTX));
+}
+
+void keccak_update(KECCAK_CTX * ctx, const uint8_t *in, size_t inlen){
+ if (ctx->rest & KECCAK_FINALIZED) {
+ local_abort("Bad keccak use");
+ }
+
+ const size_t idx = ctx->rest;
+ ctx->rest = (ctx->rest + inlen) % KECCAK_BLOCKLEN;
+
+ // fill partial block
+ if (idx) {
+ size_t left = KECCAK_BLOCKLEN - idx;
+ memcpy((char*)ctx->message + idx, in, (inlen < left ? inlen : left));
+ if (inlen < left) return;
+
+ KECCAK_PROCESS_BLOCK(ctx->hash, ctx->message);
+
+ in += left;
+ inlen -= left;
+ }
+
+ const bool is_aligned = IS_ALIGNED_64(in);
+ while (inlen >= KECCAK_BLOCKLEN) {
+ const uint64_t* aligned_message_block;
+ if (is_aligned) {
+ aligned_message_block = (uint64_t*)in;
+ } else {
+ memcpy(ctx->message, in, KECCAK_BLOCKLEN);
+ aligned_message_block = ctx->message;
+ }
+
+ KECCAK_PROCESS_BLOCK(ctx->hash, aligned_message_block);
+ in += KECCAK_BLOCKLEN;
+ inlen -= KECCAK_BLOCKLEN;
+ }
+ if (inlen) {
+ memcpy(ctx->message, in, inlen);
+ }
+}
+
+void keccak_finish(KECCAK_CTX * ctx, uint8_t *md){
+ if (!(ctx->rest & KECCAK_FINALIZED))
+ {
+ // clear the rest of the data queue
+ memset((char*)ctx->message + ctx->rest, 0, KECCAK_BLOCKLEN - ctx->rest);
+ ((char*)ctx->message)[ctx->rest] |= 0x01;
+ ((char*)ctx->message)[KECCAK_BLOCKLEN - 1] |= 0x80;
+
+ // process final block
+ KECCAK_PROCESS_BLOCK(ctx->hash, ctx->message);
+ ctx->rest = KECCAK_FINALIZED; // mark context as finalized
+ }
+
+ static_assert(KECCAK_BLOCKLEN > KECCAK_DIGESTSIZE, "");
+ if (md) {
+ memcpy(md, ctx->hash, KECCAK_DIGESTSIZE);
+ }
+}
diff --git a/src/crypto/keccak.h b/src/crypto/keccak.h
index fb9d8bd04..9123c7a3b 100644
--- a/src/crypto/keccak.h
+++ b/src/crypto/keccak.h
@@ -15,6 +15,17 @@
#define ROTL64(x, y) (((x) << (y)) | ((x) >> (64 - (y))))
#endif
+// SHA3 Algorithm context.
+typedef struct KECCAK_CTX
+{
+ // 1600 bits algorithm hashing state
+ uint64_t hash[25];
+ // 1088-bit buffer for leftovers, block size = 136 B for 256-bit keccak
+ uint64_t message[17];
+ // count of bytes in the message[] buffer
+ size_t rest;
+} KECCAK_CTX;
+
// compute a keccak hash (md) of given byte length from "in"
void keccak(const uint8_t *in, size_t inlen, uint8_t *md, int mdlen);
@@ -23,4 +34,7 @@ void keccakf(uint64_t st[25], int norounds);
void keccak1600(const uint8_t *in, size_t inlen, uint8_t *md);
+void keccak_init(KECCAK_CTX * ctx);
+void keccak_update(KECCAK_CTX * ctx, const uint8_t *in, size_t inlen);
+void keccak_finish(KECCAK_CTX * ctx, uint8_t *md);
#endif
diff --git a/src/crypto/slow-hash.c b/src/crypto/slow-hash.c
index 9d4fc0dfa..a4d2b58de 100644
--- a/src/crypto/slow-hash.c
+++ b/src/crypto/slow-hash.c
@@ -38,6 +38,7 @@
#include "common/int-util.h"
#include "hash-ops.h"
#include "oaes_lib.h"
+#include "variant2_int_sqrt.h"
#define MEMORY (1 << 21) // 2MB scratchpad
#define ITER (1 << 20)
@@ -50,7 +51,7 @@ extern int aesb_single_round(const uint8_t *in, uint8_t*out, const uint8_t *expa
