in src/main/java/org/mariadb/jdbc/internal/com/send/authentication/ed25519/math/ed25519/Ed25519FieldElement.java [193:437]
public FieldElement multiply(FieldElement val) {
int[] g =
((org.mariadb.jdbc.internal.com.send.authentication.ed25519.math.ed25519
.Ed25519FieldElement)
val)
.t;
int g1_19 = 19 * g[1]; /* 1.959375*2^29 */
int g2_19 = 19 * g[2]; /* 1.959375*2^30; still ok */
int g3_19 = 19 * g[3];
int g4_19 = 19 * g[4];
int g5_19 = 19 * g[5];
int g6_19 = 19 * g[6];
int g7_19 = 19 * g[7];
int g8_19 = 19 * g[8];
int g9_19 = 19 * g[9];
int f1_2 = 2 * t[1];
int f3_2 = 2 * t[3];
int f5_2 = 2 * t[5];
int f7_2 = 2 * t[7];
int f9_2 = 2 * t[9];
long f0g0 = t[0] * (long) g[0];
long f0g1 = t[0] * (long) g[1];
long f0g2 = t[0] * (long) g[2];
long f0g3 = t[0] * (long) g[3];
long f0g4 = t[0] * (long) g[4];
long f0g5 = t[0] * (long) g[5];
long f0g6 = t[0] * (long) g[6];
long f0g7 = t[0] * (long) g[7];
long f0g8 = t[0] * (long) g[8];
long f0g9 = t[0] * (long) g[9];
long f1g0 = t[1] * (long) g[0];
long f1g1_2 = f1_2 * (long) g[1];
long f1g2 = t[1] * (long) g[2];
long f1g3_2 = f1_2 * (long) g[3];
long f1g4 = t[1] * (long) g[4];
long f1g5_2 = f1_2 * (long) g[5];
long f1g6 = t[1] * (long) g[6];
long f1g7_2 = f1_2 * (long) g[7];
long f1g8 = t[1] * (long) g[8];
long f1g9_38 = f1_2 * (long) g9_19;
long f2g0 = t[2] * (long) g[0];
long f2g1 = t[2] * (long) g[1];
long f2g2 = t[2] * (long) g[2];
long f2g3 = t[2] * (long) g[3];
long f2g4 = t[2] * (long) g[4];
long f2g5 = t[2] * (long) g[5];
long f2g6 = t[2] * (long) g[6];
long f2g7 = t[2] * (long) g[7];
long f2g8_19 = t[2] * (long) g8_19;
long f2g9_19 = t[2] * (long) g9_19;
long f3g0 = t[3] * (long) g[0];
long f3g1_2 = f3_2 * (long) g[1];
long f3g2 = t[3] * (long) g[2];
long f3g3_2 = f3_2 * (long) g[3];
long f3g4 = t[3] * (long) g[4];
long f3g5_2 = f3_2 * (long) g[5];
long f3g6 = t[3] * (long) g[6];
long f3g7_38 = f3_2 * (long) g7_19;
long f3g8_19 = t[3] * (long) g8_19;
long f3g9_38 = f3_2 * (long) g9_19;
long f4g0 = t[4] * (long) g[0];
long f4g1 = t[4] * (long) g[1];
long f4g2 = t[4] * (long) g[2];
long f4g3 = t[4] * (long) g[3];
long f4g4 = t[4] * (long) g[4];
long f4g5 = t[4] * (long) g[5];
long f4g6_19 = t[4] * (long) g6_19;
long f4g7_19 = t[4] * (long) g7_19;
long f4g8_19 = t[4] * (long) g8_19;
long f4g9_19 = t[4] * (long) g9_19;
long f5g0 = t[5] * (long) g[0];
long f5g1_2 = f5_2 * (long) g[1];
long f5g2 = t[5] * (long) g[2];
long f5g3_2 = f5_2 * (long) g[3];
long f5g4 = t[5] * (long) g[4];
long f5g5_38 = f5_2 * (long) g5_19;
long f5g6_19 = t[5] * (long) g6_19;
long f5g7_38 = f5_2 * (long) g7_19;
long f5g8_19 = t[5] * (long) g8_19;
long f5g9_38 = f5_2 * (long) g9_19;
long f6g0 = t[6] * (long) g[0];
long f6g1 = t[6] * (long) g[1];
long f6g2 = t[6] * (long) g[2];
long f6g3 = t[6] * (long) g[3];
long f6g4_19 = t[6] * (long) g4_19;
long f6g5_19 = t[6] * (long) g5_19;
long f6g6_19 = t[6] * (long) g6_19;
long f6g7_19 = t[6] * (long) g7_19;
long f6g8_19 = t[6] * (long) g8_19;
long f6g9_19 = t[6] * (long) g9_19;
long f7g0 = t[7] * (long) g[0];
long f7g1_2 = f7_2 * (long) g[1];
long f7g2 = t[7] * (long) g[2];
long f7g3_38 = f7_2 * (long) g3_19;
long f7g4_19 = t[7] * (long) g4_19;
long f7g5_38 = f7_2 * (long) g5_19;
long f7g6_19 = t[7] * (long) g6_19;
long f7g7_38 = f7_2 * (long) g7_19;
long f7g8_19 = t[7] * (long) g8_19;
long f7g9_38 = f7_2 * (long) g9_19;
long f8g0 = t[8] * (long) g[0];
long f8g1 = t[8] * (long) g[1];
long f8g2_19 = t[8] * (long) g2_19;
long f8g3_19 = t[8] * (long) g3_19;
long f8g4_19 = t[8] * (long) g4_19;
long f8g5_19 = t[8] * (long) g5_19;
long f8g6_19 = t[8] * (long) g6_19;
long f8g7_19 = t[8] * (long) g7_19;
long f8g8_19 = t[8] * (long) g8_19;
long f8g9_19 = t[8] * (long) g9_19;
long f9g0 = t[9] * (long) g[0];
long f9g1_38 = f9_2 * (long) g1_19;
long f9g2_19 = t[9] * (long) g2_19;
long f9g3_38 = f9_2 * (long) g3_19;
long f9g4_19 = t[9] * (long) g4_19;
