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More improvements to the macros
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@eggrobin
eggrobin committed Jan 1, 2025
1 parent 8a54073 commit d6a22b9
Showing 1 changed file with 61 additions and 52 deletions.
113 changes: 61 additions & 52 deletions numerics/sin_cos.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -15,29 +15,28 @@
#include "quantities/elementary_functions.hpp"

#define OSACA_ANALYSED_FUNCTION Cos
#define UNDER_OSACA_HYPOTHESES(expression) \
[] { \
constexpr bool UseHardwareFMA = true; \
constexpr double θ = 3; \
/* From argument reduction. */ \
constexpr std::int64_t n = \
static_cast<std::int64_t>(θ * (2 / π) + 0.5); \
constexpr double reduction_value = θ - n * π_over_2_high; \
constexpr double reduction_error = n * π_over_2_low; \
/* Used to determine whether a better argument reduction is needed. */ \
constexpr DoublePrecision<double> θ_reduced = \
QuickTwoDifference(reduction_value, reduction_error); \
/* Used in Sin to detect the near-0 case. */ \
constexpr double abs_x = \
θ_reduced.value > 0 ? θ_reduced.value : -θ_reduced.value; \
/* Used throughout the top-level functions. */ \
constexpr std::int64_t quadrant = n & 0b11; \
/* Used in DetectDangerousRounding. */ \
constexpr double normalized_error = 0; \
/* Not NaN is the only part that matters; used at the end of the */ \
/* top-level functions to determine whether to call the slow path. */ \
constexpr double value = 1; \
return expression; \
#define UNDER_OSACA_HYPOTHESES(expression) \
[&] { \
constexpr bool UseHardwareFMA = true; \
constexpr double θ = 0.1; \
/* From argument reduction. */ \
constexpr std::int64_t n = static_cast<std::int64_t>(θ * (2 / π) + 0.5); \
constexpr double reduction_value = θ - n * π_over_2_high; \
constexpr double reduction_error = n * π_over_2_low; \
/* Used to determine whether a better argument reduction is needed. */ \
constexpr DoublePrecision<double> θ_reduced = \
QuickTwoDifference(reduction_value, reduction_error); \
/* Used in Sin to detect the near-0 case. */ \
constexpr double abs_x = \
θ_reduced.value > 0 ? θ_reduced.value : -θ_reduced.value; \
/* Used throughout the top-level functions. */ \
constexpr std::int64_t quadrant = n & 0b11; \
/* Used in DetectDangerousRounding. */ \
constexpr double normalized_error = 0; \
/* Not NaN is the only part that matters; used at the end of the */ \
/* top-level functions to determine whether to call the slow path. */ \
constexpr double value = 1; \
return expression; \
}()

#if defined(OSACA_ANALYSED_FUNCTION)
Expand Down Expand Up @@ -126,27 +125,37 @@
// — Return statements may be in if statements, and there may be several of
// them, so they cannot be the end of a loop started unconditionally. Instead
// we loop with goto.
// — We need to prevent the compiler from moving the start and end markers into
// the middle of register saving and restoring code, which would mess up the
// dependency analysis. This is done with additional conditional gotos.
// — Some volatile reads and writes are used to clarify identity of the
// registers in the generated code (where the names of `OSACA_result` and, if
// `OSACA_CARRY_LOOP_THROUGH_REGISTER`, `OSACA_loop_carry` appear in movsd
// instructions) and to improve the structure of the generated graph.
// `OSACA_CARRY_LOOP_THROUGH_REGISTER` is set to 0, `OSACA_loop_carry` appear
// in movsd instructions).
//
// Putting a load of the input from memory in the analysed section prevents the
// compiler from reusing intermediate values in the next iteration, e.g., if the
// absolute value of the result is computed first, the compiler might reuse it
// instead of computing the absolute value of the input. However:
// Carrying the loop dependency through a memory load and store can make the
// dependency graph easier to understand, as it forces any usage of the input to
// depend on the initial movsd, with the loop carried by a single backward edge
// to that initial movsd.
// If the loop is carried through a register, multiple usages of the input may
// result in multiple back edges from the final instruction that computed the
// result. Carrying the loop through the memory could also potentially prevent
// the compiler from reusing intermediate values in the next iteration, e.g., if
// the the computation of f(x) depends on -x and produces -f(x) before f(x), as
// in an even function defined in terms of its positive half, the compiler might
// reuse -f(x₀)=-x₁ instead of computing -x₁ from x₁=f(x₀). However:
// — it adds a spurious move to the latency;
// — some tools (IACA, LLVM-MCA) cannot see the dependency through memory.
// Set OSACA_CARRY_LOOP_THROUGH_REGISTER to 1 to carry the loop dependency
// through a register instead.
// — some tools (IACA) cannot see the dependency through memory.
// Set OSACA_CARRY_LOOP_THROUGH_REGISTER to 0 to carry the loop through memory.

#define OSACA_EVALUATE_CONDITIONS 1
#define OSACA_CARRY_LOOP_THROUGH_REGISTER 0
#define OSACA_CARRY_LOOP_THROUGH_REGISTER 1

static bool OSACA_loop_terminator = false;

#define OSACA_FUNCTION_BEGIN(arg) \
double OSACA_LOOP_CARRY_QUALIFIER OSACA_loop_carry = arg; \
OSACA_outer_loop: \
if constexpr (std::string_view(__func__) == \
STRINGIFY_EXPANSION(OSACA_ANALYSED_FUNCTION)) { \
IACA_VC64_START; \
Expand All @@ -157,25 +166,25 @@ static bool OSACA_loop_terminator = false;
_Pragma("warning(pop)"); \
arg = OSACA_loop_carry

#define OSACA_RETURN(result) \
do { \
if constexpr (std::string_view(__func__) == \
STRINGIFY_EXPANSION(OSACA_ANALYSED_FUNCTION)) { \
OSACA_loop_carry = (result); \
if (!OSACA_loop_terminator) { \
goto OSACA_loop; \
} \
double volatile OSACA_result = OSACA_loop_carry; \
IACA_VC64_END; \
/* The second goto prevents the the end marker from being interleaved */ \
/* with register restoring moves. */ \
if (!OSACA_loop_terminator) { \
goto OSACA_loop; \
} \
return OSACA_result; \
} else { \
return (result); \
} \
#define OSACA_RETURN(result) \
do { \
if constexpr (std::string_view(__func__) == \
STRINGIFY_EXPANSION(OSACA_ANALYSED_FUNCTION)) { \
OSACA_loop_carry = (result); \
if (!OSACA_loop_terminator) { \
goto OSACA_loop; \
} \
double volatile OSACA_result = OSACA_loop_carry; \
IACA_VC64_END; \
/* The outer loop prevents the the start and end marker from being */ \
/* interleaved with register saving and restoring moves. */ \
if (!OSACA_loop_terminator) { \
goto OSACA_outer_loop; \
} \
return OSACA_result; \
} else { \
return (result); \
} \
} while (false)

#if OSACA_CARRY_LOOP_THROUGH_REGISTER
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