- #include <openssl/bn.h>
-
- #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && !defined(OPENSSL_WINDOWS)
-
- #include "../internal.h"
-
- /* x86_64 BIGNUM accelerator version 0.1, December 2002.
- *
- * Implemented by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
- * project.
- *
- * Rights for redistribution and usage in source and binary forms are
- * granted according to the OpenSSL license. Warranty of any kind is
- * disclaimed.
- *
- * Q. Version 0.1? It doesn't sound like Andy, he used to assign real
- * versions, like 1.0...
- * A. Well, that's because this code is basically a quick-n-dirty
- * proof-of-concept hack. As you can see it's implemented with
- * inline assembler, which means that you're bound to GCC and that
- * there might be enough room for further improvement.
- *
- * Q. Why inline assembler?
- * A. x86_64 features own ABI which I'm not familiar with. This is
- * why I decided to let the compiler take care of subroutine
- * prologue/epilogue as well as register allocation. For reference.
- * Win64 implements different ABI for AMD64, different from Linux.
- *
- * Q. How much faster does it get?
- * A. 'apps/openssl speed rsa dsa' output with no-asm:
- *
- * sign verify sign/s verify/s
- * rsa 512 bits 0.0006s 0.0001s 1683.8 18456.2
- * rsa 1024 bits 0.0028s 0.0002s 356.0 6407.0
- * rsa 2048 bits 0.0172s 0.0005s 58.0 1957.8
- * rsa 4096 bits 0.1155s 0.0018s 8.7 555.6
- * sign verify sign/s verify/s
- * dsa 512 bits 0.0005s 0.0006s 2100.8 1768.3
- * dsa 1024 bits 0.0014s 0.0018s 692.3 559.2
- * dsa 2048 bits 0.0049s 0.0061s 204.7 165.0
- *
- * 'apps/openssl speed rsa dsa' output with this module:
- *
- * sign verify sign/s verify/s
- * rsa 512 bits 0.0004s 0.0000s 2767.1 33297.9
- * rsa 1024 bits 0.0012s 0.0001s 867.4 14674.7
- * rsa 2048 bits 0.0061s 0.0002s 164.0 5270.0
- * rsa 4096 bits 0.0384s 0.0006s 26.1 1650.8
- * sign verify sign/s verify/s
- * dsa 512 bits 0.0002s 0.0003s 4442.2 3786.3
- * dsa 1024 bits 0.0005s 0.0007s 1835.1 1497.4
- * dsa 2048 bits 0.0016s 0.0020s 620.4 504.6
- *
- * For the reference. IA-32 assembler implementation performs
- * very much like 64-bit code compiled with no-asm on the same
- * machine.
- */
-
- /* TODO(davidben): Get this file working on Windows x64. */
-
- #undef mul
- #undef mul_add
-
- #define asm __asm__
-
- /*
- * "m"(a), "+m"(r) is the way to favor DirectPath µ-code;
- * "g"(0) let the compiler to decide where does it
- * want to keep the value of zero;
- */
- #define mul_add(r, a, word, carry) \
- do { \
- register BN_ULONG high, low; \
- asm("mulq %3" : "=a"(low), "=d"(high) : "a"(word), "m"(a) : "cc"); \
- asm("addq %2,%0; adcq %3,%1" \
- : "+r"(carry), "+d"(high) \
- : "a"(low), "g"(0) \
- : "cc"); \
- asm("addq %2,%0; adcq %3,%1" \
- : "+m"(r), "+d"(high) \
- : "r"(carry), "g"(0) \
- : "cc"); \
- carry = high; \
