diff --git a/src/tests/CMakeLists.txt b/src/tests/CMakeLists.txt
index baddc1ada..f5aa9a4a8 100644
--- a/src/tests/CMakeLists.txt
+++ b/src/tests/CMakeLists.txt
@@ -14,6 +14,7 @@ add_executable(tests
     audio_core/audio_fixures.h
     audio_core/decoder_tests.cpp
     video_core/shader/shader_jit_compiler.cpp
+    video_core/pica_float.cpp
     audio_core/merryhime_3ds_audio/merry_audio/merry_audio.cpp
     audio_core/merryhime_3ds_audio/merry_audio/merry_audio.h
     audio_core/merryhime_3ds_audio/merry_audio/service_fixture.cpp
diff --git a/src/tests/video_core/pica_float.cpp b/src/tests/video_core/pica_float.cpp
new file mode 100644
index 000000000..394420c99
--- /dev/null
+++ b/src/tests/video_core/pica_float.cpp
@@ -0,0 +1,30 @@
+// Copyright 2024 Citra Emulator Project
+// Licensed under GPLv2 or any later version
+// Refer to the license.txt file included.
+
+#include <cmath>
+#include <catch2/catch_approx.hpp>
+#include <catch2/catch_test_macros.hpp>
+#include "video_core/pica_types.h"
+
+using Pica::f24;
+
+TEST_CASE("Infinities", "[video_core][pica_float]") {
+    REQUIRE(std::isinf(f24::FromFloat32(INFINITY).ToFloat32()));
+    REQUIRE(std::isinf(f24::FromFloat32(1.e20f).ToFloat32()));
+    REQUIRE(std::isinf(f24::FromFloat32(-1.e20f).ToFloat32()));
+}
+
+TEST_CASE("Subnormals", "[video_core][pica_float]") {
+    REQUIRE(f24::FromFloat32(1e-20f).ToFloat32() == 0.f);
+}
+
+TEST_CASE("NaN", "[video_core][pica_float]") {
+    const auto inf = f24::FromFloat32(INFINITY);
+    const auto nan = f24::FromFloat32(NAN);
+
+    REQUIRE(std::isnan(nan.ToFloat32()));
+    REQUIRE(std::isnan((nan * f24::Zero()).ToFloat32()));
+    REQUIRE(std::isnan((inf - inf).ToFloat32()));
+    REQUIRE((inf * f24::Zero()).ToFloat32() == 0.f);
+}
diff --git a/src/tests/video_core/shader/shader_jit_compiler.cpp b/src/tests/video_core/shader/shader_jit_compiler.cpp
index 01698a2e1..579bf7e99 100644
--- a/src/tests/video_core/shader/shader_jit_compiler.cpp
+++ b/src/tests/video_core/shader/shader_jit_compiler.cpp
@@ -260,7 +260,7 @@ TEST_CASE("LG2", "[video_core][shader][shader_jit]") {
     REQUIRE(std::isinf(shader.Run(0.f).x));
     REQUIRE(shader.Run(4.f).x == Catch::Approx(2.f));
     REQUIRE(shader.Run(64.f).x == Catch::Approx(6.f));
-    REQUIRE(shader.Run(1.e24f).x == Catch::Approx(79.7262742773f));
+    // REQUIRE(std::isinf(shader.Run(INFINITY).x));
 }
 
 TEST_CASE("EX2", "[video_core][shader][shader_jit]") {
@@ -277,8 +277,9 @@ TEST_CASE("EX2", "[video_core][shader][shader_jit]") {
     REQUIRE(shader.Run(0.f).x == Catch::Approx(1.f));
     REQUIRE(shader.Run(2.f).x == Catch::Approx(4.f));
     REQUIRE(shader.Run(6.f).x == Catch::Approx(64.f));
-    REQUIRE(shader.Run(79.7262742773f).x == Catch::Approx(1.e24f));
     REQUIRE(std::isinf(shader.Run(800.f).x));
+    // If we respect f24 precision, 2^79 = inf, as 79 > 63
+    // REQUIRE(std::isinf(shader.Run(79.7262742773f).x));
 }
 
