bignum module wrapper for kokke/tiny-bignum-c

thirdparty/bignum/README.md

@@ -0,0 +1,2 @@
+This folder contains bn.h and bn.c files
+from https://github.com/kokke/tiny-bignum-c

thirdparty/bignum/bn.c

@@ -0,0 +1,664 @@
+/*
+
+Big number library - arithmetic on multiple-precision unsigned integers.
+
+This library is an implementation of arithmetic on arbitrarily large integers.
+
+The difference between this and other implementations, is that the data structure
+has optimal memory utilization (i.e. a 1024 bit integer takes up 128 bytes RAM),
+and all memory is allocated statically: no dynamic allocation for better or worse.
+
+Primary goals are correctness, clarity of code and clean, portable implementation.
+Secondary goal is a memory footprint small enough to make it suitable for use in
+embedded applications.
+
+
+The current state is correct functionality and adequate performance.
+There may well be room for performance-optimizations and improvements.
+
+*/
+
+#include <stdio.h>
+#include <stdbool.h>
+#include <assert.h>
+#include "bn.h"
+
+
+
+/* Functions for shifting number in-place. */
+static void _lshift_one_bit(struct bn* a);
+static void _rshift_one_bit(struct bn* a);
+static void _lshift_word(struct bn* a, int nwords);
+static void _rshift_word(struct bn* a, int nwords);
+
+
+
+/* Public / Exported functions. */
+void bignum_init(struct bn* n)
+{
+  require(n, "n is null");
+
+  int i;
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    n->array[i] = 0;
+  }
+}
+
+
+void bignum_from_int(struct bn* n, DTYPE_TMP i)
+{
+  require(n, "n is null");
+
+  bignum_init(n);
+
+  /* Endianness issue if machine is not little-endian? */
+#ifdef WORD_SIZE
+ #if (WORD_SIZE == 1)
+  n->array[0] = (i & 0x000000ff);
+  n->array[1] = (i & 0x0000ff00) >> 8;
+  n->array[2] = (i & 0x00ff0000) >> 16;
+  n->array[3] = (i & 0xff000000) >> 24;
+ #elif (WORD_SIZE == 2)
+  n->array[0] = (i & 0x0000ffff);
+  n->array[1] = (i & 0xffff0000) >> 16;
+ #elif (WORD_SIZE == 4)
+  n->array[0] = i;
+  DTYPE_TMP num_32 = 32;
+  DTYPE_TMP tmp = i >> num_32; /* bit-shift with U64 operands to force 64-bit results */
+  n->array[1] = tmp;
+ #endif
+#endif
+}
+
+
+int bignum_to_int(struct bn* n)
+{
+  require(n, "n is null");
+
+  int ret = 0;
+
+  /* Endianness issue if machine is not little-endian? */
+#if (WORD_SIZE == 1)
+  ret += n->array[0];
+  ret += n->array[1] << 8;
+  ret += n->array[2] << 16;
+  ret += n->array[3] << 24;  
+#elif (WORD_SIZE == 2)
+  ret += n->array[0];
+  ret += n->array[1] << 16;
+#elif (WORD_SIZE == 4)
+  ret += n->array[0];
+#endif
+
+  return ret;
+}
+
+
+void bignum_from_string(struct bn* n, char* str, int nbytes)
+{
+  require(n, "n is null");
+  require(str, "str is null");
+  require(nbytes > 0, "nbytes must be positive");
+  require((nbytes & 1) == 0, "string format must be in hex -> equal number of bytes");
+
+  bignum_init(n);
+
+  DTYPE tmp;                        /* DTYPE is defined in bn.h - uint{8,16,32,64}_t */
+  int i = nbytes - (2 * WORD_SIZE); /* index into string */
+  int j = 0;                        /* index into array */
+
+  /* reading last hex-byte "MSB" from string first -> big endian */
+  /* MSB ~= most significant byte / block ? :) */
+  while (i >= 0)
+  {
+    tmp = 0;
+    sscanf(&str[i], SSCANF_FORMAT_STR, &tmp);
+    n->array[j] = tmp;
+    i -= (2 * WORD_SIZE); /* step WORD_SIZE hex-byte(s) back in the string. */
+    j += 1;               /* step one element forward in the array. */
+  }
+}
+
+
+void bignum_to_string(struct bn* n, char* str, int nbytes)
+{
+  require(n, "n is null");
+  require(str, "str is null");
+  require(nbytes > 0, "nbytes must be positive");
