sagemath/sagemath-ntl9.patch

diff -up src/sage/rings/bernmm/bernmm-test.cpp.orig src/sage/rings/bernmm/bernmm-test.cpp
--- src/sage/rings/bernmm/bernmm-test.cpp.orig	2015-10-11 18:17:42.808860675 -0300
+++ src/sage/rings/bernmm/bernmm-test.cpp	2015-10-11 18:18:44.684863044 -0300
@@ -70,7 +70,7 @@ void bern_naive(mpq_t* res, long n)
 */
 int testcase__bern_modp_powg(long p, long k, mpq_t b)
 {
-   double pinv = 1 / ((double) p);
+   mulmod_t pinv = PrepMulMod(p);
 
    // compute B_k mod p using _bern_modp_powg()
    long x = _bern_modp_powg(p, pinv, k);
@@ -147,7 +147,7 @@ int test__bern_modp_powg()
 */
 int testcase__bern_modp_pow2(long p, long k)
 {
-   double pinv = 1 / ((double) p);
+   mulmod_t pinv = PrepMulMod(p);
 
    if (PowerMod(2, k, p, pinv) == 1)
       return 1;
diff -up src/sage/rings/bernmm/bern_modp.cpp.orig src/sage/rings/bernmm/bern_modp.cpp
--- src/sage/rings/bernmm/bern_modp.cpp.orig	2015-10-11 18:17:42.814860675 -0300
+++ src/sage/rings/bernmm/bern_modp.cpp	2015-10-11 18:20:28.077867003 -0300
@@ -43,14 +43,14 @@ namespace bernmm {
       pinv = 1 / ((double) p)
       g = a multiplicative generator of GF(p), in [0, p)
 */
-long bernsum_powg(long p, double pinv, long k, long g)
+long bernsum_powg(long p, mulmod_t pinv, long k, long g)
 {
    long half_gm1 = (g + ((g & 1) ? 0 : p) - 1) / 2;    // (g-1)/2 mod p
    long g_to_jm1 = 1;
    long g_to_km1 = PowerMod(g, k-1, p, pinv);
    long g_to_km1_to_j = g_to_km1;
    long sum = 0;
-   double g_pinv = ((double) g) / ((double) p);
+   muldivrem_t g_pinv = PrepMulDivRem(g, p);
    mulmod_precon_t g_to_km1_pinv = PrepMulModPrecon(g_to_km1, p, pinv);
 
    for (long j = 1; j <= (p-1)/2; j++)
@@ -224,7 +224,7 @@ public:
 #error Number of bits in a long must be divisible by TABLE_LG_SIZE
 #endif
 
-long bernsum_pow2(long p, double pinv, long k, long g, long n)
+long bernsum_pow2(long p, mulmod_t pinv, long k, long g, long n)
 {
    // In the main summation loop we accumulate data into the _tables_ array;
    // tables[y][z] contributes to the final answer with a weight of
@@ -481,7 +481,7 @@ long PrepRedc(long n)
    (See bernsum_pow2() for code comments; we only add comments here where
    something is different from bernsum_pow2())
 */
-long bernsum_pow2_redc(long p, double pinv, long k, long g, long n)
+long bernsum_pow2_redc(long p, mulmod_t pinv, long k, long g, long n)
 {
    long pinv2 = PrepRedc(p);
    long F = (1L << (ULONG_BITS/2)) % p;
@@ -655,7 +655,7 @@ long bernsum_pow2_redc(long p, double pi
 
    Algorithm: uses bernsum_powg() to compute the main sum.
 */
-long _bern_modp_powg(long p, double pinv, long k)
+long _bern_modp_powg(long p, mulmod_t pinv, long k)
 {
    Factorisation F(p-1);
    long g = primitive_root(p, pinv, F);
@@ -685,7 +685,7 @@ long _bern_modp_powg(long p, double pinv
    Algorithm: uses bernsum_pow2() (or bernsum_pow2_redc() if p is small
    enough) to compute the main sum.
 */
-long _bern_modp_pow2(long p, double pinv, long k)
+long _bern_modp_pow2(long p, mulmod_t pinv, long k)
 {
    Factorisation F(p-1);
    long g = primitive_root(p, pinv, F);
@@ -765,7 +765,7 @@ long bern_modp(long p, long k)
    if (m == 0)
       return -1;
 
