sc_mul and sc_muladd

1 files changed, 652 insertions, 0 deletions

diff --git a/src/crypto/crypto-ops.c b/src/crypto/crypto-ops.c
index 4edfee0ce..1e4969558 100644
--- a/src/crypto/crypto-ops.c
+++ b/src/crypto/crypto-ops.c
@@ -2898,6 +2898,658 @@ void sc_mulsub(unsigned char *s, const unsigned char *a, const unsigned char *b,
   s[31] = s11 >> 17;
 }
 
+//copied from above and modified
+/*
+Input:
+  a[0]+256*a[1]+...+256^31*a[31] = a
+  b[0]+256*b[1]+...+256^31*b[31] = b
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = (ab) mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+void sc_mul(unsigned char *s, const unsigned char *a, const unsigned char *b) {
+  int64_t a0 = 2097151 & load_3(a);
+  int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
+  int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
+  int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
+  int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
+  int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
+  int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
+  int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
+  int64_t a8 = 2097151 & load_3(a + 21);
+  int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
+  int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+  int64_t a11 = (load_4(a + 28) >> 7);
+  int64_t b0 = 2097151 & load_3(b);
+  int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
+  int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
+  int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
+  int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
+  int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
+  int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
+  int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
+  int64_t b8 = 2097151 & load_3(b + 21);
+  int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
+  int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+  int64_t b11 = (load_4(b + 28) >> 7);
+  int64_t s0;
+  int64_t s1;
+  int64_t s2;
+  int64_t s3;
+  int64_t s4;
+  int64_t s5;
+  int64_t s6;
+  int64_t s7;
+  int64_t s8;
+  int64_t s9;
+  int64_t s10;
+  int64_t s11;
+  int64_t s12;
+  int64_t s13;
+  int64_t s14;
+  int64_t s15;
+  int64_t s16;
+  int64_t s17;
+  int64_t s18;
+  int64_t s19;
+  int64_t s20;
+  int64_t s21;
+  int64_t s22;
+  int64_t s23;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+  int64_t carry10;
+  int64_t carry11;
+  int64_t carry12;
+  int64_t carry13;
+  int64_t carry14;
+  int64_t carry15;
+  int64_t carry16;
+  int64_t carry17;
+  int64_t carry18;
+  int64_t carry19;
+  int64_t carry20;
+  int64_t carry21;
+  int64_t carry22;
+
+  s0 = a0*b0;
+  s1 = (a0*b1 + a1*b0);
+  s2 = (a0*b2 + a1*b1 + a2*b0);
+  s3 = (a0*b3 + a1*b2 + a2*b1 + a3*b0);
+  s4 = (a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0);
+  s5 = (a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0);
+  s6 = (a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0);
+  s7 = (a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0);
+  s8 = (a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0);
+  s9 = (a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0);
+  s10 = (a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0);
+  s11 = (a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0);
+  s12 = (a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1);
+  s13 = (a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2);
+  s14 = (a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3);
+  s15 = (a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4);
+  s16 = (a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5);
+  s17 = (a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6);
+  s18 = (a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7);
+  s19 = (a8*b11 + a9*b10 + a10*b9 + a11*b8);
+  s20 = (a9*b11 + a10*b10 + a11*b9);
+  s21 = (a10*b11 + a11*b10);
+  s22 = a11*b11;
+  s23 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+  carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
+  carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
+  carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+  carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
+  carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
+  carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
+
+  s11 += s23 * 666643;
+  s12 += s23 * 470296;
+  s13 += s23 * 654183;
+  s14 -= s23 * 997805;
+  s15 += s23 * 136657;
+  s16 -= s23 * 683901;
+
+  s10 += s22 * 666643;
+  s11 += s22 * 470296;
+  s12 += s22 * 654183;
+  s13 -= s22 * 997805;
+  s14 += s22 * 136657;
+  s15 -= s22 * 683901;
+
+  s9 += s21 * 666643;
+  s10 += s21 * 470296;