+  require((nbytes & 1) == 0, "string format must be in hex -> equal number of bytes");
+
+  int j = BN_ARRAY_SIZE - 1; /* index into array - reading "MSB" first -> big-endian */
+  int i = 0;                 /* index into string representation. */
+
+  /* reading last array-element "MSB" first -> big endian */
+  while ((j >= 0) && (nbytes > (i + 1)))
+  {
+    sprintf(&str[i], SPRINTF_FORMAT_STR, n->array[j]);
+    i += (2 * WORD_SIZE); /* step WORD_SIZE hex-byte(s) forward in the string. */
+    j -= 1;               /* step one element back in the array. */
+  }
+
+  /* Count leading zeros: */
+  j = 0;
+  while (str[j] == '0')
+  {
+    j += 1;
+  }
+ 
+  /* Move string j places ahead, effectively skipping leading zeros */ 
+  for (i = 0; i < (nbytes - j); ++i)
+  {
+    str[i] = str[i + j];
+  }
+
+  /* Zero-terminate string */
+  str[i] = 0;
+}
+
+
+void bignum_dec(struct bn* n)
+{
+  require(n, "n is null");
+
+  DTYPE tmp; /* copy of n */
+  DTYPE res;
+
+  int i;
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    tmp = n->array[i];
+    res = tmp - 1;
+    n->array[i] = res;
+
+    if (!(res > tmp))
+    {
+      break;
+    }
+  }
+}
+
+
+void bignum_inc(struct bn* n)
+{
+  require(n, "n is null");
+
+  DTYPE res;
+  DTYPE_TMP tmp; /* copy of n */
+
+  int i;
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    tmp = n->array[i];
+    res = tmp + 1;
+    n->array[i] = res;
+
+    if (res > tmp)
+    {
+      break;
+    }
+  }
+}
+
+
+void bignum_add(struct bn* a, struct bn* b, struct bn* c)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+  require(c, "c is null");
+
+  DTYPE_TMP tmp;
+  int carry = 0;
+  int i;
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    tmp = (DTYPE_TMP)a->array[i] + b->array[i] + carry;
+    carry = (tmp > MAX_VAL);
+    c->array[i] = (tmp & MAX_VAL);
+  }
+}
+
+
+void bignum_sub(struct bn* a, struct bn* b, struct bn* c)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+  require(c, "c is null");
+
+  DTYPE_TMP res;
+  DTYPE_TMP tmp1;
+  DTYPE_TMP tmp2;
+  int borrow = 0;
+  int i;
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    tmp1 = (DTYPE_TMP)a->array[i] + (MAX_VAL + 1); /* + number_base */
+    tmp2 = (DTYPE_TMP)b->array[i] + borrow;;
+    res = (tmp1 - tmp2);
+    c->array[i] = (DTYPE)(res & MAX_VAL); /* "modulo number_base" == "% (number_base - 1)" if number_base is 2^N */
+    borrow = (res <= MAX_VAL);
+  }
+}
+
+
+void bignum_mul(struct bn* a, struct bn* b, struct bn* c)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+  require(c, "c is null");
+
+  struct bn row;
+  struct bn tmp;
+  int i, j;
+
+  bignum_init(c);
+
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    bignum_init(&row);
+
+    for (j = 0; j < BN_ARRAY_SIZE; ++j)
+    {
+      if (i + j < BN_ARRAY_SIZE)
+      {
+        bignum_init(&tmp);
+        DTYPE_TMP intermediate = ((DTYPE_TMP)a->array[i] * (DTYPE_TMP)b->array[j]);
+        bignum_from_int(&tmp, intermediate);
+        _lshift_word(&tmp, i + j);
+        bignum_add(&tmp, &row, &row);
+      }
+    }
+    bignum_add(c, &row, c);
+  }
+}
+
+
+void bignum_div(struct bn* a, struct bn* b, struct bn* c)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+  require(c, "c is null");
+
+  struct bn current;
+  struct bn denom;
+  struct bn tmp;
+
+  bignum_from_int(&current, 1);               // int current = 1;
+  bignum_assign(&denom, b);                   // denom = b
+  bignum_assign(&tmp, a);                     // tmp   = a
+
+  const DTYPE_TMP half_max = 1 + (DTYPE_TMP)(MAX_VAL / 2);
+  bool overflow = false;
+  while (bignum_cmp(&denom, a) != LARGER)     // while (denom <= a) {
+  {
+    if (denom.array[BN_ARRAY_SIZE - 1] >= half_max)
