void
mpn_toom6h_mul (mp_ptr pp,
mp_srcptr ap, mp_size_t an,
mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
{
mp_size_t n, s, t;
int p, q, half;
int sign;
/***************************** decomposition *******************************/
ASSERT (an >= bn);
/* Can not handle too much unbalancement */
ASSERT (bn >= 42);
/* Can not handle too much unbalancement */
ASSERT ((an*3 < bn * 8) || (bn >= 46 && an * 6 < bn * 17));
/* Limit num/den is a rational number between
(12/11)^(log(4)/log(2*4-1)) and (12/11)^(log(6)/log(2*6-1)) */
#define LIMIT_numerator (18)
#define LIMIT_denominat (17)
if (LIKELY (an * LIMIT_denominat < LIMIT_numerator * bn)) /* is 6*... < 6*... */
{
n = 1 + (an - 1) / (size_t) 6;
p = q = 5;
half = 0;
s = an - 5 * n;
t = bn - 5 * n;
}
else {
if (an * 5 * LIMIT_numerator < LIMIT_denominat * 7 * bn)
{ p = 7; q = 6; }
else if (an * 5 * LIMIT_denominat < LIMIT_numerator * 7 * bn)
{ p = 7; q = 5; }
else if (an * LIMIT_numerator < LIMIT_denominat * 2 * bn) /* is 4*... < 8*... */
{ p = 8; q = 5; }
else if (an * LIMIT_denominat < LIMIT_numerator * 2 * bn) /* is 4*... < 8*... */
{ p = 8; q = 4; }
else
{ p = 9; q = 4; }
half = (p ^ q) & 1;
n = 1 + (q * an >= p * bn ? (an - 1) / (size_t) p : (bn - 1) / (size_t) q);
p--; q--;
s = an - p * n;
t = bn - q * n;
/* With LIMIT = 16/15, the following recover is needed only if bn<=73*/
if (half) { /* Recover from badly chosen splitting */
if (UNLIKELY (s<1)) {p--; s+=n; half=0;}
else if (UNLIKELY (t<1)) {q--; t+=n; half=0;}
}
}
#undef LIMIT_numerator
#undef LIMIT_denominat
ASSERT (0 < s && s <= n);
ASSERT (0 < t && t <= n);
ASSERT (half || s + t > 3);
ASSERT (n > 2);
#define r4 (pp + 3 * n) /* 3n+1 */
#define r2 (pp + 7 * n) /* 3n+1 */
#define r0 (pp +11 * n) /* s+t <= 2*n */
#define r5 (scratch) /* 3n+1 */
#define r3 (scratch + 3 * n + 1) /* 3n+1 */
#define r1 (scratch + 6 * n + 2) /* 3n+1 */
#define v0 (pp + 7 * n) /* n+1 */
#define v1 (pp + 8 * n+1) /* n+1 */
#define v2 (pp + 9 * n+2) /* n+1 */
#define v3 (scratch + 9 * n + 3) /* n+1 */
#define wsi (scratch + 9 * n + 3) /* 3n+1 */
#define wse (scratch +10 * n + 4) /* 2n+1 */
/* Alloc also 3n+1 limbs for wsi... toom_interpolate_12pts may
need all of them */
/* if (scratch == NULL) */
/* scratch = TMP_SALLOC_LIMBS(mpn_toom6_sqr_itch(n * 6)); */
ASSERT (12 * n + 6 <= mpn_toom6h_mul_itch(an,bn));
ASSERT (12 * n + 6 <= mpn_toom6_sqr_itch(n * 6));
/********************** evaluation and recursive calls *********************/
/* $\pm1/2$ */
sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 1, pp) ^
mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 1, pp);
/* A(-1/2)*B(-1/2)*2^. */ /* A(+1/2)*B(+1/2)*2^. */
TOOM6H_MUL_N_REC(pp, v0, v1, 2, r5, v2, v3, n + 1, wse);
mpn_toom_couple_handling (r5, 2 * n + 1, pp, sign, n, 1+half , half);
/* $\pm1$ */
sign = mpn_toom_eval_pm1 (v2, v0, p, ap, n, s, pp);
if (UNLIKELY (q == 3))
sign ^= mpn_toom_eval_dgr3_pm1 (v3, v1, bp, n, t, pp);
else
sign ^= mpn_toom_eval_pm1 (v3, v1, q, bp, n, t, pp);