 TEST_CASE("MUL", "[video_core][shader][shader_jit]") {
@@ -469,7 +470,7 @@ TEST_CASE("Uniform Read", "[video_core][shader][shader_jit]") {
         const float color = (i * 2.0f) / 255.0f;
         const auto color_f24 = Pica::f24::FromFloat32(color);
         shader.shader_setup->uniforms.f[i] = {color_f24, color_f24, color_f24, Pica::f24::One()};
-        f_uniforms[i] = {color, color, color, 1.0f};
+        f_uniforms[i] = {color_f24.ToFloat32(), color_f24.ToFloat32(), color_f24.ToFloat32(), 1.0f};
     }
 
     for (u32 i = 0; i < 96; ++i) {
@@ -506,7 +507,8 @@ TEST_CASE("Address Register Offset", "[video_core][shader][shader_jit]") {
             const auto color_f24 = Pica::f24::FromFloat32(color);
             shader.shader_setup->uniforms.f[i] = {color_f24, color_f24, color_f24,
                                                   Pica::f24::One()};
-            f_uniforms[i] = {color, color, color, 1.f};
+            f_uniforms[i] = {color_f24.ToFloat32(), color_f24.ToFloat32(), color_f24.ToFloat32(),
+                             1.f};
         } else if (i >= 0x60 && i < 0x64) {
             const u8 color = static_cast<u8>((i - 0x60) * 0x10);
             shader.shader_setup->uniforms.i[i - 0x60] = {color, color, color, 255};
diff --git a/src/video_core/pica_types.h b/src/video_core/pica_types.h
index 4fd27f9fe..043691e87 100644
--- a/src/video_core/pica_types.h
+++ b/src/video_core/pica_types.h
@@ -4,8 +4,10 @@
 
 #pragma once
 
+#include <bit>
 #include <cmath>
 #include <cstring>
+#include <limits>
 #include <boost/serialization/access.hpp>
 #include "common/common_types.h"
 
@@ -28,6 +30,41 @@ public:
     static constexpr Float<M, E> FromFloat32(float val) {
         Float<M, E> ret;
         ret.value = val;
+        return Trunc(ret);
+    }
+
+    static constexpr Float<M, E> MinNormal() {
+        Float<M, E> ret;
+        // Mininum normal value = 1.0 / (1 << ((1 << (E - 1)) - 2));
+        if constexpr (E == 5) {
+            ret.value = 0x1.p-14;
+        } else {
+            // E == 7
+            ret.value = (0x1.p-62);
+        }
+        return ret;
+    }
+
+    // these values are approximate, rounded up
+    static constexpr Float<M, E> Max() {
+        Float<M, E> ret;
+        if constexpr (E == 5) {
+            ret.value = 0x1.p16;
+        } else {
+            // E == 7
+            ret.value = 0x1.p64;
+        }
+        return ret;
+    }
+
+    // before C++23 std::isnormal and std::abs aren't considered constexpr so this function can't be
+    // used as constexpr until the compilers support that.
+    static constexpr Float<M, E> Trunc(const Float<M, E>& val) {
+        Float<M, E> ret = val.Flushed().InfChecked();
+        if (std::isnormal(val.ToFloat32())) {
+            u32 hex = std::bit_cast<u32>(ret.ToFloat32()) & (0xffffffff ^ ((1 << (23 - M)) - 1));
+            ret.value = std::bit_cast<float>(hex);
+        }
         return ret;
     }
 
@@ -50,17 +87,21 @@ public:
             hex = sign;
         }
 
-        std::memcpy(&res.value, &hex, sizeof(float));
+        res.value = std::bit_cast<float>(hex);
 
         return res;
     }
 
     static constexpr Float<M, E> Zero() {
-        return FromFloat32(0.f);
+        Float<M, E> ret;
+        ret.value = 0.f;
+        return ret;
     }
 
     static constexpr Float<M, E> One() {
-        return FromFloat32(1.f);
+        Float<M, E> ret;
+        ret.value = 1.f;
+        return ret;
     }
 
     // Not recommended for anything but logging
@@ -68,6 +109,24 @@ public:
         return value;
     }
 
+    constexpr Float<M, E> Flushed() const {
+        Float<M, E> ret;
+        ret.value = value;
+        if (std::abs(value) < MinNormal().ToFloat32()) {
+            ret.value = 0;
+        }
+        return ret;
+    }
+
+    constexpr Float<M, E> InfChecked() const {
+        Float<M, E> ret;
+        ret.value = value;
+        if (std::abs(value) > Max().ToFloat32()) {
+            ret.value = value * std::numeric_limits<float>::infinity();
+        }
+        return ret;
+    }
+
     constexpr Float<M, E> operator*(const Float<M, E>& flt) const {
         float result = value * flt.ToFloat32();
         // PICA gives 0 instead of NaN when multiplying by inf
@@ -95,22 +154,24 @@ public:
     }
 
     constexpr Float<M, E>& operator/=(const Float<M, E>& flt) {
-        value /= flt.ToFloat32();
+        value = operator/(flt).value;
         return *this;
     }
 
     constexpr Float<M, E>& operator+=(const Float<M, E>& flt) {
-        value += flt.ToFloat32();
+        value = operator+(flt).value;
         return *this;
     }
 
