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clamscan/libclamav/tomsfastmath/mont/fp_montgomery_calc_normalization.c

@@ -0,0 +1,43 @@
+/* TomsFastMath, a fast ISO C bignum library.
+ * 
+ * This project is meant to fill in where LibTomMath
+ * falls short.  That is speed ;-)
+ *
+ * This project is public domain and free for all purposes.
+ * 
+ * Tom St Denis, tomstdenis@gmail.com
+ */
+#include "bignum_fast.h"
+
+/* computes a = B**n mod b without division or multiplication useful for
+ * normalizing numbers in a Montgomery system.
+ */
+void fp_montgomery_calc_normalization(fp_int *a, fp_int *b)
+{
+  int     x, bits;
+
+  /* how many bits of last digit does b use */
+  bits = fp_count_bits (b) % DIGIT_BIT;
+  if (!bits) bits = DIGIT_BIT;
+
+  /* compute A = B^(n-1) * 2^(bits-1) */
+  if (b->used > 1) {
+     fp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1);
+  } else {
+     fp_set(a, 1);
+     bits = 1;
+  }
+
+  /* now compute C = A * B mod b */
+  for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
+    fp_mul_2 (a, a);
+    if (fp_cmp_mag (a, b) != FP_LT) {
+      s_fp_sub (a, b, a);
+    }
+  }
+}
+
+
+/* $Source: /cvs/libtom/tomsfastmath/src/mont/fp_montgomery_calc_normalization.c,v $ */
+/* $Revision: 1.1 $ */
+/* $Date: 2006/12/31 21:25:53 $ */

clamscan/libclamav/tomsfastmath/mont/fp_montgomery_reduce.c

@@ -0,0 +1,556 @@
+/* TomsFastMath, a fast ISO C bignum library.
+ * 
+ * This project is meant to fill in where LibTomMath
+ * falls short.  That is speed ;-)
+ *
+ * This project is public domain and free for all purposes.
+ * 
+ * Tom St Denis, tomstdenis@gmail.com
+ */
+#include "bignum_fast.h"
+
+/******************************************************************/
+#if defined(TFM_X86) && !defined(TFM_SSE2) 
+/* x86-32 code */
+
+#define MONT_START 
+#define MONT_FINI
+#define LOOP_END
+#define LOOP_START \
+   mu = c[x] * mp
+
+#define INNERMUL                                          \
+asm(                                                      \
+   "movl %5,%%eax \n\t"                                   \
+   "mull %4       \n\t"                                   \
+   "addl %1,%%eax \n\t"                                   \
+   "adcl $0,%%edx \n\t"                                   \
+   "addl %%eax,%0 \n\t"                                   \
+   "adcl $0,%%edx \n\t"                                   \
+   "movl %%edx,%1 \n\t"                                   \
+:"=g"(_c[LO]), "=r"(cy)                                   \
+:"0"(_c[LO]), "1"(cy), "g"(mu), "g"(*tmpm++)              \
+: "%eax", "%edx", "cc")
+
+#define PROPCARRY                           \
+asm(                                        \
+   "addl   %1,%0    \n\t"                   \
+   "setb   %%al     \n\t"                   \
+   "movzbl %%al,%1 \n\t"                    \
+:"=g"(_c[LO]), "=r"(cy)                     \
+:"0"(_c[LO]), "1"(cy)                       \
+: "%eax", "cc")
+
+/******************************************************************/
+#elif defined(TFM_X86_64)
+/* x86-64 code */
+
+#define MONT_START 
+#define MONT_FINI
+#define LOOP_END
+#define LOOP_START \
+   mu = c[x] * mp
+
+#define INNERMUL                                          \
+asm(                                                      \
