104 changes: 104 additions & 0 deletions libc/src/stdfix/expk.cpp
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//===-- Implementation of expk function ----------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#include "expk.h"
#include "src/__support/CPP/bit.h"
#include "src/__support/common.h"
#include "src/__support/fixed_point/fx_bits.h"

namespace LIBC_NAMESPACE {

namespace {

// Look up tables for exp(hi) and exp(mid).
// Generated with Sollya:
// > for i from 0 to 23 do {
// hi = i - 11;
// e_hi = nearestint(exp(hi) * 2^15) * 2^-15;
// print(e_hi, "k,");
// };
static constexpr accum EXP_HI[24] = {
0x1p-15k, 0x1p-15k, 0x1p-13k, 0x1.6p-12k,
0x1.ep-11k, 0x1.44p-9k, 0x1.bap-8k, 0x1.2cp-6k,
0x1.97cp-5k, 0x1.153p-3k, 0x1.78b8p-2k, 0x1p0k,
0x1.5bf1p1k, 0x1.d8e68p2k, 0x1.415e6p4k, 0x1.b4c9p5k,
0x1.28d388p7k, 0x1.936dc6p8k, 0x1.1228858p10k, 0x1.749ea7cp11k,
0x1.fa7157cp12k, 0x1.5829dcf8p14k, 0x1.d3c4489p15k, ACCUM_MAX,
};

// Generated with Sollya:
// > for i from 0 to 15 do {
// m = i/16 - 0.0625;
// e_m = nearestint(exp(m) * 2^15) * 2^-15;
// print(e_m, "k,");
// };
static constexpr accum EXP_MID[16] = {
0x1.e0fcp-1k, 0x1p0k, 0x1.1082p0k, 0x1.2216p0k,
0x1.34ccp0k, 0x1.48b6p0k, 0x1.5deap0k, 0x1.747ap0k,
0x1.8c8p0k, 0x1.a612p0k, 0x1.c14cp0k, 0x1.de46p0k,
0x1.fd1ep0k, 0x1.0efap1k, 0x1.2074p1k, 0x1.330ep1k,
};

} // anonymous namespace

LLVM_LIBC_FUNCTION(accum, expk, (accum x)) {
using FXRep = fixed_point::FXRep<accum>;
using StorageType = typename FXRep::StorageType;
// Output overflow
// > floor(log(2^16) * 2^15) * 2^-15
if (LIBC_UNLIKELY(x >= 0x1.62e4p3k))
return FXRep::MAX();
// Lower bound where exp(x) -> 0:
// floor(log(2^-16) * 2^15) * 2^-15
if (LIBC_UNLIKELY(x <= -0x1.62e44p3k))
return FXRep::ZERO();

// Current range of x:
// -0x1.62e4p3 <= x <= 0x1.62e3cp3
// Range reduction:
// x = hi + mid + lo,
// where:
// hi is an integer
// mid * 2^4 is an integer
// |lo| <= 2^-5.
// Then exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo)
// ~ exp(hi) * exp(mid) * (1 + lo + lo^2 / 2)
// with relative errors < |lo|^3/2 <= 2^-16.
// exp(hi) and exp(mid) are extracted from small lookup tables.

// Round-to-nearest 1/16, tie-to-(+Int):
constexpr accum ONE_THIRTY_SECOND = 0x1.0p-5k;
// x_rounded = floor(x + 1/16).
accum x_rounded = ((x + ONE_THIRTY_SECOND) >> (FXRep::FRACTION_LEN - 4))
<< (FXRep::FRACTION_LEN - 4);
accum lo = x - x_rounded;

// Range of x_rounded:
// x_rounded >= floor((-0x1.62e4p3 + 0x1.0p-5) * 2^4) * 2^-4
// = -0x1.62p3 = -11.0625
// To get the indices, we shift the values so that it start with 0.
// Range of indices: 0 <= indices <= 355.
StorageType indices = cpp::bit_cast<StorageType>((x_rounded + 0x1.62p3k) >>
(FXRep::FRACTION_LEN - 4));
// So we have the following relation:
// indices = (hi + mid + 177/16) * 16
// That implies:
// hi + mid = indices/16 - 11.0625
// So for lookup tables, we can use the upper 4 bits to get:
// exp( floor(indices / 16) - 11 )
// and lower 4 bits for:
// exp( (indices - floor(indices)) - 0.0625 )
accum exp_hi = EXP_HI[indices >> 4];
accum exp_mid = EXP_MID[indices & 0xf];
// exp(x) ~ exp(hi) * exp(mid) * (1 + lo);
accum l1 = 0x1.0p0k + (lo >> 1); // = 1 + lo / 2
accum l2 = 0x1.0p0k + lo * l1; // = 1 + lo * (1 + lo / 2) = 1 + lo + lo^2/2
return (exp_hi * (exp_mid * l2));
}

