--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libtommath/bn_mp_prime_strong_lucas_selfridge.c	Mon Sep 16 15:50:38 2019 +0200
@@ -0,0 +1,411 @@
+#include "tommath_private.h"
+#ifdef BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C
+
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * SPDX-License-Identifier: Unlicense
+ */
+
+/*
+ *  See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
+ */
+#ifndef LTM_USE_FIPS_ONLY
+
+/*
+ *  8-bit is just too small. You can try the Frobenius test
+ *  but that frobenius test can fail, too, for the same reason.
+ */
+#ifndef MP_8BIT
+
+/*
+ * multiply bigint a with int d and put the result in c
+ * Like mp_mul_d() but with a signed long as the small input
+ */
+static int s_mp_mul_si(const mp_int *a, long d, mp_int *c)
+{
+   mp_int t;
+   int err, neg = 0;
+
+   if ((err = mp_init(&t)) != MP_OKAY) {
+      return err;
+   }
+   if (d < 0) {
+      neg = 1;
+      d = -d;
+   }
+
+   /*
+    * mp_digit might be smaller than a long, which excludes
+    * the use of mp_mul_d() here.
+    */
+   if ((err = mp_set_long(&t, (unsigned long) d)) != MP_OKAY) {
+      goto LBL_MPMULSI_ERR;
+   }
+   if ((err = mp_mul(a, &t, c)) != MP_OKAY) {
+      goto LBL_MPMULSI_ERR;
+   }
+   if (neg ==  1) {
+      c->sign = (a->sign == MP_NEG) ? MP_ZPOS: MP_NEG;
+   }
+LBL_MPMULSI_ERR:
+   mp_clear(&t);
+   return err;
+}
+/*
+    Strong Lucas-Selfridge test.
+    returns MP_YES if it is a strong L-S prime, MP_NO if it is composite
+
+    Code ported from  Thomas Ray Nicely's implementation of the BPSW test
+    at http://www.trnicely.net/misc/bpsw.html
+
+    Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>.
+    Released into the public domain by the author, who disclaims any legal
+    liability arising from its use
+
+    The multi-line comments are made by Thomas R. Nicely and are copied verbatim.
+    Additional comments marked "CZ" (without the quotes) are by the code-portist.
+
+    (If that name sounds familiar, he is the guy who found the fdiv bug in the
+     Pentium (P5x, I think) Intel processor)
+*/
+int mp_prime_strong_lucas_selfridge(const mp_int *a, int *result)
+{
+   /* CZ TODO: choose better variable names! */
+   mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz;
+   /* CZ TODO: Some of them need the full 32 bit, hence the (temporary) exclusion of MP_8BIT */
+   int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits;
+   int e;
+   int isset, oddness;
+
+   *result = MP_NO;
+   /*
+   Find the first element D in the sequence {5, -7, 9, -11, 13, ...}
+   such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory
+   indicates that, if N is not a perfect square, D will "nearly
+   always" be "small." Just in case, an overflow trap for D is
+   included.
+   */
+
+   if ((e = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz,
+                          NULL)) != MP_OKAY) {
+      return e;
+   }
+
+   D = 5;
+   sign = 1;
+
+   for (;;) {
+      Ds   = sign * D;
+      sign = -sign;
+      if ((e = mp_set_long(&Dz, (unsigned long)D)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((e = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      /* if 1 < GCD < N then N is composite with factor "D", and
+         Jacobi(D,N) is technically undefined (but often returned
+         as zero). */
+      if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) {
+         goto LBL_LS_ERR;
+      }
+      if (Ds < 0) {
+         Dz.sign = MP_NEG;
+      }
+      if ((e = mp_kronecker(&Dz, a, &J)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+
+      if (J == -1) {
+         break;
+      }
+      D += 2;
+
+      if (D > (INT_MAX - 2)) {
+         e = MP_VAL;
+         goto LBL_LS_ERR;
+      }
+   }
+
+
+
+   P = 1;              /* Selfridge's choice */
+   Q = (1 - Ds) / 4;   /* Required so D = P*P - 4*Q */
+
+   /* NOTE: The conditions (a) N does not divide Q, and
+      (b) D is square-free or not a perfect square, are included by
+      some authors; e.g., "Prime numbers and computer methods for
+      factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston),
+      p. 130. For this particular application of Lucas sequences,
+      these conditions were found to be immaterial. */
+
+   /* Now calculate N - Jacobi(D,N) = N + 1 (even), and calculate the
+      odd positive integer d and positive integer s for which
+      N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test).
