/* Multiply {ap,an} by {bp,bn}, and put the result in {pp, an+bn} */ void mpn_nussbaumer_mul (mp_ptr pp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn) { mp_size_t rn; mp_ptr tp; TMP_DECL; ASSERT (an >= bn); ASSERT (bn > 0); TMP_MARK; if ((ap == bp) && (an == bn)) { rn = mpn_sqrmod_bnm1_next_size (2*an); tp = TMP_ALLOC_LIMBS (mpn_sqrmod_bnm1_itch (rn, an)); mpn_sqrmod_bnm1 (pp, rn, ap, an, tp); } else { rn = mpn_mulmod_bnm1_next_size (an + bn); tp = TMP_ALLOC_LIMBS (mpn_mulmod_bnm1_itch (rn, an, bn)); mpn_mulmod_bnm1 (pp, rn, ap, an, bp, bn, tp); } TMP_FREE; }
/* Computes {rp,MIN(rn,2an)} <- {ap,an}^2 Mod(B^rn-1) * * The result is expected to be ZERO if and only if the operand * already is. Otherwise the class [0] Mod(B^rn-1) is represented by * B^rn-1. * It should not be a problem if sqrmod_bnm1 is used to * compute the full square with an <= 2*rn, because this condition * implies (B^an-1)^2 < (B^rn-1) . * * Requires rn/4 < an <= rn * Scratch need: rn/2 + (need for recursive call OR rn + 3). This gives * * S(n) <= rn/2 + MAX (rn + 4, S(n/2)) <= 3/2 rn + 4 */ void mpn_sqrmod_bnm1 (mp_ptr rp, mp_size_t rn, mp_srcptr ap, mp_size_t an, mp_ptr tp) { ASSERT (0 < an); ASSERT (an <= rn); if ((rn & 1) != 0 || BELOW_THRESHOLD (rn, SQRMOD_BNM1_THRESHOLD)) { if (UNLIKELY (an < rn)) { if (UNLIKELY (2*an <= rn)) { mpn_sqr (rp, ap, an); } else { mp_limb_t cy; mpn_sqr (tp, ap, an); cy = mpn_add (rp, tp, rn, tp + rn, 2*an - rn); MPN_INCR_U (rp, rn, cy); } } else mpn_bc_sqrmod_bnm1 (rp, ap, rn, tp); } else { mp_size_t n; mp_limb_t cy; mp_limb_t hi; n = rn >> 1; ASSERT (2*an > n); /* Compute xm = a^2 mod (B^n - 1), xp = a^2 mod (B^n + 1) and crt together as x = -xp * B^n + (B^n + 1) * [ (xp + xm)/2 mod (B^n-1)] */ #define a0 ap #define a1 (ap + n) #define xp tp /* 2n + 2 */ /* am1 maybe in {xp, n} */ #define sp1 (tp + 2*n + 2) /* ap1 maybe in {sp1, n + 1} */ { mp_srcptr am1; mp_size_t anm; mp_ptr so; if (LIKELY (an > n)) { so = xp + n; am1 = xp; cy = mpn_add (xp, a0, n, a1, an - n); MPN_INCR_U (xp, n, cy); anm = n; } else { so = xp; am1 = a0; anm = an; } mpn_sqrmod_bnm1 (rp, n, am1, anm, so); } { int k; mp_srcptr ap1; mp_size_t anp; if (LIKELY (an > n)) { ap1 = sp1; cy = mpn_sub (sp1, a0, n, a1, an - n); sp1[n] = 0; MPN_INCR_U (sp1, n + 1, cy); anp = n + ap1[n]; } else { ap1 = a0; anp = an; } if (BELOW_THRESHOLD (n, MUL_FFT_MODF_THRESHOLD)) k=0; else { int mask; k = mpn_fft_best_k (n, 1); mask = (1<<k) -1; while (n & mask) {k--; mask >>=1;}; } if (k >= FFT_FIRST_K) xp[n] = mpn_mul_fft (xp, n, ap1, anp, ap1, anp, k); else if (UNLIKELY (ap1 == a0)) { ASSERT (anp <= n); ASSERT (2*anp > n); mpn_sqr (xp, a0, an); anp = 2*an - n; cy = mpn_sub (xp, xp, n, xp + n, anp); xp[n] = 