+    {
+      overflow = true;
+      break;
+    }
+    _lshift_one_bit(&current);                //   current <<= 1;
+    _lshift_one_bit(&denom);                  //   denom <<= 1;
+  }
+  if (!overflow)
+  {
+    _rshift_one_bit(&denom);                  // denom >>= 1;
+    _rshift_one_bit(&current);                // current >>= 1;
+  }
+  bignum_init(c);                             // int answer = 0;
+
+  while (!bignum_is_zero(&current))           // while (current != 0)
+  {
+    if (bignum_cmp(&tmp, &denom) != SMALLER)  //   if (dividend >= denom)
+    {
+      bignum_sub(&tmp, &denom, &tmp);         //     dividend -= denom;
+      bignum_or(c, &current, c);              //     answer |= current;
+    }
+    _rshift_one_bit(&current);                //   current >>= 1;
+    _rshift_one_bit(&denom);                  //   denom >>= 1;
+  }                                           // return answer;
+}
+
+
+void bignum_lshift(struct bn* a, struct bn* b, int nbits)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+  require(nbits >= 0, "no negative shifts");
+
+  bignum_assign(b, a);
+  /* Handle shift in multiples of word-size */
+  const int nbits_pr_word = (WORD_SIZE * 8);
+  int nwords = nbits / nbits_pr_word;
+  if (nwords != 0)
+  {
+    _lshift_word(b, nwords);
+    nbits -= (nwords * nbits_pr_word);
+  }
+
+  if (nbits != 0)
+  {
+    int i;
+    for (i = (BN_ARRAY_SIZE - 1); i > 0; --i)
+    {
+      b->array[i] = (b->array[i] << nbits) | (b->array[i - 1] >> ((8 * WORD_SIZE) - nbits));
+    }
+    b->array[i] <<= nbits;
+  }
+}
+
+
+void bignum_rshift(struct bn* a, struct bn* b, int nbits)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+  require(nbits >= 0, "no negative shifts");
+  
+  bignum_assign(b, a);
+  /* Handle shift in multiples of word-size */
+  const int nbits_pr_word = (WORD_SIZE * 8);
+  int nwords = nbits / nbits_pr_word;
+  if (nwords != 0)
+  {
+    _rshift_word(b, nwords);
+    nbits -= (nwords * nbits_pr_word);
+  }
+
+  if (nbits != 0)
+  {
+    int i;
+    for (i = 0; i < (BN_ARRAY_SIZE - 1); ++i)
+    {
+      b->array[i] = (b->array[i] >> nbits) | (b->array[i + 1] << ((8 * WORD_SIZE) - nbits));
+    }
+    b->array[i] >>= nbits;
+  }
+  
+}
+
+
+void bignum_mod(struct bn* a, struct bn* b, struct bn* c)
+{
+  /*
+    Take divmod and throw away div part
+  */
+  require(a, "a is null");
+  require(b, "b is null");
+  require(c, "c is null");
+
+  struct bn tmp;
+
+  bignum_divmod(a,b,&tmp,c);
+}
+
+void bignum_divmod(struct bn* a, struct bn* b, struct bn* c, struct bn* d)
+{
+  /*
+    Puts a%b in d
+    and a/b in c
+
+    mod(a,b) = a - ((a / b) * b)
+
+    example:
+      mod(8, 3) = 8 - ((8 / 3) * 3) = 2
+  */
+  require(a, "a is null");
+  require(b, "b is null");
+  require(c, "c is null");
+
+  struct bn tmp;
+
+  /* c = (a / b) */
+  bignum_div(a, b, c);
+
+  /* tmp = (c * b) */
+  bignum_mul(c, b, &tmp);
+
+  /* c = a - tmp */
+  bignum_sub(a, &tmp, d);
+}
+
+
+void bignum_and(struct bn* a, struct bn* b, struct bn* c)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+  require(c, "c is null");
+
+  int i;
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    c->array[i] = (a->array[i] & b->array[i]);
+  }
+}
+
+
+void bignum_or(struct bn* a, struct bn* b, struct bn* c)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+  require(c, "c is null");
+
+  int i;
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    c->array[i] = (a->array[i] | b->array[i]);
+  }
+}
+
+
+void bignum_xor(struct bn* a, struct bn* b, struct bn* c)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+  require(c, "c is null");
+
+  int i;
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    c->array[i] = (a->array[i] ^ b->array[i]);
