diff --git a/CMakeLists.txt b/CMakeLists.txt
index e51b764a..a98a9c4a 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,5 +1,5 @@
cmake_minimum_required(VERSION 3.8)
-project(dynarmic C CXX)
+project(dynarmic C CXX ASM)
# Determine if we're built as a subproject (using add_subdirectory)
# or if this is the master project.
diff --git a/src/backend/x64/emit_x64_floating_point.cpp b/src/backend/x64/emit_x64_floating_point.cpp
index e307f99a..a5710614 100644
--- a/src/backend/x64/emit_x64_floating_point.cpp
+++ b/src/backend/x64/emit_x64_floating_point.cpp
@@ -995,6 +995,111 @@ static void EmitFPRSqrtEstimate(BlockOfCode& code, EmitContext& ctx, IR::Inst* i
ctx.reg_alloc.DefineValue(inst, result);
return;
}
+
+ // TODO: VRSQRT14SS implementation (AVX512F)
+
+ auto args = ctx.reg_alloc.GetArgumentInfo(inst);
+
+ const Xbyak::Xmm operand = ctx.reg_alloc.UseXmm(args[0]);
+ const Xbyak::Xmm result = ctx.reg_alloc.ScratchXmm();
+ const Xbyak::Xmm value = ctx.reg_alloc.ScratchXmm();
+ [[maybe_unused]] const Xbyak::Reg32 tmp = ctx.reg_alloc.ScratchGpr().cvt32();
+
+ Xbyak::Label fallback, bad_values, end;
+
+ if constexpr (fsize == 64) {
+ code.cvtsd2ss(value, operand);
+
+ if (ctx.FPCR().RMode() == FP::RoundingMode::TowardsMinusInfinity || ctx.FPCR().RMode() == FP::RoundingMode::TowardsZero) {
+ code.ucomiss(value, code.MConst(xword, FP::FPInfo<u32>::MaxNormal(false)));
+ code.je(bad_values, code.T_NEAR);
+ }
+ } else {
+ code.movaps(value, operand);
+ }
+
+ code.movaps(xmm0, code.MConst(xword, 0xFFFF8000));
+ code.pand(value, xmm0);
+ code.por(value, code.MConst(xword, 0x00008000));
+
+ // Detect NaNs, negatives, zeros, denormals and infinities
+ code.ucomiss(value, code.MConst(xword, 0x00800000));
+ code.jna(bad_values, code.T_NEAR);
+
+ code.sqrtss(value, value);
+
+ code.movd(result, code.MConst(xword, 0x3F800000));
+ code.divss(result, value);
+
+ code.paddd(result, code.MConst(xword, 0x00004000));
+ code.pand(result, xmm0);
+
+ if constexpr (fsize == 64) {
+ code.cvtss2sd(result, result);
+ }
+ code.L(end);
+
+ code.SwitchToFarCode();
+
+ code.L(bad_values);
+ bool needs_fallback = false;
+ if constexpr (fsize == 32) {
+ Xbyak::Label default_nan;
+
+ code.movd(tmp, operand);
+
+ if (!ctx.FPCR().FZ()) {
+ if (ctx.FPCR().DN()) {
+ // a > 0x80000000
+ code.cmp(tmp, 0x80000000);
+ code.ja(default_nan, code.T_NEAR);
+ }
+
+ // a > 0 && a < 0x00800000;
+ code.sub(tmp, 1);
+ code.cmp(tmp, 0x007FFFFF);
+ code.jb(fallback);
+ needs_fallback = true;
+ }
+
+ code.rsqrtss(result, operand);
+
+ if (ctx.FPCR().DN()) {
+ code.ucomiss(result, result);