+   "movq %5,%%rax \n\t"                                   \
+   "mulq %4       \n\t"                                   \
+   "addq %1,%%rax \n\t"                                   \
+   "adcq $0,%%rdx \n\t"                                   \
+   "addq %%rax,%0 \n\t"                                   \
+   "adcq $0,%%rdx \n\t"                                   \
+   "movq %%rdx,%1 \n\t"                                   \
+:"=g"(_c[LO]), "=r"(cy)                                   \
+:"0"(_c[LO]), "1"(cy), "r"(mu), "r"(*tmpm++)              \
+: "%rax", "%rdx", "cc")
+
+#define INNERMUL8 \
+ asm(                  \
+ "movq 0(%5),%%rax    \n\t"  \
+ "movq 0(%2),%%r10    \n\t"  \
+ "movq 0x8(%5),%%r11  \n\t"  \
+ "mulq %4             \n\t"  \
+ "addq %%r10,%%rax    \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq 0x8(%2),%%r10  \n\t"  \
+ "addq %3,%%rax       \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq %%rax,0(%0)    \n\t"  \
+ "movq %%rdx,%1       \n\t"  \
+ \
+ "movq %%r11,%%rax    \n\t"  \
+ "movq 0x10(%5),%%r11 \n\t"  \
+ "mulq %4             \n\t"  \
+ "addq %%r10,%%rax    \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq 0x10(%2),%%r10 \n\t"  \
+ "addq %3,%%rax       \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq %%rax,0x8(%0)  \n\t"  \
+ "movq %%rdx,%1       \n\t"  \
+ \
+ "movq %%r11,%%rax    \n\t"  \
+ "movq 0x18(%5),%%r11 \n\t"  \
+ "mulq %4             \n\t"  \
+ "addq %%r10,%%rax    \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq 0x18(%2),%%r10 \n\t"  \
+ "addq %3,%%rax       \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq %%rax,0x10(%0) \n\t"  \
+ "movq %%rdx,%1       \n\t"  \
+ \
+ "movq %%r11,%%rax    \n\t"  \
+ "movq 0x20(%5),%%r11 \n\t"  \
+ "mulq %4             \n\t"  \
+ "addq %%r10,%%rax    \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq 0x20(%2),%%r10 \n\t"  \
+ "addq %3,%%rax       \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq %%rax,0x18(%0) \n\t"  \
+ "movq %%rdx,%1       \n\t"  \
+ \
+ "movq %%r11,%%rax    \n\t"  \
+ "movq 0x28(%5),%%r11 \n\t"  \
+ "mulq %4             \n\t"  \
+ "addq %%r10,%%rax    \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq 0x28(%2),%%r10 \n\t"  \
+ "addq %3,%%rax       \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq %%rax,0x20(%0) \n\t"  \
+ "movq %%rdx,%1       \n\t"  \
+ \
+ "movq %%r11,%%rax    \n\t"  \
+ "movq 0x30(%5),%%r11 \n\t"  \
+ "mulq %4             \n\t"  \
+ "addq %%r10,%%rax    \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq 0x30(%2),%%r10 \n\t"  \
+ "addq %3,%%rax       \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq %%rax,0x28(%0) \n\t"  \
+ "movq %%rdx,%1       \n\t"  \
+ \
+ "movq %%r11,%%rax    \n\t"  \
+ "movq 0x38(%5),%%r11 \n\t"  \
+ "mulq %4             \n\t"  \
+ "addq %%r10,%%rax    \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq 0x38(%2),%%r10 \n\t"  \
+ "addq %3,%%rax       \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq %%rax,0x30(%0) \n\t"  \
+ "movq %%rdx,%1       \n\t"  \
+ \
+ "movq %%r11,%%rax    \n\t"  \
+ "mulq %4             \n\t"  \
+ "addq %%r10,%%rax    \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "addq %3,%%rax       \n\t"  \
+ "adcq $0,%%rdx       \n\t"  \