+  }
+}
+
+
+int bignum_cmp(struct bn* a, struct bn* b)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+
+  int i = BN_ARRAY_SIZE;
+  do
+  {
+    i -= 1; /* Decrement first, to start with last array element */
+    if (a->array[i] > b->array[i])
+    {
+      return LARGER;
+    }
+    else if (a->array[i] < b->array[i])
+    {
+      return SMALLER;
+    }
+  }
+  while (i != 0);
+
+  return EQUAL;
+}
+
+
+int bignum_is_zero(struct bn* n)
+{
+  require(n, "n is null");
+
+  int i;
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    if (n->array[i])
+    {
+      return 0;
+    }
+  }
+
+  return 1;
+}
+
+
+void bignum_pow(struct bn* a, struct bn* b, struct bn* c)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+  require(c, "c is null");
+
+  struct bn tmp;
+
+  bignum_init(c);
+
+  if (bignum_cmp(b, c) == EQUAL)
+  {
+    /* Return 1 when exponent is 0 -- n^0 = 1 */
+    bignum_inc(c);
+  }
+  else
+  {
+    struct bn bcopy;
+    bignum_assign(&bcopy, b);
+
+    /* Copy a -> tmp */
+    bignum_assign(&tmp, a);
+
+    bignum_dec(&bcopy);
+ 
+    /* Begin summing products: */
+    while (!bignum_is_zero(&bcopy))
+    {
+
+      /* c = tmp * tmp */
+      bignum_mul(&tmp, a, c);
+      /* Decrement b by one */
+      bignum_dec(&bcopy);
+
+      bignum_assign(&tmp, c);
+    }
+
+    /* c = tmp */
+    bignum_assign(c, &tmp);
+  }
+}
+
+void bignum_isqrt(struct bn *a, struct bn* b)
+{
+  require(a, "a is null");
+  require(b, "b is null");
+
+  struct bn low, high, mid, tmp;
+
+  bignum_init(&low);
+  bignum_assign(&high, a);
+  bignum_rshift(&high, &mid, 1);
+  bignum_inc(&mid);
+
+  while (bignum_cmp(&high, &low) > 0) 
+  {
+    bignum_mul(&mid, &mid, &tmp);
+    if (bignum_cmp(&tmp, a) > 0) 
+    {
+      bignum_assign(&high, &mid);
+      bignum_dec(&high);
+    }
+    else 
+    {
+      bignum_assign(&low, &mid);
+    }
+    bignum_sub(&high,&low,&mid);
+    _rshift_one_bit(&mid);
+    bignum_add(&low,&mid,&mid);
+    bignum_inc(&mid);
+  }
+  bignum_assign(b,&low);
+}
+
+
+void bignum_assign(struct bn* dst, struct bn* src)
+{
+  require(dst, "dst is null");
+  require(src, "src is null");
+
+  int i;
+  for (i = 0; i < BN_ARRAY_SIZE; ++i)
+  {
+    dst->array[i] = src->array[i];
+  }
+}
+
+
+/* Private / Static functions. */
+static void _rshift_word(struct bn* a, int nwords)
+{
+  /* Naive method: */
+  require(a, "a is null");
+  require(nwords >= 0, "no negative shifts");
+
+  int i;
+  if (nwords >= BN_ARRAY_SIZE)
+  {
+    for (i = 0; i < BN_ARRAY_SIZE; ++i)
+    {
+      a->array[i] = 0;
+    }
+    return;
+  }
+
+  for (i = 0; i < BN_ARRAY_SIZE - nwords; ++i)
+  {
+    a->array[i] = a->array[i + nwords];
+  }
+  for (; i < BN_ARRAY_SIZE; ++i)
+  {
+    a->array[i] = 0;
+  }
+}
+
+
+static void _lshift_word(struct bn* a, int nwords)
+{
+  require(a, "a is null");
+  require(nwords >= 0, "no negative shifts");
+
+  int i;
+  /* Shift whole words */
+  for (i = (BN_ARRAY_SIZE - 1); i >= nwords; --i)
+  {
+    a->array[i] = a->array[i - nwords];
+  }
+  /* Zero pad shifted words. */
+  for (; i >= 0; --i)
+  {
+    a->array[i] = 0;
+  }  
+}
+
+
+static void _lshift_one_bit(struct bn* a)
+{
+  require(a, "a is null");
+
+  int i;
+  for (i = (BN_ARRAY_SIZE - 1); i > 0; --i)
+  {
+    a->array[i] = (a->array[i] << 1) | (a->array[i - 1] >> ((8 * WORD_SIZE) - 1));
+  }
+  a->array[0] <<= 1;
+}
+
+
+static void _rshift_one_bit(struct bn* a)
+{
+  require(a, "a is null");
+
+  int i;
+  for (i = 0; i < (BN_ARRAY_SIZE - 1); ++i)
+  {
+    a->array[i] = (a->array[i] >> 1) | (a->array[i + 1] << ((8 * WORD_SIZE) - 1));
+  }
+  a->array[BN_ARRAY_SIZE - 1] >>= 1;
+}
+
+

