void fp2_mulc_low(dv2_t c, fp2_t a, fp2_t b) {
align dig_t t0[2 * FP_DIGS], t1[2 * FP_DIGS], t2[2 * FP_DIGS];
/* Karatsuba algorithm. */
/* t0 = a_0 + a_1, t1 = b_0 + b_1. */
fp_addn_low(t0, a[0], a[1]);
fp_addn_low(t1, b[0], b[1]);
/* c_0 = a_0 * b_0, c_1 = a_1 * b_1, t2 = (a_0 + a_1) * (b_0 + b_1). */
fp_muln_low(c[0], a[0], b[0]);
fp_muln_low(c[1], a[1], b[1]);
fp_muln_low(t2, t0, t1);
/* t0 = (a_0 * b_0) + (a_1 * b_1). */
fp_addd_low(t0, c[0], c[1]);
/* c_0 = (a_0 * b_0) + u^2 * (a_1 * b_1). */
fp_subd_low(c[0], c[0], c[1]);
#ifndef FP_QNRES
/* t1 = u^2 * (a_1 * b_1). */
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_subd_low(c[0], c[0], c[1]);
}
#endif
/* c_1 = (t2 - t0). */
fp_subd_low(c[1], t2, t0);
/* c_0 = c_0 + 2^N * p/4. */
bn_lshb_low(c[0] + FP_DIGS - 1, c[0] + FP_DIGS - 1, FP_DIGS + 1, 2);
fp_addn_low(c[0] + FP_DIGS, c[0] + FP_DIGS, fp_prime_get());
bn_rshb_low(c[0] + FP_DIGS - 1, c[0] + FP_DIGS - 1, FP_DIGS + 1, 2);
}
void fp2_mul_basic(fp2_t c, fp2_t a, fp2_t b) {
dv_t t0, t1, t2, t3, t4;
dv_null(t0);
dv_null(t1);
dv_null(t2);
dv_null(t3);
dv_null(t4);
TRY {
dv_new(t0);
dv_new(t1);
dv_new(t2);
dv_new(t3);
dv_new(t4);
/* Karatsuba algorithm. */
/* t2 = a_0 + a_1, t1 = b0 + b1. */
fp_add(t2, a[0], a[1]);
fp_add(t1, b[0], b[1]);
/* t3 = (a_0 + a_1) * (b0 + b1). */
fp_muln_low(t3, t2, t1);
/* t0 = a_0 * b0, t4 = a_1 * b1. */
fp_muln_low(t0, a[0], b[0]);
fp_muln_low(t4, a[1], b[1]);
/* t2 = (a_0 * b0) + (a_1 * b1). */
fp_addc_low(t2, t0, t4);
/* t1 = (a_0 * b0) + u^2 * (a_1 * b1). */
fp_subc_low(t1, t0, t4);
/* t1 = u^2 * (a_1 * b1). */
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_subc_low(t1, t1, t4);
}
/* c_0 = t1 mod p. */
fp_rdc(c[0], t1);
/* t4 = t3 - t2. */
fp_subc_low(t4, t3, t2);
/* c_1 = t4 mod p. */
fp_rdc(c[1], t4);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
dv_free(t0);
dv_free(t1);
dv_free(t2);
dv_free(t3);
dv_free(t4);
}
}
void fp_mul_karat(fp_t c, const fp_t a, const fp_t b) {
dv_t t;
dv_null(t);
TRY {
/* We need a temporary variable so that c can be a or b. */
dv_new(t);
dv_zero(t, 2 * FP_DIGS);
if (FP_DIGS > 1) {
fp_mul_karat_imp(t, a, b, FP_DIGS, FP_KARAT);
} else {
fp_muln_low(t, a, b);
}
fp_rdc(c, t);
} CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
dv_free(t);
}
}
void fp2_muln_low(dv2_t c, fp2_t a, fp2_t b) {
align dig_t t0[2 * FP_DIGS], t1[2 * FP_DIGS], t2[2 * FP_DIGS];
