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 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_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 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 fp2_addm_low(fp2_t c, fp2_t a, fp2_t b) {
fp_addm_low(c[0], a[0], b[0]);
fp_addm_low(c[1], a[1], b[1]);
}
void fp3_addm_low(fp3_t c, fp3_t a, fp3_t b) {
fp_addm_low(c[0], a[0], b[0]);
fp_addm_low(c[1], a[1], b[1]);
fp_addm_low(c[2], a[2], b[2]);
}