thirdparty/bignum/bn.h

@@ -0,0 +1,123 @@
+#ifndef __BIGNUM_H__
+#define __BIGNUM_H__
+/*
+
+Big number library - arithmetic on multiple-precision unsigned integers.
+
+This library is an implementation of arithmetic on arbitrarily large integers.
+
+The difference between this and other implementations, is that the data structure
+has optimal memory utilization (i.e. a 1024 bit integer takes up 128 bytes RAM),
+and all memory is allocated statically: no dynamic allocation for better or worse.
+
+Primary goals are correctness, clarity of code and clean, portable implementation.
+Secondary goal is a memory footprint small enough to make it suitable for use in
+embedded applications.
+
+
+The current state is correct functionality and adequate performance.
+There may well be room for performance-optimizations and improvements.
+
+*/
+
+#include <stdint.h>
+#include <assert.h>
+
+
+/* This macro defines the word size in bytes of the array that constitues the big-number data structure. */
+#ifndef WORD_SIZE
+  #define WORD_SIZE 4
+#endif
+
+/* Size of big-numbers in bytes */
+#define BN_ARRAY_SIZE    (128 / WORD_SIZE)
+
+
+/* Here comes the compile-time specialization for how large the underlying array size should be. */
+/* The choices are 1, 2 and 4 bytes in size with uint32, uint64 for WORD_SIZE==4, as temporary. */
+#ifndef WORD_SIZE
+  #error Must define WORD_SIZE to be 1, 2, 4
+#elif (WORD_SIZE == 1)
+  /* Data type of array in structure */
+  #define DTYPE                    uint8_t
+  /* bitmask for getting MSB */
+  #define DTYPE_MSB                ((DTYPE_TMP)(0x80))
+  /* Data-type larger than DTYPE, for holding intermediate results of calculations */
+  #define DTYPE_TMP                uint32_t
+  /* sprintf format string */
+  #define SPRINTF_FORMAT_STR       "%.02x"
+  #define SSCANF_FORMAT_STR        "%2hhx"
+  /* Max value of integer type */
+  #define MAX_VAL                  ((DTYPE_TMP)0xFF)
+#elif (WORD_SIZE == 2)
+  #define DTYPE                    uint16_t
+  #define DTYPE_TMP                uint32_t
+  #define DTYPE_MSB                ((DTYPE_TMP)(0x8000))
+  #define SPRINTF_FORMAT_STR       "%.04x"
+  #define SSCANF_FORMAT_STR        "%4hx"
+  #define MAX_VAL                  ((DTYPE_TMP)0xFFFF)
+#elif (WORD_SIZE == 4)
+  #define DTYPE                    uint32_t
+  #define DTYPE_TMP                uint64_t
+  #define DTYPE_MSB                ((DTYPE_TMP)(0x80000000))
+  #define SPRINTF_FORMAT_STR       "%.08x"
+  #define SSCANF_FORMAT_STR        "%8x"
+  #define MAX_VAL                  ((DTYPE_TMP)0xFFFFFFFF)
+#endif
+#ifndef DTYPE
+  #error DTYPE must be defined to uint8_t, uint16_t uint32_t or whatever
+#endif
+
+
+/* Custom assert macro - easy to disable */
+#define require(p, msg) assert(p && #msg)
+
+
+/* Data-holding structure: array of DTYPEs */
+struct bn
+{
+  DTYPE array[BN_ARRAY_SIZE];
+};
+
+
+
+/* Tokens returned by bignum_cmp() for value comparison */
+enum { SMALLER = -1, EQUAL = 0, LARGER = 1 };
+
+
+
+/* Initialization functions: */
+void bignum_init(struct bn* n);
+void bignum_from_int(struct bn* n, DTYPE_TMP i);
+int  bignum_to_int(struct bn* n);
+void bignum_from_string(struct bn* n, char* str, int nbytes);
+void bignum_to_string(struct bn* n, char* str, int maxsize);
+
+/* Basic arithmetic operations: */
+void bignum_add(struct bn* a, struct bn* b, struct bn* c); /* c = a + b */
+void bignum_sub(struct bn* a, struct bn* b, struct bn* c); /* c = a - b */
+void bignum_mul(struct bn* a, struct bn* b, struct bn* c); /* c = a * b */
+void bignum_div(struct bn* a, struct bn* b, struct bn* c); /* c = a / b */
+void bignum_mod(struct bn* a, struct bn* b, struct bn* c); /* c = a % b */
+void bignum_divmod(struct bn* a, struct bn* b, struct bn* c, struct bn* d); /* c = a/b, d = a%b */
+
+/* Bitwise operations: */
+void bignum_and(struct bn* a, struct bn* b, struct bn* c); /* c = a & b */
+void bignum_or(struct bn* a, struct bn* b, struct bn* c);  /* c = a | b */
+void bignum_xor(struct bn* a, struct bn* b, struct bn* c); /* c = a ^ b */
+void bignum_lshift(struct bn* a, struct bn* b, int nbits); /* b = a << nbits */
+void bignum_rshift(struct bn* a, struct bn* b, int nbits); /* b = a >> nbits */
+
+/* Special operators and comparison */
+int  bignum_cmp(struct bn* a, struct bn* b);               /* Compare: returns LARGER, EQUAL or SMALLER */
+int  bignum_is_zero(struct bn* n);                         /* For comparison with zero */
+void bignum_inc(struct bn* n);                             /* Increment: add one to n */
+void bignum_dec(struct bn* n);                             /* Decrement: subtract one from n */
+void bignum_pow(struct bn* a, struct bn* b, struct bn* c); /* Calculate a^b -- e.g. 2^10 => 1024 */
+void bignum_isqrt(struct bn* a, struct bn* b);             /* Integer square root -- e.g. isqrt(5) => 2*/
+void bignum_assign(struct bn* dst, struct bn* src);        /* Copy src into dst -- dst := src */
+
+
+#endif /* #ifndef __BIGNUM_H__ */
+
+