+ code.jnp(end, code.T_NEAR);
+ } else {
+ // FZ ? (a >= 0x80800000 && a <= 0xFF800000) : (a >= 0x80000001 && a <= 0xFF800000)
+ // !FZ path takes into account the subtraction by one from the earlier block
+ code.add(tmp, ctx.FPCR().FZ() ? 0x7F800000 : 0x80000000);
+ code.cmp(tmp, ctx.FPCR().FZ() ? 0x7F000001 : 0x7F800000);
+ code.jnb(end, code.T_NEAR);
+ }
+
+ code.L(default_nan);
+ code.movd(result, code.MConst(xword, 0x7FC00000));
+ code.jmp(end, code.T_NEAR);
+ } else {
+ needs_fallback = true;
+ }
+
+ code.L(fallback);
+ if (needs_fallback) {
+ code.sub(rsp, 8);
+ ABI_PushCallerSaveRegistersAndAdjustStackExcept(code, HostLocXmmIdx(result.getIdx()));
+ code.movq(code.ABI_PARAM1, operand);
+ code.mov(code.ABI_PARAM2.cvt32(), ctx.FPCR().Value());
+ code.lea(code.ABI_PARAM3, code.ptr[code.r15 + code.GetJitStateInfo().offsetof_fpsr_exc]);
+ code.CallFunction(&FP::FPRSqrtEstimate<FPT>);
+ code.movq(result, rax);
+ ABI_PopCallerSaveRegistersAndAdjustStackExcept(code, HostLocXmmIdx(result.getIdx()));
+ code.add(rsp, 8);
+ code.jmp(end, code.T_NEAR);
+ }
+
+ code.SwitchToNearCode();
+
+ ctx.reg_alloc.DefineValue(inst, result);
+ return;
}
auto args = ctx.reg_alloc.GetArgumentInfo(inst);
diff --git a/src/backend/x64/emit_x64_vector_floating_point.cpp b/src/backend/x64/emit_x64_vector_floating_point.cpp
index 9041b3fb..9e578460 100644
--- a/src/backend/x64/emit_x64_vector_floating_point.cpp
+++ b/src/backend/x64/emit_x64_vector_floating_point.cpp
@@ -406,22 +406,17 @@ void EmitThreeOpVectorOperation(BlockOfCode& code, EmitContext& ctx, IR::Inst* i
ctx.reg_alloc.DefineValue(inst, result);
}
-template<size_t fpcr_controlled_arg_index = 1, typename Lambda>
-void EmitTwoOpFallback(BlockOfCode& code, EmitContext& ctx, IR::Inst* inst, Lambda lambda) {
+template<typename Lambda>
+void EmitTwoOpFallbackWithoutRegAlloc(BlockOfCode& code, EmitContext& ctx, Xbyak::Xmm result, Xbyak::Xmm arg1, Lambda lambda, bool fpcr_controlled) {
const auto fn = static_cast<mp::equivalent_function_type<Lambda>*>(lambda);
- auto args = ctx.reg_alloc.GetArgumentInfo(inst);
- const bool fpcr_controlled = args[fpcr_controlled_arg_index].GetImmediateU1();
- const Xbyak::Xmm arg1 = ctx.reg_alloc.UseXmm(args[0]);
- const Xbyak::Xmm result = ctx.reg_alloc.ScratchXmm();
- ctx.reg_alloc.EndOfAllocScope();
- ctx.reg_alloc.HostCall(nullptr);
+ const u32 fpcr = ctx.FPCR(fpcr_controlled).Value();
constexpr u32 stack_space = 2 * 16;
code.sub(rsp, stack_space + ABI_SHADOW_SPACE);
code.lea(code.ABI_PARAM1, ptr[rsp + ABI_SHADOW_SPACE + 0 * 16]);