/* Karatsuba algorithm. */
/* t0 = a_0 + a_1, t1 = b_0 + b_1. */
#ifdef FP_SPACE
fp_addn_low(t0, a[0], a[1]);
fp_addn_low(t1, b[0], b[1]);
#else
fp_addm_low(t0, a[0], a[1]);
fp_addm_low(t1, b[0], b[1]);
#endif
/* c_0 = a_0 * b_0, c_1 = a_1 * b_1. */
fp_muln_low(c[0], a[0], b[0]);
fp_muln_low(c[1], a[1], b[1]);
/* t2 = (a_0 + a_1) * (b_0 + b_1). */
fp_muln_low(t2, t0, t1);
/* t0 = (a_0 * b_0) + (a_1 * b_1). */
#ifdef FP_SPACE
fp_addd_low(t0, c[0], c[1]);
#else
fp_addc_low(t0, c[0], c[1]);
#endif
/* c_0 = (a_0 * b_0) + u^2 * (a_1 * b_1). */
fp_subc_low(c[0], c[0], c[1]);
#ifndef FP_QNRES
/* t1 = u^2 * (a_1 * b_1). */
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_subc_low(c[0], c[0], c[1]);
}
for (int i = 0; i <= fp_prime_get_qnr(); i++) {
fp_addc_low(c[0], c[0], c[1]);
}
#endif
/* c_1 = t2 - t0. */
#ifdef FP_SPACE
fp_subd_low(c[1], t2, t0);
#else
fp_subc_low(c[1], t2, t0);
#endif
}
void fp3_sqrn_low(dv3_t c, fp3_t a) {
align dig_t t0[2 * FP_DIGS], t1[2 * FP_DIGS], t2[2 * FP_DIGS];
align dig_t t3[2 * FP_DIGS], t4[2 * FP_DIGS], t5[2 * FP_DIGS];
/* t0 = a_0^2. */
fp_sqrn_low(t0, a[0]);
/* t1 = 2 * a_1 * a_2. */
#ifdef FP_SPACE
fp_dbln_low(t2, a[1]);
#else
fp_dblm_low(t2, a[1]);
#endif
fp_muln_low(t1, t2, a[2]);
/* t2 = a_2^2. */
fp_sqrn_low(t2, a[2]);
/* t3 = (a_0 + a_2 + a_1)^2, t4 = (a_0 + a_2 - a_1)^2. */
#ifdef FP_SPACE
fp_addn_low(t3, a[0], a[2]);
fp_addn_low(t4, t3, a[1]);
#else
fp_addm_low(t3, a[0], a[2]);
fp_addm_low(t4, t3, a[1]);
#endif
fp_subm_low(t5, t3, a[1]);
fp_sqrn_low(t3, t4);
fp_sqrn_low(t4, t5);
/* t4 = (t4 + t3)/2. */
fp_addd_low(t4, t4, t3);
fp_hlvd_low(t4, t4);
/* t3 = t3 - t4 - t1. */
fp_addc_low(t5, t1, t4);
fp_subc_low(t3, t3, t5);
/* c_2 = t4 - t0 - t2. */
fp_addc_low(t5, t0, t2);
fp_subc_low(c[2], t4, t5);
/* c_0 = t0 + t1 * B. */
fp_subc_low(c[0], t0, t1);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_subc_low(c[0], c[0], t1);
}
/* c_1 = t3 + t2 * B. */
fp_subc_low(c[1], t3, t2);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_subc_low(c[1], c[1], t2);
}
}
void fp3_muln_low(dv3_t c, fp3_t a, fp3_t b) {
align dig_t t0[2 * FP_DIGS], t1[2 * FP_DIGS], t2[2 * FP_DIGS], t3[2 * FP_DIGS];
align dig_t t4[2 * FP_DIGS], t5[2 * FP_DIGS], t6[2 * FP_DIGS];
/* Karatsuba algorithm. */
/* t0 = a_0 * b_0, t1 = a_1 * b_1, t2 = a_2 * b_2. */
fp_muln_low(t0, a[0], b[0]);
fp_muln_low(t1, a[1], b[1]);