- } while (0)
-
- #define mul(r, a, word, carry) \
- do { \
- register BN_ULONG high, low; \
- asm("mulq %3" : "=a"(low), "=d"(high) : "a"(word), "g"(a) : "cc"); \
- asm("addq %2,%0; adcq %3,%1" \
- : "+r"(carry), "+d"(high) \
- : "a"(low), "g"(0) \
- : "cc"); \
- (r) = carry, carry = high; \
- } while (0)
- #undef sqr
- #define sqr(r0, r1, a) asm("mulq %2" : "=a"(r0), "=d"(r1) : "a"(a) : "cc");
-
- BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
- BN_ULONG w) {
- BN_ULONG c1 = 0;
-
- if (num <= 0) {
- return (c1);
- }
-
- while (num & ~3) {
- mul_add(rp[0], ap[0], w, c1);
- mul_add(rp[1], ap[1], w, c1);
- mul_add(rp[2], ap[2], w, c1);
- mul_add(rp[3], ap[3], w, c1);
- ap += 4;
- rp += 4;
- num -= 4;
- }
- if (num) {
- mul_add(rp[0], ap[0], w, c1);
- if (--num == 0) {
- return c1;
- }
- mul_add(rp[1], ap[1], w, c1);
- if (--num == 0) {
- return c1;
- }
- mul_add(rp[2], ap[2], w, c1);
- return c1;
- }
-
- return c1;
- }
-
- BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w) {
- BN_ULONG c1 = 0;
-
- if (num <= 0) {
- return c1;
- }
-
- while (num & ~3) {
- mul(rp[0], ap[0], w, c1);
- mul(rp[1], ap[1], w, c1);
- mul(rp[2], ap[2], w, c1);
- mul(rp[3], ap[3], w, c1);
- ap += 4;
- rp += 4;
- num -= 4;
- }
- if (num) {
- mul(rp[0], ap[0], w, c1);
- if (--num == 0) {
- return c1;
- }
- mul(rp[1], ap[1], w, c1);
- if (--num == 0) {
- return c1;
- }
- mul(rp[2], ap[2], w, c1);
- }
- return c1;
- }
-
- void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n) {
- if (n <= 0) {
- return;
- }
-
- while (n & ~3) {
- sqr(r[0], r[1], a[0]);
- sqr(r[2], r[3], a[1]);
- sqr(r[4], r[5], a[2]);
- sqr(r[6], r[7], a[3]);
- a += 4;
- r += 8;
- n -= 4;
- }
- if (n) {
- sqr(r[0], r[1], a[0]);
- if (--n == 0) {
- return;
- }
- sqr(r[2], r[3], a[1]);
- if (--n == 0) {
- return;
- }
- sqr(r[4], r[5], a[2]);
- }
- }
-
- BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) {
- BN_ULONG ret, waste;
-
- asm("divq %4" : "=a"(ret), "=d"(waste) : "a"(l), "d"(h), "g"(d) : "cc");
-
- return ret;
- }
-
- BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
- int n) {
- BN_ULONG ret;
- size_t i = 0;
-
- if (n <= 0) {
- return 0;
- }
-
- asm volatile (
- " subq %0,%0 \n" /* clear carry */
- " jmp 1f \n"
- ".p2align 4 \n"
- "1: movq (%4,%2,8),%0 \n"
- " adcq (%5,%2,8),%0 \n"
- " movq %0,(%3,%2,8) \n"
- " lea 1(%2),%2 \n"
- " loop 1b \n"
- " sbbq %0,%0 \n"
- : "=&r"(ret), "+c"(n), "+r"(i)
- : "r"(rp), "r"(ap), "r"(bp)
- : "cc", "memory");
-
- return ret & 1;
- }
-
- #ifndef SIMICS
- BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
- int n) {
- BN_ULONG ret;
- size_t i = 0;
-
- if (n <= 0) {
- return 0;
- }
-
- asm volatile (
- " subq %0,%0 \n" /* clear borrow */
- " jmp 1f \n"
- ".p2align 4 \n"
- "1: movq (%4,%2,8),%0 \n"
- " sbbq (%5,%2,8),%0 \n"
- " movq %0,(%3,%2,8) \n"
- " lea 1(%2),%2 \n"
- " loop 1b \n"