code.lea(code.ABI_PARAM2, ptr[rsp + ABI_SHADOW_SPACE + 1 * 16]);
- code.mov(code.ABI_PARAM3.cvt32(), ctx.FPCR(fpcr_controlled).Value());
+ code.mov(code.ABI_PARAM3.cvt32(), fpcr);
code.lea(code.ABI_PARAM4, code.ptr[code.r15 + code.GetJitStateInfo().offsetof_fpsr_exc]);
code.movaps(xword[code.ABI_PARAM2], arg1);
@@ -429,6 +424,19 @@ void EmitTwoOpFallback(BlockOfCode& code, EmitContext& ctx, IR::Inst* inst, Lamb
code.movaps(result, xword[rsp + ABI_SHADOW_SPACE + 0 * 16]);
code.add(rsp, stack_space + ABI_SHADOW_SPACE);
+}
+
+template<size_t fpcr_controlled_arg_index = 1, typename Lambda>
+void EmitTwoOpFallback(BlockOfCode& code, EmitContext& ctx, IR::Inst* inst, Lambda lambda) {
+ auto args = ctx.reg_alloc.GetArgumentInfo(inst);
+ const Xbyak::Xmm arg1 = ctx.reg_alloc.UseXmm(args[0]);
+ const Xbyak::Xmm result = ctx.reg_alloc.ScratchXmm();
+ ctx.reg_alloc.EndOfAllocScope();
+ ctx.reg_alloc.HostCall(nullptr);
+
+ const bool fpcr_controlled = args[fpcr_controlled_arg_index].GetImmediateU1();
+
+ EmitTwoOpFallbackWithoutRegAlloc(code, ctx, result, arg1, lambda, fpcr_controlled);
ctx.reg_alloc.DefineValue(inst, result);
}
@@ -1435,6 +1443,12 @@ template<size_t fsize>
static void EmitRSqrtEstimate(BlockOfCode& code, EmitContext& ctx, IR::Inst* inst) {
using FPT = mp::unsigned_integer_of_size<fsize>;
+ const auto fallback_fn = [](VectorArray<FPT>& result, const VectorArray<FPT>& operand, FP::FPCR fpcr, FP::FPSR& fpsr) {
+ for (size_t i = 0; i < result.size(); i++) {
+ result[i] = FP::FPRSqrtEstimate<FPT>(operand[i], fpcr, fpsr);
+ }
+ };
+
if constexpr (fsize != 16) {
if (ctx.HasOptimization(OptimizationFlag::Unsafe_ReducedErrorFP)) {
auto args = ctx.reg_alloc.GetArgumentInfo(inst);
@@ -1454,11 +1468,7 @@ static void EmitRSqrtEstimate(BlockOfCode& code, EmitContext& ctx, IR::Inst* ins
}
}
- EmitTwoOpFallback(code, ctx, inst, [](VectorArray<FPT>& result, const VectorArray<FPT>& operand, FP::FPCR fpcr, FP::FPSR& fpsr) {
- for (size_t i = 0; i < result.size(); i++) {
- result[i] = FP::FPRSqrtEstimate<FPT>(operand[i], fpcr, fpsr);
- }
- });
+ EmitTwoOpFallback(code, ctx, inst, fallback_fn);
}
void EmitX64::EmitFPVectorRSqrtEstimate16(EmitContext& ctx, IR::Inst* inst) {
diff --git a/src/common/fp/op/FPRSqrtEstimate.cpp b/src/common/fp/op/FPRSqrtEstimate.cpp
index 23bb4141..09f8ffe7 100644
--- a/src/common/fp/op/FPRSqrtEstimate.cpp
+++ b/src/common/fp/op/FPRSqrtEstimate.cpp
@@ -35,6 +35,7 @@ FPT FPRSqrtEstimate(FPT op, FPCR fpcr, FPSR& fpsr) {
}
if (type == FPType::Infinity) {
+ // Note: Just +Inf reaches here, negatives are handled in the case above.