fp_muln_low(t2, a[2], b[2]);
/* t3 = (a_1 + a_2) * (b_1 + b_2). */
#ifdef FP_SPACE
fp_addn_low(t3, a[1], a[2]);
fp_addn_low(t4, b[1], b[2]);
#else
fp_addm_low(t3, a[1], a[2]);
fp_addm_low(t4, b[1], b[2]);
#endif
fp_muln_low(t5, t3, t4);
fp_addd_low(t6, t1, t2);
fp_subc_low(t4, t5, t6);
fp_subc_low(c[0], t0, t4);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_subc_low(c[0], c[0], t4);
}
#ifdef FP_SPACE
fp_addn_low(t4, a[0], a[1]);
fp_addn_low(t5, b[0], b[1]);
#else
fp_addm_low(t4, a[0], a[1]);
fp_addm_low(t5, b[0], b[1]);
#endif
fp_muln_low(t6, t4, t5);
fp_addd_low(t4, t0, t1);
fp_subc_low(t4, t6, t4);
fp_subc_low(c[1], t4, t2);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_subc_low(c[1], c[1], t2);
}
#ifdef FP_SPACE
fp_addn_low(t5, a[0], a[2]);
fp_addn_low(t6, b[0], b[2]);
#else
fp_addm_low(t5, a[0], a[2]);
fp_addm_low(t6, b[0], b[2]);
#endif
fp_muln_low(t4, t5, t6);
fp_addd_low(t6, t0, t2);
fp_subc_low(t5, t4, t6);
fp_addc_low(c[2], t5, t1);
}
void fp_mul_comba(fp_t c, const fp_t a, const fp_t b) {
dv_t t;
dv_null(t);
TRY {
/* We need a temporary variable so that c can be a or b. */
dv_new(t);
fp_muln_low(t, a, b);
fp_rdc(c, t);
dv_free(t);
} CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
dv_free(t);
}
}
void fp12_mul_dxs_lazyr(fp12_t c, fp12_t a, fp12_t b) {
fp6_t t0;
dv6_t u0, u1, u2;
fp6_null(t0);
dv6_null(u0);
dv6_null(u1);
dv6_null(u2);
TRY {
fp6_new(t0);
dv6_new(u0);
dv6_new(u1);
dv6_new(u2);
if (ep2_curve_is_twist() == EP_DTYPE) {
#if EP_ADD == BASIC
/* t0 = a_0 * b_0. */
fp_muln_low(u0[0][0], a[0][0][0], b[0][0][0]);
fp_muln_low(u0[0][1], a[0][0][1], b[0][0][0]);
fp_muln_low(u0[1][0], a[0][1][0], b[0][0][0]);
fp_muln_low(u0[1][1], a[0][1][1], b[0][0][0]);
fp_muln_low(u0[2][0], a[0][2][0], b[0][0][0]);
fp_muln_low(u0[2][1], a[0][2][1], b[0][0][0]);
/* t2 = b_0 + b_1. */
fp_add(t0[0][0], b[0][0][0], b[1][0][0]);
fp_copy(t0[0][1], b[1][0][1]);
fp2_copy(t0[1], b[1][1]);
#elif EP_ADD == PROJC
/* t0 = a_0 * b_0. */
#ifdef RLC_FP_ROOM
fp2_mulc_low(u0[0], a[0][0], b[0][0]);
fp2_mulc_low(u0[1], a[0][1], b[0][0]);
fp2_mulc_low(u0[2], a[0][2], b[0][0]);
#else
fp2_muln_low(u0[0], a[0][0], b[0][0]);
fp2_muln_low(u0[1], a[0][1], b[0][0]);
fp2_muln_low(u0[2], a[0][2], b[0][0]);
#endif
/* t2 = b_0 + b_1. */
fp2_add(t0[0], b[0][0], b[1][0]);
fp2_copy(t0[1], b[1][1]);
#endif
/* t1 = a_1 * b_1. */
fp6_mul_dxs_unr_lazyr(u1, a[1], b[1]);
