/* x86_64 BIGNUM accelerator version 0.1, December 2002. * * Implemented by Andy Polyakov 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. */ #include // TODO(davidben): Get this file working on Windows x64. #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && defined(__GNUC__) #include "../internal.h" #undef mul #undef mul_add // "m"(a), "+m"(r) is the way to favor DirectPath ยต-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, size_t 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, size_t 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, size_t 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_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, size_t 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; } BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, size_t 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; } // 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[16], BN_ULONG a[8], BN_ULONG b[8]) { 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[8], BN_ULONG a[4], BN_ULONG b[4]) { 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[16], const BN_ULONG a[8]) { 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[8], const BN_ULONG a[4]) { 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; } #undef mul_add #undef mul #undef sqr #undef mul_add_c #undef sqr_add_c #undef mul_add_c2 #undef sqr_add_c2 #endif // !NO_ASM && X86_64 && __GNUC__