Document the new DPF surfaces in one command set, and test the field, half-tree, and multipoint edges.

Co-authored-by: Cursor <cursoragent@cursor.com>

test/tests/fp61_test.cpp

@@ -0,0 +1,57 @@
+#include <gtest/gtest.h>
+
+#include <cstdint>
+#include <limits>
+#include <sstream>
+
+#include "dpf/fp61.hpp"
+
+namespace
+{
+
+using dpf::fp61;
+using dpf::fp61_mod;
+
+}  // namespace
+
+TEST(Fp61, ReduceCanonicalizesTheModulus)
+{
+    EXPECT_EQ(fp61::reduce(0), 0u);
+    EXPECT_EQ(fp61::reduce(1), 1u);
+    EXPECT_EQ(fp61::reduce(fp61_mod), 0u);
+    EXPECT_EQ(fp61::reduce(fp61_mod + 1), 1u);
+    EXPECT_EQ(fp61::reduce(std::uint64_t{1} << 61), 1u);
+    EXPECT_EQ(fp61::reduce(std::numeric_limits<std::uint64_t>::max()), 7u);
+    EXPECT_EQ(fp61::reduce(fp61::reduce(fp61_mod + 9)), fp61::reduce(9));
+}
+
+TEST(Fp61, ArithmeticWrapsInTheField)
+{
+    const fp61 a{fp61_mod - 1};
+    const fp61 b{3};
+    EXPECT_EQ((a + b).raw(), 2u);
+    EXPECT_EQ((b - a).raw(), 4u);
+    EXPECT_EQ((-a).raw(), 1u);
+    EXPECT_EQ((-fp61{0}).raw(), 0u);
+    EXPECT_EQ((a - a).raw(), 0u);
+    EXPECT_EQ((-(-a)).raw(), a.raw());
+    EXPECT_EQ((a * fp61{1}).raw(), a.raw());
+    EXPECT_EQ((a * fp61{0}).raw(), 0u);
+    EXPECT_EQ((fp61{2} * fp61{3}).raw(), 6u);
+}
+
+TEST(Fp61, MultiplicationDistributes)
+{
+    const fp61 a{1000};
+    const fp61 b{fp61_mod - 5};
+    const fp61 c{17};
+    EXPECT_EQ(((a + b) * c).raw(), (a * c + b * c).raw());
+    EXPECT_EQ((a * b).raw(), (b * a).raw());
+}
+
+TEST(Fp61, StreamPrintsTheReducedValue)
+{
+    std::ostringstream os;
+    os << fp61{fp61_mod + 4};
+    EXPECT_EQ(os.str(), "4");
+}