} else {
/* t0 = a_0 * b_0. */
fp6_mul_dxs_unr_lazyr(u0, a[0], b[0]);
#if EP_ADD == BASIC
/* t0 = a_0 * b_0. */
fp_muln_low(u1[1][0], a[1][2][0], b[1][1][0]);
fp_muln_low(u1[1][1], a[1][2][1], b[1][1][0]);
fp2_nord_low(u1[0], u1[1]);
fp_muln_low(u1[1][0], a[1][0][0], b[1][1][0]);
fp_muln_low(u1[1][1], a[1][0][1], b[1][1][0]);
fp_muln_low(u1[2][0], a[1][1][0], b[1][1][0]);
fp_muln_low(u1[2][1], a[1][1][1], b[1][1][0]);
/* t2 = b_0 + b_1. */
fp2_copy(t0[0], b[0][0]);
fp_add(t0[1][0], b[0][1][0], b[1][1][0]);
fp_copy(t0[1][1], b[0][1][1]);
#elif EP_ADD == PROJC
/* t1 = a_1 * b_1. */
fp2_muln_low(u1[1], a[1][2], b[1][1]);
fp2_nord_low(u1[0], u1[1]);
fp2_muln_low(u1[1], a[1][0], b[1][1]);
fp2_muln_low(u1[2], a[1][1], b[1][1]);
/* t2 = b_0 + b_1. */
fp2_copy(t0[0], b[0][0]);
fp2_add(t0[1], b[0][1], b[1][1]);
#endif
}
/* c_1 = a_0 + a_1. */
fp6_add(c[1], a[0], a[1]);
/* c_1 = (a_0 + a_1) * (b_0 + b_1) */
fp6_mul_dxs_unr_lazyr(u2, c[1], t0);
for (int i = 0; i < 3; i++) {
fp2_subc_low(u2[i], u2[i], u0[i]);
fp2_subc_low(u2[i], u2[i], u1[i]);
}
fp2_rdcn_low(c[1][0], u2[0]);
fp2_rdcn_low(c[1][1], u2[1]);
fp2_rdcn_low(c[1][2], u2[2]);
fp2_nord_low(u2[0], u1[2]);
fp2_addc_low(u0[0], u0[0], u2[0]);
fp2_addc_low(u0[1], u0[1], u1[0]);
fp2_addc_low(u0[2], u0[2], u1[1]);
/* c_0 = a_0b_0 + v * a_1b_1. */
fp2_rdcn_low(c[0][0], u0[0]);
fp2_rdcn_low(c[0][1], u0[1]);
fp2_rdcn_low(c[0][2], u0[2]);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp6_free(t0);
dv6_free(u0);
dv6_free(u1);
dv6_free(u2);
}
}
void fp3_sqr_basic(fp3_t c, fp3_t a) {
dv_t t0, t1, t2, t3, t4, t5;
dv_null(t0);
dv_null(t1);
dv_null(t2);
dv_null(t3);
dv_null(t4);
dv_null(t5);
TRY {
dv_new(t0);
dv_new(t1);
dv_new(t2);
dv_new(t3);
dv_new(t4);
dv_new(t5);
/* t0 = a_0^2. */
fp_sqrn_low(t0, a[0]);
/* t1 = 2 * a_1 * a_2. */
fp_dbl(t2, a[1]);
fp_muln_low(t1, t2, a[2]);
/* t2 = a_2^2. */
fp_sqrn_low(t2, a[2]);
/* t3 = (a_0 + a_2 + a_1)^2, t4 = (a_0 + a_2 - a_1)^2. */
fp_add(t3, a[0], a[2]);
fp_add(t4, t3, a[1]);
fp_sub(t5, t3, a[1]);
fp_sqrn_low(t3, t4);
fp_sqrn_low(t4, t5);
/* t4 = (t4 + t3)/2. */
fp_addd_low(t4, t4, t3);
fp_hlvd_low(t4, t4);
/* t3 = t3 - t4 - t1. */
fp_addc_low(t5, t1, t4);
fp_subc_low(t3, t3, t5);
/* c_2 = t4 - t0 - t2. */
fp_addc_low(t5, t0, t2);
fp_subc_low(t4, t4, t5);
fp_rdc(c[2], t4);
/* c_0 = t0 + t1 * B. */
fp_subc_low(t0, t0, t1);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_subc_low(t0, t0, t1);
