felem_scalar(inx2, in, 2);
felem_scalar(inx4, in, 4);
- /*-
- * We have many cases were we want to do
- * in[x] * in[y] +
- * in[y] * in[x]
- * This is obviously just
- * 2 * in[x] * in[y]
- * However, rather than do the doubling on the 128 bit result, we
- * double one of the inputs to the multiplication by reading from
- * |inx2| */
+ /*-
+ * We have many cases were we want to do
+ * in[x] * in[y] +
+ * in[y] * in[x]
+ * This is obviously just
+ * 2 * in[x] * in[y]
+ * However, rather than do the doubling on the 128 bit result, we
+ * double one of the inputs to the multiplication by reading from
+ * |inx2|
+ */
out[0] = ((uint128_t) in[0]) * in[0];
out[1] = ((uint128_t) in[0]) * inx2[1];
out[1] += ((limb) in[0]) >> 58;
out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6;
- /*-
- * out[1] < 2^58 + 2^6 + 2^58
- * = 2^59 + 2^6
- */
+ /*-
+ * out[1] < 2^58 + 2^6 + 2^58
+ * = 2^59 + 2^6
+ */
out[2] += ((limb) (in[0] >> 64)) >> 52;
out[2] += ((limb) in[1]) >> 58;
out[8] += ((limb) in[7]) >> 58;
out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6;
- /*-
- * out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12
- * < 2^59 + 2^13
- */
+ /*-
+ * out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12
+ * < 2^59 + 2^13
+ */
overflow1 = ((limb) (in[7] >> 64)) >> 52;
overflow1 += ((limb) in[8]) >> 58;
out[1] += out[0] >> 58;
out[0] &= bottom58bits;
- /*-
- * out[0] < 2^58
- * out[1] < 2^59 + 2^6 + 2^13 + 2^2
- * < 2^59 + 2^14
- */
+ /*-
+ * out[0] < 2^58
+ * out[1] < 2^59 + 2^6 + 2^13 + 2^2
+ * < 2^59 + 2^14
+ */
}
static void felem_square_reduce(felem out, const felem in)
felem_scalar64(ftmp2, 3);
/* ftmp2[i] < 3*2^60 + 3*2^15 */
felem_mul(tmp, ftmp, ftmp2);
- /*-
- * tmp[i] < 17(3*2^121 + 3*2^76)
- * = 61*2^121 + 61*2^76
- * < 64*2^121 + 64*2^76
- * = 2^127 + 2^82
- * < 2^128
- */
+ /*-
+ * tmp[i] < 17(3*2^121 + 3*2^76)
+ * = 61*2^121 + 61*2^76
+ * < 64*2^121 + 64*2^76
+ * = 2^127 + 2^82
+ * < 2^128
+ */
felem_reduce(alpha, tmp);
/* x' = alpha^2 - 8*beta */
felem_diff64(beta, x_out);
/* beta[i] < 2^61 + 2^60 + 2^16 */
felem_mul(tmp, alpha, beta);
- /*-
- * tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16))
- * = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30)
- * = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30)
- * < 2^128
- */
+ /*-
+ * tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16))
+ * = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30)
+ * = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30)
+ * < 2^128
+ */
felem_square(tmp2, gamma);
- /*-
- * tmp2[i] < 17*(2^59 + 2^14)^2
- * = 17*(2^118 + 2^74 + 2^28)
- */
+ /*-
+ * tmp2[i] < 17*(2^59 + 2^14)^2
+ * = 17*(2^118 + 2^74 + 2^28)
+ */
felem_scalar128(tmp2, 8);
- /*-
- * tmp2[i] < 8*17*(2^118 + 2^74 + 2^28)
- * = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31
- * < 2^126
- */
+ /*-
+ * tmp2[i] < 8*17*(2^118 + 2^74 + 2^28)
+ * = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31
+ * < 2^126
+ */
felem_diff128(tmp, tmp2);
- /*-
- * tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30)
- * = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 +
- * 2^74 + 2^69 + 2^34 + 2^30
- * < 2^128
- */
+ /*-
+ * tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30)
+ * = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 +
+ * 2^74 + 2^69 + 2^34 + 2^30
+ * < 2^128
+ */
felem_reduce(y_out, tmp);
}