extern int aesb_pseudo_round(const uint8_t *in, uint8_t *out, const uint8_t *expandedKey);
#define VARIANT1_1(p) \
- do if (variant > 0) \
+ do if (variant == 1) \
{ \
const uint8_t tmp = ((const uint8_t*)(p))[11]; \
static const uint32_t table = 0x75310; \
@@ -59,7 +60,7 @@ extern int aesb_pseudo_round(const uint8_t *in, uint8_t *out, const uint8_t *exp
} while(0)
#define VARIANT1_2(p) \
- do if (variant > 0) \
+ do if (variant == 1) \
{ \
xor64(p, tweak1_2); \
} while(0)
@@ -67,7 +68,7 @@ extern int aesb_pseudo_round(const uint8_t *in, uint8_t *out, const uint8_t *exp
#define VARIANT1_CHECK() \
do if (length < 43) \
{ \
- fprintf(stderr, "Cryptonight variants need at least 43 bytes of data"); \
+ fprintf(stderr, "Cryptonight variant 1 needs at least 43 bytes of data"); \
_exit(1); \
} while(0)
@@ -75,7 +76,7 @@ extern int aesb_pseudo_round(const uint8_t *in, uint8_t *out, const uint8_t *exp
#define VARIANT1_PORTABLE_INIT() \
uint8_t tweak1_2[8]; \
- do if (variant > 0) \
+ do if (variant == 1) \
{ \
VARIANT1_CHECK(); \
memcpy(&tweak1_2, &state.hs.b[192], sizeof(tweak1_2)); \
@@ -83,11 +84,119 @@ extern int aesb_pseudo_round(const uint8_t *in, uint8_t *out, const uint8_t *exp
} while(0)
#define VARIANT1_INIT64() \
- if (variant > 0) \
+ if (variant == 1) \
{ \
VARIANT1_CHECK(); \
} \
- const uint64_t tweak1_2 = variant > 0 ? (state.hs.w[24] ^ (*((const uint64_t*)NONCE_POINTER))) : 0
+ const uint64_t tweak1_2 = (variant == 1) ? (state.hs.w[24] ^ (*((const uint64_t*)NONCE_POINTER))) : 0
+
+#define VARIANT2_INIT64() \
+ uint64_t division_result = 0; \
+ uint64_t sqrt_result = 0; \
+ do if (variant >= 2) \
+ { \
+ U64(b)[2] = state.hs.w[8] ^ state.hs.w[10]; \
+ U64(b)[3] = state.hs.w[9] ^ state.hs.w[11]; \
+ division_result = state.hs.w[12]; \
+ sqrt_result = state.hs.w[13]; \
+ } while (0)
+
+#define VARIANT2_PORTABLE_INIT() \
+ uint64_t division_result = 0; \
+ uint64_t sqrt_result = 0; \
+ do if (variant >= 2) \
+ { \
+ memcpy(b + AES_BLOCK_SIZE, state.hs.b + 64, AES_BLOCK_SIZE); \
+ xor64(b + AES_BLOCK_SIZE, state.hs.b + 80); \
+ xor64(b + AES_BLOCK_SIZE + 8, state.hs.b + 88); \
+ division_result = state.hs.w[12]; \
+ sqrt_result = state.hs.w[13]; \
+ } while (0)
+
+#define VARIANT2_SHUFFLE_ADD_SSE2(base_ptr, offset) \
+ do if (variant >= 2) \
+ { \
+ const __m128i chunk1 = _mm_load_si128((__m128i *)((base_ptr) + ((offset) ^ 0x10))); \
+ const __m128i chunk2 = _mm_load_si128((__m128i *)((base_ptr) + ((offset) ^ 0x20))); \
+ const __m128i chunk3 = _mm_load_si128((__m128i *)((base_ptr) + ((offset) ^ 0x30))); \
+ _mm_store_si128((__m128i *)((base_ptr) + ((offset) ^ 0x10)), _mm_add_epi64(chunk3, _b1)); \
+ _mm_store_si128((__m128i *)((base_ptr) + ((offset) ^ 0x20)), _mm_add_epi64(chunk1, _b)); \
+ _mm_store_si128((__m128i *)((base_ptr) + ((offset) ^ 0x30)), _mm_add_epi64(chunk2, _a)); \
+ } while (0)
+
+#define VARIANT2_SHUFFLE_ADD_NEON(base_ptr, offset) \
+ do if (variant >= 2) \
+ { \
+ const uint64x2_t chunk1 = vld1q_u64(U64((base_ptr) + ((offset) ^ 0x10))); \
