org.whispersystems.curve25519.java.fe_mul Maven / Gradle / Ivy
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Curve25519 library for Java
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package org.whispersystems.curve25519.java;
public class fe_mul {
//CONVERT #include "fe.h"
//CONVERT #include "long.h"
/*
h = f * g
Can overlap h with f or g.
Preconditions:
|f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
|g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
Postconditions:
|h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/
/*
Notes on implementation strategy:
Using schoolbook multiplication.
Karatsuba would save a little in some cost models.
Most multiplications by 2 and 19 are 32-bit precomputations;
cheaper than 64-bit postcomputations.
There is one remaining multiplication by 19 in the carry chain;
one *19 precomputation can be merged into this,
but the resulting data flow is considerably less clean.
There are 12 carries below.
10 of them are 2-way parallelizable and vectorizable.
Can get away with 11 carries, but then data flow is much deeper.
With tighter constraints on inputs can squeeze carries into int32.
*/
public static long[] fe_mul1(int[] f, int[] g) {
int f0 = f[0];
int f1 = f[1];
int f2 = f[2];
int f3 = f[3];
int f4 = f[4];
int f5 = f[5];
int f6 = f[6];
int f7 = f[7];
int f8 = f[8];
int f9 = f[9];
int g0 = g[0];
int g1 = g[1];
int g2 = g[2];
int g3 = g[3];
int g4 = g[4];
int g5 = g[5];
int g6 = g[6];
int g7 = g[7];
int g8 = g[8];
int g9 = g[9];
int g1_19 = 19 * g1; /* 1.959375*2^29 */
int g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
int g3_19 = 19 * g3;
int g4_19 = 19 * g4;
int g5_19 = 19 * g5;
int g6_19 = 19 * g6;
int g7_19 = 19 * g7;
int g8_19 = 19 * g8;
int g9_19 = 19 * g9;
int f1_2 = 2 * f1;
int f3_2 = 2 * f3;
int f5_2 = 2 * f5;
int f7_2 = 2 * f7;
int f9_2 = 2 * f9;
long f0g0 = f0 * (long) g0;
long f0g1 = f0 * (long) g1;
long f0g2 = f0 * (long) g2;
long f0g3 = f0 * (long) g3;
long f0g4 = f0 * (long) g4;
long f0g5 = f0 * (long) g5;
long f0g6 = f0 * (long) g6;
long f0g7 = f0 * (long) g7;
long f0g8 = f0 * (long) g8;
long f0g9 = f0 * (long) g9;
long f1g0 = f1 * (long) g0;
long f1g1_2 = f1_2 * (long) g1;
long f1g2 = f1 * (long) g2;
long f1g3_2 = f1_2 * (long) g3;
long f1g4 = f1 * (long) g4;
long f1g5_2 = f1_2 * (long) g5;
long f1g6 = f1 * (long) g6;
long f1g7_2 = f1_2 * (long) g7;
long f1g8 = f1 * (long) g8;
long f1g9_38 = f1_2 * (long) g9_19;
long f2g0 = f2 * (long) g0;
long f2g1 = f2 * (long) g1;
long f2g2 = f2 * (long) g2;
long f2g3 = f2 * (long) g3;
long f2g4 = f2 * (long) g4;
long f2g5 = f2 * (long) g5;
long f2g6 = f2 * (long) g6;
long f2g7 = f2 * (long) g7;
long f2g8_19 = f2 * (long) g8_19;
long f2g9_19 = f2 * (long) g9_19;
long f3g0 = f3 * (long) g0;
long f3g1_2 = f3_2 * (long) g1;
long f3g2 = f3 * (long) g2;
long f3g3_2 = f3_2 * (long) g3;
long f3g4 = f3 * (long) g4;
long f3g5_2 = f3_2 * (long) g5;
long f3g6 = f3 * (long) g6;
long f3g7_38 = f3_2 * (long) g7_19;
long f3g8_19 = f3 * (long) g8_19;
long f3g9_38 = f3_2 * (long) g9_19;
