[libc-commits] [libc] a5466f0 - [libc] Improve the performance of expm1f.
Tue Ly via libc-commits
libc-commits at lists.llvm.org
Wed Mar 30 16:23:41 PDT 2022
Author: Tue Ly
Date: 2022-03-30T19:23:25-04:00
New Revision: a5466f0436d2c287a20882cd1beae3e6cf56fea4
URL: https://github.com/llvm/llvm-project/commit/a5466f0436d2c287a20882cd1beae3e6cf56fea4
DIFF: https://github.com/llvm/llvm-project/commit/a5466f0436d2c287a20882cd1beae3e6cf56fea4.diff
LOG: [libc] Improve the performance of expm1f.
Improve the performance of expm1f:
- Rearrange the selection logic for different cases to improve the overall
throughput.
- Use the same degree-4 polynomial for large inputs as `expf`
(https://reviews.llvm.org/D122418), reduced from a degree-7 polynomial.
Performance benchmark using perf tool from CORE-MATH project
(https://gitlab.inria.fr/core-math/core-math/-/tree/master):
Before this patch:
```
$ ./perf.sh expm1f
CORE-MATH reciprocal throughput : 15.362
System LIBC reciprocal throughput : 53.288
LIBC reciprocal throughput : 54.572
$ ./perf.sh expm1f --latency
CORE-MATH latency : 57.759
System LIBC latency : 147.146
LIBC latency : 118.057
```
After this patch:
```
$ ./perf.sh expm1f
CORE-MATH reciprocal throughput : 15.359
System LIBC reciprocal throughput : 53.188
LIBC reciprocal throughput : 14.600
$ ./perf.sh expm1f --latency
CORE-MATH latency : 57.774
System LIBC latency : 147.119
LIBC latency : 60.280
```
Reviewed By: michaelrj, santoshn, zimmermann6
Differential Revision: https://reviews.llvm.org/D122538
Added:
Modified:
libc/src/math/generic/expm1f.cpp
libc/test/src/math/exhaustive/exhaustive_test.cpp
libc/test/src/math/exhaustive/expm1f_test.cpp
libc/test/src/math/expm1f_test.cpp
Removed:
################################################################################
diff --git a/libc/src/math/generic/expm1f.cpp b/libc/src/math/generic/expm1f.cpp
index 7256c4fd75f56..b0544b76e09ac 100644
--- a/libc/src/math/generic/expm1f.cpp
+++ b/libc/src/math/generic/expm1f.cpp
@@ -24,41 +24,59 @@ LLVM_LIBC_FUNCTION(float, expm1f, (float x)) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
- // When x < log(2^-25) or nan
- if (unlikely(xbits.uintval() >= 0xc18a'a123U)) {
- // exp(-Inf) = 0
- if (xbits.is_inf())
- return -1.0f;
- // exp(nan) = nan
- if (xbits.is_nan())
- return x;
+ uint32_t x_u = xbits.uintval();
+ uint32_t x_abs = x_u & 0x7fff'ffffU;
+
+ // Exceptional value
+ if (unlikely(x_u == 0x3e35'bec5U)) { // x = 0x1.6b7d8ap-3f
int round_mode = fputil::get_round();
- if (round_mode == FE_UPWARD || round_mode == FE_TOWARDZERO)
- return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
- return -1.0f;
+ if (round_mode == FE_TONEAREST || round_mode == FE_UPWARD)
+ return 0x1.8dbe64p-3f;
+ return 0x1.8dbe62p-3f;
}
- // x >= 89 or nan
- if (unlikely(!xbits.get_sign() && (xbits.uintval() >= 0x42b2'0000))) {
- if (xbits.uintval() < 0x7f80'0000U) {
- int rounding = fputil::get_round();
- if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
- return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
- errno = ERANGE;
+ // When |x| > 25*log(2), or nan
+ if (unlikely(x_abs >= 0x418a'a123U)) {
+ // x < log(2^-25)
+ if (xbits.get_sign()) {
+ // exp(-Inf) = 0
+ if (xbits.is_inf())
+ return -1.0f;
+ // exp(nan) = nan
+ if (xbits.is_nan())
+ return x;
+ int round_mode = fputil::get_round();
+ if (round_mode == FE_UPWARD || round_mode == FE_TOWARDZERO)
+ return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f
+ return -1.0f;
+ } else {
+ // x >= 89 or nan
+ if (xbits.uintval() >= 0x42b2'0000) {
+ if (xbits.uintval() < 0x7f80'0000U) {
+ int rounding = fputil::get_round();
+ if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
+ return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
+
+ errno = ERANGE;
+ }
+ return x + static_cast<float>(FPBits::inf());
+ }
}
- return x + static_cast<float>(FPBits::inf());
}
- int unbiased_exponent = static_cast<int>(xbits.get_unbiased_exponent());
// |x| < 2^-4
- if (unbiased_exponent < 123) {
+ if (x_abs < 0x3d80'0000U) {
// |x| < 2^-25
- if (unbiased_exponent < 102) {
+ if (x_abs < 0x3300'0000U) {
// x = -0.0f
if (unlikely(xbits.uintval() == 0x8000'0000U))
return x;
- // When |x| < 2^-25, the relative error:
- // |(e^x - 1) - x| / |x| < |x^2| / |x| = |x| < 2^-25 < epsilon(1)/2.
