algo.3 oppsite of real numbers

src/epsilon/r.hpp

@@ -35,6 +35,15 @@ constexpr r<C> add(r<C> x, r<C> y) {
   };
 }
 
+template <container C>
+constexpr r<C> opp(r<C> x) {
+  return [x = std::move(x)](unsigned int n) -> coro::lazy<z<C>> {
+    auto xn = co_await x(n);
+    negate(xn);
+    co_return xn;
+  };
+}
+
 }  // namespace epx
 
 #endif  // EPSILON_INC_R_HPP

src/epsilon/z.hpp

@@ -133,6 +133,9 @@ constexpr z<C>& normalize(z<C>& num) noexcept {
 
 template <container C>
 constexpr z<C>& negate(z<C>& num) noexcept {
+  if (is_zero(num)) {
+    return num;
+  }
   num.sgn = is_positive(num) ? sign::negative : sign::positive;
   return num;
 }

src/ut/r_tests.cpp

@@ -98,4 +98,24 @@ TEST(r_tests, add) {
   }
 }
 
+TEST(r_tests, opp) {
+  {
+    auto x = epx::make_q(stosz("0"), stosz("1"));
+    auto expr = epx::opp(x);
+    EXPECT_EQ("0", epx::to_string(expr, 0));
+    EXPECT_EQ("0.00000", epx::to_string(expr, 5));
+  }
+  {
+    auto x = epx::make_q(stosz("1"), stosz("1"));
+    auto expr = epx::opp(x);
+    EXPECT_EQ("-1", epx::to_string(expr, 0));
+    EXPECT_EQ("-1.00000", epx::to_string(expr, 5));
+  }
+  {
+    auto x = epx::make_q(stosz("-1"), stosz("7"));
+    auto expr = epx::opp(x);
+    EXPECT_EQ("0.14285714285714285714286", epx::to_string(expr, 23));
+  }
+}
+
 }  // namespace epxut

src/ut/z_tests.cpp

@@ -61,6 +61,26 @@ TEST(z_tests, normalize) {
   }
 }
 
+TEST(z_tests, negate) {
+  {
+    sz zero;
+    epx::negate(zero);
+    EXPECT_TRUE(epx::is_zero(zero));
+  }
+  {
+    sz num = {.digits = {1}};
+    sz expected = {.digits = {1}, .sgn = epx::sign::negative};
+    epx::negate(num);
+    EXPECT_EQ(expected, num);
+  }
+  {
+    sz num = {.digits = {1}, .sgn = epx::sign::negative};
+    sz expected = {.digits = {1}};
+    epx::negate(num);
+    EXPECT_EQ(expected, num);
+  }
+}
+
 TEST(z_tests, add) {
   {
     sz zero, one{.digits = {1}}, minus_one{.digits = {1}, .sgn = epx::sign::negative};