vlib/bignum/bignum.v

@@ -0,0 +1,195 @@
+module bignum
+
+// Wrapper for https://github.com/kokke/tiny-bignum-c
+
+#flag -I @VROOT/thirdparty/bignum
+#flag @VROOT/thirdparty/bignum/bn.o
+#include "bn.h"
+
+const (
+	STRING_BUFFER_SIZE = 8192
+)
+
+pub struct Number {
+	array [32]u32
+}
+
+fn C.bignum_init( n &Number )
+fn C.bignum_from_int( n &Number, i u64 )
+fn C.bignum_to_int( n &Number ) int
+fn C.bignum_from_string( n &Number, s byteptr, nbytes int)
+fn C.bignum_to_string( n &Number, s byteptr, maxsize int)
+
+fn C.bignum_add( a &Number, b &Number, c &Number) // c = a + b
+fn C.bignum_sub( a &Number, b &Number, c &Number) // c = a - b
+fn C.bignum_mul( a &Number, b &Number, c &Number) // c = a * b
+fn C.bignum_div( a &Number, b &Number, c &Number) // c = a / b
+fn C.bignum_mod( a &Number, b &Number, c &Number) // c = a % b
+fn C.bignum_divmod( a &Number, b &Number, c &Number, d &Number)  // c = a/b d=a%b
+
+fn C.bignum_and( a &Number, b &Number, c &Number) // c = a & b
+fn C.bignum_or( a &Number, b &Number, c &Number)  // c = a | b
+fn C.bignum_xor( a &Number, b &Number, c &Number) // c = a xor b
+fn C.bignum_lshift( a &Number, b &Number, nbits int) // b = a << nbits
+fn C.bignum_rshift( a &Number, b &Number, nbits int) // b = a >> nbits
+
+fn C.bignum_cmp( a &Number, b &Number) int 
+fn C.bignum_is_zero( a &Number) int
+fn C.bignum_inc(n &Number)
+fn C.bignum_dec(n &Number)
+fn C.bignum_pow( a &Number, b &Number, c &Number) // c = a ^ b
+fn C.bignum_isqrt( a &Number, b &Number) // b = integer_square_root_of(a)
+fn C.bignum_assign( dst &Number, src &Number) // copy src number to dst number
+
+////////////////////////////////////////////////////////////
+// conversion actions to/from big numbers:
+pub fn new_bignum() Number {
+	return Number{}
+}
+pub fn from_int(i int) Number {
+	n := Number{}
+	C.bignum_from_int( &n, i)
+	return n
+}
+
+pub fn from_u64(u u64) Number {
+	n := Number{}
+	C.bignum_from_int( &n, u)
+	return n
+}
+pub fn from_string(s string) Number {
+	n := Number{}
+	C.bignum_from_string(&n, s.str, s.len)
+	return n
+}
+
+pub fn (n Number) int() int {
+	r := C.bignum_to_int(&n)
+	return r
+}
+
+pub fn (n Number) str() string {
+	// TODO: return a decimal representation of the bignumber n.
+	// A decimal representation will be easier to use in the repl
+	// but will be slower to calculate. Also, it is not implemented
+	// in the bn library.
+	return 'Number (in hex): ' + n.hexstr()
+}
+
+pub fn (n Number) hexstr() string {
+	mut buf := [STRING_BUFFER_SIZE]byte
+	C.bignum_to_string( &n, buf, STRING_BUFFER_SIZE)
+	// NB: bignum_to_string , returns the HEXADECIMAL representation of the bignum n
+	s := tos_clone( buf )
+	if s.len == 0 { return '0' }
+	return s
+}
+////////////////////////////////////////////////////////////
+// overloaded ops for the numbers:
+pub fn (a Number) + (b Number) Number {
+	c := Number{}
+	C.bignum_add(&a, &b, &c)
+	return c
+}
+
+pub fn (a Number) - (b Number) Number {
+	c := Number{}
+	C.bignum_sub(&a, &b, &c)
+	return c
+}
+
+pub fn (a Number) * (b Number) Number {
+	c := Number{}
+	C.bignum_mul(&a, &b, &c)
+	return c
+}
+
+pub fn (a Number) / (b Number) Number {
+	c := Number{}
+	C.bignum_div(&a, &b, &c)
+	return c
+}
+
+pub fn (a Number) % (b Number) Number {
+	c := Number{}
+	C.bignum_mod(&a, &b, &c)
+	return c
+}
+
+pub fn divmod( a &Number, b &Number, c &Number) Number {
+	d := Number{}
+	C.bignum_divmod( a, b, c, &d)
+	return d
+}
+////////////////////////////////////////////////////////////
+pub fn cmp(a Number, b Number) int {
+	return C.bignum_cmp(&a,&b)
+}
+pub fn (a Number) is_zero() bool {
+	return int(C.bignum_is_zero(&a)) != 0
+}
+pub fn (a mut Number) inc() {
+	C.bignum_inc(a)
+}
+pub fn (a mut Number) dec() {
+	C.bignum_dec(a)
+}
+pub fn pow(a Number, b Number) Number {
+	c := Number{}
+	C.bignum_pow(&a,&b,&c)
+	return c
+}
+pub fn (a Number) isqrt() Number {
+	b := Number{}
+	C.bignum_isqrt(&a,&b)
+	return b
+}
+////////////////////////////////////////////////////////////
+pub fn b_and(a Number, b Number) Number {
+	c := Number{}
+	C.bignum_and(&a,&b,&c)
+	return c
+}
+pub fn b_or(a Number, b Number) Number {
+	c := Number{}
+	C.bignum_or(&a,&b,&c)
+	return c
+}
+pub fn b_xor(a Number, b Number) Number {
+	c := Number{}
+	C.bignum_xor(&a,&b,&c)
+	return c
+}
+pub fn (a Number) lshift(nbits int) Number {
+	b := Number{}
+	C.bignum_lshift(&a,&b,nbits)
+	return b
+}
+pub fn (a Number) rshift(nbits int) Number {
+	b := Number{}
+	C.bignum_rshift(&a,&b,nbits)
+	return b
+}
+pub fn (a Number) clone() Number {
+	b := Number{}
+	C.bignum_assign(&b,&a)
+	return b
+}
+////////////////////////////////////////////////////////////
+pub fn factorial(nn bignum.Number) bignum.Number {
+	mut n := nn.clone()
+	mut a := nn.clone()
+	n.dec()
+	mut i:=1
+	for !n.is_zero() {
+		res := a * n
+		n.dec()
+		a = res
+		i++
+	}
+	return a
+}
+
+pub fn fact(n int) bignum.Number {
+	return factorial( bignum.from_int(n) )
+}