- " sbbq %0,%0 \n"
- : "=&r"(ret), "+c"(n), "+r"(i)
- : "r"(rp), "r"(ap), "r"(bp)
- : "cc", "memory");
-
- return ret & 1;
- }
- #else
- /* Simics 1.4<7 has buggy sbbq:-( */
- #define BN_MASK2 0xffffffffffffffffL
- BN_ULONG bn_sub_words(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n) {
- BN_ULONG t1, t2;
- int c = 0;
-
- if (n <= 0) {
- return (BN_ULONG)0;
- }
-
- for (;;) {
- t1 = a[0];
- t2 = b[0];
- r[0] = (t1 - t2 - c) & BN_MASK2;
- if (t1 != t2) {
- c = (t1 < t2);
- }
- if (--n <= 0) {
- break;
- }
-
- t1 = a[1];
- t2 = b[1];
- r[1] = (t1 - t2 - c) & BN_MASK2;
- if (t1 != t2) {
- c = (t1 < t2);
- }
- if (--n <= 0) {
- break;
- }
-
- t1 = a[2];
- t2 = b[2];
- r[2] = (t1 - t2 - c) & BN_MASK2;
- if (t1 != t2) {
- c = (t1 < t2);
- }
- if (--n <= 0) {
- break;
- }
-
- t1 = a[3];
- t2 = b[3];
- r[3] = (t1 - t2 - c) & BN_MASK2;
- if (t1 != t2) {
- c = (t1 < t2);
- }
- if (--n <= 0) {
- break;
- }
-
- a += 4;
- b += 4;
- r += 4;
- }
- return c;
- }
- #endif
-
- /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
- /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
- /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
- /* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0)
- */
-
- /* Keep in mind that carrying into high part of multiplication result can not
- * overflow, because it cannot be all-ones. */
- #define mul_add_c(a, b, c0, c1, c2) \
- do { \
- BN_ULONG t1, t2; \
- asm("mulq %3" : "=a"(t1), "=d"(t2) : "a"(a), "m"(b) : "cc"); \
- asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \
- : "+r"(c0), "+r"(c1), "+r"(c2) \
- : "r"(t1), "r"(t2), "g"(0) \
- : "cc"); \
- } while (0)
-
- #define sqr_add_c(a, i, c0, c1, c2) \
- do { \
- BN_ULONG t1, t2; \
- asm("mulq %2" : "=a"(t1), "=d"(t2) : "a"(a[i]) : "cc"); \
- asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \
- : "+r"(c0), "+r"(c1), "+r"(c2) \
- : "r"(t1), "r"(t2), "g"(0) \
- : "cc"); \
- } while (0)
-
- #define mul_add_c2(a, b, c0, c1, c2) \
- do { \
- BN_ULONG t1, t2; \
- asm("mulq %3" : "=a"(t1), "=d"(t2) : "a"(a), "m"(b) : "cc"); \
- asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \
- : "+r"(c0), "+r"(c1), "+r"(c2) \
- : "r"(t1), "r"(t2), "g"(0) \
- : "cc"); \
- asm("addq %3,%0; adcq %4,%1; adcq %5,%2" \
- : "+r"(c0), "+r"(c1), "+r"(c2) \
- : "r"(t1), "r"(t2), "g"(0) \
- : "cc"); \
- } while (0)
-
- #define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2)
-
- void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) {
- BN_ULONG c1, c2, c3;
-
- c1 = 0;
- c2 = 0;
- c3 = 0;
- mul_add_c(a[0], b[0], c1, c2, c3);
- r[0] = c1;
- c1 = 0;
- mul_add_c(a[0], b[1], c2, c3, c1);
- mul_add_c(a[1], b[0], c2, c3, c1);
- r[1] = c2;
- c2 = 0;
- mul_add_c(a[2], b[0], c3, c1, c2);
- mul_add_c(a[1], b[1], c3, c1, c2);
- mul_add_c(a[0], b[2], c3, c1, c2);
- r[2] = c3;
- c3 = 0;
- mul_add_c(a[0], b[3], c1, c2, c3);