+ // When |x| < 2^-25, the relative error of the approximation e^x - 1 ~ x
+ // is:
+ // |(e^x - 1) - x| / |e^x - 1| < |x^2| / |x|
+ // = |x|
+ // < 2^-25
+ // < epsilon(1)/2.
// So the correctly rounded values of expm1(x) are:
// = x + eps(x) if rounding mode = FE_UPWARD,
// or (rounding mode = FE_TOWARDZERO and x is negative),
@@ -67,20 +85,21 @@ LLVM_LIBC_FUNCTION(float, expm1f, (float x)) {
// fma(x, x, x) ~ x + x^2 instead.
return fputil::fma(x, x, x);
}
+
// 2^-25 <= |x| < 2^-4
double xd = static_cast<double>(x);
double xsq = xd * xd;
// Degree-8 minimax polynomial generated by Sollya with:
// > display = hexadecimal;
- // > P = fpminimax(expm1(x)/x, 7, [|D...|], [-2^-4, 2^-4]);
+ // > P = fpminimax((expm1(x) - x)/x^2, 6, [|D...|], [-2^-4, 2^-4]);
double r =
- fputil::polyeval(xd, 0x1p-1, 0x1.55555555559abp-3, 0x1.55555555551a7p-5,
- 0x1.111110f70f2a4p-7, 0x1.6c16c17639e82p-10,
- 0x1.a02526febbea6p-13, 0x1.a01dc40888fcdp-16);
+ fputil::polyeval(xd, 0x1p-1, 0x1.55555555557ddp-3, 0x1.55555555552fap-5,
+ 0x1.111110fcd58b7p-7, 0x1.6c16c1717660bp-10,
+ 0x1.a0241f0006d62p-13, 0x1.a01e3f8d3c06p-16);
return static_cast<float>(fputil::fma(r, xsq, xd));
}
- // For -18 < x < 89, to compute exp(x), we perform the following range
+ // For -18 < x < 89, to compute expm1(x), we perform the following range
// reduction: find hi, mid, lo such that:
// x = hi + mid + lo, in which
// hi is an integer,
@@ -89,48 +108,30 @@ LLVM_LIBC_FUNCTION(float, expm1f, (float x)) {
// In particular,
// hi + mid = round(x * 2^7) * 2^(-7).
// Then,
- // exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo).
+ // expm1(x) = exp(hi + mid + lo) - 1 = exp(hi) * exp(mid) * exp(lo) - 1.
// We store exp(hi) and exp(mid) in the lookup tables EXP_M1 and EXP_M2
- // respectively. exp(lo) is computed using a degree-7 minimax polynomial
+ // respectively. exp(lo) is computed using a degree-4 minimax polynomial
// generated by Sollya.
- // Exceptional value
- if (xbits.uintval() == 0xbdc1'c6cbU) {
- // x = -0x1.838d96p-4f
- int round_mode = fputil::get_round();
- if (round_mode == FE_TONEAREST || round_mode == FE_DOWNWARD)
- return -0x1.71c884p-4f;
- return -0x1.71c882p-4f;
- }
-
// x_hi = hi + mid.
- int x_hi = static_cast<int>(x * 0x1.0p7f);
+ int x_hi = static_cast<int>(x * 0x1.0p7f + (xbits.get_sign() ? -0.5f : 0.5f));
// Subtract (hi + mid) from x to get lo.
x -= static_cast<float>(x_hi) * 0x1.0p-7f;
double xd = static_cast<double>(x);
- // Make sure that -2^(-8) <= lo < 2^-8.
