/* Toom 4 interpolation. Interpolates the value at 2^(sn*B) of a polynomial p(x) with 7 coefficients given the values p(oo), p(2), p(1), p(-1), 2^6*p(1/2), 2^6*p(-1/2), p(0). The output is placed in rp and the final number of limbs of the output is given in rpn. The 4th and 6th values may be negative, and if so, n4 and n6 should be set to a negative value respectively. To save space we pass r3, r5, r7 in place in the output rp. The other r's are stored separately in space tp. The low limb of r3 is stored in r30, as it will be overwritten by the high limb of r5. rp rp1 rp2 rp3 rp4 rp5 rp6 rp7 <----------- r7-----------><------------r5--------------> <-------------r3-------------> We assume that r1 is stored at tp, r2 at (tp + t4), r4 at (tp + 2*t4) and r6 (tp + 3*t4). Each of these r's has t4 = s4 + 1 limbs allocated. */ void mpn_toom4_interpolate(mp_ptr rp, mp_size_t * rpn, mp_size_t sn, mp_ptr tp, mp_size_t s4, mp_size_t n4, mp_size_t n6, mp_limb_t r30) { mp_size_t n1, n2, n3, n5, n7, t4; mp_limb_t saved, saved2, cy; t4 = s4 + 1; mpn_add_n(r2, r2, r5, s4); if (n6 < 0) mpn_add_n(r6, r5, r6, s4); else mpn_sub_n(r6, r5, r6, s4); /* r6 is now in twos complement format */ saved = r3[0]; r3[0] = r30; if (n4 < 0) mpn_add_n(r4, r3, r4, s4); else mpn_sub_n(r4, r3, r4, s4); r3[0] = saved; /* r4 is now in twos complement format */ mpn_sub_n(r5, r5, r1, s4); #if HAVE_NATIVE_mpn_sublsh_n r5[s4-1] -= mpn_sublsh_n(r5, r5, r7, s4-1, 6); #else r5[s4-1] -= mpn_submul_1(r5, r7, s4-1, 64); #endif TC4_RSHIFT1(r4, s4); saved = r3[0]; r3[0] = r30; mpn_sub_n(r3, r3, r4, s4); r30 = r3[0]; r3[0] = saved; mpn_double(r5, s4); mpn_sub_n(r5, r5, r6, s4); saved = r3[0]; r3[0] = r30; mpn_submul_1(r2, r3, s4, 65); r3[0] = saved; saved2 = r7[s4-1]; r7[s4-1] = CNST_LIMB(0); // r7 is always positive so no sign extend needed saved = r3[0]; r3[0] = r30; #if HAVE_NATIVE_mpn_subadd_n mpn_subadd_n(r3, r3, r7, r1, s4); #else mpn_sub_n(r3, r3, r7, s4); mpn_sub_n(r3, r3, r1, s4); #endif r7[s4-1] = saved2; r30 = r3[0]; mpn_addmul_1(r2, r3, s4, 45); #if HAVE_NATIVE_mpn_sublsh_n cy = mpn_sublsh_n(r5, r5, r3, s4 - 1, 3); #else cy = mpn_submul_1(r5, r3, s4 - 1, 8); #endif r3[0] = saved; r3[0] -= (cy + 8*r3[s4-1]); mpn_rshift(r5, r5, s4, 3); mpn_divexact_by3(r5, r5, s4); mpn_sub_n(r6, r6, r2, s4); #if HAVE_NATIVE_mpn_sublsh_n mpn_sublsh_n(r2, r2, r4, s4, 4); #else mpn_submul_1(r2, r4, s4, 16); #endif mpn_rshift(r2, r2, s4, 1); mpn_divexact_by3(r2, r2, s4); mpn_divexact_by3(r2, r2, s4); saved = r3[0]; r3[0] = r30; cy = mpn_sub_n(r3, r3, r5, s4 - 1); r30 = r3[0]; r3[0] = saved; r3[s4-1] -= (cy + r5[s4-1]); mpn_sub_n(r4, r4, r2, s4); mpn_addmul_1(r6, r2, s4, 30); mpn_divexact_byfobm1(r6, r6, s4, CNST_LIMB(15), CNST_LIMB(~0/15)); mpn_rshift(r6, r6, s4, 2); mpn_sub_n(r2, r2, r6, s4); TC4_NORM(r1, n1, s4); TC4_NORM(r2, n2, s4); (*rpn) = 6*sn+1; cy = mpn_add_1(r3, r3, *rpn - 4*sn, r30); /* don't forget to add r3[0] back in */ if (cy) { rp[*rpn] = cy; (*rpn)++; } tc4_copy(rp, rpn, 5*sn, r2, n2); tc4_copy(rp, rpn, 6*sn, r1, n1); tc4_copy(rp, rpn, sn, r6, s4); tc4_copy(rp, rpn, 3*sn, r4, s4); }