return FPInfo<FPT>::Zero(false);
}
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index f4a596c2..105a4a00 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -19,6 +19,13 @@ add_executable(dynarmic_tests
rand_int.h
)
+if (NOT MSVC)
+ target_sources(dynarmic_tests PRIVATE
+ rsqrt_test.cpp
+ rsqrt_test_fn.s
+ )
+endif()
+
if (DYNARMIC_TESTS_USE_UNICORN)
target_sources(dynarmic_tests PRIVATE
A32/fuzz_arm.cpp
@@ -47,7 +54,7 @@ create_target_directory_groups(dynarmic_print_info)
target_link_libraries(dynarmic_tests PRIVATE dynarmic boost catch fmt mp xbyak)
target_include_directories(dynarmic_tests PRIVATE . ../src)
target_compile_options(dynarmic_tests PRIVATE ${DYNARMIC_CXX_FLAGS})
-target_compile_definitions(dynarmic_tests PRIVATE FMT_USE_USER_DEFINED_LITERALS=0)
+target_compile_definitions(dynarmic_tests PRIVATE FMT_USE_USER_DEFINED_LITERALS=0 CATCH_CONFIG_ENABLE_BENCHMARKING=1)
target_link_libraries(dynarmic_print_info PRIVATE dynarmic boost catch fmt mp)
target_include_directories(dynarmic_print_info PRIVATE . ../src)
diff --git a/tests/rsqrt_test.cpp b/tests/rsqrt_test.cpp
new file mode 100644
index 00000000..911b2030
--- /dev/null
+++ b/tests/rsqrt_test.cpp
@@ -0,0 +1,148 @@
+/* This file is part of the dynarmic project.
+ * Copyright (c) 2021 MerryMage
+ * SPDX-License-Identifier: 0BSD
+ */
+
+#include <catch.hpp>
+#include <fmt/printf.h>
+
+#include "common/common_types.h"
+#include "common/fp/fpcr.h"
+#include "common/fp/fpsr.h"
+#include "common/fp/op/FPRSqrtEstimate.h"
+
+extern "C" u32 rsqrt_inaccurate(u32);
+extern "C" u32 rsqrt_full(u32);
+extern "C" u32 rsqrt_full_gpr(u32);
+extern "C" u32 rsqrt_full_nb(u32);
+extern "C" u32 rsqrt_full_nb2(u32);
+extern "C" u32 rsqrt_full_nb_gpr(u32);
+extern "C" u32 rsqrt_newton(u32);
+extern "C" u32 rsqrt_hack(u32);
+
+using namespace Dynarmic;
+
+extern "C" u32 rsqrt_fallback(u32 value) {
+ FP::FPCR fpcr;
+ FP::FPSR fpsr;
+ return FP::FPRSqrtEstimate(value, fpcr, fpsr);
+}
+
+void Test(u32 value) {
+ FP::FPCR fpcr;
+ FP::FPSR fpsr;
+
+ const u32 expect = FP::FPRSqrtEstimate(value, fpcr, fpsr);
+ const u32 full = rsqrt_full(value);
+ const u32 full_gpr = rsqrt_full_gpr(value);
+ const u32 newton = rsqrt_newton(value);
+ const u32 hack = rsqrt_hack(value);
+
+ if (expect != full || expect != full_gpr || expect != newton || expect != hack) {
+ fmt::print("{:08x} = {:08x} : {:08x} : {:08x} : {:08x} : {:08x}\n", value, expect, full, full_gpr, newton, hack);
+
+ REQUIRE(expect == full);
+ REQUIRE(expect == full_gpr);
