Starting design of big integer class.

Operators defined: A+B, -A

bigdecimal.xcodeproj/project.pbxproj

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include/biginteger.h

@@ -0,0 +1,59 @@
+//
+//  biginteger.h
+//  bigdecimal
+//
+//  Created by Sam Jaffe on 6/30/17.
+//
+
+#pragma once
+
+#include <string>
+#include <vector>
+
+namespace math {
+  class biginteger {
+  public:
+    using data_type = std::vector<int32_t>;
+    static constexpr int32_t const MAX_SEG   { 999999999};
+    static constexpr int32_t const OVER_SEG  {1000000000};
+    static constexpr int32_t const SEG_DIGITS{         9};
+  public:
+    // Constructors
+    biginteger();
+    biginteger(int32_t);
+    biginteger(uint32_t);
+    biginteger(int64_t);
+    biginteger(uint64_t);
+    biginteger(char const *);
+    // Unary operators
+    biginteger operator-() const;
+    // Binary operators
+    friend biginteger operator+(biginteger const &, biginteger const &);
+    friend biginteger operator-(biginteger const &, biginteger const &);
+    friend biginteger operator*(biginteger const &, biginteger const &);
+    friend biginteger operator/(biginteger const &, biginteger const &);
+    friend biginteger & operator+=(biginteger &, biginteger const &);
+    friend biginteger & operator-=(biginteger &, biginteger const &);
+    friend biginteger & operator*=(biginteger &, biginteger const &);
+    friend biginteger & operator/=(biginteger &, biginteger const &);
+    // Output
+    std::string to_string() const;
+    // Comparison
+    friend bool operator==(biginteger const &, biginteger const &);
+    friend bool operator!=(biginteger const &, biginteger const &);
+    friend bool operator<=(biginteger const &, biginteger const &);
+    friend bool operator< (biginteger const &, biginteger const &);
+    friend bool operator>=(biginteger const &, biginteger const &);
+    friend bool operator> (biginteger const &, biginteger const &);
+  private:
+    biginteger(bool, uint64_t);
+    biginteger(bool, data_type &&);
+    friend void swap(biginteger & rhs, biginteger & lhs) {
+      using std::swap;
+      swap(rhs.is_negative, lhs.is_negative);
+      swap(rhs.data, lhs.data);
+    }
+    bool is_negative;
+    data_type data{};
+  };
+}