+ "movq %%rax,0x38(%0) \n\t"  \
+ "movq %%rdx,%1       \n\t"  \
+ \
+:"=r"(_c), "=r"(cy)                    \
+: "0"(_c),  "1"(cy), "g"(mu), "r"(tmpm)\
+: "%rax", "%rdx", "%r10", "%r11", "cc")
+
+
+#define PROPCARRY                           \
+asm(                                        \
+   "addq   %1,%0    \n\t"                   \
+   "setb   %%al     \n\t"                   \
+   "movzbq %%al,%1 \n\t"                    \
+:"=g"(_c[LO]), "=r"(cy)                     \
+:"0"(_c[LO]), "1"(cy)                       \
+: "%rax", "cc")
+
+/******************************************************************/
+#elif defined(TFM_SSE2)  
+/* SSE2 code (assumes 32-bit fp_digits) */
+/* XMM register assignments:
+ * xmm0  *tmpm++, then Mu * (*tmpm++)
+ * xmm1  c[x], then Mu
+ * xmm2  mp
+ * xmm3  cy
+ * xmm4  _c[LO]
+ */
+
+#define MONT_START \
+   asm("movd %0,%%mm2"::"g"(mp))
+
+#define MONT_FINI \
+   asm("emms")
+
+#define LOOP_START          \
+asm(                        \
+"movd %0,%%mm1        \n\t" \
+"pxor %%mm3,%%mm3     \n\t" \
+"pmuludq %%mm2,%%mm1  \n\t" \
+:: "g"(c[x]))
+
+/* pmuludq on mmx registers does a 32x32->64 multiply. */
+#define INNERMUL               \
+asm(                           \
+   "movd %1,%%mm4        \n\t" \
+   "movd %2,%%mm0        \n\t" \
+   "paddq %%mm4,%%mm3    \n\t" \
+   "pmuludq %%mm1,%%mm0  \n\t" \
+   "paddq %%mm0,%%mm3    \n\t" \
+   "movd %%mm3,%0        \n\t" \
+   "psrlq $32, %%mm3     \n\t" \
+:"=g"(_c[LO]) : "0"(_c[LO]), "g"(*tmpm++) );
+
+#define INNERMUL8 \
+asm(                           \
+   "movd 0(%1),%%mm4     \n\t" \
+   "movd 0(%2),%%mm0     \n\t" \
+   "paddq %%mm4,%%mm3    \n\t" \
+   "pmuludq %%mm1,%%mm0  \n\t" \
+   "movd 4(%2),%%mm5     \n\t" \
+   "paddq %%mm0,%%mm3    \n\t" \
+   "movd 4(%1),%%mm6     \n\t" \
+   "movd %%mm3,0(%0)     \n\t" \
+   "psrlq $32, %%mm3     \n\t" \
+\
+   "paddq %%mm6,%%mm3    \n\t" \
+   "pmuludq %%mm1,%%mm5  \n\t" \
+   "movd 8(%2),%%mm6     \n\t" \
+   "paddq %%mm5,%%mm3    \n\t" \
+   "movd 8(%1),%%mm7     \n\t" \
+   "movd %%mm3,4(%0)     \n\t" \
+   "psrlq $32, %%mm3     \n\t" \
+\
+   "paddq %%mm7,%%mm3    \n\t" \
+   "pmuludq %%mm1,%%mm6  \n\t" \
+   "movd 12(%2),%%mm7    \n\t" \
+   "paddq %%mm6,%%mm3    \n\t" \
+   "movd 12(%1),%%mm5     \n\t" \
+   "movd %%mm3,8(%0)     \n\t" \
+   "psrlq $32, %%mm3     \n\t" \
+\
+   "paddq %%mm5,%%mm3    \n\t" \
+   "pmuludq %%mm1,%%mm7  \n\t" \
+   "movd 16(%2),%%mm5    \n\t" \
+   "paddq %%mm7,%%mm3    \n\t" \
+   "movd 16(%1),%%mm6    \n\t" \
+   "movd %%mm3,12(%0)    \n\t" \
+   "psrlq $32, %%mm3     \n\t" \
+\
+   "paddq %%mm6,%%mm3    \n\t" \
+   "pmuludq %%mm1,%%mm5  \n\t" \
+   "movd 20(%2),%%mm6    \n\t" \
+   "paddq %%mm5,%%mm3    \n\t" \
+   "movd 20(%1),%%mm7    \n\t" \
+   "movd %%mm3,16(%0)    \n\t" \
+   "psrlq $32, %%mm3     \n\t" \
+\
+   "paddq %%mm7,%%mm3    \n\t" \
+   "pmuludq %%mm1,%%mm6  \n\t" \
+   "movd 24(%2),%%mm7    \n\t" \
+   "paddq %%mm6,%%mm3    \n\t" \
+   "movd 24(%1),%%mm5     \n\t" \
+   "movd %%mm3,20(%0)    \n\t" \
+   "psrlq $32, %%mm3     \n\t" \
+\
+   "paddq %%mm5,%%mm3    \n\t" \
+   "pmuludq %%mm1,%%mm7  \n\t" \
+   "movd 28(%2),%%mm5    \n\t" \
+   "paddq %%mm7,%%mm3    \n\t" \
+   "movd 28(%1),%%mm6    \n\t" \
+   "movd %%mm3,24(%0)    \n\t" \
