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Merge pull request #464 from czurnieden/fix_sigma_div_recursive

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Corrected startvalue for sigma and changed cutoff in mp_div
This commit is contained in:
Steffen Jaeckel 2019-11-25 11:04:35 +01:00 committed by GitHub
commit fc5f50768b
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GPG Key ID: 4AEE18F83AFDEB23
2 changed files with 16 additions and 35 deletions
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2
mp_div.c
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@ -26,7 +26,7 @@ mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
}
if (MP_HAS(S_MP_DIV_RECURSIVE)
&& (b->used > MP_MUL_KARATSUBA_CUTOFF)
&& (b->used > (2 * MP_MUL_KARATSUBA_CUTOFF))
&& (b->used <= ((a->used/3)*2))) {
err = s_mp_div_recursive(a, b, c, d);
} else if (MP_HAS(S_MP_DIV_SCHOOL)) {

49
s_mp_div_recursive.c
View File

@ -20,7 +20,7 @@ static mp_err s_recursion(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
mp_int A1, A2, B1, B0, Q1, Q0, R1, R0, t;
int m = a->used - b->used, k = m/2;
if (m < MP_MUL_KARATSUBA_CUTOFF) {
if (m < (MP_MUL_KARATSUBA_CUTOFF)) {
return s_mp_div_school(a, b, q, r);
}
@ -43,15 +43,16 @@ static mp_err s_recursion(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
if ((err = mp_sub(&A1, &t, &A1)) != MP_OKAY) goto LBL_ERR;
/* while A1 < 0 do Q1 = Q1 - 1, A1 = A1 + (beta^k * B) */
if ((err = mp_mul_2d(b, k * MP_DIGIT_BIT, &t)) != MP_OKAY) goto LBL_ERR;
while (mp_cmp_d(&A1, 0uL) == MP_LT) {
if ((err = mp_decr(&Q1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&A1, &t, &A1)) != MP_OKAY) goto LBL_ERR;
if (mp_cmp_d(&A1, 0uL) == MP_LT) {
if ((err = mp_mul_2d(b, k * MP_DIGIT_BIT, &t)) != MP_OKAY) goto LBL_ERR;
do {
if ((err = mp_decr(&Q1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&A1, &t, &A1)) != MP_OKAY) goto LBL_ERR;
} while (mp_cmp_d(&A1, 0uL) == MP_LT);
}
/* (Q0, R0) = RecursiveDivRem(A1 / beta^(k), B1) */
if ((err = mp_div_2d(&A1, k * MP_DIGIT_BIT, &A1, &t)) != MP_OKAY) goto LBL_ERR;
if ((err = s_recursion(&A1, &B1, &Q0, &R0)) != MP_OKAY) goto LBL_ERR;
if ((err = s_recursion(&A1, &B1, &Q0, &R0)) != MP_OKAY) goto LBL_ERR;
/* A2 = (R0*beta^k) + (A1 % beta^k) - (Q0*B0) */
if ((err = mp_lshd(&R0, k)) != MP_OKAY) goto LBL_ERR;
@ -65,13 +66,10 @@ static mp_err s_recursion(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
if ((err = mp_add(&A2, b, &A2)) != MP_OKAY) goto LBL_ERR;
}
/* return q = (Q1*beta^k) + Q0, r = A2 */
if (q != NULL) {
if ((err = mp_lshd(&Q1, k)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&Q1, &Q0, q)) != MP_OKAY) goto LBL_ERR;
}
if (r != NULL) {
if ((err = mp_copy(&A2, r)) != MP_OKAY) goto LBL_ERR;
}
if ((err = mp_lshd(&Q1, k)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&Q1, &Q0, q)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_copy(&A2, r)) != MP_OKAY) goto LBL_ERR;
LBL_ERR:
mp_clear_multi(&A1, &A2, &B1, &B0, &Q1, &Q0, &R1, &R0, &t, NULL);
@ -94,24 +92,7 @@ mp_err s_mp_div_recursive(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
/* most significant bit of a limb */
/* assumes MP_DIGIT_MAX < (sizeof(mp_digit) * CHAR_BIT) */
msb = (MP_DIGIT_MAX + (mp_digit)(1)) >> 1;
/*
Method to compute sigma shamelessly stolen from
J. Burnikel and J. Ziegler, "Fast recursive division", Research Report
MPI-I-98-1-022, Max-Planck-Institut fuer Informatik, Saarbruecken, Germany,
October 1998. (available online)
Vid. section 2.3.
*/
m = MP_MUL_KARATSUBA_CUTOFF;
while (m <= b->used) {
m <<= 1;
}
j = (b->used + m - 1) / m;
n = j * m;
sigma = MP_DIGIT_BIT * (n - b->used);
sigma = 0;
msb_b = b->dp[b->used - 1];
while (msb_b < msb) {
sigma++;
@ -139,7 +120,7 @@ mp_err s_mp_div_recursive(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
/* Q = 0 */
mp_zero(&Q);
while (m > n) {
/* (q, r) = RecursveDivRem(A / (beta^(m-n)), B) */
/* (q, r) = RecursiveDivRem(A / (beta^(m-n)), B) */
j = (m - n) * MP_DIGIT_BIT;
if ((err = mp_div_2d(&A, j, &A_div, &A_mod)) != MP_OKAY) goto LBL_ERR;
if ((err = s_recursion(&A_div, &B, &Q1, &R)) != MP_OKAY) goto LBL_ERR;
@ -152,7 +133,7 @@ mp_err s_mp_div_recursive(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
/* m = m - n */
m = m - n;
}
/* (q, r) = RecursveDivRem(A, B) */
/* (q, r) = RecursiveDivRem(A, B) */
if ((err = s_recursion(&A, &B, &Q1, &R)) != MP_OKAY) goto LBL_ERR;
/* Q = (Q * beta^m) + q, R = r */
if ((err = mp_mul_2d(&Q, m * MP_DIGIT_BIT, &Q)) != MP_OKAY) goto LBL_ERR;