- mul_add_c(a[1], b[2], c1, c2, c3);
- mul_add_c(a[2], b[1], c1, c2, c3);
- mul_add_c(a[3], b[0], c1, c2, c3);
- r[3] = c1;
- c1 = 0;
- mul_add_c(a[4], b[0], c2, c3, c1);
- mul_add_c(a[3], b[1], c2, c3, c1);
- mul_add_c(a[2], b[2], c2, c3, c1);
- mul_add_c(a[1], b[3], c2, c3, c1);
- mul_add_c(a[0], b[4], c2, c3, c1);
- r[4] = c2;
- c2 = 0;
- mul_add_c(a[0], b[5], c3, c1, c2);
- mul_add_c(a[1], b[4], c3, c1, c2);
- mul_add_c(a[2], b[3], c3, c1, c2);
- mul_add_c(a[3], b[2], c3, c1, c2);
- mul_add_c(a[4], b[1], c3, c1, c2);
- mul_add_c(a[5], b[0], c3, c1, c2);
- r[5] = c3;
- c3 = 0;
- mul_add_c(a[6], b[0], c1, c2, c3);
- mul_add_c(a[5], b[1], c1, c2, c3);
- mul_add_c(a[4], b[2], c1, c2, c3);
- mul_add_c(a[3], b[3], c1, c2, c3);
- mul_add_c(a[2], b[4], c1, c2, c3);
- mul_add_c(a[1], b[5], c1, c2, c3);
- mul_add_c(a[0], b[6], c1, c2, c3);
- r[6] = c1;
- c1 = 0;
- mul_add_c(a[0], b[7], c2, c3, c1);
- mul_add_c(a[1], b[6], c2, c3, c1);
- mul_add_c(a[2], b[5], c2, c3, c1);
- mul_add_c(a[3], b[4], c2, c3, c1);
- mul_add_c(a[4], b[3], c2, c3, c1);
- mul_add_c(a[5], b[2], c2, c3, c1);
- mul_add_c(a[6], b[1], c2, c3, c1);
- mul_add_c(a[7], b[0], c2, c3, c1);
- r[7] = c2;
- c2 = 0;
- mul_add_c(a[7], b[1], c3, c1, c2);
- mul_add_c(a[6], b[2], c3, c1, c2);
- mul_add_c(a[5], b[3], c3, c1, c2);
- mul_add_c(a[4], b[4], c3, c1, c2);
- mul_add_c(a[3], b[5], c3, c1, c2);
- mul_add_c(a[2], b[6], c3, c1, c2);
- mul_add_c(a[1], b[7], c3, c1, c2);
- r[8] = c3;
- c3 = 0;
- mul_add_c(a[2], b[7], c1, c2, c3);
- mul_add_c(a[3], b[6], c1, c2, c3);
- mul_add_c(a[4], b[5], c1, c2, c3);
- mul_add_c(a[5], b[4], c1, c2, c3);
- mul_add_c(a[6], b[3], c1, c2, c3);
- mul_add_c(a[7], b[2], c1, c2, c3);
- r[9] = c1;
- c1 = 0;
- mul_add_c(a[7], b[3], c2, c3, c1);
- mul_add_c(a[6], b[4], c2, c3, c1);
- mul_add_c(a[5], b[5], c2, c3, c1);
- mul_add_c(a[4], b[6], c2, c3, c1);
- mul_add_c(a[3], b[7], c2, c3, c1);
- r[10] = c2;
- c2 = 0;
- mul_add_c(a[4], b[7], c3, c1, c2);
- mul_add_c(a[5], b[6], c3, c1, c2);
- mul_add_c(a[6], b[5], c3, c1, c2);
- mul_add_c(a[7], b[4], c3, c1, c2);
- r[11] = c3;
- c3 = 0;
- mul_add_c(a[7], b[5], c1, c2, c3);
- mul_add_c(a[6], b[6], c1, c2, c3);
- mul_add_c(a[5], b[7], c1, c2, c3);
- r[12] = c1;
- c1 = 0;
- mul_add_c(a[6], b[7], c2, c3, c1);
- mul_add_c(a[7], b[6], c2, c3, c1);
- r[13] = c2;
- c2 = 0;
- mul_add_c(a[7], b[7], c3, c1, c2);
- r[14] = c3;
- r[15] = c1;
- }
-
- void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) {
- BN_ULONG c1, c2, c3;
-
- c1 = 0;
- c2 = 0;
- c3 = 0;
- mul_add_c(a[0], b[0], c1, c2, c3);
- r[0] = c1;
- c1 = 0;
- mul_add_c(a[0], b[1], c2, c3, c1);
- mul_add_c(a[1], b[0], c2, c3, c1);
- r[1] = c2;
- c2 = 0;
- mul_add_c(a[2], b[0], c3, c1, c2);
- mul_add_c(a[1], b[1], c3, c1, c2);
- mul_add_c(a[0], b[2], c3, c1, c2);
- r[2] = c3;
- c3 = 0;
- mul_add_c(a[0], b[3], c1, c2, c3);