+   "psrlq $32, %%mm3     \n\t" \
+\
+   "paddq %%mm6,%%mm3    \n\t" \
+   "pmuludq %%mm1,%%mm5  \n\t" \
+   "paddq %%mm5,%%mm3    \n\t" \
+   "movd %%mm3,28(%0)    \n\t" \
+   "psrlq $32, %%mm3     \n\t" \
+:"=r"(_c) : "0"(_c), "g"(tmpm) );
+
+#define LOOP_END \
+asm( "movd %%mm3,%0  \n" :"=r"(cy))
+
+#define PROPCARRY                           \
+asm(                                        \
+   "addl   %1,%0    \n\t"                   \
+   "setb   %%al     \n\t"                   \
+   "movzbl %%al,%1 \n\t"                    \
+:"=g"(_c[LO]), "=r"(cy)                     \
+:"0"(_c[LO]), "1"(cy)                       \
+: "%eax", "cc")
+
+/******************************************************************/
+#elif defined(TFM_ARM)
+   /* ARMv4 code */
+
+#define MONT_START 
+#define MONT_FINI
+#define LOOP_END
+#define LOOP_START \
+   mu = c[x] * mp
+
+#define INNERMUL                    \
+asm(                                \
+    " LDR    r0,%1            \n\t" \
+    " ADDS   r0,r0,%0         \n\t" \
+    " MOVCS  %0,#1            \n\t" \
+    " MOVCC  %0,#0            \n\t" \
+    " UMLAL  r0,%0,%3,%4      \n\t" \
+    " STR    r0,%1            \n\t" \
+:"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(*tmpm++),"1"(_c[0]):"r0","cc");
+
+#define PROPCARRY                  \
+asm(                               \
+    " LDR   r0,%1            \n\t" \
+    " ADDS  r0,r0,%0         \n\t" \
+    " STR   r0,%1            \n\t" \
+    " MOVCS %0,#1            \n\t" \
+    " MOVCC %0,#0            \n\t" \
+:"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"r0","cc");
+
+/******************************************************************/
+#elif defined(TFM_PPC32)
+
+/* PPC32 */
+#define MONT_START 
+#define MONT_FINI
+#define LOOP_END
+#define LOOP_START \
+   mu = c[x] * mp
+
+#define INNERMUL                     \
+asm(                                 \
+   " mullw    16,%3,%4       \n\t"   \
+   " mulhwu   17,%3,%4       \n\t"   \
+   " addc     16,16,%0       \n\t"   \
+   " addze    17,17          \n\t"   \
+   " lwz      18,%1          \n\t"   \
+   " addc     16,16,18       \n\t"   \
+   " addze    %0,17          \n\t"   \
+   " stw      16,%1          \n\t"   \
+:"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(tmpm[0]),"1"(_c[0]):"16", "17", "18","cc"); ++tmpm;
+
+#define PROPCARRY                    \
+asm(                                 \
+   " lwz      16,%1         \n\t"    \
+   " addc     16,16,%0      \n\t"    \
+   " stw      16,%1         \n\t"    \
+   " xor      %0,%0,%0      \n\t"    \
+   " addze    %0,%0         \n\t"    \
+:"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"16","cc");
+
+/******************************************************************/
+#elif defined(TFM_PPC64)
+
+/* PPC64 */
+#define MONT_START 
+#define MONT_FINI
+#define LOOP_END
+#define LOOP_START \
+   mu = c[x] * mp
+
+#define INNERMUL                     \
+asm(                                 \
+   " mulld    r16,%3,%4       \n\t"   \
+   " mulhdu   r17,%3,%4       \n\t"   \
+   " addc     r16,16,%0       \n\t"   \
+   " addze    r17,r17          \n\t"   \
+   " ldx      r18,0,%1        \n\t"   \
+   " addc     r16,r16,r18       \n\t"   \
+   " addze    %0,r17          \n\t"   \