-   double pinv = 1 / ((double) p);
+   mulmod_t pinv = PrepMulMod(p);
    long x = _bern_modp(p, pinv, m);    // = B_m/m mod p
    return MulMod(x, k, p, pinv);
 }
diff -up src/sage/rings/bernmm/bern_modp.h.orig src/sage/rings/bernmm/bern_modp.h
--- src/sage/rings/bernmm/bern_modp.h.orig	2015-10-11 18:17:42.820860675 -0300
+++ src/sage/rings/bernmm/bern_modp.h	2015-10-11 18:20:53.453867975 -0300
@@ -12,6 +12,7 @@
 #ifndef BERNMM_BERN_MODP_H
 #define BERNMM_BERN_MODP_H
 
+#include <NTL/ZZ.h>
 
 namespace bernmm {
 
@@ -29,8 +30,8 @@ long bern_modp(long p, long k);
 /*
    Exported for testing.
 */
-long _bern_modp_powg(long p, double pinv, long k);
-long _bern_modp_pow2(long p, double pinv, long k);
+long _bern_modp_powg(long p, NTL::mulmod_t pinv, long k);
+long _bern_modp_pow2(long p, NTL::mulmod_t pinv, long k);
 
 
 };
diff -up src/sage/rings/bernmm/bern_modp_util.cpp.orig src/sage/rings/bernmm/bern_modp_util.cpp
--- src/sage/rings/bernmm/bern_modp_util.cpp.orig	2015-10-11 18:17:42.825860675 -0300
+++ src/sage/rings/bernmm/bern_modp_util.cpp	2015-10-11 18:21:24.653869170 -0300
@@ -20,7 +20,7 @@ NTL_CLIENT;
 namespace bernmm {
 
 
-long PowerMod(long a, long ee, long n, double ninv)
+long PowerMod(long a, long ee, long n, mulmod_t ninv)
 {
    long x, y;
 
@@ -89,7 +89,7 @@ PrimeTable::PrimeTable(long bound)
 }
 
 
-long order(long x, long p, double pinv, const Factorisation& F)
+long order(long x, long p, mulmod_t pinv, const Factorisation& F)
 {
    // in the loop below, m is always some multiple of the order of x
    long m = p - 1;
@@ -113,7 +113,7 @@ long order(long x, long p, double pinv,
 
 
 
-long primitive_root(long p, double pinv, const Factorisation& F)
+long primitive_root(long p, mulmod_t pinv, const Factorisation& F)
 {
    if (p == 2)
       return 1;
diff -up src/sage/rings/bernmm/bern_modp_util.h.orig src/sage/rings/bernmm/bern_modp_util.h
--- src/sage/rings/bernmm/bern_modp_util.h.orig	2015-10-11 18:17:42.830860676 -0300
+++ src/sage/rings/bernmm/bern_modp_util.h	2015-10-11 18:21:58.044870449 -0300
@@ -17,6 +17,7 @@
 #include <vector>
 #include <cassert>
 #include <climits>
+#include <NTL/ZZ.h>
 
 
 #if ULONG_MAX == 4294967295U
@@ -39,7 +40,7 @@ namespace bernmm {
 
    (Implementation is adapted from ZZ.c in NTL 5.4.1.)
 */
-long PowerMod(long a, long ee, long n, double ninv);
+long PowerMod(long a, long ee, long n, NTL::mulmod_t ninv);
 
 
 /*
@@ -123,13 +124,13 @@ long next_prime(long p);
 /*
    Computes order of x mod p, given the factorisation F of p-1.
 */
-long order(long x, long p, double pinv, const Factorisation& F);
+long order(long x, long p, NTL::mulmod_t pinv, const Factorisation& F);
 
 
 /*
    Finds the smallest primitive root mod p, given the factorisation F of p-1.
 */
-long primitive_root(long p, double pinv, const Factorisation& F);
+long primitive_root(long p, NTL::mulmod_t pinv, const Factorisation& F);
 
 
 };    // end namespace
diff -up src/sage/rings/bernmm/bern_modp.cpp.orig src/sage/rings/bernmm/bern_modp.cpp
--- src/sage/rings/bernmm/bern_modp.cpp.orig	2015-11-02 23:58:56.669503117 -0200
+++ src/sage/rings/bernmm/bern_modp.cpp	2015-11-02 23:59:15.683503846 -0200
@@ -717,7 +717,7 @@ long _bern_modp_pow2(long p, mulmod_t pi
       2 <= k <= p-3, k even
       pinv = 1 / ((double) p)
 */
-long _bern_modp(long p, double pinv, long k)
+long _bern_modp(long p, mulmod_t pinv, long k)
 {
    if (PowerMod(2, k, p, pinv) != 1)
       // 2^k != 1 mod p, so we use the faster version