+      The strong Lucas-Selfridge test then returns N as a strong
+      Lucas probable prime (slprp) if any of the following
+      conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0,
+      V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0
+      (all equalities mod N). Thus d is the highest index of U that
+      must be computed (since V_2m is independent of U), compared
+      to U_{N+1} for the standard Lucas-Selfridge test; and no
+      index of V beyond (N+1)/2 is required, just as in the
+      standard Lucas-Selfridge test. However, the quantity Q^d must
+      be computed for use (if necessary) in the latter stages of
+      the test. The result is that the strong Lucas-Selfridge test
+      has a running time only slightly greater (order of 10 %) than
+      that of the standard Lucas-Selfridge test, while producing
+      only (roughly) 30 % as many pseudoprimes (and every strong
+      Lucas pseudoprime is also a standard Lucas pseudoprime). Thus
+      the evidence indicates that the strong Lucas-Selfridge test is
+      more effective than the standard Lucas-Selfridge test, and a
+      Baillie-PSW test based on the strong Lucas-Selfridge test
+      should be more reliable. */
+
+   if ((e = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) {
+      goto LBL_LS_ERR;
+   }
+   s = mp_cnt_lsb(&Np1);
+
+   /* CZ
+    * This should round towards zero because
+    * Thomas R. Nicely used GMP's mpz_tdiv_q_2exp()
+    * and mp_div_2d() is equivalent. Additionally:
+    * dividing an even number by two does not produce
+    * any leftovers.
+    */
+   if ((e = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) {
+      goto LBL_LS_ERR;
+   }
+   /* We must now compute U_d and V_d. Since d is odd, the accumulated
+      values U and V are initialized to U_1 and V_1 (if the target
+      index were even, U and V would be initialized instead to U_0=0
+      and V_0=2). The values of U_2m and V_2m are also initialized to
+      U_1 and V_1; the FOR loop calculates in succession U_2 and V_2,
+      U_4 and V_4, U_8 and V_8, etc. If the corresponding bits
+      (1, 2, 3, ...) of t are on (the zero bit having been accounted
+      for in the initialization of U and V), these values are then
+      combined with the previous totals for U and V, using the
+      composition formulas for addition of indices. */
+
+   mp_set(&Uz, 1uL);    /* U=U_1 */
+   mp_set(&Vz, (mp_digit)P);    /* V=V_1 */
+   mp_set(&U2mz, 1uL);  /* U_1 */
+   mp_set(&V2mz, (mp_digit)P);  /* V_1 */
+
+   if (Q < 0) {
+      Q = -Q;
+      if ((e = mp_set_long(&Qmz, (unsigned long)Q)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      /* Initializes calculation of Q^d */
+      if ((e = mp_set_long(&Qkdz, (unsigned long)Q)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      Qmz.sign = MP_NEG;
+      Q2mz.sign = MP_NEG;
+      Qkdz.sign = MP_NEG;
+      Q = -Q;
+   } else {
+      if ((e = mp_set_long(&Qmz, (unsigned long)Q)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      /* Initializes calculation of Q^d */
+      if ((e = mp_set_long(&Qkdz, (unsigned long)Q)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+   }
+
+   Nbits = mp_count_bits(&Dz);
+
+   for (u = 1; u < Nbits; u++) { /* zero bit off, already accounted for */
+      /* Formulas for doubling of indices (carried out mod N). Note that
+       * the indices denoted as "2m" are actually powers of 2, specifically
+       * 2^(ul-1) beginning each loop and 2^ul ending each loop.
