| /* 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. |
| */ |
| |
| #include <openssl/bn.h> |
| |
| // 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" |
| " dec %1 \n" |
| " jnz 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" |
| " dec %1 \n" |
| " jnz 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], const BN_ULONG a[8], const 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], const BN_ULONG a[4], const 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__ |
