+# ifdef BN_LLONG
+/*
+ * Keep in mind that additions to multiplication result can not
+ * overflow, because its high half cannot be all-ones.
+ */
+# define mul_add_c(a,b,c0,c1,c2) do { \
+ BN_ULONG hi; \
+ BN_ULLONG t = (BN_ULLONG)(a)*(b); \
+ t += c0; /* no carry */ \
+ c0 = (BN_ULONG)Lw(t); \
+ hi = (BN_ULONG)Hw(t); \
+ c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
+ } while(0)
+
+# define mul_add_c2(a,b,c0,c1,c2) do { \
+ BN_ULONG hi; \
+ BN_ULLONG t = (BN_ULLONG)(a)*(b); \
+ BN_ULLONG tt = t+c0; /* no carry */ \
+ c0 = (BN_ULONG)Lw(tt); \
+ hi = (BN_ULONG)Hw(tt); \
+ c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
+ t += c0; /* no carry */ \
+ c0 = (BN_ULONG)Lw(t); \
+ hi = (BN_ULONG)Hw(t); \
+ c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
+ } while(0)
+
+# define sqr_add_c(a,i,c0,c1,c2) do { \
+ BN_ULONG hi; \
+ BN_ULLONG t = (BN_ULLONG)a[i]*a[i]; \
+ t += c0; /* no carry */ \
+ c0 = (BN_ULONG)Lw(t); \
+ hi = (BN_ULONG)Hw(t); \
+ c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
+ } while(0)
+
+# define sqr_add_c2(a,i,j,c0,c1,c2) \
+ mul_add_c2((a)[i],(a)[j],c0,c1,c2)
+
+# elif defined(BN_UMULT_LOHI)
+/*
+ * Keep in mind that additions to hi can not overflow, because
+ * the high word of a multiplication result cannot be all-ones.
+ */
+# define mul_add_c(a,b,c0,c1,c2) do { \
+ BN_ULONG ta = (a), tb = (b); \
+ BN_ULONG lo, hi; \
+ BN_UMULT_LOHI(lo,hi,ta,tb); \
+ c0 += lo; hi += (c0<lo)?1:0; \
+ c1 += hi; c2 += (c1<hi)?1:0; \
+ } while(0)
+
+# define mul_add_c2(a,b,c0,c1,c2) do { \
+ BN_ULONG ta = (a), tb = (b); \
+ BN_ULONG lo, hi, tt; \
+ BN_UMULT_LOHI(lo,hi,ta,tb); \
+ c0 += lo; tt = hi+((c0<lo)?1:0); \
+ c1 += tt; c2 += (c1<tt)?1:0; \
+ c0 += lo; hi += (c0<lo)?1:0; \
+ c1 += hi; c2 += (c1<hi)?1:0; \
+ } while(0)
+
+# define sqr_add_c(a,i,c0,c1,c2) do { \
+ BN_ULONG ta = (a)[i]; \
+ BN_ULONG lo, hi; \
+ BN_UMULT_LOHI(lo,hi,ta,ta); \
+ c0 += lo; hi += (c0<lo)?1:0; \
+ c1 += hi; c2 += (c1<hi)?1:0; \
+ } while(0)
+
+# define sqr_add_c2(a,i,j,c0,c1,c2) \
+ mul_add_c2((a)[i],(a)[j],c0,c1,c2)
+
+# elif defined(BN_UMULT_HIGH)
+/*
+ * Keep in mind that additions to hi can not overflow, because
+ * the high word of a multiplication result cannot be all-ones.
+ */
+# define mul_add_c(a,b,c0,c1,c2) do { \
+ BN_ULONG ta = (a), tb = (b); \
+ BN_ULONG lo = ta * tb; \
+ BN_ULONG hi = BN_UMULT_HIGH(ta,tb); \
+ c0 += lo; hi += (c0<lo)?1:0; \
+ c1 += hi; c2 += (c1<hi)?1:0; \
+ } while(0)
+
+# define mul_add_c2(a,b,c0,c1,c2) do { \
+ BN_ULONG ta = (a), tb = (b), tt; \
+ BN_ULONG lo = ta * tb; \
+ BN_ULONG hi = BN_UMULT_HIGH(ta,tb); \
+ c0 += lo; tt = hi + ((c0<lo)?1:0); \
+ c1 += tt; c2 += (c1<tt)?1:0; \
+ c0 += lo; hi += (c0<lo)?1:0; \
+ c1 += hi; c2 += (c1<hi)?1:0; \
+ } while(0)
+
+# define sqr_add_c(a,i,c0,c1,c2) do { \
+ BN_ULONG ta = (a)[i]; \
+ BN_ULONG lo = ta * ta; \
+ BN_ULONG hi = BN_UMULT_HIGH(ta,ta); \
+ c0 += lo; hi += (c0<lo)?1:0; \
+ c1 += hi; c2 += (c1<hi)?1:0; \
+ } while(0)
+
+# define sqr_add_c2(a,i,j,c0,c1,c2) \
+ mul_add_c2((a)[i],(a)[j],c0,c1,c2)
+
+# else /* !BN_LLONG */
+/*
+ * Keep in mind that additions to hi can not overflow, because
+ * the high word of a multiplication result cannot be all-ones.