0; MPN_INCR_U (xp, n+1, cy); } else mpn_bc_sqrmod_bnp1 (xp, ap1, n, xp); } /* Here the CRT recomposition begins. xm <- (xp + xm)/2 = (xp + xm)B^n/2 mod (B^n-1) Division by 2 is a bitwise rotation. Assumes xp normalised mod (B^n+1). The residue class [0] is represented by [B^n-1]; except when both input are ZERO. */ #if HAVE_NATIVE_mpn_rsh1add_n || HAVE_NATIVE_mpn_rsh1add_nc #if HAVE_NATIVE_mpn_rsh1add_nc cy = mpn_rsh1add_nc(rp, rp, xp, n, xp[n]); /* B^n = 1 */ hi = cy << (GMP_NUMB_BITS - 1); cy = 0; /* next update of rp[n-1] will set cy = 1 only if rp[n-1]+=hi overflows, i.e. a further increment will not overflow again. */ #else /* ! _nc */ cy = xp[n] + mpn_rsh1add_n(rp, rp, xp, n); /* B^n = 1 */ hi = (cy<<(GMP_NUMB_BITS-1))&GMP_NUMB_MASK; /* (cy&1) << ... */ cy >>= 1; /* cy = 1 only if xp[n] = 1 i.e. {xp,n} = ZERO, this implies that the rsh1add was a simple rshift: the top bit is 0. cy=1 => hi=0. */ #endif #if GMP_NAIL_BITS == 0 add_ssaaaa(cy, rp[n-1], cy, rp[n-1], CNST_LIMB(0), hi); #else cy += (hi & rp[n-1]) >> (GMP_NUMB_BITS-1); rp[n-1] ^= hi; #endif #else /* ! HAVE_NATIVE_mpn_rsh1add_n */ #if HAVE_NATIVE_mpn_add_nc cy = mpn_add_nc(rp, rp, xp, n, xp[n]); #else /* ! _nc */ cy = xp[n] + mpn_add_n(rp, rp, xp, n); /* xp[n] == 1 implies {xp,n} == ZERO */ #endif cy += (rp[0]&1); mpn_rshift(rp, rp, n, 1); ASSERT (cy <= 2); hi = (cy<<(GMP_NUMB_BITS-1))&GMP_NUMB_MASK; /* (cy&1) << ... */ cy >>= 1; /* We can have cy != 0 only if hi = 0... */ ASSERT ((rp[n-1] & GMP_NUMB_HIGHBIT) == 0); rp[n-1] |= hi; /* ... rp[n-1] + cy can not overflow, the following INCR is correct. */ #endif ASSERT (cy <= 1); /* Next increment can not overflow, read the previous comments about cy. */ ASSERT ((cy == 0) || ((rp[n-1] & GMP_NUMB_HIGHBIT) == 0)); MPN_INCR_U(rp, n, cy); /* Compute the highest half: ([(xp + xm)/2 mod (B^n-1)] - xp ) * B^n */ if (UNLIKELY (2*an < rn)) { /* Note that in this case, the only way the result can equal zero mod B^{rn} - 1 is if the input is zero, and then the output of both the recursive calls and this CRT reconstruction is zero, not B^{rn} - 1. */ cy = mpn_sub_n (rp + n, rp, xp, 2*an - n); /* FIXME: This subtraction of the high parts is not really necessary, we do it to get the carry out, and for sanity checking. */ cy = xp[n] + mpn_sub_nc (xp + 2*an - n, rp + 2*an - n, xp + 2*an - n, rn - 2*an, cy); ASSERT (mpn_zero_p (xp + 2*an - n+1, rn - 1 - 2*an)); cy = mpn_sub_1 (rp, rp, 2*an, cy); ASSERT (cy == (xp + 2*an - n)[0]); } else { cy = xp[n] + mpn_sub_n (rp + n, rp, xp, n); /* cy = 1 only if {xp,n+1} is not ZERO, i.e. {rp,n} is not ZERO. DECR will affect _at most_ the lowest n limbs. */ MPN_DECR_U (rp, 2*n, cy); } #undef a0 #undef a1 #undef xp #undef sp1 } }