+ REQUIRE(expect == newton);
+ REQUIRE(expect == hack);
+ }
+}
+
+TEST_CASE("RSqrt Tests", "[fp][.]") {
+ Test(0x00000000);
+ Test(0x80000000);
+ Test(0x7f8b7201);
+ Test(0x7f800000);
+ Test(0x7fc00000);
+ Test(0xff800000);
+ Test(0xffc00000);
+ Test(0xff800001);
+
+ for (u64 i = 0; i < 0x1'0000'0000; i++) {
+ const u32 value = static_cast<u32>(i);
+ Test(value);
+ }
+}
+
+TEST_CASE("Benchmark RSqrt", "[fp][.]") {
+ BENCHMARK("Inaccurate") {
+ u64 total = 0;
+ for (u64 i = 0; i < 0x1'0000'0000; i += 0x1234) {
+ const u32 value = static_cast<u32>(i);
+ total += rsqrt_inaccurate(value);
+ }
+ return total;
+ };
+
+ BENCHMARK("Full divss") {
+ u64 total = 0;
+ for (u64 i = 0; i < 0x1'0000'0000; i += 0x1234) {
+ const u32 value = static_cast<u32>(i);
+ total += rsqrt_full(value);
+ }
+ return total;
+ };
+
+ BENCHMARK("Full divss (GPR)") {
+ u64 total = 0;
+ for (u64 i = 0; i < 0x1'0000'0000; i += 0x1234) {
+ const u32 value = static_cast<u32>(i);
+ total += rsqrt_full_gpr(value);
+ }
+ return total;
+ };
+
+ BENCHMARK("Full divss (NB)") {
+ u64 total = 0;
+ for (u64 i = 0; i < 0x1'0000'0000; i += 0x1234) {
+ const u32 value = static_cast<u32>(i);
+ total += rsqrt_full_nb(value);
+ }
+ return total;
+ };
+
+ BENCHMARK("Full divss (NB2)") {
+ u64 total = 0;
+ for (u64 i = 0; i < 0x1'0000'0000; i += 0x1234) {
+ const u32 value = static_cast<u32>(i);
+ total += rsqrt_full_nb2(value);
+ }
+ return total;
+ };
+
+ BENCHMARK("Full divss (NB + GPR)") {
+ u64 total = 0;
+ for (u64 i = 0; i < 0x1'0000'0000; i += 0x1234) {
+ const u32 value = static_cast<u32>(i);
+ total += rsqrt_full_nb_gpr(value);
+ }
+ return total;
+ };
+
+ BENCHMARK("One Newton iteration") {
+ u64 total = 0;
+ for (u64 i = 0; i < 0x1'0000'0000; i += 0x1234) {
+ const u32 value = static_cast<u32>(i);
+ total += rsqrt_newton(value);
+ }
+ return total;
+ };
+
+ BENCHMARK("Ugly Hack") {
+ u64 total = 0;
+ for (u64 i = 0; i < 0x1'0000'0000; i += 0x1234) {
+ const u32 value = static_cast<u32>(i);
+ total += rsqrt_hack(value);
+ }
+ return total;
+ };
+
+ BENCHMARK("Softfloat") {
+ u64 total = 0;
+ for (u64 i = 0; i < 0x1'0000'0000; i += 0x1234) {
+ const u32 value = static_cast<u32>(i);
+ total += rsqrt_fallback(value);
+ }
+ return total;
+ };
+}
diff --git a/tests/rsqrt_test_fn.s b/tests/rsqrt_test_fn.s
new file mode 100644
index 00000000..8e985917
--- /dev/null
+++ b/tests/rsqrt_test_fn.s
@@ -0,0 +1,303 @@
+.global _rsqrt_inaccurate
+.global rsqrt_inaccurate
+.global _rsqrt_full
+.global rsqrt_full
+.global _rsqrt_full_gpr