/* We have {v0,2k} {v1,2k+1} {c+4k+1,r+r2-1} v0 v1 {-}vinf vinf0 is the first limb of vinf, which is overwritten by v1 {vm1,2k+1} {v2, 2k+1} ws is temporary space sa is the sign of vm1 rr2 is r+r2 We want to compute t1 <- (3*v0+2*vm1+v2)/6-2*vinf t2 <- (v1+vm1)/2 then the result is c0+c1*t+c2*t^2+c3*t^3+c4*t^4 where c0 <- v0 c1 <- v1 - t1 c2 <- t2 - v0 - vinf c3 <- t1 - t2 c4 <- vinf */ void mpn_toom3_interpolate (mp_ptr c, mp_ptr v1, mp_ptr v2, mp_ptr vm1, mp_ptr vinf, mp_size_t k, mp_size_t rr2, int sa, mp_limb_t vinf0, mp_ptr ws) { mp_limb_t cy, saved; mp_size_t twok = k + k; mp_size_t kk1 = twok + 1; mp_ptr c1, c2, c3, c4, c5; mp_limb_t cout; /* final carry, should be zero at the end */ c1 = c + k; c2 = c1 + k; c3 = c2 + k; c4 = c3 + k; c5 = c4 + k; #define v0 (c) /* {c,2k} {c+2k,2k+1} {c+4k+1,r+r2-1} v0 v1 {-}vinf {vm1,2k+1} {v2, 2k+1} */ /* v2 <- v2 - vm1 */ if (sa < 0) { mpn_add_n(v2, v2, vm1, kk1); } else { mpn_sub_n(v2, v2, vm1, kk1); } ASSERT_NOCARRY (mpn_divexact_by3 (v2, v2, kk1)); /* v2 <- v2 / 3 */ /* vm1 <- t2 := (v1 - sa*vm1) / 2 */ if (sa < 0) { #ifdef HAVE_NATIVE_mpn_rsh1add_n mpn_rsh1add_n (vm1, v1, vm1, kk1); #else mpn_add_n (vm1, vm1, v1, kk1); mpn_half (vm1, kk1); #endif } else { #ifdef HAVE_NATIVE_mpn_rsh1sub_n mpn_rsh1sub_n (vm1, v1, vm1, kk1); #else mpn_sub_n (vm1, v1, vm1, kk1); mpn_half (vm1, kk1); #endif } /* v1 <- v1 - v0 - vinf */ saved = c4[0]; c4[0] = vinf0; #if HAVE_NATIVE_mpn_subadd_n cy = mpn_subadd_n(v1, v1, v0, c4, rr2); #else cy = mpn_sub_n(v1, v1, v0, rr2); cy += mpn_sub_n(v1, v1, c4, rr2); #endif c4[0] = saved; if (rr2 < twok) { v1[twok] -= mpn_sub_n(v1 + rr2, v1 + rr2, v0 + rr2, twok - rr2); MPN_DECR_U(v1 + rr2, kk1 - rr2, cy); } else v1[twok] -= cy; saved = c4[0]; c4[0] = vinf0; /* subtract 5*vinf from v2, */ cy = mpn_submul_1 (v2, c4, rr2, CNST_LIMB(5)); MPN_DECR_U (v2 + rr2, kk1 - rr2, cy); c4[0] = saved; /* v2 = (v2 - v1)/2 (exact) */ #ifdef HAVE_NATIVE_mpn_rsh1sub_n mpn_rsh1sub_n (v2, v2, v1, kk1); #else mpn_sub_n (v2, v2, v1, kk1); mpn_half (v2, kk1); #endif /* v1 = v1 - vm1 */ mpn_sub_n(v1, v1, vm1, kk1); /* vm1 = vm1 - v2 and add vm1 in {c+k, ...} */ #if HAVE_NATIVE_mpn_addsub_n cy = mpn_addsub_n(c1, c1, vm1, v2, kk1); #else mpn_sub_n(vm1, vm1, v2, kk1); cy = mpn_add_n (c1, c1, vm1, kk1); #endif ASSERT_NOCARRY (mpn_add_1(c3 + 1, c3 + 1, rr2 + k - 1, cy)); /* 4k+rr2-(3k+1) = rr2+k-1 */ /* don't forget to add vinf0 in {c+4k, ...} */ ASSERT_NOCARRY (mpn_add_1(c4, c4, rr2, vinf0)); /* add v2 in {c+3k, ...} */ if (rr2 <= k + 1) ASSERT_NOCARRY (mpn_add_n (c3, c3, v2, k+rr2)); else { cy = mpn_add_n (c3, c3, v2, kk1); if (cy) ASSERT_NOCARRY (mpn_add_1(c5 + 1, c5 + 1, rr2 - k - 1, cy)); /* 4k+rr2-(5k+1) = rr2-k-1 */ } #undef v0 }