+       *
+       * U_2m = U_m*V_m
+       * V_2m = V_m*V_m - 2*Q^m
+       */
+
+      if ((e = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((e = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((e = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((e = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((e = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      /* Must calculate powers of Q for use in V_2m, also for Q^d later */
+      if ((e = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      /* prevents overflow */ /* CZ  still necessary without a fixed prealloc'd mem.? */
+      if ((e = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((isset = mp_get_bit(&Dz, u)) == MP_VAL) {
+         e = isset;
+         goto LBL_LS_ERR;
+      }
+      if (isset == MP_YES) {
+         /* Formulas for addition of indices (carried out mod N);
+          *
+          * U_(m+n) = (U_m*V_n + U_n*V_m)/2
+          * V_(m+n) = (V_m*V_n + D*U_m*U_n)/2
+          *
+          * Be careful with division by 2 (mod N)!
+          */
+         if ((e = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((e = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((e = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((e = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((e = s_mp_mul_si(&T4z, (long)Ds, &T4z)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((e = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if (mp_isodd(&Uz) != MP_NO) {
+            if ((e = mp_add(&Uz, a, &Uz)) != MP_OKAY) {
+               goto LBL_LS_ERR;
+            }
+         }
+         /* CZ
+          * This should round towards negative infinity because
+          * Thomas R. Nicely used GMP's mpz_fdiv_q_2exp().
+          * But mp_div_2() does not do so, it is truncating instead.
+          */
+         oddness = mp_isodd(&Uz);
+         if ((e = mp_div_2(&Uz, &Uz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((Uz.sign == MP_NEG) && (oddness != MP_NO)) {
+            if ((e = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) {
+               goto LBL_LS_ERR;
+            }
+         }
+         if ((e = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if (mp_isodd(&Vz) != MP_NO) {
+            if ((e = mp_add(&Vz, a, &Vz)) != MP_OKAY) {
+               goto LBL_LS_ERR;
+            }
+         }
+         oddness = mp_isodd(&Vz);
+         if ((e = mp_div_2(&Vz, &Vz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((Vz.sign == MP_NEG) && (oddness != MP_NO)) {
+            if ((e = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) {
+               goto LBL_LS_ERR;
+            }
+         }
+         if ((e = mp_mod(&Uz, a, &Uz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((e = mp_mod(&Vz, a, &Vz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         /* Calculating Q^d for later use */
+         if ((e = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((e = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+      }
+   }
+
+   /* If U_d or V_d is congruent to 0 mod N, then N is a prime or a
+      strong Lucas pseudoprime. */
+   if ((mp_iszero(&Uz) != MP_NO) || (mp_iszero(&Vz) != MP_NO)) {
+      *result = MP_YES;
+      goto LBL_LS_ERR;
+   }
+
+   /* NOTE: Ribenboim ("The new book of prime number records," 3rd ed.,
+      1995/6) omits the condition V0 on p.142, but includes it on
+      p. 130. The condition is NECESSARY; otherwise the test will
+      return false negatives---e.g., the primes 29 and 2000029 will be
+      returned as composite. */
+
+   /* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d}
+      by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of
+      these are congruent to 0 mod N, then N is a prime or a strong
+      Lucas pseudoprime. */
+
+   /* Initialize 2*Q^(d*2^r) for V_2m */
+   if ((e = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) {
+      goto LBL_LS_ERR;
+   }
+
+   for (r = 1; r < s; r++) {
+      if ((e = mp_sqr(&Vz, &Vz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((e = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if ((e = mp_mod(&Vz, a, &Vz)) != MP_OKAY) {
+         goto LBL_LS_ERR;
+      }
+      if (mp_iszero(&Vz) != MP_NO) {
+         *result = MP_YES;
+         goto LBL_LS_ERR;
+      }
+      /* Calculate Q^{d*2^r} for next r (final iteration irrelevant). */
+      if (r < (s - 1)) {
+         if ((e = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((e = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+         if ((e = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) {
+            goto LBL_LS_ERR;
+         }
+      }
+   }
+LBL_LS_ERR:
+   mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL);
+   return e;
+}
+#endif
+#endif
+#endif
+
+/* ref:         HEAD -> master, tag: v1.1.0 */
+/* git commit:  08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
+/* commit time: 2019-01-28 20:32:32 +0100 */