+   " sdx      r16,0,%1        \n\t"   \
+:"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(tmpm[0]),"1"(_c[0]):"r16", "r17", "r18","cc"); ++tmpm;
+
+#define PROPCARRY                    \
+asm(                                 \
+   " ldx      r16,0,%1       \n\t"    \
+   " addc     r16,r16,%0      \n\t"    \
+   " sdx      r16,0,%1       \n\t"    \
+   " xor      %0,%0,%0      \n\t"    \
+   " addze    %0,%0         \n\t"    \
+:"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"r16","cc");
+
+/******************************************************************/
+#elif defined(TFM_AVR32)
+
+/* AVR32 */
+#define MONT_START 
+#define MONT_FINI
+#define LOOP_END
+#define LOOP_START \
+   mu = c[x] * mp
+
+#define INNERMUL                    \
+asm(                                \
+    " ld.w   r2,%1            \n\t" \
+    " add    r2,%0            \n\t" \
+    " eor    r3,r3            \n\t" \
+    " acr    r3               \n\t" \
+    " macu.d r2,%3,%4         \n\t" \
+    " st.w   %1,r2            \n\t" \
+    " mov    %0,r3            \n\t" \
+:"=r"(cy),"=r"(_c):"0"(cy),"r"(mu),"r"(*tmpm++),"1"(_c):"r2","r3");
+
+#define PROPCARRY                    \
+asm(                                 \
+   " ld.w     r2,%1         \n\t"    \
+   " add      r2,%0         \n\t"    \
+   " st.w     %1,r2         \n\t"    \
+   " eor      %0,%0         \n\t"    \
+   " acr      %0            \n\t"    \
+:"=r"(cy),"=r"(&_c[0]):"0"(cy),"1"(&_c[0]):"r2","cc");
+
+/******************************************************************/
+#elif defined(TFM_MIPS)
+
+/* MIPS */
+#define MONT_START 
+#define MONT_FINI
+#define LOOP_END
+#define LOOP_START \
+   mu = c[x] * mp
+
+#define INNERMUL                     \
+asm(                                 \
+   " multu    %3,%4          \n\t"   \
+   " mflo     $12            \n\t"   \
+   " mfhi     $13            \n\t"   \
+   " addu     $12,$12,%0     \n\t"   \
+   " sltu     $10,$12,%0     \n\t"   \
+   " addu     $13,$13,$10    \n\t"   \
+   " lw       $10,%1         \n\t"   \
+   " addu     $12,$12,$10    \n\t"   \
+   " sltu     $10,$12,$10    \n\t"   \
+   " addu     %0,$13,$10     \n\t"   \
+   " sw       $12,%1         \n\t"   \
+:"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(tmpm[0]),"1"(_c[0]):"$10","$12","$13"); ++tmpm;
+
+#define PROPCARRY                    \
+asm(                                 \
+   " lw       $10,%1        \n\t"    \
+   " addu     $10,$10,%0    \n\t"    \
+   " sw       $10,%1        \n\t"    \
+   " sltu     %0,$10,%0     \n\t"    \
+:"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"$10");
+
+/******************************************************************/
+#else
+
+/* ISO C code */
+#define MONT_START 
+#define MONT_FINI
+#define LOOP_END
+#define LOOP_START \
+   mu = c[x] * mp
+
+#define INNERMUL                                      \
+   do { fp_word t;                                    \
+   _c[0] = t  = ((fp_word)_c[0] + (fp_word)cy) +      \
+                (((fp_word)mu) * ((fp_word)*tmpm++)); \
+   cy = (t >> DIGIT_BIT);                             \
+   } while (0)
+
+#define PROPCARRY \
+   do { fp_digit t = _c[0] += cy; cy = (t < cy); } while (0)
+
+#endif