+ const uint64x2_t chunk2 = vld1q_u64(U64((base_ptr) + ((offset) ^ 0x20))); \
+ const uint64x2_t chunk3 = vld1q_u64(U64((base_ptr) + ((offset) ^ 0x30))); \
+ vst1q_u64(U64((base_ptr) + ((offset) ^ 0x10)), vaddq_u64(chunk3, vreinterpretq_u64_u8(_b1))); \
+ vst1q_u64(U64((base_ptr) + ((offset) ^ 0x20)), vaddq_u64(chunk1, vreinterpretq_u64_u8(_b))); \
+ vst1q_u64(U64((base_ptr) + ((offset) ^ 0x30)), vaddq_u64(chunk2, vreinterpretq_u64_u8(_a))); \
+ } while (0)
+
+#define VARIANT2_PORTABLE_SHUFFLE_ADD(base_ptr, offset) \
+ do if (variant >= 2) \
+ { \
+ uint64_t* chunk1 = U64((base_ptr) + ((offset) ^ 0x10)); \
+ uint64_t* chunk2 = U64((base_ptr) + ((offset) ^ 0x20)); \
+ uint64_t* chunk3 = U64((base_ptr) + ((offset) ^ 0x30)); \
+ \
+ const uint64_t chunk1_old[2] = { chunk1[0], chunk1[1] }; \
+ \
+ uint64_t b1[2]; \
+ memcpy(b1, b + 16, 16); \
+ chunk1[0] = chunk3[0] + b1[0]; \
+ chunk1[1] = chunk3[1] + b1[1]; \
+ \
+ uint64_t a0[2]; \
+ memcpy(a0, a, 16); \
+ chunk3[0] = chunk2[0] + a0[0]; \
+ chunk3[1] = chunk2[1] + a0[1]; \
+ \
+ uint64_t b0[2]; \
+ memcpy(b0, b, 16); \
+ chunk2[0] = chunk1_old[0] + b0[0]; \
+ chunk2[1] = chunk1_old[1] + b0[1]; \
+ } while (0)
+
+#define VARIANT2_INTEGER_MATH_DIVISION_STEP(b, ptr) \
+ ((uint64_t*)(b))[0] ^= division_result ^ (sqrt_result << 32); \
+ { \
+ const uint64_t dividend = ((uint64_t*)(ptr))[1]; \
+ const uint32_t divisor = (((uint64_t*)(ptr))[0] + (uint32_t)(sqrt_result << 1)) | 0x80000001UL; \
+ division_result = ((uint32_t)(dividend / divisor)) + \
+ (((uint64_t)(dividend % divisor)) << 32); \
+ } \
+ const uint64_t sqrt_input = ((uint64_t*)(ptr))[0] + division_result
+
+#define VARIANT2_INTEGER_MATH_SSE2(b, ptr) \
+ do if (variant >= 2) \
+ { \
+ VARIANT2_INTEGER_MATH_DIVISION_STEP(b, ptr); \
+ VARIANT2_INTEGER_MATH_SQRT_STEP_SSE2(); \
+ VARIANT2_INTEGER_MATH_SQRT_FIXUP(sqrt_result); \
+ } while(0)
+
+#if defined DBL_MANT_DIG && (DBL_MANT_DIG >= 50)
+ // double precision floating point type has enough bits of precision on current platform
+ #define VARIANT2_PORTABLE_INTEGER_MATH(b, ptr) \
+ do if (variant >= 2) \
+ { \
+ VARIANT2_INTEGER_MATH_DIVISION_STEP(b, ptr); \
+ VARIANT2_INTEGER_MATH_SQRT_STEP_FP64(); \
+ VARIANT2_INTEGER_MATH_SQRT_FIXUP(sqrt_result); \
+ } while (0)
+#else
+ // double precision floating point type is not good enough on current platform
+ // fall back to the reference code (integer only)
+ #define VARIANT2_PORTABLE_INTEGER_MATH(b, ptr) \
+ do if (variant >= 2) \
+ { \
+ VARIANT2_INTEGER_MATH_DIVISION_STEP(b, ptr); \
+ VARIANT2_INTEGER_MATH_SQRT_STEP_REF(); \
+ } while (0)
+#endif
#if !defined NO_AES && (defined(__x86_64__) || (defined(_MSC_VER) && defined(_WIN64)))
// Optimised code below, uses x86-specific intrinsics, SSE2, AES-NI
@@ -164,19 +273,22 @@ extern int aesb_pseudo_round(const uint8_t *in, uint8_t *out, const uint8_t *exp
* This code is based upon an optimized implementation by dga.
