/* mpn_toom42_mulmid -- toom42 middle product Copyright (C) 2009, David Harvey All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #include "mpir.h" #include "gmp-impl.h" /* Let a = sum_0^{m-1} a_i B^i and b = sum_0^{n-1} b_j B^j then MP(a, m, b, n) = sum_{0<=i= 4. See mpn_toom42_mulmid_itch() for the amount of scratch space required. FIXME: this code assumes that n is small compared to GMP_NUMB_MAX. The exact requirements should be clarified. */ void mpn_toom42_mulmid (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n, mp_ptr scratch) { mp_limb_t cy, e[12], t0, t1; mp_size_t m; int neg; ASSERT (n >= 4); ASSERT (! MPN_OVERLAP_P (rp, n + 2, ap, 2*n - 1)); ASSERT (! MPN_OVERLAP_P (rp, n + 2, bp, n)); ap += n & 1; /* handle odd row and diagonal later */ m = n / 2; /* (e0h:e0l) etc are correction terms, in 2's complement */ #define e0l (e[0]) #define e0h (e[1]) #define e1l (e[2]) #define e1h (e[3]) #define e2l (e[4]) #define e2h (e[5]) #define e3l (e[6]) #define e3h (e[7]) #define e4l (e[8]) #define e4h (e[9]) #define e5l (e[10]) #define e5h (e[11]) #define s scratch #define d rp #define p0 rp #define p1 (scratch + 2*m - 1) #define p2 (rp + m) #define rec_scratch (scratch + 3*m + 1) /* rp scratch |---------|-----------| |---------|---------|----------| 0 m 2m+2 0 m 2m 3m+1 <----d---><---p2-----> <-------------s-------------> <----p0----> <----p1----> */ /* transposed interpolation, and compute correction terms */ cy = mpn_add_err1_n (s, ap, ap + m, &e0l, bp + m, m - 1, 0); cy = mpn_add_err2_n (s + m - 1, ap + m - 1, ap + 2*m - 1, &e1l, bp + m, bp, m, cy); mpn_add_err1_n (s + 2*m - 1, ap + 2*m - 1, ap + 3*m - 1, &e3l, bp, m, cy); if (mpn_cmp (bp + m, bp, m) < 0) { ASSERT_NOCARRY (mpn_sub_err2_n (d, bp, bp + m, &e4l, ap + m - 1, ap + 2*m - 1, m, 0)); neg = 1; } else { ASSERT_NOCARRY (mpn_sub_err2_n (d, bp + m, bp, &e4l, ap + m - 1, ap + 2*m - 1, m, 0)); neg = 0; } /* recursive middle products. The picture is: b[2m-1] A A A B B B - - - - - ... - A A A B B B - - - - b[m] - - A A A B B B - - - b[m-1] - - - C C C D D D - - ... - - - - C C C D D D - b[0] - - - - - C C C D D D a[0] ... a[m] ... a[2m] ... a[4m-2] */ if (m < MULMID_TOOM42_THRESHOLD) { /* C + D */ mpn_mulmid_basecase (p2, s + m, 2*m - 1, bp, m); t0 = p2[0], t1 = p2[1]; /* save first two limbs of p2 */ /* B - C (or C - B if neg == 1) */ mpn_mulmid_basecase (p1, ap + m, 2*m - 1, d, m); /* A + B */ mpn_mulmid_basecase (p0, s, 2*m - 1, bp + m, m); } else { /* as above, but call toom42 instead */ mpn_toom42_mulmid (p2, s + m, bp, m, rec_scratch); t0 = p2[0], t1 = p2[1]; mpn_toom42_mulmid (p1, ap + m, d, m, rec_scratch); mpn_toom42_mulmid (p0, s, bp + m, m, rec_scratch); } /* apply correction terms */ /* -e0 at p0[0] */ SUBC_LIMB (cy, p0[0], p0[0], e0l); e0h += cy; SUBC_LIMB (cy, p0[1], p0[1], e0h); if (UNLIKELY (cy)) e2h += mpn_sub_1 (p0 + 2, p0 + 2, m - 1, 1); /* absorb t0 into e1 */ ADDC_LIMB (cy, e1l, e1l, t0); e1h += cy; /* e1 at p0[m] */ ADDC_LIMB (cy, p0[m], p0[m], e1l); p0[m + 1] += e1h + cy; /* add back t1 */ ADDC_LIMB (cy, p2[1], p2[1], t1); if (UNLIKELY (cy)) mpn_add_1 (p2 + 2, p2 + 2, m, 1); /* -e2 at p2[0] */ SUBC_LIMB (cy, p2[0], p2[0], e2l); e2h += cy; SUBC_LIMB (cy, p2[1], p2[1], e2h); if (UNLIKELY (cy)) mpn_sub_1 (p2 + 2, p2 + 2, m, 1); /* e3 at p2[m] */ ADDC_LIMB (cy, p2[m], p2[m], e3l); p2[m + 1] = (p2[m + 1] + e3h + cy) & GMP_NUMB_MASK; /* e4 at p1[0] */ ADDC_LIMB (cy, p1[0], p1[0], e4l); e4h += cy; ADDC_LIMB (cy, p1[1], p1[1], e4h); if (UNLIKELY (cy)) mpn_add_1 (p1 + 2, p1 + 2, m, 1); /* -e5 at p1[m] */ SUBC_LIMB (cy, p1[m], p1[m], e5l); p1[m + 1] = (p1[m + 1] - e5h - cy) & GMP_NUMB_MASK; /* adjustment if p1 ends up negative */ cy = (p1[m + 1] & GMP_NUMB_HIGHBIT) != 0; /* transposed evaluation */ if (neg) { mpn_sub_1 (rp + m + 2, rp + m + 2, m, cy); mpn_add (rp, rp, 2*m + 2, p1, m + 2); /* A + C */ mpn_sub_n (rp + m, rp + m, p1, m + 2); /* B + D */ } else { mpn_add_1 (rp + m + 2, rp + m + 2, m, cy); mpn_sub (rp, rp, 2*m + 2, p1, m + 2); /* A + C */ mpn_add_n (rp + m, rp + m, p1, m + 2); /* B + D */ } /* odd row and diagonal */ if (n & 1) { /* Cells marked E are already done. We need to do cells marked O. OOOOO---- -EEEEO--- --EEEEO-- ---EEEEO- ----EEEEO */ /* first row of O's */ cy = mpn_addmul_1 (rp, ap - 1, n, bp[n - 1]); ADDC_LIMB (rp[n + 1], rp[n], rp[n], cy); /* O's on diagonal */ /* FIXME: should probably define an interface "mpn_mulmid_diag_1" that can handle the sum below. Currently we're relying on mulmid_basecase being pretty fast for a diagonal sum like this, which is true at least for the K8 asm verion, but surely false for the generic version. */ mpn_mulmid_basecase (e, ap + n - 1, n - 1, bp, n - 1); mpn_add_n (rp + n - 1, rp + n - 1, e, 3); } }