}
fp_rdc(c[0], t0);
/* c_1 = t3 + t2 * B. */
fp_subc_low(t3, t3, t2);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_subc_low(t3, t3, t2);
}
fp_rdc(c[1], t3);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
dv_free(t0);
dv_free(t1);
dv_free(t2);
dv_free(t3);
dv_free(t4);
dv_free(t5);
}
}
void fp_mulm_low(dig_t *c, const dig_t *a, const dig_t *b) {
dig_t align t[2 * FP_DIGS];
fp_muln_low(t, a, b);
fp_rdc(c, t);
}
void fp2_sqrn_low(dv2_t c, fp2_t a) {
align dig_t t0[2 * FP_DIGS], t1[2 * FP_DIGS], t2[2 * FP_DIGS];
/* t0 = (a0 + a1). */
#ifdef FP_SPACE
/* if we have room for carries, we can avoid reductions here. */
fp_addn_low(t0, a[0], a[1]);
#else
fp_addm_low(t0, a[0], a[1]);
#endif
/* t1 = (a0 - a1). */
fp_subm_low(t1, a[0], a[1]);
#ifdef FP_QNRES
#ifdef FP_SPACE
fp_dbln_low(t2, a[0]);
#else
fp_dblm_low(t2, a[0]);
#endif
/* c1 = 2 * a0 * a1. */
fp_muln_low(c[1], t2, a[1]);
/* c_0 = a_0^2 + a_1^2 * u^2. */
fp_muln_low(c[0], t0, t1);
#else /* !FP_QNRES */
/* t1 = u^2 * (a1 * b1). */
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_subm_low(t1, t1, a[1]);
}
if (fp_prime_get_qnr() == -1) {
/* t2 = 2 * a0. */
fp_dbl(t2, a[0]);
/* c1 = 2 * a0 * a1. */
fp_muln_low(c[1], t2, a[1]);
/* c0 = a0^2 + b_0^2 * u^2. */
fp_muln_low(c[0], t0, t1);
} else {
/* c1 = a0 * a1. */
fp_muln_low(c[1], a[0], a[1]);
/* c0 = a0^2 + b_0^2 * u^2. */
fp_muln_low(c[0], t0, t1);
#ifdef FP_SPACE
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_addd_low(c[0], c[0], c[1]);
}
/* c1 = 2 * a0 * a1. */
fp_addd_low(c[1], c[1], c[1]);
#else
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_addc_low(c[0], c[0], c[1]);
}
/* c1 = 2 * a0 * a1. */
fp_addc_low(c[1], c[1], c[1]);
#endif
}
#endif
/* c = c0 + c1 * u. */
}
void pp_dbl_k2_projc_lazyr(fp2_t l, ep_t r, ep_t p, ep_t q) {
fp_t t0, t1, t2, t3, t4, t5;
dv_t u0, u1;
fp_null(t0);
fp_null(t1);
fp_null(t2);
fp_null(t3);
fp_null(t4);
fp_null(t5);
dv_null(u0);
dv_null(u1);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
fp_new(t3);
fp_new(t4);
fp_new(t5);
dv_new(u0);
dv_new(u1);
/* For these curves, we always can choose a = -3. */
/* dbl-2001-b formulas: 3M + 5S + 8add + 1*4 + 2*8 + 1*3 */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b */
/* t0 = delta = z1^2. */
fp_sqr(t0, p->z);
/* t1 = gamma = y1^2. */
fp_sqr(t1, p->y);
/* t2 = beta = x1 * y1^2. */