+.global rsqrt_full_gpr
+.global _rsqrt_full_nb
+.global rsqrt_full_nb
+.global _rsqrt_full_nb2
+.global rsqrt_full_nb2
+.global _rsqrt_full_nb_gpr
+.global rsqrt_full_nb_gpr
+.global _rsqrt_newton
+.global rsqrt_newton
+.global _rsqrt_hack
+.global rsqrt_hack
+.global _rsqrt_fallback
+
+.text
+.intel_syntax
+
+.align 16
+min_pos_denorm:
+.long 0x00800000,0,0,0
+penultimate_bit:
+.long 0x00008000,0,0,0
+ultimate_bit:
+.long 0x00004000,0,0,0
+top_mask:
+.long 0xFFFF8000,0,0,0
+one:
+.long 0x3f800000,0,0,0
+half:
+.long 0x3f000000,0,0,0
+one_point_five:
+.long 0x3fc00000,0,0,0
+magic1:
+.long 0x60000000,0,0,0
+magic2:
+.long 0x3c000000,0,0,0
+magic3:
+.long 0x000047ff,0,0,0
+
+_rsqrt_inaccurate:
+rsqrt_inaccurate:
+ movd xmm0, edi
+
+ rsqrtss xmm0, xmm0
+
+ movd eax, xmm0
+ ret
+
+_rsqrt_full:
+rsqrt_full:
+ movd xmm0, edi
+
+ pand xmm0, [rip + top_mask]
+ por xmm0, [rip + penultimate_bit]
+
+ vcmpngt_uqss xmm1, xmm0, [rip + min_pos_denorm]
+ ptest xmm1, xmm1
+ jnz rsqrt_full_bad
+
+ sqrtss xmm0, xmm0
+
+ movd xmm1, [rip + one]
+ divss xmm1, xmm0
+
+ paddd xmm1, [rip + ultimate_bit]
+ pand xmm1, [rip + top_mask]
+
+ movd eax, xmm1
+ ret
+
+_rsqrt_full_gpr:
+rsqrt_full_gpr:
+ movd eax, xmm0 # Emulate regalloc mov
+
+ mov eax, edi
+ and eax, 0xFFFF8000
+ or eax, 0x00008000
+
+ movd xmm0, eax
+ vcmpngt_uqss xmm1, xmm0, [rip + min_pos_denorm]
+ ptest xmm1, xmm1
+ jnz rsqrt_full_bad
+
+ sqrtss xmm0, xmm0
+
+ movd xmm1, [rip + one]
+ divss xmm1, xmm0
+ movd eax, xmm1
+
+ add eax, 0x00004000
+ and eax, 0xffff8000
+
+ movd xmm0, eax # Emulate regalloc mov
+ ret
+
+_rsqrt_full_nb2:
+rsqrt_full_nb2:
+ movd xmm0, edi
+
+ pand xmm0, [rip + top_mask]
+ por xmm0, [rip + penultimate_bit]
+
+ ucomiss xmm0, [rip + min_pos_denorm]
+ jna rsqrt_full_bad_new1
+
+ sqrtss xmm0, xmm0
+
+ movd xmm1, [rip + one]
+ divss xmm1, xmm0
+
+ paddd xmm1, [rip + ultimate_bit]
+ pand xmm1, [rip + top_mask]
+
+ movd eax, xmm1
+ ret
+
+_rsqrt_full_nb:
+rsqrt_full_nb:
+ movd xmm0, edi
+
+ pand xmm0, [rip + top_mask]
+ por xmm0, [rip + penultimate_bit]
+
+ vcmpngt_uqss xmm1, xmm0, [rip + min_pos_denorm]
+ ptest xmm1, xmm1
+ jnz rsqrt_full_bad_new1
+
+ sqrtss xmm0, xmm0
+
+ movd xmm1, [rip + one]
+ divss xmm1, xmm0
+
+ paddd xmm1, [rip + ultimate_bit]
+ pand xmm1, [rip + top_mask]
+
+ movd eax, xmm1
+ ret
+
+rsqrt_full_bad_new1:
+ cmp edi, 0x00800000
+ jb rsqrt_full_bad_new_fallback1
+
+ movd xmm0, edi
+ rsqrtss xmm1, xmm0
+
+ ucomiss xmm1, xmm1
+ jp rsqrt_full_bad_new1_nan
+
+ movd eax, xmm1
+ ret
+
