78 changes: 9 additions & 69 deletions libc/src/math/generic/sinpif16.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -7,52 +7,23 @@
//===----------------------------------------------------------------------===//

#include "src/math/sinpif16.h"
#include "hdr/errno_macros.h"
#include "hdr/fenv_macros.h"
#include "sincosf16_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/cast.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"

namespace LIBC_NAMESPACE_DECL {

// Lookup table for sin(k * pi / 32) with k = 0, ..., 63.
// Table is generated with Sollya as follows:
// > display = hexadecimmal;
// > for k from 0 to 63 do { round(sin(k * pi/32), SG, RN); };
static constexpr float SIN_K_PI_OVER_32[64] = {
0x0.0p0, 0x1.917a6cp-4, 0x1.8f8b84p-3, 0x1.294062p-2,
0x1.87de2ap-2, 0x1.e2b5d4p-2, 0x1.1c73b4p-1, 0x1.44cf32p-1,
0x1.6a09e6p-1, 0x1.8bc806p-1, 0x1.a9b662p-1, 0x1.c38b3p-1,
0x1.d906bcp-1, 0x1.e9f416p-1, 0x1.f6297cp-1, 0x1.fd88dap-1,
0x1p0, 0x1.fd88dap-1, 0x1.f6297cp-1, 0x1.e9f416p-1,
0x1.d906bcp-1, 0x1.c38b3p-1, 0x1.a9b662p-1, 0x1.8bc806p-1,
0x1.6a09e6p-1, 0x1.44cf32p-1, 0x1.1c73b4p-1, 0x1.e2b5d4p-2,
0x1.87de2ap-2, 0x1.294062p-2, 0x1.8f8b84p-3, 0x1.917a6cp-4,
0x0.0p0, -0x1.917a6cp-4, -0x1.8f8b84p-3, -0x1.294062p-2,
-0x1.87de2ap-2, -0x1.e2b5d4p-2, -0x1.1c73b4p-1, -0x1.44cf32p-1,
-0x1.6a09e6p-1, -0x1.8bc806p-1, -0x1.a9b662p-1, -0x1.c38b3p-1,
-0x1.d906bcp-1, -0x1.e9f416p-1, -0x1.f6297ep-1, -0x1.fd88dap-1,
-0x1p0, -0x1.fd88dap-1, -0x1.f6297cp-1, -0x1.e9f416p-1,
-0x1.d906bcp-1, -0x1.c38b3p-1, -0x1.a9b662p-1, -0x1.8bc806p-1,
-0x1.6a09e6p-1, -0x1.44cf32p-1, -0x1.1c73b4p-1, -0x1.e2b5d4p-2,
-0x1.87de2ap-2, -0x1.294062p-2, -0x1.8f8b84p-3, -0x1.917a6cp-4};

static LIBC_INLINE int32_t range_reduction(float x, float &y) {
float kf = fputil::nearest_integer(x * 32);
y = fputil::multiply_add<float>(x, 32.0, -kf);

return static_cast<int32_t>(kf);
}

LLVM_LIBC_FUNCTION(float16, sinpif16, (float16 x)) {
using FPBits = typename fputil::FPBits<float16>;
FPBits xbits(x);

uint16_t x_u = xbits.uintval();
uint16_t x_abs = x_u & 0x7fff;
float xf = x;

// Range reduction:
// For |x| > 1/32, we perform range reduction as follows:
Expand All @@ -68,12 +39,8 @@ LLVM_LIBC_FUNCTION(float16, sinpif16, (float16 x)) {
// Once k and y are computed, we then deduce the answer by the sine of sum
// formula:
// sin(x * pi) = sin((k + y) * pi/32)
// = sin(k * pi/32) * cos(y * pi/32) + sin (y * pi/32) * cos (k *
// pi/32)
// The values of sin(k * pi/32) and cos (k * pi/32) for k = 0...63 are
// precomputed and stored using a vector of 64 single precision floats. sin(y
// * pi/32) and cos(y * pi/32) are computed using degree-9 chebyshev
// polynomials generated by Sollya.
// = sin(k * pi/32) * cos(y * pi/32) +
// sin(y * pi/32) * cos(k * pi/32)