- if (x >= 0x1.0p-8f) {
- ++x_hi;
- xd -= 0x1.0p-7;
- }
- if (x < -0x1.0p-8f) {
- --x_hi;
- xd += 0x1.0p-7;
- }
x_hi += 104 << 7;
// hi = x_hi >> 7
double exp_hi = EXP_M1[x_hi >> 7];
// lo = x_hi & 0x0000'007fU;
double exp_mid = EXP_M2[x_hi & 0x7f];
double exp_hi_mid = exp_hi * exp_mid;
- // Degree-7 minimax polynomial generated by Sollya with the following
+ // Degree-4 minimax polynomial generated by Sollya with the following
// commands:
// > display = hexadecimal;
- // > Q = fpminimax(expm1(x)/x, 6, [|D...|], [-2^-8, 2^-8]);
+ // > Q = fpminimax(expm1(x)/x, 3, [|D...|], [-2^-8, 2^-8]);
// > Q;
- double exp_lo = fputil::polyeval(
- xd, 0x1p0, 0x1p0, 0x1p-1, 0x1.5555555555555p-3, 0x1.55555555553ap-5,
- 0x1.1111111204dfcp-7, 0x1.6c16cb2da593ap-10, 0x1.9ff1648996d2ep-13);
+ double exp_lo =
+ fputil::polyeval(xd, 0x1.0p0, 0x1.ffffffffff777p-1, 0x1.000000000071cp-1,
+ 0x1.555566668e5e7p-3, 0x1.55555555ef243p-5);
return static_cast<float>(fputil::fma(exp_hi_mid, exp_lo, -1.0));
}
diff --git a/libc/test/src/math/exhaustive/exhaustive_test.cpp b/libc/test/src/math/exhaustive/exhaustive_test.cpp
index 227a9a113ba84..1b713eb92ed98 100644
--- a/libc/test/src/math/exhaustive/exhaustive_test.cpp
+++ b/libc/test/src/math/exhaustive/exhaustive_test.cpp
@@ -15,6 +15,7 @@
#include <vector>
#include "exhaustive_test.h"
+#include "src/__support/FPUtil/FPBits.h"
#include "utils/UnitTest/Test.h"
template <typename T>
@@ -28,14 +29,26 @@ void LlvmLibcExhaustiveTest<T>::test_full_range(T start, T stop, int nthreads,
thread_list.emplace_back([this, begin, end, rounding]() {
std::stringstream msg;
msg << "-- Testing from " << begin << " to " << end << " [0x" << std::hex
- << begin << ", 0x" << end << ") ..." << std::endl;
+ << begin << ", 0x" << end << "), [" << std::hexfloat
+ << float(__llvm_libc::fputil::FPBits<float>(
+ static_cast<uint32_t>(begin)))
+ << ", "
+ << float(
+ __llvm_libc::fputil::FPBits<float>(static_cast<uint32_t>(end)))
+ << ") ..." << std::endl;
std::cout << msg.str();
msg.str("");
bool result = check(begin, end, rounding);
msg << "** Finished testing from " << std::dec << begin << " to " << end
- << " [0x" << std::hex << begin << ", 0x" << end
+ << " [0x" << std::hex << begin << ", 0x" << end << "), ["
+ << std::hexfloat
+ << float(__llvm_libc::fputil::FPBits<float>(
+ static_cast<uint32_t>(begin)))
+ << ", "
+ << float(
+ __llvm_libc::fputil::FPBits<float>(static_cast<uint32_t>(end)))
<< ") : " << (result ? "PASSED" : "FAILED") << std::endl;
std::cout << msg.str();
});
diff --git a/libc/test/src/math/exhaustive/expm1f_test.cpp b/libc/test/src/math/exhaustive/expm1f_test.cpp
index 8a4cf762b2695..5131f1de6025e 100644
--- a/libc/test/src/math/exhaustive/expm1f_test.cpp
+++ b/libc/test/src/math/exhaustive/expm1f_test.cpp
@@ -12,6 +12,8 @@
#include "utils/MPFRWrapper/MPFRUtils.h"
#include "utils/UnitTest/FPMatcher.h"
+#include <thread>
+
using FPBits = __llvm_libc::fputil::FPBits<float>;
namespace mpfr = __llvm_libc::testing::mpfr;
@@ -20,18 +22,19 @@ struct LlvmLibcExpfExhaustiveTest : public LlvmLibcExhaustiveTest<uint32_t> {
bool check(uint32_t start, uint32_t stop,
mpfr::RoundingMode rounding) override {
mpfr::ForceRoundingMode r(rounding);
- uint32_t bits = start;
+ uint32_t bits = stop;
bool result = true;
do {
FPBits xbits(bits);
float x = float(xbits);
result &= EXPECT_MPFR_MATCH(mpfr::Operation::Expm1, x,
__llvm_libc::expm1f(x), 0.5, rounding);
- } while (bits++ < stop);
+ } while (bits-- > start);
+ return result;
}
};
-static constexpr int NUM_THREADS = 16;
+static const int NUM_THREADS = std::thread::hardware_concurrency();
// Range: [0, 89];
static constexpr uint32_t POS_START = 0x0000'0000U;
diff --git a/libc/test/src/math/expm1f_test.cpp b/libc/test/src/math/expm1f_test.cpp
index 0971b708b6d86..78be76ec57f73 100644
--- a/libc/test/src/math/expm1f_test.cpp
+++ b/libc/test/src/math/expm1f_test.cpp
@@ -92,6 +92,11 @@ TEST(LlvmLibcExpm1fTest, Borderline) {
ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Expm1, x,
__llvm_libc::expm1f(x), 0.5);
EXPECT_MATH_ERRNO(0);
+
+ x = float(FPBits(0x3e35bec5U));
+ ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Expm1, x,
+ __llvm_libc::expm1f(x), 0.5);
+ EXPECT_MATH_ERRNO(0);
}
TEST(LlvmLibcExpm1fTest, InFloatRange) {
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