long f9g5_38 = f9_2 * (long) g5_19;
long f9g6_19 = t[9] * (long) g6_19;
long f9g7_38 = f9_2 * (long) g7_19;
long f9g8_19 = t[9] * (long) g8_19;
long f9g9_38 = f9_2 * (long) g9_19;
/**
* Remember: 2^255 congruent 19 modulo p. h = h0 * 2^0 + h1 * 2^26 + h2 * 2^(26+25) + h3 *
* 2^(26+25+26) + ... + h9 * 2^(5*26+5*25). So to get the real number we would have to multiply
* the coefficients with the corresponding powers of 2. To get an idea what is going on below,
* look at the calculation of h0: h0 is the coefficient to the power 2^0 so it collects (sums)
* all products that have the power 2^0. f0 * g0 really is f0 * 2^0 * g0 * 2^0 = (f0 * g0) *
* 2^0. f1 * g9 really is f1 * 2^26 * g9 * 2^230 = f1 * g9 * 2^256 = 2 * f1 * g9 * 2^255
* congruent 2 * 19 * f1 * g9 * 2^0 modulo p. f2 * g8 really is f2 * 2^51 * g8 * 2^204 = f2 * g8
* * 2^255 congruent 19 * f2 * g8 * 2^0 modulo p. and so on...
*/
long h0 =
f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19
+ f9g1_38;
long h1 =
f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
long h2 =
f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
long h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
long h4 =
f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
long h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
long h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
long h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
long h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
long h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
long carry0;
long carry1;
long carry2;
long carry3;
long carry4;
long carry5;
long carry6;
long carry7;
long carry8;
long carry9;
/*
|h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
|h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
*/
carry0 = (h0 + (long) (1 << 25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
carry4 = (h4 + (long) (1 << 25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
/* |h0| <= 2^25 */
/* |h4| <= 2^25 */
/* |h1| <= 1.71*2^59 */
/* |h5| <= 1.71*2^59 */
carry1 = (h1 + (long) (1 << 24)) >> 25;
h2 += carry1;
h1 -= carry1 << 25;
carry5 = (h5 + (long) (1 << 24)) >> 25;
h6 += carry5;
h5 -= carry5 << 25;
/* |h1| <= 2^24; from now on fits into int32 */
/* |h5| <= 2^24; from now on fits into int32 */
/* |h2| <= 1.41*2^60 */
/* |h6| <= 1.41*2^60 */
carry2 = (h2 + (long) (1 << 25)) >> 26;
h3 += carry2;
h2 -= carry2 << 26;
carry6 = (h6 + (long) (1 << 25)) >> 26;
h7 += carry6;
h6 -= carry6 << 26;
/* |h2| <= 2^25; from now on fits into int32 unchanged */
/* |h6| <= 2^25; from now on fits into int32 unchanged */
/* |h3| <= 1.71*2^59 */
/* |h7| <= 1.71*2^59 */
carry3 = (h3 + (long) (1 << 24)) >> 25;
h4 += carry3;
h3 -= carry3 << 25;
carry7 = (h7 + (long) (1 << 24)) >> 25;
h8 += carry7;
h7 -= carry7 << 25;
/* |h3| <= 2^24; from now on fits into int32 unchanged */
/* |h7| <= 2^24; from now on fits into int32 unchanged */
/* |h4| <= 1.72*2^34 */
/* |h8| <= 1.41*2^60 */
carry4 = (h4 + (long) (1 << 25)) >> 26;
h5 += carry4;
h4 -= carry4 << 26;
carry8 = (h8 + (long) (1 << 25)) >> 26;
h9 += carry8;
h8 -= carry8 << 26;
/* |h4| <= 2^25; from now on fits into int32 unchanged */
/* |h8| <= 2^25; from now on fits into int32 unchanged */
/* |h5| <= 1.01*2^24 */
/* |h9| <= 1.71*2^59 */
carry9 = (h9 + (long) (1 << 24)) >> 25;
h0 += carry9 * 19;
h9 -= carry9 << 25;
/* |h9| <= 2^24; from now on fits into int32 unchanged */
/* |h0| <= 1.1*2^39 */
carry0 = (h0 + (long) (1 << 25)) >> 26;
h1 += carry0;
h0 -= carry0 << 26;
/* |h0| <= 2^25; from now on fits into int32 unchanged */
/* |h1| <= 1.01*2^24 */
int[] h = new int[10];
h[0] = (int) h0;
h[1] = (int) h1;
h[2] = (int) h2;
h[3] = (int) h3;
h[4] = (int) h4;
h[5] = (int) h5;
h[6] = (int) h6;
h[7] = (int) h7;
h[8] = (int) h8;
h[9] = (int) h9;
return new org.mariadb.jdbc.internal.com.send.authentication.ed25519.math.ed25519
.Ed25519FieldElement(f, h);
}