} // namespace LIBC_NAMESPACE
20 changes: 20 additions & 0 deletions libc/src/stdfix/expk.h
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//===-- Implementation header for expk --------------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_LIBC_SRC_STDFIX_EXPK_H
#define LLVM_LIBC_SRC_STDFIX_EXPK_H

#include "include/llvm-libc-macros/stdfix-macros.h"

namespace LIBC_NAMESPACE {

accum expk(accum x);

} // namespace LIBC_NAMESPACE

#endif // LLVM_LIBC_SRC_STDFIX_EXPK_H
36 changes: 36 additions & 0 deletions libc/test/src/stdfix/CMakeLists.txt
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Expand Up @@ -96,3 +96,39 @@ add_libc_test(
libc.src.__support.FPUtil.basic_operations
libc.src.__support.FPUtil.sqrt
)

add_libc_test(
exphk_test
SUITE
libc-stdfix-tests
HDRS
ExpTest.h
SRCS
exphk_test.cpp
COMPILE_OPTIONS
-O3
DEPENDS
libc.src.stdfix.exphk
libc.src.math.exp
libc.src.__support.CPP.bit
libc.src.__support.fixed_point.fx_rep
libc.src.__support.FPUtil.basic_operations
)

add_libc_test(
expk_test
SUITE
libc-stdfix-tests
HDRS
ExpTest.h
SRCS
expk_test.cpp
COMPILE_OPTIONS
-O3
DEPENDS
libc.src.stdfix.expk
libc.src.math.exp
libc.src.__support.CPP.bit
libc.src.__support.fixed_point.fx_rep
libc.src.__support.FPUtil.basic_operations
)
77 changes: 77 additions & 0 deletions libc/test/src/stdfix/ExpTest.h
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//===-- Utility class to test integer sqrt ----------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"

#include "src/__support/CPP/bit.h"
#include "src/__support/FPUtil/BasicOperations.h"
#include "src/__support/fixed_point/fx_rep.h"
#include "src/__support/fixed_point/sqrt.h"

#include "src/math/exp.h"

template <typename T> class ExpTest : public LIBC_NAMESPACE::testing::Test {

using FXRep = LIBC_NAMESPACE::fixed_point::FXRep<T>;
static constexpr T zero = FXRep::ZERO();
static constexpr T one = static_cast<T>(1);
static constexpr T eps = FXRep::EPS();

public:
typedef T (*ExpFunc)(T);

void test_special_numbers(ExpFunc func) {
EXPECT_EQ(one, func(T(0)));
EXPECT_EQ(FXRep::MAX(), func(T(30)));
EXPECT_EQ(zero, func(T(-30)));
}

void test_range_with_step(ExpFunc func, T step, bool rel_error) {
constexpr int COUNT = 255;
constexpr double ERR = 3.0 * static_cast<double>(eps);
double x_d = 0.0;
T x = step;
for (int i = 0; i < COUNT; ++i) {
x += step;
x_d = static_cast<double>(x);
double y_d = static_cast<double>(func(x));
double result = LIBC_NAMESPACE::exp(x_d);
double errors = rel_error
? LIBC_NAMESPACE::fputil::abs((y_d / result) - 1.0)
: LIBC_NAMESPACE::fputil::abs(y_d - result);
if (errors > ERR) {
// Print out the failure input and output.
EXPECT_EQ(x, T(0));
EXPECT_EQ(func(x), zero);
}
ASSERT_TRUE(errors <= ERR);
}
}

void test_positive_range(ExpFunc func) {
test_range_with_step(func, T(0x1.0p-6), /*rel_error*/ true);
}

void test_negative_range(ExpFunc func) {
test_range_with_step(func, T(-0x1.0p-6), /*rel_error*/ false);
}
};

#define LIST_EXP_TESTS(Name, T, func) \
using LlvmLibcExp##Name##Test = ExpTest<T>; \
TEST_F(LlvmLibcExp##Name##Test, SpecialNumbers) { \
test_special_numbers(&func); \
} \
TEST_F(LlvmLibcExp##Name##Test, PositiveRange) { \
test_positive_range(&func); \
} \
TEST_F(LlvmLibcExp##Name##Test, NegativeRange) { \
test_negative_range(&func); \
} \
static_assert(true, "Require semicolon.")
13 changes: 13 additions & 0 deletions libc/test/src/stdfix/exphk_test.cpp
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//===-- Unittests for exphk -----------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#include "ExpTest.h"

#include "src/stdfix/exphk.h"

LIST_EXP_TESTS(hk, short accum, LIBC_NAMESPACE::exphk);
13 changes: 13 additions & 0 deletions libc/test/src/stdfix/expk_test.cpp
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@@ -0,0 +1,13 @@
//===-- Unittests for expk ------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#include "ExpTest.h"

#include "src/stdfix/expk.h"

LIST_EXP_TESTS(k, accum, LIBC_NAMESPACE::expk);