+  s11 += s21 * 654183;
+  s12 -= s21 * 997805;
+  s13 += s21 * 136657;
+  s14 -= s21 * 683901;
+
+  s8 += s20 * 666643;
+  s9 += s20 * 470296;
+  s10 += s20 * 654183;
+  s11 -= s20 * 997805;
+  s12 += s20 * 136657;
+  s13 -= s20 * 683901;
+
+  s7 += s19 * 666643;
+  s8 += s19 * 470296;
+  s9 += s19 * 654183;
+  s10 -= s19 * 997805;
+  s11 += s19 * 136657;
+  s12 -= s19 * 683901;
+
+  s6 += s18 * 666643;
+  s7 += s18 * 470296;
+  s8 += s18 * 654183;
+  s9 -= s18 * 997805;
+  s10 += s18 * 136657;
+  s11 -= s18 * 683901;
+
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+
+  s5 += s17 * 666643;
+  s6 += s17 * 470296;
+  s7 += s17 * 654183;
+  s8 -= s17 * 997805;
+  s9 += s17 * 136657;
+  s10 -= s17 * 683901;
+
+  s4 += s16 * 666643;
+  s5 += s16 * 470296;
+  s6 += s16 * 654183;
+  s7 -= s16 * 997805;
+  s8 += s16 * 136657;
+  s9 -= s16 * 683901;
+
+  s3 += s15 * 666643;
+  s4 += s15 * 470296;
+  s5 += s15 * 654183;
+  s6 -= s15 * 997805;
+  s7 += s15 * 136657;
+  s8 -= s15 * 683901;
+
+  s2 += s14 * 666643;
+  s3 += s14 * 470296;
+  s4 += s14 * 654183;
+  s5 -= s14 * 997805;
+  s6 += s14 * 136657;
+  s7 -= s14 * 683901;
+
+  s1 += s13 * 666643;
+  s2 += s13 * 470296;
+  s3 += s13 * 654183;
+  s4 -= s13 * 997805;
+  s5 += s13 * 136657;
+  s6 -= s13 * 683901;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  s[0] = s0 >> 0;
+  s[1] = s0 >> 8;
+  s[2] = (s0 >> 16) | (s1 << 5);
+  s[3] = s1 >> 3;
+  s[4] = s1 >> 11;
+  s[5] = (s1 >> 19) | (s2 << 2);
+  s[6] = s2 >> 6;
+  s[7] = (s2 >> 14) | (s3 << 7);
+  s[8] = s3 >> 1;
+  s[9] = s3 >> 9;
+  s[10] = (s3 >> 17) | (s4 << 4);
+  s[11] = s4 >> 4;
+  s[12] = s4 >> 12;
+  s[13] = (s4 >> 20) | (s5 << 1);
+  s[14] = s5 >> 7;
+  s[15] = (s5 >> 15) | (s6 << 6);
+  s[16] = s6 >> 2;
+  s[17] = s6 >> 10;
+  s[18] = (s6 >> 18) | (s7 << 3);
+  s[19] = s7 >> 5;
+  s[20] = s7 >> 13;
+  s[21] = s8 >> 0;
+  s[22] = s8 >> 8;
+  s[23] = (s8 >> 16) | (s9 << 5);
+  s[24] = s9 >> 3;
+  s[25] = s9 >> 11;
+  s[26] = (s9 >> 19) | (s10 << 2);
+  s[27] = s10 >> 6;
+  s[28] = (s10 >> 14) | (s11 << 7);
+  s[29] = s11 >> 1;
+  s[30] = s11 >> 9;
+  s[31] = s11 >> 17;
+}
+
+//copied from above and modified
+/*
+Input:
+  a[0]+256*a[1]+...+256^31*a[31] = a
+  b[0]+256*b[1]+...+256^31*b[31] = b
+  c[0]+256*c[1]+...+256^31*c[31] = c
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = (c+ab) mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) {
+  int64_t a0 = 2097151 & load_3(a);
+  int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
+  int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
+  int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
+  int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
+  int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
+  int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
+  int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
+  int64_t a8 = 2097151 & load_3(a + 21);
+  int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
+  int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+  int64_t a11 = (load_4(a + 28) >> 7);
+  int64_t b0 = 2097151 & load_3(b);
+  int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
+  int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
+  int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
+  int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
+  int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
+  int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
+  int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
+  int64_t b8 = 2097151 & load_3(b + 21);
+  int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
+  int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+  int64_t b11 = (load_4(b + 28) >> 7);
+  int64_t c0 = 2097151 & load_3(c);
+  int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
+  int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
+  int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
+  int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
+  int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
+  int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
+  int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
+  int64_t c8 = 2097151 & load_3(c + 21);
+  int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
+  int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
+  int64_t c11 = (load_4(c + 28) >> 7);
+  int64_t s0;
+  int64_t s1;
+  int64_t s2;
+  int64_t s3;
+  int64_t s4;
+  int64_t s5;
+  int64_t s6;
+  int64_t s7;
+  int64_t s8;
+  int64_t s9;
+  int64_t s10;
+  int64_t s11;
+  int64_t s12;
+  int64_t s13;
+  int64_t s14;
+  int64_t s15;
+  int64_t s16;
+  int64_t s17;
+  int64_t s18;
+  int64_t s19;