long f4g0 = f4 * (long) g0;
long f4g1 = f4 * (long) g1;
long f4g2 = f4 * (long) g2;
long f4g3 = f4 * (long) g3;
long f4g4 = f4 * (long) g4;
long f4g5 = f4 * (long) g5;
long f4g6_19 = f4 * (long) g6_19;
long f4g7_19 = f4 * (long) g7_19;
long f4g8_19 = f4 * (long) g8_19;
long f4g9_19 = f4 * (long) g9_19;
long f5g0 = f5 * (long) g0;
long f5g1_2 = f5_2 * (long) g1;
long f5g2 = f5 * (long) g2;
long f5g3_2 = f5_2 * (long) g3;
long f5g4 = f5 * (long) g4;
long f5g5_38 = f5_2 * (long) g5_19;
long f5g6_19 = f5 * (long) g6_19;
long f5g7_38 = f5_2 * (long) g7_19;
long f5g8_19 = f5 * (long) g8_19;
long f5g9_38 = f5_2 * (long) g9_19;
long f6g0 = f6 * (long) g0;
long f6g1 = f6 * (long) g1;
long f6g2 = f6 * (long) g2;
long f6g3 = f6 * (long) g3;
long f6g4_19 = f6 * (long) g4_19;
long f6g5_19 = f6 * (long) g5_19;
long f6g6_19 = f6 * (long) g6_19;
long f6g7_19 = f6 * (long) g7_19;
long f6g8_19 = f6 * (long) g8_19;
long f6g9_19 = f6 * (long) g9_19;
long f7g0 = f7 * (long) g0;
long f7g1_2 = f7_2 * (long) g1;
long f7g2 = f7 * (long) g2;
long f7g3_38 = f7_2 * (long) g3_19;
long f7g4_19 = f7 * (long) g4_19;
long f7g5_38 = f7_2 * (long) g5_19;
long f7g6_19 = f7 * (long) g6_19;
long f7g7_38 = f7_2 * (long) g7_19;
long f7g8_19 = f7 * (long) g8_19;
long f7g9_38 = f7_2 * (long) g9_19;
long f8g0 = f8 * (long) g0;
long f8g1 = f8 * (long) g1;
long f8g2_19 = f8 * (long) g2_19;
long f8g3_19 = f8 * (long) g3_19;
long f8g4_19 = f8 * (long) g4_19;
long f8g5_19 = f8 * (long) g5_19;
long f8g6_19 = f8 * (long) g6_19;
long f8g7_19 = f8 * (long) g7_19;
long f8g8_19 = f8 * (long) g8_19;
long f8g9_19 = f8 * (long) g9_19;
long f9g0 = f9 * (long) g0;
long f9g1_38 = f9_2 * (long) g1_19;
long f9g2_19 = f9 * (long) g2_19;
long f9g3_38 = f9_2 * (long) g3_19;
long f9g4_19 = f9 * (long) g4_19;
long f9g5_38 = f9_2 * (long) g5_19;
long f9g6_19 = f9 * (long) g6_19;
long f9g7_38 = f9_2 * (long) g7_19;
long f9g8_19 = f9 * (long) g8_19;
long f9g9_38 = f9_2 * (long) g9_19;
long[] h = new long[10];
h[0] = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
h[1] = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
h[2] = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
h[3] = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
h[4] = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
h[5] = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
h[6] = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
h[7] = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
h[8] = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
h[9] = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
return h;
}
public static void fe_mul(int[] h, int[] f, int[] g) {
long[] hr = fe_mul1(f, g);
long h0 = hr[0];
long h1 = hr[1];
long h2 = hr[2];
long h3 = hr[3];
long h4 = hr[4];
long h5 = hr[5];
long h6 = hr[6];
long h7 = hr[7];
long h8 = hr[8];
long h9 = hr[9];
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 */
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;
}
}
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