vlib/bignum/bignum_test.v

@@ -0,0 +1,86 @@
+import bignum
+
+fn test_new_bignum(){
+	n := bignum.new_bignum()
+	assert sizeof( bignum.Number ) == 128
+	assert n.hexstr() == '0'
+}
+
+fn test_from_int(){
+	assert bignum.from_int(255).hexstr() == 'ff'
+	assert bignum.from_int(127).hexstr() == '7f'
+	assert bignum.from_int(1024).hexstr() == '400'
+	assert bignum.from_int(2147483647).hexstr() == '7fffffff'
+	assert bignum.from_int(-1).hexstr() == 'ffffffffffffffff'
+}
+
+fn test_from_u64(){
+	assert bignum.from_u64(255).hexstr() == 'ff'
+	assert bignum.from_u64(127).hexstr() == '7f'
+	assert bignum.from_u64(1024).hexstr() == '400'
+	assert bignum.from_u64(4294967295).hexstr() == 'ffffffff'
+	assert bignum.from_u64(4398046511104).hexstr() == '40000000000'
+	assert bignum.from_u64(-1).hexstr() == 'ffffffffffffffff'
+}
+
+fn test_plus(){
+	a := bignum.from_u64(2)
+	b := bignum.from_u64(3)
+	c := a + b
+	assert c.hexstr() == '5'
+	assert (bignum.from_u64(1024) + bignum.from_u64(1024)).hexstr() == '800'
+}
+
+fn test_minus(){
+	a := bignum.from_u64(2)
+	b := bignum.from_u64(3)
+	c := b - a
+	assert c.hexstr() == '1'
+	e := bignum.from_u64(1024)
+	ee := e - e
+	assert ee.hexstr() == '0'
+}
+
+fn test_divide(){
+	a := bignum.from_u64(2)
+	b := bignum.from_u64(3)
+	c := b / a
+	assert c.hexstr() == '1'
+	assert (b % a ).hexstr() == '1'
+	e := bignum.from_u64(1024) // dec(1024) == hex(0x400)
+	ee := e / e
+	assert ee.hexstr() == '1'
+	assert (e / a).hexstr() == '200'
+	assert (e / (a*a)).hexstr() == '100'
+}
+
+fn test_multiply(){
+	a := bignum.from_u64(2)
+	b := bignum.from_u64(3)
+	c := b * a
+	assert c.hexstr() == '6'
+	e := bignum.from_u64(1024)
+	e2 := e * e
+	e4 := e2 * e2
+	e8 := e2 * e2 * e2 * e2
+	e9 := e8 + bignum.from_u64(1)
+	d  := ((e9 * e9) + b) * c
+	assert e4.hexstr() == '10000000000'
+	assert e8.hexstr() == '100000000000000000000'
+	assert e9.hexstr() == '100000000000000000001'
+	assert d.hexstr() == '60000000000000000000c00000000000000000018'
+}
+
+fn test_mod(){
+	assert (bignum.from_u64(13) % bignum.from_u64(10) ).int() == 3
+	assert (bignum.from_u64(13) % bignum.from_u64(9) ).int()  == 4
+	assert (bignum.from_u64(7) % bignum.from_u64(5) ).int() == 2
+}
+
+
+fn test_factorial(){
+	f5 := bignum.factorial( bignum.from_u64(5) )
+	assert f5.hexstr() == '78'
+	f100 := bignum.factorial( bignum.from_u64(100) )
+	assert f100.hexstr() == '1b30964ec395dc24069528d54bbda40d16e966ef9a70eb21b5b2943a321cdf10391745570cca9420c6ecb3b72ed2ee8b02ea2735c61a000000000000000000000000'
+}

vlib/compiler/expression.v

@@ -448,34 +448,29 @@ fn (p mut Parser) expression() string {
 		// Make sure operators are used with correct types
 		if !p.pref.translated && !is_str && !is_ustr && !is_num {
 			T := p.table.find_type(typ)
-			if tok_op == .plus {
+			if      tok_op == .plus {  p.handle_operator('+', typ, 'op_plus', ph, T)  }
-				if T.has_method('+') {
+			else if tok_op == .minus { p.handle_operator('-', typ, 'op_minus', ph, T) }
-					p.cgen.set_placeholder(ph, typ + '_plus(')
-					p.gen(')')
-				}
-				else {
-					p.error('operator + not defined on `$typ`')
-				}
-			}
-			else if tok_op == .minus {
-				if T.has_method('-') {
-					p.cgen.set_placeholder(ph, '${typ}_minus(')
-					p.gen(')')
-				}
-				else {
-					p.error('operator - not defined on `$typ`')
-				}
-			}
 		}
 	}
 	return typ
 }
 
+fn (p mut Parser) handle_operator(op string, typ string, cpostfix string, ph int, T &Type) {
+	if T.has_method( op ) {
+		p.cgen.set_placeholder(ph, '${typ}_${cpostfix}(')
+		p.gen(')')
+	}
+	else {
+		p.error('operator $op not defined on `$typ`')
+	}
+}  
+
 fn (p mut Parser) term() string {
 	line_nr := p.scanner.line_nr
 	//if p.fileis('fn_test') {
 		//println('\nterm() $line_nr')
 	//}
+	ph := p.cgen.add_placeholder()
 	typ := p.unary()
 	//if p.fileis('fn_test') {
 		//println('2: $line_nr')
@@ -491,11 +486,28 @@ fn (p mut Parser) term() string {
 		// is_mul := tok == .mod
 		p.next()
 		p.gen(tok.str())// + ' /*op2*/ ')
+		oph := p.cgen.add_placeholder()
 		p.fgen(' ' + tok.str() + ' ')
 		if (is_div || is_mod) && p.tok == .number && p.lit == '0' {
 			p.error('division or modulo by zero')
 		}
 		expr_type := p.unary()
+
+		if !is_primitive_type(expr_type) && expr_type == typ {
+			p.check_types(expr_type, typ)
+			T := p.table.find_type(typ)
+			// NB: oph is a char index just after the OP
+			before_oph := p.cgen.cur_line[..oph-1]
+			after_oph := p.cgen.cur_line[oph..]
+			p.cgen.cur_line = before_oph + ',' + after_oph
+			match tok {
+				.mul {   p.handle_operator('*', typ, 'op_mul', ph, T) }
+				.div {   p.handle_operator('/', typ, 'op_div', ph, T) }
+				.mod {   p.handle_operator('%', typ, 'op_mod', ph, T) }
+			}
+			continue
+		}
+		
 		if is_mod {
 			if !(is_integer_type(expr_type) && is_integer_type(typ)) {
 				p.error('operator `mod` requires integer types')