- mul_add_c(a[1], b[2], c1, c2, c3);
- mul_add_c(a[2], b[1], c1, c2, c3);
- mul_add_c(a[3], b[0], c1, c2, c3);
- r[3] = c1;
- c1 = 0;
- mul_add_c(a[3], b[1], c2, c3, c1);
- mul_add_c(a[2], b[2], c2, c3, c1);
- mul_add_c(a[1], b[3], c2, c3, c1);
- r[4] = c2;
- c2 = 0;
- mul_add_c(a[2], b[3], c3, c1, c2);
- mul_add_c(a[3], b[2], c3, c1, c2);
- r[5] = c3;
- c3 = 0;
- mul_add_c(a[3], b[3], c1, c2, c3);
- r[6] = c1;
- r[7] = c2;
- }
-
- void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a) {
- BN_ULONG c1, c2, c3;
-
- c1 = 0;
- c2 = 0;
- c3 = 0;
- sqr_add_c(a, 0, c1, c2, c3);
- r[0] = c1;
- c1 = 0;
- sqr_add_c2(a, 1, 0, c2, c3, c1);
- r[1] = c2;
- c2 = 0;
- sqr_add_c(a, 1, c3, c1, c2);
- sqr_add_c2(a, 2, 0, c3, c1, c2);
- r[2] = c3;
- c3 = 0;
- sqr_add_c2(a, 3, 0, c1, c2, c3);
- sqr_add_c2(a, 2, 1, c1, c2, c3);
- r[3] = c1;
- c1 = 0;
- sqr_add_c(a, 2, c2, c3, c1);
- sqr_add_c2(a, 3, 1, c2, c3, c1);
- sqr_add_c2(a, 4, 0, c2, c3, c1);
- r[4] = c2;
- c2 = 0;
- sqr_add_c2(a, 5, 0, c3, c1, c2);
- sqr_add_c2(a, 4, 1, c3, c1, c2);
- sqr_add_c2(a, 3, 2, c3, c1, c2);
- r[5] = c3;
- c3 = 0;
- sqr_add_c(a, 3, c1, c2, c3);
- sqr_add_c2(a, 4, 2, c1, c2, c3);
- sqr_add_c2(a, 5, 1, c1, c2, c3);
- sqr_add_c2(a, 6, 0, c1, c2, c3);
- r[6] = c1;
- c1 = 0;
- sqr_add_c2(a, 7, 0, c2, c3, c1);
- sqr_add_c2(a, 6, 1, c2, c3, c1);
- sqr_add_c2(a, 5, 2, c2, c3, c1);
- sqr_add_c2(a, 4, 3, c2, c3, c1);
- r[7] = c2;
- c2 = 0;
- sqr_add_c(a, 4, c3, c1, c2);
- sqr_add_c2(a, 5, 3, c3, c1, c2);
- sqr_add_c2(a, 6, 2, c3, c1, c2);
- sqr_add_c2(a, 7, 1, c3, c1, c2);
- r[8] = c3;
- c3 = 0;
- sqr_add_c2(a, 7, 2, c1, c2, c3);
- sqr_add_c2(a, 6, 3, c1, c2, c3);
- sqr_add_c2(a, 5, 4, c1, c2, c3);
- r[9] = c1;
- c1 = 0;
- sqr_add_c(a, 5, c2, c3, c1);
- sqr_add_c2(a, 6, 4, c2, c3, c1);
- sqr_add_c2(a, 7, 3, c2, c3, c1);
- r[10] = c2;
- c2 = 0;
- sqr_add_c2(a, 7, 4, c3, c1, c2);
- sqr_add_c2(a, 6, 5, c3, c1, c2);
- r[11] = c3;
- c3 = 0;
- sqr_add_c(a, 6, c1, c2, c3);
- sqr_add_c2(a, 7, 5, c1, c2, c3);
- r[12] = c1;
- c1 = 0;
- sqr_add_c2(a, 7, 6, c2, c3, c1);
- r[13] = c2;
- c2 = 0;
- sqr_add_c(a, 7, c3, c1, c2);
- r[14] = c3;
- r[15] = c1;
- }
-
- void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a) {
- BN_ULONG c1, c2, c3;
-
- c1 = 0;
- c2 = 0;
- c3 = 0;
- sqr_add_c(a, 0, c1, c2, c3);
- r[0] = c1;
- c1 = 0;
- sqr_add_c2(a, 1, 0, c2, c3, c1);
- r[1] = c2;
- c2 = 0;
- sqr_add_c(a, 1, c3, c1, c2);
- sqr_add_c2(a, 2, 0, c3, c1, c2);
- r[2] = c3;
- c3 = 0;
- sqr_add_c2(a, 3, 0, c1, c2, c3);
- sqr_add_c2(a, 2, 1, c1, c2, c3);
- r[3] = c1;
- c1 = 0;
- sqr_add_c(a, 2, c2, c3, c1);
- sqr_add_c2(a, 3, 1, c2, c3, c1);
- r[4] = c2;
- c2 = 0;
- sqr_add_c2(a, 3, 2, c3, c1, c2);
- r[5] = c3;
- c3 = 0;
- sqr_add_c(a, 3, c1, c2, c3);
- r[6] = c1;
- r[7] = c2;
- }
-
- #endif /* !NO_ASM && X86_64 && !WINDOWS */
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