+/******************************************************************/
+
+
+#define LO  0
+
+#ifdef TFM_SMALL_MONT_SET
+#include "fp_mont_small.i"
+#endif
+
+/* computes x/R == x (mod N) via Montgomery Reduction */
+void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
+{
+   fp_digit c[FP_SIZE], *_c, *tmpm, mu;
+   int      oldused, x, y, pa;
+
+   /* bail if too large */
+   if (m->used > (FP_SIZE/2)) {
+      return;
+   }
+
+#ifdef TFM_SMALL_MONT_SET
+   if (m->used <= 16) {
+      fp_montgomery_reduce_small(a, m, mp);
+      return;
+   }
+#endif
+
+#if defined(USE_MEMSET)
+   /* now zero the buff */
+   memset(c, 0, sizeof c);
+#endif
+   pa = m->used;
+
+   /* copy the input */
+   oldused = a->used;
+   for (x = 0; x < oldused; x++) {
+       c[x] = a->dp[x];
+   }
+#if !defined(USE_MEMSET)
+   for (; x < 2*pa+1; x++) {
+       c[x] = 0;
+   }
+#endif
+   MONT_START;
+
+   for (x = 0; x < pa; x++) {
+       fp_digit cy = 0;
+       /* get Mu for this round */
+       LOOP_START;
+       _c   = c + x;
+       tmpm = m->dp;
+       y = 0;
+       #if (defined(TFM_SSE2) || defined(TFM_X86_64))
+        for (; y < (pa & ~7); y += 8) {
+              INNERMUL8;
+              _c   += 8;
+              tmpm += 8;
+           }
+       #endif
+
+       for (; y < pa; y++) {
+          INNERMUL;
+          ++_c;
+       }
+       LOOP_END;
+       while (cy) {
+           PROPCARRY;
+           ++_c;
+       }
+  }         
+
+  /* now copy out */
+  _c   = c + pa;
+  tmpm = a->dp;
+  for (x = 0; x < pa+1; x++) {
+     *tmpm++ = *_c++;
+  }
+
+  for (; x < oldused; x++)   {
+     *tmpm++ = 0;
+  }
+
+  MONT_FINI;
+
+  a->used = pa+1;
+  fp_clamp(a);
+  
+  /* if A >= m then A = A - m */
+  if (fp_cmp_mag (a, m) != FP_LT) {
+    s_fp_sub (a, m, a);
+  }
+}
+
+
+/* $Source: /cvs/libtom/tomsfastmath/src/mont/fp_montgomery_reduce.c,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2007/03/14 23:47:42 $ */

clamscan/libclamav/tomsfastmath/mont/fp_montgomery_setup.c

@@ -0,0 +1,48 @@
+/* TomsFastMath, a fast ISO C bignum library.
+ * 
+ * This project is meant to fill in where LibTomMath
+ * falls short.  That is speed ;-)
+ *
+ * This project is public domain and free for all purposes.
+ * 
+ * Tom St Denis, tomstdenis@gmail.com
+ */
+#include "bignum_fast.h"
+
+/* setups the montgomery reduction */
+int fp_montgomery_setup(fp_int *a, fp_digit *rho)
+{
+  fp_digit x, b;
+
+/* fast inversion mod 2**k
+ *
+ * Based on the fact that
+ *
+ * XA = 1 (mod 2**n)  =>  (X(2-XA)) A = 1 (mod 2**2n)
+ *                    =>  2*X*A - X*X*A*A = 1
+ *                    =>  2*(1) - (1)     = 1
+ */
+  b = a->dp[0];
+
+  if ((b & 1) == 0) {
+    return FP_VAL;
+  }
+
+  x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
+  x *= 2 - b * x;               /* here x*a==1 mod 2**8 */
+  x *= 2 - b * x;               /* here x*a==1 mod 2**16 */
+  x *= 2 - b * x;               /* here x*a==1 mod 2**32 */
+#ifdef FP_64BIT
+  x *= 2 - b * x;               /* here x*a==1 mod 2**64 */
+#endif
+
+  /* rho = -1/m mod b */
+  *rho = (((fp_word) 1 << ((fp_word) DIGIT_BIT)) - ((fp_word)x));
+
+  return FP_OKAY;
+}
+
+
+/* $Source: /cvs/libtom/tomsfastmath/src/mont/fp_montgomery_setup.c,v $ */
+/* $Revision: 1.1 $ */
+/* $Date: 2006/12/31 21:25:53 $ */