*/
#define post_aes() \
+ VARIANT2_SHUFFLE_ADD_SSE2(hp_state, j); \
_mm_store_si128(R128(c), _c); \
- _b = _mm_xor_si128(_b, _c); \
- _mm_store_si128(R128(&hp_state[j]), _b); \
+ _mm_store_si128(R128(&hp_state[j]), _mm_xor_si128(_b, _c)); \
VARIANT1_1(&hp_state[j]); \
j = state_index(c); \
p = U64(&hp_state[j]); \
b[0] = p[0]; b[1] = p[1]; \
+ VARIANT2_INTEGER_MATH_SSE2(b, c); \
__mul(); \
+ VARIANT2_SHUFFLE_ADD_SSE2(hp_state, j); \
a[0] += hi; a[1] += lo; \
p = U64(&hp_state[j]); \
p[0] = a[0]; p[1] = a[1]; \
a[0] ^= b[0]; a[1] ^= b[1]; \
VARIANT1_2(p + 1); \
+ _b1 = _b; \
_b = _c; \
#if defined(_MSC_VER)
@@ -570,10 +682,10 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
uint8_t text[INIT_SIZE_BYTE];
RDATA_ALIGN16 uint64_t a[2];
- RDATA_ALIGN16 uint64_t b[2];
+ RDATA_ALIGN16 uint64_t b[4];
RDATA_ALIGN16 uint64_t c[2];
union cn_slow_hash_state state;
- __m128i _a, _b, _c;
+ __m128i _a, _b, _b1, _c;
uint64_t hi, lo;
size_t i, j;
@@ -599,6 +711,7 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
memcpy(text, state.init, INIT_SIZE_BYTE);
VARIANT1_INIT64();
+ VARIANT2_INIT64();
/* CryptoNight Step 2: Iteratively encrypt the results from Keccak to fill
* the 2MB large random access buffer.
@@ -637,6 +750,7 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
*/
_b = _mm_load_si128(R128(b));
+ _b1 = _mm_load_si128(R128(b) + 1);
// Two independent versions, one with AES, one without, to ensure that
// the useAes test is only performed once, not every iteration.
if(useAes)
@@ -761,19 +875,22 @@ union cn_slow_hash_state
_a = vld1q_u8((const uint8_t *)a); \
#define post_aes() \
+ VARIANT2_SHUFFLE_ADD_NEON(hp_state, j); \
vst1q_u8((uint8_t *)c, _c); \
- _b = veorq_u8(_b, _c); \
- vst1q_u8(&hp_state[j], _b); \
+ vst1q_u8(&hp_state[j], veorq_u8(_b, _c)); \
VARIANT1_1(&hp_state[j]); \
j = state_index(c); \
p = U64(&hp_state[j]); \
b[0] = p[0]; b[1] = p[1]; \
+ VARIANT2_PORTABLE_INTEGER_MATH(b, c); \
__mul(); \
+ VARIANT2_SHUFFLE_ADD_NEON(hp_state, j); \
a[0] += hi; a[1] += lo; \
p = U64(&hp_state[j]); \
p[0] = a[0]; p[1] = a[1]; \
a[0] ^= b[0]; a[1] ^= b[1]; \
VARIANT1_2(p + 1); \
+ _b1 = _b; \
_b = _c; \
@@ -912,10 +1029,10 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
uint8_t text[INIT_SIZE_BYTE];
RDATA_ALIGN16 uint64_t a[2];
- RDATA_ALIGN16 uint64_t b[2];
+ RDATA_ALIGN16 uint64_t b[4];
RDATA_ALIGN16 uint64_t c[2];
union cn_slow_hash_state state;
- uint8x16_t _a, _b, _c, zero = {0};
+ uint8x16_t _a, _b, _b1, _c, zero = {0};
uint64_t hi, lo;
size_t i, j;
@@ -936,6 +1053,7 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
memcpy(text, state.init, INIT_SIZE_BYTE);
VARIANT1_INIT64();
+ VARIANT2_INIT64();
/* CryptoNight Step 2: Iteratively encrypt the results from Keccak to fill
* the 2MB large random access buffer.