src/biginteger.cpp

@@ -0,0 +1,161 @@
+//
+//  biginteger.cpp
+//  bigdecimal
+//
+//  Created by Sam Jaffe on 6/30/17.
+//
+
+#include "biginteger.h"
+
+using namespace math;
+
+namespace detail {
+  using data_type = biginteger::data_type;
+  // 1 => GREATER, 0 => EQUAL, -1 => LESS
+  int compare(data_type const & rhs, data_type const & lhs);
+  data_type add(data_type const & rhs, data_type const & lhs);
+  data_type subtract_nounderflow(data_type const & rhs, data_type const & lhs);
+}
+
+static void swap(biginteger & rhs, biginteger && lhs) {
+  swap(rhs, lhs);
+}
+
+biginteger::biginteger()
+: biginteger(false, 0) {}
+
+biginteger::biginteger(int32_t value)
+: biginteger(static_cast<int64_t>(value)) {}
+
+biginteger::biginteger(uint32_t value)
+: biginteger(static_cast<uint64_t>(value)) {}
+
+biginteger::biginteger(int64_t value) :
+biginteger(value < 0, static_cast<uint64_t>(value < 0 ? -value : value)) {}
+
+biginteger::biginteger(uint64_t value)
+: biginteger(false, value) {}
+
+biginteger::biginteger(bool neg, uint64_t value) :
+is_negative(neg) {
+  uint64_t next{0};
+  do {
+    next = value / OVER_SEG;
+    data.push_back(static_cast<int32_t>(value - (OVER_SEG * next)));
+  } while ((value = next) > 0);
+}
+
+biginteger::biginteger(bool neg, data_type && dt) :
+is_negative(neg), data(std::move(dt)) {}
+
+biginteger & operator+=(biginteger & rhs, biginteger const & lhs) {
+  swap(rhs, rhs + lhs);
+  return rhs;
+}
+
+//biginteger & operator-=(biginteger & rhs, biginteger const & lhs) {
+//  swap(rhs, rhs - lhs);
+//  return rhs;
+//}
+//
+//biginteger & operator*=(biginteger & rhs, biginteger const & lhs) {
+//  swap(rhs, rhs * lhs);
+//  return rhs;
+//}
+//
+//biginteger & operator/=(biginteger & rhs, biginteger const & lhs) {
+//  swap(rhs, rhs / lhs);
+//  return rhs;
+//}
+
+biginteger biginteger::operator-() const {
+  biginteger tmp{*this};
+  tmp.is_negative = !tmp.is_negative;
+  return tmp;
+}
+
+biginteger math::operator+(biginteger const & rhs, biginteger const & lhs) {
+  if (rhs.is_negative == lhs.is_negative) {
+    return {rhs.is_negative, detail::add(rhs.data, lhs.data)};
+  } else {
+    auto cmp = detail::compare(rhs.data, lhs.data);
+    if (cmp == 0) {
+      return 0;
+    } else if (cmp > 0) {
+      return {rhs.is_negative, detail::subtract_nounderflow(rhs.data, lhs.data)};
+    } else {
+      return {lhs.is_negative, detail::subtract_nounderflow(lhs.data, rhs.data)};
+    }
+  }
+}
+
+namespace detail {
+#define IMPL_COMPARE(expr) \
+  if (rhs expr < lhs expr) return -1; \
+  else if (lhs expr < rhs expr) return 1
+  
+  int compare(data_type const & rhs, data_type const & lhs) {
+    IMPL_COMPARE(.size());
+    for (data_type::size_type i = rhs.size(); i > 0; --i) {
+      IMPL_COMPARE([i-1]);
+    }
+    return 0;
+  }
+#undef IMPL_COMPARE
+  
+  data_type add(data_type const & rhs, data_type const & lhs) {
+    data_type::size_type const rbnd = rhs.size(), lbnd = lhs.size();
+    data_type::size_type const ubnd = std::max(rbnd, lbnd);
+    data_type rval(ubnd);
+    // Add
+    for (data_type::size_type i = 0; i < rbnd; ++i) {
+      rval[i] += rhs[i];
+    }
+    for (data_type::size_type i = 0; i < lbnd; ++i) {
+      rval[i] += lhs[i];
+    }
+    // Carry
+    for (data_type::size_type i = 0; i < ubnd-1; ++i) {
+      if (rval[i] > biginteger::MAX_SEG) {
+        rval[i] -= biginteger::OVER_SEG;
+        rval[i+1] += 1;
+      }
+    }
+    if (rval[ubnd-1] > biginteger::MAX_SEG) {
+      rval[ubnd-1] -= biginteger::OVER_SEG;
+      rval.push_back(1);
+    }
+    return rval;
+  }
+  
+  data_type subtract_nounderflow(data_type const & rhs, data_type const & lhs) {
+    data_type::size_type const rbnd = rhs.size(), lbnd = lhs.size();
+    data_type rval{rhs};
+    // Subtract
+    for (data_type::size_type i = 0; i < lbnd; ++i) {
+      rval[i] -= lhs[i];
+    }
+    // Borrow
+    for (data_type::size_type i = 0; i < rbnd; ++i) {
+      if (rval[i] < 0) {
+        rval[i] += biginteger::OVER_SEG;
+        rval[i+1] -= 1;
+      }
+    }
+    if (rval[rbnd-1] == 0 && rbnd > 1) { rval.pop_back(); }
+    return rval;
+  }
+}
+
+#include <iomanip>
+#include <sstream>
+
+std::string biginteger::to_string() const {
+  std::stringstream ss;
+  if (is_negative) ss << '-';
+  ss << data[data.size()-1];
+  for (data_type::size_type i = data.size()-1; i > 0; --i) {
+    ss << std::setw(SEG_DIGITS) << std::setfill('0') << data[i-1];
+  }
+  return ss.str();
+}

test/biginteger.t.h

@@ -0,0 +1,35 @@
+//
+//  biginteger.t.h
+//  bigdecimal
+//
+//  Created by Sam Jaffe on 6/30/17.
+//
+
+#pragma once
+
+#include "biginteger.h"
+
+#include <cxxtest/TestSuite.h>
+
+class biginteger_TestSuite : public CxxTest::TestSuite {
+public:
+  void testAddPastBounds() {
+    math::biginteger bi{999999999ULL};
+    TS_ASSERT_EQUALS((bi+1).to_string(), "1000000000");
+  }
+  
+  void testAddReciprocalIsZero() {
+    math::biginteger bi{1000};
+    TS_ASSERT_EQUALS((bi+(-bi)).to_string(), "0");
+  }
+
+  void testAddNegativeLargerGivesNegative() {
+    math::biginteger bi{1000};
+    TS_ASSERT_EQUALS((bi+(-1001)).to_string(), "-1");
+  }
+
+  void testAddNegativeSmallerGivesPositive() {
+    math::biginteger bi{1000};
+    TS_ASSERT_EQUALS((bi+(-999)).to_string(), "1");
+  }
+};