hackney

// Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved.
//
// 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
//
//     https://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.

/* 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 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 MSVC x64.
#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
    (defined(__GNUC__) || defined(__clang__))

#include "../internal.h"


#undef mul
#undef mul_add

// "m"(a), "+m"(r)	is the way to favor DirectPath µ-code;
#define mul_add(r, a, word, carry)                                         \
  do {                                                                     \
    BN_ULONG high, low;                                                    \
    __asm__("mulq %3" : "=a"(low), "=d"(high) : "a"(word), "m"(a) : "cc"); \
    __asm__("addq %2,%0; adcq $0,%1"                                       \
            : "+r"(carry), "+d"(high)                                      \
            : "a"(low)                                                     \
            : "cc");                                                       \
    __asm__("addq %2,%0; adcq $0,%1"                                       \
            : "+m"(r), "+d"(high)                                          \
            : "r"(carry)                                                   \
            : "cc");                                                       \
    (carry) = high;                                                        \
  } while (0)

#define mul(r, a, word, carry)                                             \
  do {                                                                     \
    BN_ULONG high, low;                                                    \
    __asm__("mulq %3" : "=a"(low), "=d"(high) : "a"(word), "g"(a) : "cc"); \
    __asm__("addq %2,%0; adcq $0,%1"                                       \
            : "+r"(carry), "+d"(high)                                      \
            : "a"(low)                                                     \
            : "cc");                                                       \
    (r) = (carry);                                                         \
    (carry) = high;                                                        \
  } while (0)

// r0:r1:carry = r0:r1 + a^2 + carry:0
#define sqr_add(r0, r1, a, carry)                               \
  do {                                                          \
    BN_ULONG high, low;                                         \
    /* lo:hi = a^2 */                                           \
    __asm__("mulq %2" : "=a"(low), "=d"(high) : "a"(a) : "cc"); \
    /* carry:hi = lo:hi + carry:0 = a^2 + carry */              \
    __asm__("addq %2,%0; adcq $0,%1"                            \
            : "+r"(carry), "+d"(high)                           \
            : "a"(low)                                          \
            : "cc");                                            \
    /* r0:r1:carry = carry:hi + r0:r1 */                        \
    __asm__("addq %2,%0; adcq %3,%1; movq $0, %2; adcq $0, %2"  \
            : "+m"(r0), "+m"(r1), "+r"(carry)                   \
            : "d"(high)                                         \
            : "cc");                                            \
  } while (0)

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_add_words(BN_ULONG *r, const BN_ULONG *a, size_t n) {
  if (n == 0) {
    return;
  }

  BN_ULONG carry = 0;
  while (n & ~3) {
    sqr_add(r[0], r[1], a[0], carry);
    sqr_add(r[2], r[3], a[1], carry);
    sqr_add(r[4], r[5], a[2], carry);
    sqr_add(r[6], r[7], a[3], carry);
    a += 4;
    r += 8;
    n -= 4;
  }
  if (n) {
    sqr_add(r[0], r[1], a[0], carry);
    if (--n == 0) {
      return;
    }
    sqr_add(r[2], r[3], a[1], carry);
    if (--n == 0) {
      return;
    }
    sqr_add(r[4], r[5], a[2], carry);
  }
}

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 $0,%2"                     \
            : "+&r"(c0), "+r"(c1), "+r"(c2)                          \
            : "r"(t1), "r"(t2)                                       \
            : "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 $0,%2"                  \
            : "+&r"(c0), "+r"(c1), "+r"(c2)                       \
            : "r"(t1), "r"(t2)                                    \
            : "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 $0,%2"                     \
            : "+&r"(c0), "+r"(c1), "+r"(c2)                          \
            : "r"(t1), "r"(t2)                                       \
            : "cc");                                                 \
    __asm__("addq %3,%0; adcq %4,%1; adcq $0,%2"                     \
            : "+&r"(c0), "+r"(c1), "+r"(c2)                          \
            : "r"(t1), "r"(t2)                                       \
            : "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__ || __clang__)