@@ -959,7 +1077,7 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
*/
_b = vld1q_u8((const uint8_t *)b);
-
+ _b1 = vld1q_u8(((const uint8_t *)b) + AES_BLOCK_SIZE);
for(i = 0; i < ITER / 2; i++)
{
@@ -1075,6 +1193,11 @@ __asm__ __volatile__(
#endif /* !aarch64 */
#endif // NO_OPTIMIZED_MULTIPLY_ON_ARM
+STATIC INLINE void copy_block(uint8_t* dst, const uint8_t* src)
+{
+ memcpy(dst, src, AES_BLOCK_SIZE);
+}
+
STATIC INLINE void sum_half_blocks(uint8_t* a, const uint8_t* b)
{
uint64_t a0, a1, b0, b1;
@@ -1109,7 +1232,9 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
{
uint8_t text[INIT_SIZE_BYTE];
uint8_t a[AES_BLOCK_SIZE];
- uint8_t b[AES_BLOCK_SIZE];
+ uint8_t b[AES_BLOCK_SIZE * 2];
+ uint8_t c[AES_BLOCK_SIZE];
+ uint8_t c1[AES_BLOCK_SIZE];
uint8_t d[AES_BLOCK_SIZE];
uint8_t aes_key[AES_KEY_SIZE];
RDATA_ALIGN16 uint8_t expandedKey[256];
@@ -1138,11 +1263,12 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
}
memcpy(text, state.init, INIT_SIZE_BYTE);
- VARIANT1_INIT64();
-
aes_ctx = (oaes_ctx *) oaes_alloc();
oaes_key_import_data(aes_ctx, state.hs.b, AES_KEY_SIZE);
+ VARIANT1_INIT64();
+ VARIANT2_INIT64();
+
// use aligned data
memcpy(expandedKey, aes_ctx->key->exp_data, aes_ctx->key->exp_data_len);
for(i = 0; i < MEMORY / INIT_SIZE_BYTE; i++)
@@ -1163,23 +1289,33 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
#define state_index(x) ((*(uint32_t *) x) & MASK)
// Iteration 1
- p = &long_state[state_index(a)];
+ j = state_index(a);
+ p = &long_state[j];
aesb_single_round(p, p, a);
+ copy_block(c1, p);
- xor_blocks(b, p);
- swap_blocks(b, p);
- swap_blocks(a, b);
+ VARIANT2_PORTABLE_SHUFFLE_ADD(long_state, j);
+ xor_blocks(p, b);
VARIANT1_1(p);
// Iteration 2
- p = &long_state[state_index(a)];
-
- mul(a, p, d);
- sum_half_blocks(b, d);
- swap_blocks(b, p);
- xor_blocks(b, p);
- swap_blocks(a, b);
- VARIANT1_2(U64(p) + 1);
+ j = state_index(c1);
+ p = &long_state[j];
+ copy_block(c, p);
+
+ VARIANT2_PORTABLE_INTEGER_MATH(c, c1);
+ mul(c1, c, d);
+ VARIANT2_PORTABLE_SHUFFLE_ADD(long_state, j);
+ sum_half_blocks(a, d);
+ swap_blocks(a, c);
+ xor_blocks(a, c);
+ VARIANT1_2(U64(c) + 1);
+ copy_block(p, c);
+
+ if (variant >= 2) {
+ copy_block(b + AES_BLOCK_SIZE, b);
+ }
+ copy_block(b, c1);
}
memcpy(text, state.init, INIT_SIZE_BYTE);
@@ -1298,8 +1434,9 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
union cn_slow_hash_state state;
uint8_t text[INIT_SIZE_BYTE];
uint8_t a[AES_BLOCK_SIZE];
- uint8_t b[AES_BLOCK_SIZE];
- uint8_t c[AES_BLOCK_SIZE];
+ uint8_t b[AES_BLOCK_SIZE * 2];
+ uint8_t c1[AES_BLOCK_SIZE];
+ uint8_t c2[AES_BLOCK_SIZE];
uint8_t d[AES_BLOCK_SIZE];
size_t i, j;
uint8_t aes_key[AES_KEY_SIZE];
@@ -1315,6 +1452,7 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
aes_ctx = (oaes_ctx *) oaes_alloc();
VARIANT1_PORTABLE_INIT();
+ VARIANT2_PORTABLE_INIT();
oaes_key_import_data(aes_ctx, aes_key, AES_KEY_SIZE);
for (i = 0; i < MEMORY / INIT_SIZE_BYTE; i++) {
@@ -1324,9 +1462,9 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
memcpy(&long_state[i * INIT_SIZE_BYTE], text, INIT_SIZE_BYTE);
}
- for (i = 0; i < 16; i++) {
- a[i] = state.k[ i] ^ state.k[32 + i];
- b[i] = state.k[16 + i] ^ state.k[48 + i];
+ for (i = 0; i < AES_BLOCK_SIZE; i++) {
+ a[i] = state.k[ i] ^ state.k[AES_BLOCK_SIZE * 2 + i];
+ b[i] = state.k[AES_BLOCK_SIZE + i] ^ state.k[AES_BLOCK_SIZE * 3 + i];
}
for (i = 0; i < ITER / 2; i++) {
@@ -1335,26 +1473,32 @@ void cn_slow_hash(const void *data, size_t length, char *hash, int variant, int