     constexpr Float<M, E>& operator-=(const Float<M, E>& flt) {
-        value -= flt.ToFloat32();
+        value = operator-(flt).value;
         return *this;
     }
 
     constexpr Float<M, E> operator-() const {
-        return Float<M, E>::FromFloat32(-ToFloat32());
+        Float<M, E> ret;
+        ret.value = -value;
+        return ret;
     }
 
     constexpr bool operator<(const Float<M, E>& flt) const {
diff --git a/src/video_core/renderer_software/sw_rasterizer.cpp b/src/video_core/renderer_software/sw_rasterizer.cpp
index 36aa2b03b..d0f42fe7d 100644
--- a/src/video_core/renderer_software/sw_rasterizer.cpp
+++ b/src/video_core/renderer_software/sw_rasterizer.cpp
@@ -30,7 +30,7 @@ using Pica::Texture::TextureInfo;
 // negative/positive z values when computing with f32 precision,
 // causing some vertices to get erroneously clipped. To workaround this problem,
 // we can use a very small epsilon value for clip plane comparison.
-constexpr f32 EPSILON_Z = 0.00000001f;
+constexpr f32 EPSILON_Z = 0.f;
 
 struct Vertex : Pica::OutputVertex {
     Vertex(const OutputVertex& v) : OutputVertex(v) {}
@@ -125,9 +125,8 @@ void RasterizerSoftware::AddTriangle(const Pica::OutputVertex& v0, const Pica::O
     auto* input_list = &buffer_b;
 
     // NOTE: We clip against a w=epsilon plane to guarantee that the output has a positive w value.
-    // TODO: Not sure if this is a valid approach. Also should probably instead use the smallest
-    //       epsilon possible within f24 accuracy.
-    static constexpr f24 EPSILON = f24::FromFloat32(0.00001f);
+    // TODO: Not sure if this is a valid approach.
+    static constexpr f24 EPSILON = f24::MinNormal();
     static constexpr f24 f0 = f24::Zero();
     static constexpr f24 f1 = f24::One();
     static constexpr std::array<ClippingEdge, 7> clipping_edges = {{
@@ -287,11 +286,11 @@ void RasterizerSoftware::ProcessTriangle(const Vertex& v0, const Vertex& v1, con
     max_y = ((max_y + Fix12P4::FracMask()) & Fix12P4::IntMask());
 
     const int bias0 =
-        IsRightSideOrFlatBottomEdge(vtxpos[0].xy(), vtxpos[1].xy(), vtxpos[2].xy()) ? -1 : 0;
+        IsRightSideOrFlatBottomEdge(vtxpos[0].xy(), vtxpos[1].xy(), vtxpos[2].xy()) ? 1 : 0;
     const int bias1 =
-        IsRightSideOrFlatBottomEdge(vtxpos[1].xy(), vtxpos[2].xy(), vtxpos[0].xy()) ? -1 : 0;
+        IsRightSideOrFlatBottomEdge(vtxpos[1].xy(), vtxpos[2].xy(), vtxpos[0].xy()) ? 1 : 0;
     const int bias2 =
-        IsRightSideOrFlatBottomEdge(vtxpos[2].xy(), vtxpos[0].xy(), vtxpos[1].xy()) ? -1 : 0;
+        IsRightSideOrFlatBottomEdge(vtxpos[2].xy(), vtxpos[0].xy(), vtxpos[1].xy()) ? 1 : 0;
 
     const auto w_inverse = Common::MakeVec(v0.pos.w, v1.pos.w, v2.pos.w);
 
@@ -314,13 +313,13 @@ void RasterizerSoftware::ProcessTriangle(const Vertex& v0, const Vertex& v1, con
                 }
 
                 // Calculate the barycentric coordinates w0, w1 and w2
-                const s32 w0 = bias0 + SignedArea(vtxpos[1].xy(), vtxpos[2].xy(), {x, y});
-                const s32 w1 = bias1 + SignedArea(vtxpos[2].xy(), vtxpos[0].xy(), {x, y});
-                const s32 w2 = bias2 + SignedArea(vtxpos[0].xy(), vtxpos[1].xy(), {x, y});
+                const s32 w0 = SignedArea(vtxpos[1].xy(), vtxpos[2].xy(), {x, y});
+                const s32 w1 = SignedArea(vtxpos[2].xy(), vtxpos[0].xy(), {x, y});
+                const s32 w2 = SignedArea(vtxpos[0].xy(), vtxpos[1].xy(), {x, y});
                 const s32 wsum = w0 + w1 + w2;
 
                 // If current pixel is not covered by the current primitive
-                if (w0 < 0 || w1 < 0 || w2 < 0) {
+                if (w0 < bias0 || w1 < bias1 || w2 < bias2) {
                     continue;
                 }