+  int64_t s20;
+  int64_t s21;
+  int64_t s22;
+  int64_t s23;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+  int64_t carry10;
+  int64_t carry11;
+  int64_t carry12;
+  int64_t carry13;
+  int64_t carry14;
+  int64_t carry15;
+  int64_t carry16;
+  int64_t carry17;
+  int64_t carry18;
+  int64_t carry19;
+  int64_t carry20;
+  int64_t carry21;
+  int64_t carry22;
+
+  s0 = c0 + a0*b0;
+  s1 = c1 + (a0*b1 + a1*b0);
+  s2 = c2 + (a0*b2 + a1*b1 + a2*b0);
+  s3 = c3 + (a0*b3 + a1*b2 + a2*b1 + a3*b0);
+  s4 = c4 + (a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0);
+  s5 = c5 + (a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0);
+  s6 = c6 + (a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0);
+  s7 = c7 + (a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0);
+  s8 = c8 + (a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0);
+  s9 = c9 + (a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0);
+  s10 = c10 + (a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0);
+  s11 = c11 + (a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0);
+  s12 = (a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1);
+  s13 = (a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2);
+  s14 = (a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3);
+  s15 = (a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4);
+  s16 = (a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5);
+  s17 = (a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6);
+  s18 = (a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7);
+  s19 = (a8*b11 + a9*b10 + a10*b9 + a11*b8);
+  s20 = (a9*b11 + a10*b10 + a11*b9);
+  s21 = (a10*b11 + a11*b10);
+  s22 = a11*b11;
+  s23 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+  carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
+  carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
+  carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+  carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
+  carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
+  carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
+
+  s11 += s23 * 666643;
+  s12 += s23 * 470296;
+  s13 += s23 * 654183;
+  s14 -= s23 * 997805;
+  s15 += s23 * 136657;
+  s16 -= s23 * 683901;
+
+  s10 += s22 * 666643;
+  s11 += s22 * 470296;
+  s12 += s22 * 654183;
+  s13 -= s22 * 997805;
+  s14 += s22 * 136657;
+  s15 -= s22 * 683901;
+
+  s9 += s21 * 666643;
+  s10 += s21 * 470296;
+  s11 += s21 * 654183;
+  s12 -= s21 * 997805;
+  s13 += s21 * 136657;
+  s14 -= s21 * 683901;
+
+  s8 += s20 * 666643;
+  s9 += s20 * 470296;
+  s10 += s20 * 654183;
+  s11 -= s20 * 997805;
+  s12 += s20 * 136657;
+  s13 -= s20 * 683901;
+
+  s7 += s19 * 666643;
+  s8 += s19 * 470296;
+  s9 += s19 * 654183;
+  s10 -= s19 * 997805;
+  s11 += s19 * 136657;
+  s12 -= s19 * 683901;
+
+  s6 += s18 * 666643;
+  s7 += s18 * 470296;
+  s8 += s18 * 654183;
+  s9 -= s18 * 997805;
+  s10 += s18 * 136657;
+  s11 -= s18 * 683901;
+
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+
+  s5 += s17 * 666643;
+  s6 += s17 * 470296;
+  s7 += s17 * 654183;
+  s8 -= s17 * 997805;
+  s9 += s17 * 136657;
+  s10 -= s17 * 683901;
+
+  s4 += s16 * 666643;
+  s5 += s16 * 470296;
+  s6 += s16 * 654183;
+  s7 -= s16 * 997805;
+  s8 += s16 * 136657;
+  s9 -= s16 * 683901;
+
+  s3 += s15 * 666643;
+  s4 += s15 * 470296;
+  s5 += s15 * 654183;
+  s6 -= s15 * 997805;
+  s7 += s15 * 136657;
+  s8 -= s15 * 683901;
+
+  s2 += s14 * 666643;
+  s3 += s14 * 470296;
+  s4 += s14 * 654183;
+  s5 -= s14 * 997805;
+  s6 += s14 * 136657;
+  s7 -= s14 * 683901;
+
+  s1 += s13 * 666643;
+  s2 += s13 * 470296;
+  s3 += s13 * 654183;
+  s4 -= s13 * 997805;
+  s5 += s13 * 136657;
+  s6 -= s13 * 683901;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  s[0] = s0 >> 0;
+  s[1] = s0 >> 8;
+  s[2] = (s0 >> 16) | (s1 << 5);
+  s[3] = s1 >> 3;
+  s[4] = s1 >> 11;
+  s[5] = (s1 >> 19) | (s2 << 2);
+  s[6] = s2 >> 6;
+  s[7] = (s2 >> 14) | (s3 << 7);
+  s[8] = s3 >> 1;
+  s[9] = s3 >> 9;
+  s[10] = (s3 >> 17) | (s4 << 4);
+  s[11] = s4 >> 4;
+  s[12] = s4 >> 12;
+  s[13] = (s4 >> 20) | (s5 << 1);
+  s[14] = s5 >> 7;
+  s[15] = (s5 >> 15) | (s6 << 6);
+  s[16] = s6 >> 2;
+  s[17] = s6 >> 10;
+  s[18] = (s6 >> 18) | (s7 << 3);
+  s[19] = s7 >> 5;
+  s[20] = s7 >> 13;
+  s[21] = s8 >> 0;
+  s[22] = s8 >> 8;
+  s[23] = (s8 >> 16) | (s9 << 5);
+  s[24] = s9 >> 3;
+  s[25] = s9 >> 11;
+  s[26] = (s9 >> 19) | (s10 << 2);
+  s[27] = s10 >> 6;
+  s[28] = (s10 >> 14) | (s11 << 7);
+  s[29] = s11 >> 1;
+  s[30] = s11 >> 9;
+  s[31] = s11 >> 17;
+}
+
 /* Assumes that a != INT64_MIN */
 static int64_t signum(int64_t a) {
   return (a >> 63) - ((-a) >> 63);