* next address <-+
*/
/* Iteration 1 */
- j = e2i(a, MEMORY / AES_BLOCK_SIZE);
- copy_block(c, &long_state[j * AES_BLOCK_SIZE]);
- aesb_single_round(c, c, a);
- xor_blocks(b, c);
- swap_blocks(b, c);
- copy_block(&long_state[j * AES_BLOCK_SIZE], c);
- assert(j == e2i(a, MEMORY / AES_BLOCK_SIZE));
- swap_blocks(a, b);
- VARIANT1_1(&long_state[j * AES_BLOCK_SIZE]);
+ j = e2i(a, MEMORY / AES_BLOCK_SIZE) * AES_BLOCK_SIZE;
+ copy_block(c1, &long_state[j]);
+ aesb_single_round(c1, c1, a);
+ VARIANT2_PORTABLE_SHUFFLE_ADD(long_state, j);
+ copy_block(&long_state[j], c1);
+ xor_blocks(&long_state[j], b);
+ assert(j == e2i(a, MEMORY / AES_BLOCK_SIZE) * AES_BLOCK_SIZE);
+ VARIANT1_1(&long_state[j]);
/* Iteration 2 */
- j = e2i(a, MEMORY / AES_BLOCK_SIZE);
- copy_block(c, &long_state[j * AES_BLOCK_SIZE]);
- mul(a, c, d);
- sum_half_blocks(b, d);
- swap_blocks(b, c);
- xor_blocks(b, c);
- VARIANT1_2(c + 8);
- copy_block(&long_state[j * AES_BLOCK_SIZE], c);
- assert(j == e2i(a, MEMORY / AES_BLOCK_SIZE));
- swap_blocks(a, b);
+ j = e2i(c1, MEMORY / AES_BLOCK_SIZE) * AES_BLOCK_SIZE;
+ copy_block(c2, &long_state[j]);
+ VARIANT2_PORTABLE_INTEGER_MATH(c2, c1);
+ mul(c1, c2, d);
+ VARIANT2_PORTABLE_SHUFFLE_ADD(long_state, j);
+ swap_blocks(a, c1);
+ sum_half_blocks(c1, d);
+ swap_blocks(c1, c2);
+ xor_blocks(c1, c2);
+ VARIANT1_2(c2 + 8);
+ copy_block(&long_state[j], c2);
+ assert(j == e2i(a, MEMORY / AES_BLOCK_SIZE) * AES_BLOCK_SIZE);
+ if (variant >= 2) {
+ copy_block(b + AES_BLOCK_SIZE, b);
+ }
+ copy_block(b, a);
+ copy_block(a, c1);
}
memcpy(text, state.init, INIT_SIZE_BYTE);
diff --git a/src/crypto/variant2_int_sqrt.h b/src/crypto/variant2_int_sqrt.h
new file mode 100644
index 000000000..b405bb798
--- /dev/null
+++ b/src/crypto/variant2_int_sqrt.h
@@ -0,0 +1,163 @@
+#ifndef VARIANT2_INT_SQRT_H
+#define VARIANT2_INT_SQRT_H
+
+#include <math.h>
+#include <float.h>
+
+#define VARIANT2_INTEGER_MATH_SQRT_STEP_SSE2() \
+ do { \
+ const __m128i exp_double_bias = _mm_set_epi64x(0, 1023ULL << 52); \
+ __m128d x = _mm_castsi128_pd(_mm_add_epi64(_mm_cvtsi64_si128(sqrt_input >> 12), exp_double_bias)); \
+ x = _mm_sqrt_sd(_mm_setzero_pd(), x); \
+ sqrt_result = (uint64_t)(_mm_cvtsi128_si64(_mm_sub_epi64(_mm_castpd_si128(x), exp_double_bias))) >> 19; \
+ } while(0)
+
+#define VARIANT2_INTEGER_MATH_SQRT_STEP_FP64() \
+ do { \
+ sqrt_result = sqrt(sqrt_input + 18446744073709551616.0) * 2.0 - 8589934592.0; \
+ } while(0)
+
+#define VARIANT2_INTEGER_MATH_SQRT_STEP_REF() \
+ sqrt_result = integer_square_root_v2(sqrt_input)
+
+// Reference implementation of the integer square root for Cryptonight variant 2
+// Computes integer part of "sqrt(2^64 + n) * 2 - 2^33"
+//
+// In other words, given 64-bit unsigned integer n:
+// 1) Write it as x = 1.NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN000... in binary (1 <= x < 2, all 64 bits of n are used)
+// 2) Calculate sqrt(x) = 1.0RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR... (1 <= sqrt(x) < sqrt(2), so it will always start with "1.0" in binary)
+// 3) Take 32 bits that come after "1.0" and return them as a 32-bit unsigned integer, discard all remaining bits
+//
+// Some sample inputs and outputs:
+//
+// Input | Output | Exact value of "sqrt(2^64 + n) * 2 - 2^33"
+// -----------------|------------|-------------------------------------------
+// 0 | 0 | 0
+// 2^32 | 0 | 0.99999999994179233909330885695244...