/* A(-1)*B(-1) */ /* A(1)*B(1) */
TOOM6H_MUL_N_REC(pp, v0, v1, 2, r3, v2, v3, n + 1, wse);
mpn_toom_couple_handling (r3, 2 * n + 1, pp, sign, n, 0, 0);
/* $\pm4$ */
sign = mpn_toom_eval_pm2exp (v2, v0, p, ap, n, s, 2, pp) ^
mpn_toom_eval_pm2exp (v3, v1, q, bp, n, t, 2, pp);
/* A(-4)*B(-4) */
TOOM6H_MUL_N_REC(pp, v0, v1, 2, r1, v2, v3, n + 1, wse); /* A(+4)*B(+4) */
mpn_toom_couple_handling (r1, 2 * n + 1, pp, sign, n, 2, 4);
/* $\pm1/4$ */
sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 2, pp) ^
mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 2, pp);
/* A(-1/4)*B(-1/4)*4^. */ /* A(+1/4)*B(+1/4)*4^. */
TOOM6H_MUL_N_REC(pp, v0, v1, 2, r4, v2, v3, n + 1, wse);
mpn_toom_couple_handling (r4, 2 * n + 1, pp, sign, n, 2*(1+half), 2*(half));
/* $\pm2$ */
sign = mpn_toom_eval_pm2 (v2, v0, p, ap, n, s, pp) ^
mpn_toom_eval_pm2 (v3, v1, q, bp, n, t, pp);
/* A(-2)*B(-2) */ /* A(+2)*B(+2) */
TOOM6H_MUL_N_REC(pp, v0, v1, 2, r2, v2, v3, n + 1, wse);
mpn_toom_couple_handling (r2, 2 * n + 1, pp, sign, n, 1, 2);
#undef v0
#undef v1
#undef v2
#undef v3
#undef wse
/* A(0)*B(0) */
TOOM6H_MUL_N_REC(pp, ap, bp, 0, pp, ap, bp, n, wsi);
/* Infinity */
if (UNLIKELY (half != 0)) {
if (s > t) {
TOOM6H_MUL_REC(r0, ap + p * n, s, bp + q * n, t, wsi);
} else {
TOOM6H_MUL_REC(r0, bp + q * n, t, ap + p * n, s, wsi);
};
};
mpn_toom_interpolate_12pts (pp, r1, r3, r5, n, s+t, half, wsi);
#undef r0
#undef r1
#undef r2
#undef r3
#undef r4
#undef r5
#undef wsi
}
void
mpn_sqr (mp_ptr p, mp_srcptr a, mp_size_t n)
{
ASSERT (n >= 1);
ASSERT (! MPN_OVERLAP_P (p, 2 * n, a, n));
if (BELOW_THRESHOLD (n, SQR_BASECASE_THRESHOLD))
{ /* mul_basecase is faster than sqr_basecase on small sizes sometimes */
mpn_mul_basecase (p, a, n, a, n);
}
else if (BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD))
{
mpn_sqr_basecase (p, a, n);
}
else if (BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD))
{
/* Allocate workspace of fixed size on stack: fast! */
mp_limb_t ws[mpn_toom2_sqr_itch (SQR_TOOM3_THRESHOLD_LIMIT-1)];
ASSERT (SQR_TOOM3_THRESHOLD <= SQR_TOOM3_THRESHOLD_LIMIT);
mpn_toom2_sqr (p, a, n, ws);
}
else if (BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD))
{
mp_ptr ws;
TMP_SDECL;
TMP_SMARK;
ws = TMP_SALLOC_LIMBS (mpn_toom3_sqr_itch (n));
mpn_toom3_sqr (p, a, n, ws);
TMP_SFREE;
}
else if (BELOW_THRESHOLD (n, SQR_TOOM6_THRESHOLD))
{
mp_ptr ws;
TMP_SDECL;
TMP_SMARK;
ws = TMP_SALLOC_LIMBS (mpn_toom4_sqr_itch (n));
mpn_toom4_sqr (p, a, n, ws);
TMP_SFREE;
}
else if (BELOW_THRESHOLD (n, SQR_TOOM8_THRESHOLD))
{
mp_ptr ws;
TMP_SDECL;
TMP_SMARK;
ws = TMP_SALLOC_LIMBS (mpn_toom6_sqr_itch (n));
mpn_toom6_sqr (p, a, n, ws);
TMP_SFREE;
}
else if (BELOW_THRESHOLD (n, SQR_FFT_THRESHOLD))
{
mp_ptr ws;
TMP_DECL;
TMP_MARK;
ws = TMP_ALLOC_LIMBS (mpn_toom8_sqr_itch (n));
mpn_toom8_sqr (p, a, n, ws);
TMP_FREE;
}
else
{
/* The current FFT code allocates its own space. That should probably
change. */
mpn_fft_mul (p, a, n, a, n);
}
}