fp_mul(t2, p->x, t1);
/* t3 = alpha = 3 * (x1 - z1^2) * (x1 + z1^2). */
fp_sub(t3, p->x, t0);
fp_add(t4, p->x, t0);
fp_mul(t4, t3, t4);
fp_dbl(t3, t4);
fp_add(t3, t3, t4);
/* t2 = 4 * beta. */
fp_dbl(t2, t2);
fp_dbl(t2, t2);
/* z3 = (y1 + z1)^2 - gamma - delta. */
fp_add(r->z, p->y, p->z);
fp_sqr(r->z, r->z);
fp_sub(r->z, r->z, t1);
fp_sub(r->z, r->z, t0);
/* l0 = 2 * gamma - alpha * (delta * xq + x1). */
fp_dbl(t1, t1);
fp_mul(t5, t0, q->x);
fp_add(t5, t5, p->x);
fp_mul(t5, t5, t3);
fp_sub(l[0], t1, t5);
/* x3 = alpha^2 - 8 * beta. */
fp_dbl(t5, t2);
fp_sqr(r->x, t3);
fp_sub(r->x, r->x, t5);
/* y3 = alpha * (4 * beta - x3) - 8 * gamma^2. */
fp_sqrn_low(u0, t1);
fp_addc_low(u0, u0, u0);
fp_subm_low(r->y, t2, r->x);
fp_muln_low(u1, r->y, t3);
fp_subc_low(u1, u1, u0);
fp_rdcn_low(r->y, u1);
/* l1 = - z3 * delta * yq. */
fp_mul(l[1], r->z, t0);
fp_mul(l[1], l[1], q->y);
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
fp_free(t3);
fp_free(t4);
fp_free(t5);
dv_free(u0);
dv_free(u1);
}
}
void fp3_mul_basic(fp3_t c, fp3_t a, fp3_t b) {
dv_t t, t0, t1, t2, t3, t4, t5, t6;
dv_null(t);
dv_null(t0);
dv_null(t1);
dv_null(t2);
dv_null(t3);
dv_null(t4);
dv_null(t5);
dv_null(t6);
TRY {
dv_new(t);
dv_new(t0);
dv_new(t1);
dv_new(t2);
dv_new(t3);
dv_new(t4);
dv_new(t5);
dv_new(t6);
/* Karatsuba algorithm. */
/* t0 = a_0 * b_0, t1 = a_1 * b_1, t2 = a_2 * b_2. */
fp_muln_low(t0, a[0], b[0]);
fp_muln_low(t1, a[1], b[1]);
fp_muln_low(t2, a[2], b[2]);
/* t3 = (a_1 + a_2) * (b_1 + b_2). */
fp_add(t3, a[1], a[2]);
fp_add(t4, b[1], b[2]);
fp_muln_low(t, t3, t4);
fp_addd_low(t6, t1, t2);
fp_subc_low(t4, t, t6);
fp_subc_low(t3, t0, t4);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_subc_low(t3, t3, t4);
}
fp_add(t4, a[0], a[1]);
fp_add(t5, b[0], b[1]);
fp_muln_low(t, t4, t5);
fp_addd_low(t4, t0, t1);
fp_subc_low(t4, t, t4);
fp_subc_low(t4, t4, t2);
for (int i = -1; i > fp_prime_get_cnr(); i--) {
fp_subc_low(t4, t4, t2);
}
fp_add(t5, a[0], a[2]);
fp_add(t6, b[0], b[2]);
fp_muln_low(t, t5, t6);
fp_addd_low(t6, t0, t2);
fp_subc_low(t5, t, t6);
fp_addc_low(t5, t5, t1);
/* c_0 = t3 mod p. */
fp_rdc(c[0], t3);
/* c_1 = t4 mod p. */
fp_rdc(c[1], t4);
/* c_2 = t5 mod p. */
fp_rdc(c[2], t5);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
dv_free(t);
dv_free(t0);
dv_free(t1);
dv_free(t2);
dv_free(t3);
dv_free(t4);
dv_free(t5);
dv_free(t6);
}
}