+rsqrt_full_bad_new_fallback1:
+ call _rsqrt_fallback
+ ret
+
+rsqrt_full_bad_new1_nan:
+ ucomiss xmm0, xmm0
+ jp rsqrt_full_bad_new1_nan_ret
+
+ mov eax, 0x7FC00000
+ ret
+
+rsqrt_full_bad_new1_nan_ret:
+ ret
+
+_rsqrt_full_nb_gpr:
+rsqrt_full_nb_gpr:
+ movd eax, xmm0 # Emulate regalloc mov
+
+ mov eax, edi
+ and eax, 0xFFFF8000
+ or eax, 0x00008000
+
+ movd xmm0, eax
+ vcmpngt_uqss xmm1, xmm0, [rip + min_pos_denorm]
+ ptest xmm1, xmm1
+ jnz rsqrt_full_bad_new2
+
+ sqrtss xmm0, xmm0
+
+ movd xmm1, [rip + one]
+ divss xmm1, xmm0
+ movd eax, xmm1
+
+ add eax, 0x00004000
+ and eax, 0xffff8000
+
+ movd xmm0, eax # Emulate regalloc mov
+ ret
+
+rsqrt_full_bad_new2:
+ cmp edi, 0x00800000
+ jb rsqrt_full_bad_new_fallback2
+
+ movd xmm0, edi
+ rsqrtss xmm1, xmm0
+
+ test edi, edi
+ js rsqrt_full_bad_new2_nan
+
+ movd eax, xmm1
+ ret
+
+rsqrt_full_bad_new_fallback2:
+ call _rsqrt_fallback
+ ret
+
+rsqrt_full_bad_new2_nan:
+ mov eax, 0x7FC00000
+ ret
+
+rsqrt_full_bad:
+ xorps xmm1, xmm1
+ movd xmm0, edi
+ ucomiss xmm0, xmm1
+ jp rsqrt_full_nan
+ je rsqrt_full_zero
+ jc rsqrt_full_neg
+
+ cmp edi, 0x7F800000
+ je rsqrt_full_inf
+
+ # TODO: Full Denormal Implementation
+ call _rsqrt_fallback
+ ret
+
+rsqrt_full_neg:
+ mov eax, 0x7FC00000
+ ret
+
+rsqrt_full_inf:
+ xor eax, eax
+ ret
+
+rsqrt_full_nan:
+ mov eax, edi
+ or eax, 0x00400000
+ ret
+
+rsqrt_full_zero:
+ mov eax, edi
+ or eax, 0x7F800000
+ ret
+
+_rsqrt_newton:
+rsqrt_newton:
+ movd xmm0, edi
+
+ pand xmm0, [rip + top_mask]
+ por xmm0, [rip + penultimate_bit]
+
+ vcmpngt_uqss xmm1, xmm0, [rip + min_pos_denorm]
+ ptest xmm1, xmm1
+ jnz rsqrt_full_bad
+
+ rsqrtps xmm1, xmm0
+ mulss xmm0, [rip + half]
+ vmulss xmm2, xmm1, xmm1
+ mulss xmm2, xmm0
+ movaps xmm0, [rip + one_point_five]
+ subss xmm0, xmm2
+ mulss xmm0, xmm1
+
+ paddd xmm0, [rip + ultimate_bit]
+ pand xmm0, [rip + top_mask]
+
+ movd eax, xmm0
+ ret
+
+_rsqrt_hack:
+rsqrt_hack:
+ movd xmm9, edi
+
+ vpand xmm0, xmm9, [rip + top_mask]
+ por xmm0, [rip + penultimate_bit]
+
+ # detect NaNs, negatives, zeros, denormals and infinities
+ vcmpngt_uqss xmm1, xmm0, [rip + min_pos_denorm]
+ ptest xmm1, xmm1
+ jnz rsqrt_full_bad
+
+ # calculate x64 estimate
+ rsqrtps xmm0, xmm0
+
+ # calculate correction factor
+ vpslld xmm1, xmm9, 8
+ vpsrad xmm2, xmm1, 31
+ paddd xmm1, [rip + magic1]
+ pcmpgtd xmm1, [rip + magic2]
+ pxor xmm1, xmm2
+ movaps xmm2, [rip + magic3]
+ psubd xmm2, xmm1
+
+ # correct x64 estimate
+ paddd xmm0, xmm2
+ pand xmm0, [rip + top_mask]
+
+ movd eax, xmm0
+ ret