+// 2^32 + 1 | 1 | 1.0000000001746229827200734316305...
+// 2^50 | 262140 | 262140.00012206565608606978175873...
+// 2^55 + 20963331 | 8384515 | 8384515.9999999997673963974959744...
+// 2^55 + 20963332 | 8384516 | 8384516
+// 2^62 + 26599786 | 1013904242 | 1013904242.9999999999479374853545...
+// 2^62 + 26599787 | 1013904243 | 1013904243.0000000001561875439364...
+// 2^64 - 1 | 3558067407 | 3558067407.9041987696409179931096...
+
+// The reference implementation as it is now uses only unsigned int64 arithmetic, so it can't have undefined behavior
+// It was tested once for all edge cases and confirmed correct
+static inline uint32_t integer_square_root_v2(uint64_t n)
+{
+ uint64_t r = 1ULL << 63;
+
+ for (uint64_t bit = 1ULL << 60; bit; bit >>= 2)
+ {
+ const bool b = (n < r + bit);
+ const uint64_t n_next = n - (r + bit);
+ const uint64_t r_next = r + bit * 2;
+ n = b ? n : n_next;
+ r = b ? r : r_next;
+ r >>= 1;
+ }
+
+ return r * 2 + ((n > r) ? 1 : 0);
+}
+
+/*
+VARIANT2_INTEGER_MATH_SQRT_FIXUP checks that "r" is an integer part of "sqrt(2^64 + sqrt_input) * 2 - 2^33" and adds or subtracts 1 if needed
+It's hard to understand how it works, so here is a full calculation of formulas used in VARIANT2_INTEGER_MATH_SQRT_FIXUP
+
+The following inequalities must hold for r if it's an integer part of "sqrt(2^64 + sqrt_input) * 2 - 2^33":
+1) r <= sqrt(2^64 + sqrt_input) * 2 - 2^33
+2) r + 1 > sqrt(2^64 + sqrt_input) * 2 - 2^33
+
+We need to check them using only unsigned integer arithmetic to avoid rounding errors and undefined behavior
+
+First inequality: r <= sqrt(2^64 + sqrt_input) * 2 - 2^33
+-----------------------------------------------------------------------------------
+r <= sqrt(2^64 + sqrt_input) * 2 - 2^33
+r + 2^33 <= sqrt(2^64 + sqrt_input) * 2
+r/2 + 2^32 <= sqrt(2^64 + sqrt_input)
+(r/2 + 2^32)^2 <= 2^64 + sqrt_input
+
+Rewrite r as r = s * 2 + b (s = trunc(r/2), b is 0 or 1)
+
+((s*2+b)/2 + 2^32)^2 <= 2^64 + sqrt_input
+(s*2+b)^2/4 + 2*2^32*(s*2+b)/2 + 2^64 <= 2^64 + sqrt_input
+(s*2+b)^2/4 + 2*2^32*(s*2+b)/2 <= sqrt_input
+(s*2+b)^2/4 + 2^32*r <= sqrt_input
+(s^2*4+2*s*2*b+b^2)/4 + 2^32*r <= sqrt_input
+s^2+s*b+b^2/4 + 2^32*r <= sqrt_input
+s*(s+b) + b^2/4 + 2^32*r <= sqrt_input
+
+Let r2 = s*(s+b) + r*2^32
+r2 + b^2/4 <= sqrt_input
+
+If this inequality doesn't hold, then we must decrement r: IF "r2 + b^2/4 > sqrt_input" THEN r = r - 1
+
+b can be 0 or 1
+If b is 0 then we need to compare "r2 > sqrt_input"
+If b is 1 then b^2/4 = 0.25, so we need to compare "r2 + 0.25 > sqrt_input"
+Since both r2 and sqrt_input are integers, we can safely replace it with "r2 + 1 > sqrt_input"
+-----------------------------------------------------------------------------------
+Both cases can be merged to a single expression "r2 + b > sqrt_input"
+-----------------------------------------------------------------------------------
+There will be no overflow when calculating "r2 + b", so it's safe to compare with sqrt_input:
+r2 + b = s*(s+b) + r*2^32 + b
+The largest value s, b and r can have is s = 1779033703, b = 1, r = 3558067407 when sqrt_input = 2^64 - 1