vlib/compiler/fn.v

@@ -265,7 +265,7 @@ fn (p mut Parser) fn_decl() {
 		p.register_var(receiver)
 	}
 	// +-/* methods
-	if p.tok in [.plus, .minus, .mul] {
+	if p.tok in [.plus, .minus, .mul, .div, .mod] {
 		f.name = p.tok.str()
 		p.next()
 	}

vlib/compiler/gen_c.v

@@ -228,9 +228,15 @@ fn (table mut Table) fn_gen_name(f &Fn) string {
 	if f.is_method {
 		name = '${f.receiver_typ}_$f.name'
 		name = name.replace(' ', '')
-		name = name.replace('*', '')
+		if f.name.len == 1 {
-		name = name.replace('+', 'plus')
+			match f.name[0] {
-		name = name.replace('-', 'minus')
+				`+` { name = name.replace('+', 'op_plus') }
+				`-` { name = name.replace('-', 'op_minus') }
+				`*` { name = name.replace('*', 'op_mul') }
+				`/` { name = name.replace('/', 'op_div') }
+				`%` { name = name.replace('%', 'op_mod') }
+			}
+		}
 	}
 	// Avoid name conflicts (with things like abs(), print() etc).
 	// Generate v_abs(), v_print()

vlib/math/math.v

@@ -6,6 +6,35 @@ module math
 
 #include <math.h>
 
+fn C.acos(x f64) f64
+fn C.asin(x f64) f64
+fn C.atan(x f64) f64
+fn C.atan2(y f64, x f64) f64
+fn C.cbrt(x f64) f64
+fn C.ceil(x f64) f64
+fn C.cos(x f64) f64
+fn C.cosh(x f64) f64
+fn C.erf(x f64) f64
+fn C.erfc(x f64) f64
+fn C.exp(x f64) f64
+fn C.exp2(x f64) f64
+fn C.floor(x f64) f64
+fn C.fmod(x f64, y f64) f64
+fn C.hypot(x f64, y f64) f64
+fn C.log(x f64) f64
+fn C.log2(x f64) f64
+fn C.log10(x f64) f64
+fn C.lgamma(x f64) f64
+fn C.pow(x f64, y f64) f64
+fn C.round(x f64) f64
+fn C.sin(x f64) f64
+fn C.sqrt(x f64) f64
+fn C.tgamma(x f64) f64
+fn C.tan(x f64) f64
+fn C.tanh(x f64) f64
+fn C.trunc(x f64) f64
+
+
 // NOTE
 // When adding a new function, please make sure it's in the right place.
 // All functions are sorted alphabetically.
@@ -18,8 +47,6 @@ pub fn abs(a f64) f64 {
 	return a
 }
 
-fn C.acos(a f64) f64
-
 // acos calculates inverse cosine (arccosine).
 pub fn acos(a f64) f64 {
 	return C.acos(a)

vlib/os/os_test.v

@@ -1,5 +1,9 @@
 import os
 
+fn test_aaa_setup(){
+	cleanup_leftovers() assert true
+}
+
 fn test_setenv() {
   os.setenv('foo', 'bar', true)
   assert os.getenv('foo') == 'bar'
@@ -114,12 +118,11 @@ fn test_walk() {
 }
 
 fn test_cp() {
-  $if windows {
+    old_file_name := 'cp_example.txt'
-    old_file_name := './example.txt'
+    new_file_name := 'cp_new_example.txt'
-    new_file_name := './new_example.txt'
     
     os.write_file(old_file_name, 'Test data 1 2 3, V is awesome #$%^[]!~⭐')
-    result := os.cp(old_file_name, new_file_name) or { panic('$err: errcode: $errcode') }
+    os.cp(old_file_name, new_file_name) or { panic('$err: errcode: $errcode') }
 
     old_file := os.read_file(old_file_name) or { panic(err) }
     new_file := os.read_file(new_file_name) or { panic(err) }
@@ -128,12 +131,10 @@ fn test_cp() {
     os.rm(old_file_name)
     os.rm(new_file_name)
 }
-}
 
 fn test_cp_r() {
   //fileX -> dir/fileX
- // TODO clean up the files
+  // NB: clean up of the files happens inside the cleanup_leftovers function
- /*
   os.write_file('ex1.txt', 'wow!')
   os.mkdir('ex')
   os.cp_r('ex1.txt', 'ex', false) or { panic(err) }
@@ -148,7 +149,6 @@ fn test_cp_r() {
   assert old2 == new2
   //recurring on dir -> local dir
   os.cp_r('ex', './', true) or { panic(err) }
- */
 }
 
 //fn test_fork() {
@@ -173,3 +173,25 @@ fn test_cp_r() {
 //    println(cpid)
 //  }
 //}
+
+fn test_zzz_cleanup(){
+	cleanup_leftovers() assert true
+}
+
+
+// this function is called by both test_aaa_setup & test_zzz_cleanup
+// it ensures that os tests do not polute the filesystem with leftover
+// files so that they can be run several times in a row.
+fn cleanup_leftovers(){
+	// possible leftovers from test_cp
+	os.rm('cp_example.txt')
+	os.rm('cp_new_example.txt')
+	
+	// possible leftovers from test_cp_r
+	os.rm('ex/ex2/ex2.txt')
+	os.rm('ex/ex2')
+	os.rm('ex/ex1.txt')
+	os.rm('ex')  
+	os.rm('ex2/ex2.txt')
+	os.rm('ex2')  
+}