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x86_64-gcc.c

/*
 * 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.
 */

#define BN_ULONG unsigned long

/*
 * "m"(a), "+m"(r)      is the way to favor DirectPath -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)

#define sqr(r0,r1,a)                \
      asm ("mulq %2"                \
            : "=a"(r0),"=d"(r1)     \
            : "a"(a)          \
            : "cc");

BN_ULONG bn_mul_add_words(BN_ULONG *rp, 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, 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, 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, BN_ULONG *ap, BN_ULONG *bp,int n)
{ BN_ULONG ret=0,i=0;

      if (n <= 0) return 0;

      asm (
      "     subq  %2,%2       \n"
      ".align 16              \n"
      "1:   movq  (%4,%2,8),%0      \n"
      "     adcq  (%5,%2,8),%0      \n"
      "     movq  %0,(%3,%2,8)      \n"
      "     leaq  1(%2),%2    \n"
      "     loop  1b          \n"
      "     sbbq  %0,%0       \n"
            : "=&a"(ret),"+c"(n),"=&r"(i)
            : "r"(rp),"r"(ap),"r"(bp)
            : "cc"
      );

  return ret&1;
}

#ifndef SIMICS
BN_ULONG bn_sub_words (BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int n)
{ BN_ULONG ret=0,i=0;

      if (n <= 0) return 0;

      asm (
      "     subq  %2,%2       \n"
      ".align 16              \n"
      "1:   movq  (%4,%2,8),%0      \n"
      "     sbbq  (%5,%2,8),%0      \n"
      "     movq  %0,(%3,%2,8)      \n"
      "     leaq  1(%2),%2    \n"
      "     loop  1b          \n"
      "     sbbq  %0,%0       \n"
            : "=&a"(ret),"+c"(n),"=&r"(i)
            : "r"(rp),"r"(ap),"r"(bp)
            : "cc"
      );

  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) */

#if 0
/* original macros are kept for reference purposes */
#define mul_add_c(a,b,c0,c1,c2) {   \
      BN_ULONG ta=(a),tb=(b);       \
      t1 = ta * tb;                 \
      t2 = BN_UMULT_HIGH(ta,tb);    \
      c0 += t1; t2 += (c0<t1)?1:0;  \
      c1 += t2; c2 += (c1<t2)?1:0;  \
      }

#define mul_add_c2(a,b,c0,c1,c2) {  \
      BN_ULONG ta=(a),tb=(b),t0;    \
      t1 = BN_UMULT_HIGH(ta,tb);    \
      t0 = ta * tb;                 \
      t2 = t1+t1; c2 += (t2<t1)?1:0;      \
      t1 = t0+t0; t2 += (t1<t0)?1:0;      \
      c0 += t1; t2 += (c0<t1)?1:0;  \
      c1 += t2; c2 += (c1<t2)?1:0;  \
      }
#else
#define mul_add_c(a,b,c0,c1,c2)     do {  \
      asm ("mulq %3"                \
            : "=a"(t1),"=d"(t2)     \
            : "a"(a),"m"(b)         \
            : "cc");          \
      asm ("addq %2,%0; adcq %3,%1" \
            : "+r"(c0),"+d"(t2)     \
            : "a"(t1),"g"(0)  \
            : "cc");          \
      asm ("addq %2,%0; adcq %3,%1" \
            : "+r"(c1),"+r"(c2)     \
            : "d"(t2),"g"(0)  \
            : "cc");          \
      } while (0)

#define sqr_add_c(a,i,c0,c1,c2)     do {  \
      asm ("mulq %2"                \
            : "=a"(t1),"=d"(t2)     \
            : "a"(a[i])       \
            : "cc");          \
      asm ("addq %2,%0; adcq %3,%1" \
            : "+r"(c0),"+d"(t2)     \
            : "a"(t1),"g"(0)  \
            : "cc");          \
      asm ("addq %2,%0; adcq %3,%1" \
            : "+r"(c1),"+r"(c2)     \
            : "d"(t2),"g"(0)  \
            : "cc");          \
      } while (0)

#define mul_add_c2(a,b,c0,c1,c2) do {     \
      asm ("mulq %3"                \
            : "=a"(t1),"=d"(t2)     \
            : "a"(a),"m"(b)         \
            : "cc");          \
      asm ("addq %0,%0; adcq %2,%1" \
            : "+d"(t2),"+r"(c2)     \
            : "g"(0)          \
            : "cc");          \
      asm ("addq %0,%0; adcq %2,%1" \
            : "+a"(t1),"+d"(t2)     \
            : "g"(0)          \
            : "cc");          \
      asm ("addq %2,%0; adcq %3,%1" \
            : "+r"(c0),"+d"(t2)     \
            : "a"(t1),"g"(0)  \
            : "cc");          \
      asm ("addq %2,%0; adcq %3,%1" \
            : "+r"(c1),"+r"(c2)     \
            : "d"(t2),"g"(0)  \
            : "cc");          \
      } while (0)
#endif

#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 t1,t2;
      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 t1,t2;
      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, BN_ULONG *a)
      {
      BN_ULONG t1,t2;
      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, BN_ULONG *a)
      {
      BN_ULONG t1,t2;
      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;
      }

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