+r2 + b <= 1779033703*1779033704 + 3558067407*2^32 + 1 = 18446744068217447385 < 2^64
+
+Second inequality: r + 1 > sqrt(2^64 + sqrt_input) * 2 - 2^33
+-----------------------------------------------------------------------------------
+r + 1 > sqrt(2^64 + sqrt_input) * 2 - 2^33
+r + 1 + 2^33 > sqrt(2^64 + sqrt_input) * 2
+((r+1)/2 + 2^32)^2 > 2^64 + sqrt_input
+
+Rewrite r as r = s * 2 + b (s = trunc(r/2), b is 0 or 1)
+
+((s*2+b+1)/2 + 2^32)^2 > 2^64 + sqrt_input
+(s*2+b+1)^2/4 + 2*(s*2+b+1)/2*2^32 + 2^64 > 2^64 + sqrt_input
+(s*2+b+1)^2/4 + (s*2+b+1)*2^32 > sqrt_input
+(s*2+b+1)^2/4 + (r+1)*2^32 > sqrt_input
+(s*2+(b+1))^2/4 + r*2^32 + 2^32 > sqrt_input
+(s^2*4+2*s*2*(b+1)+(b+1)^2)/4 + r*2^32 + 2^32 > sqrt_input
+s^2+s*(b+1)+(b+1)^2/4 + r*2^32 + 2^32 > sqrt_input
+s*(s+b) + s + (b+1)^2/4 + r*2^32 + 2^32 > sqrt_input
+
+Let r2 = s*(s+b) + r*2^32
+
+r2 + s + (b+1)^2/4 + 2^32 > sqrt_input
+r2 + 2^32 + (b+1)^2/4 > sqrt_input - s
+
+If this inequality doesn't hold, then we must decrement r: IF "r2 + 2^32 + (b+1)^2/4 <= sqrt_input - s" THEN r = r - 1
+b can be 0 or 1
+If b is 0 then we need to compare "r2 + 2^32 + 1/4 <= sqrt_input - s" which is equal to "r2 + 2^32 < sqrt_input - s" because all numbers here are integers
+If b is 1 then (b+1)^2/4 = 1, so we need to compare "r2 + 2^32 + 1 <= sqrt_input - s" which is also equal to "r2 + 2^32 < sqrt_input - s"
+-----------------------------------------------------------------------------------
+Both cases can be merged to a single expression "r2 + 2^32 < sqrt_input - s"
+-----------------------------------------------------------------------------------
+There will be no overflow when calculating "r2 + 2^32":
+r2 + 2^32 = s*(s+b) + r*2^32 + 2^32 = s*(s+b) + (r+1)*2^32
+The largest value s, b and r can have is s = 1779033703, b = 1, r = 3558067407 when sqrt_input = 2^64 - 1
+r2 + b <= 1779033703*1779033704 + 3558067408*2^32 = 18446744072512414680 < 2^64
+
+There will be no integer overflow when calculating "sqrt_input - s", i.e. "sqrt_input >= s" at all times:
+s = trunc(r/2) = trunc(sqrt(2^64 + sqrt_input) - 2^32) < sqrt(2^64 + sqrt_input) - 2^32 + 1
+sqrt_input > sqrt(2^64 + sqrt_input) - 2^32 + 1
+sqrt_input + 2^32 - 1 > sqrt(2^64 + sqrt_input)
+(sqrt_input + 2^32 - 1)^2 > sqrt_input + 2^64
+sqrt_input^2 + 2*sqrt_input*(2^32 - 1) + (2^32-1)^2 > sqrt_input + 2^64
+sqrt_input^2 + sqrt_input*(2^33 - 2) + (2^32-1)^2 > sqrt_input + 2^64
+sqrt_input^2 + sqrt_input*(2^33 - 3) + (2^32-1)^2 > 2^64
+sqrt_input^2 + sqrt_input*(2^33 - 3) + 2^64-2^33+1 > 2^64
+sqrt_input^2 + sqrt_input*(2^33 - 3) - 2^33 + 1 > 0
+This inequality is true if sqrt_input > 1 and it's easy to check that s = 0 if sqrt_input is 0 or 1, so there will be no integer overflow
+*/
+
+#define VARIANT2_INTEGER_MATH_SQRT_FIXUP(r) \
+ do { \
+ const uint64_t s = r >> 1; \
+ const uint64_t b = r & 1; \
+ const uint64_t r2 = (uint64_t)(s) * (s + b) + (r << 32); \
+ r += ((r2 + b > sqrt_input) ? -1 : 0) + ((r2 + (1ULL << 32) < sqrt_input - s) ? 1 : 0); \
+ } while(0)
+
+#endif
generated by cgit v1.2.3 (git 2.25.1) at 2025-01-21 11:04:45 +0000