+ */
+# define mul_add_c(a,b,c0,c1,c2) do { \
+ BN_ULONG lo = LBITS(a), hi = HBITS(a); \
+ BN_ULONG bl = LBITS(b), bh = HBITS(b); \
+ mul64(lo,hi,bl,bh); \
+ c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \
+ c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
+ } while(0)
+
+# define mul_add_c2(a,b,c0,c1,c2) do { \
+ BN_ULONG tt; \
+ BN_ULONG lo = LBITS(a), hi = HBITS(a); \
+ BN_ULONG bl = LBITS(b), bh = HBITS(b); \
+ mul64(lo,hi,bl,bh); \
+ tt = hi; \
+ c0 = (c0+lo)&BN_MASK2; if (c0<lo) tt++; \
+ c1 = (c1+tt)&BN_MASK2; if (c1<tt) c2++; \
+ c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \
+ c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
+ } while(0)
+
+# define sqr_add_c(a,i,c0,c1,c2) do { \
+ BN_ULONG lo, hi; \
+ sqr64(lo,hi,(a)[i]); \
+ c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \
+ c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
+ } while(0)
+
+# define sqr_add_c2(a,i,j,c0,c1,c2) \
+ mul_add_c2((a)[i],(a)[j],c0,c1,c2)
+# endif /* !BN_LLONG */
+
+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;
+}
+
+# ifdef OPENSSL_NO_ASM
+# ifdef OPENSSL_BN_ASM_MONT
+# include <alloca.h>
+/*
+ * This is essentially reference implementation, which may or may not
+ * result in performance improvement. E.g. on IA-32 this routine was
+ * observed to give 40% faster rsa1024 private key operations and 10%
+ * faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only
+ * by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a
+ * reference implementation, one to be used as starting point for
+ * platform-specific assembler. Mentioned numbers apply to compiler
+ * generated code compiled with and without -DOPENSSL_BN_ASM_MONT and
+ * can vary not only from platform to platform, but even for compiler
+ * versions. Assembler vs. assembler improvement coefficients can
+ * [and are known to] differ and are to be documented elsewhere.
+ */
+int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
+ const BN_ULONG *np, const BN_ULONG *n0p, int num)
+{
+ BN_ULONG c0, c1, ml, *tp, n0;
+# ifdef mul64
+ BN_ULONG mh;
+# endif
+ volatile BN_ULONG *vp;
+ int i = 0, j;
+
+# if 0 /* template for platform-specific
+ * implementation */
+ if (ap == bp)
+ return bn_sqr_mont(rp, ap, np, n0p, num);
+# endif
+ vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
+
+ n0 = *n0p;
+
+ c0 = 0;
+ ml = bp[0];
+# ifdef mul64
+ mh = HBITS(ml);
+ ml = LBITS(ml);
+ for (j = 0; j < num; ++j)
+ mul(tp[j], ap[j], ml, mh, c0);
+# else
+ for (j = 0; j < num; ++j)
+ mul(tp[j], ap[j], ml, c0);
+# endif
+
+ tp[num] = c0;
+ tp[num + 1] = 0;
+ goto enter;
+
+ for (i = 0; i < num; i++) {
+ c0 = 0;
+ ml = bp[i];
+# ifdef mul64
+ mh = HBITS(ml);
+ ml = LBITS(ml);
+ for (j = 0; j < num; ++j)
+ mul_add(tp[j], ap[j], ml, mh, c0);
+# else
+ for (j = 0; j < num; ++j)
+ mul_add(tp[j], ap[j], ml, c0);
+# endif
+ c1 = (tp[num] + c0) & BN_MASK2;
+ tp[num] = c1;
+ tp[num + 1] = (c1 < c0 ? 1 : 0);
+ enter:
+ c1 = tp[0];
+ ml = (c1 * n0) & BN_MASK2;
+ c0 = 0;
+# ifdef mul64
+ mh = HBITS(ml);
+ ml = LBITS(ml);
+ mul_add(c1, np[0], ml, mh, c0);
+# else
+ mul_add(c1, ml, np[0], c0);
+# endif
+ for (j = 1; j < num; j++) {
+ c1 = tp[j];
+# ifdef mul64
+ mul_add(c1, np[j], ml, mh, c0);
+# else
+ mul_add(c1, ml, np[j], c0);
+# endif
+ tp[j - 1] = c1 & BN_MASK2;
+ }
+ c1 = (tp[num] + c0) & BN_MASK2;
+ tp[num - 1] = c1;
+ tp[num] = tp[num + 1] + (c1 < c0 ? 1 : 0);
+ }
+
+ if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
+ c0 = bn_sub_words(rp, tp, np, num);
+ if (tp[num] != 0 || c0 == 0) {
+ for (i = 0; i < num + 2; i++)
+ vp[i] = 0;
+ return 1;
+ }
+ }
+ for (i = 0; i < num; i++)
+ rp[i] = tp[i], vp[i] = 0;
+ vp[num] = 0;
+ vp[num + 1] = 0;
+ return 1;
+}
+# else
+/*
+ * Return value of 0 indicates that multiplication/convolution was not
+ * performed to signal the caller to fall down to alternative/original
+ * code-path.
+ */
+int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
+ const BN_ULONG *np, const BN_ULONG *n0, int num)
+{
+ return 0;
+}
+# endif /* OPENSSL_BN_ASM_MONT */
+# endif