// For signed zeros
if (LIBC_UNLIKELY(x_abs == 0U))
Expand All @@ -94,36 +61,8 @@ LLVM_LIBC_FUNCTION(float16, sinpif16, (float16 x)) {
return FPBits::zero(xbits.sign()).get_val();
}

float f32 = x;
float y;
int32_t k = range_reduction(f32, y);

float sin_k = SIN_K_PI_OVER_32[k & 63];
float cos_k = SIN_K_PI_OVER_32[(k + 16) & 63];

// Recall;
// sin(x * pi/32) = sin((k + y) * pi/32)
// = sin(y * pi/32) * cos(k * pi/32) + cos(y * pi/32) * sin(k *
// pi/32) Recall, after range reduction, -0.5 <= y <= 0.5. For very small
// values of y, calculating sin(y * p/32) can be inaccurate. Generating a
// polynomial for sin(y * p/32)/y instead significantly reduces the relative
// errors.
float ysq = y * y;

// Degree-6 minimax even polynomial for sin(y*pi/32)/y generated by Sollya
// with: > Q = fpminimax(sin(y*pi/32)/y, [|0, 2, 4, 6|], [|SG...|], [0, 0.5]);
float sin_y = y * fputil::polyeval(ysq, 0x1.921fb6p-4f, -0x1.4aeabcp-13f,
0x1.a03354p-21f, -0x1.ad02d2p-20f);

// Note that cosm1_y = cos(y*pi/32) - 1 = cos_y - 1
// Derivation:
// sin(x * pi) = sin((k + y) * pi/32)
// = sin_y * cos_k + cos_y * sin_k
// = cos_k * sin_y + sin_k * (1 + cos_y - 1)
// Degree-6 minimax even polynomial for cos(y*pi/32) generated by Sollya with:
// > P = fpminimax(cos(y*pi/32), [|0, 2, 4, 6|],[|1, SG...|], [0, 0.5]);
float cosm1_y = ysq * fputil::polyeval(ysq, -0x1.3bd3ccp-8f, 0x1.03a61ap-18f,
0x1.a6f7a2p-29f);
float sin_k, cos_k, sin_y, cosm1_y;
sincospif16_eval(xf, sin_k, cos_k, sin_y, cosm1_y);

if (LIBC_UNLIKELY(sin_y == 0 && sin_k == 0))
return FPBits::zero(xbits.sign()).get_val();
Expand All @@ -133,4 +72,5 @@ LLVM_LIBC_FUNCTION(float16, sinpif16, (float16 x)) {
return fputil::cast<float16>(fputil::multiply_add(
sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k)));
}

} // namespace LIBC_NAMESPACE_DECL
11 changes: 11 additions & 0 deletions libc/test/src/math/CMakeLists.txt
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Expand Up @@ -45,6 +45,17 @@ add_fp_unittest(
)


add_fp_unittest(
cospif16_test
NEED_MPFR
SUITE
libc-math-unittests
SRCS
cospif16_test.cpp
DEPENDS
libc.src.math.cospif16
)

add_fp_unittest(
daddl_test
NEED_MPFR
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40 changes: 40 additions & 0 deletions libc/test/src/math/cospif16_test.cpp
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@@ -0,0 +1,40 @@
//===-- Exhaustive test for cospif16 --------------------------------------===//
//
// 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 "src/math/cospif16.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"
#include "utils/MPFRWrapper/MPFRUtils.h"

using LlvmLibcCospif16Test = LIBC_NAMESPACE::testing::FPTest<float16>;

namespace mpfr = LIBC_NAMESPACE::testing::mpfr;

// Range: [0, Inf]
static constexpr uint16_t POS_START = 0x0000U;
static constexpr uint16_t POS_STOP = 0x7c00U;

// Range: [-Inf, 0]
static constexpr uint16_t NEG_START = 0x8000U;
static constexpr uint16_t NEG_STOP = 0xfc00U;

TEST_F(LlvmLibcCospif16Test, PositiveRange) {
for (uint16_t v = POS_START; v <= POS_STOP; ++v) {
float16 x = FPBits(v).get_val();
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cospi, x,
LIBC_NAMESPACE::cospif16(x), 0.5);
}
}

TEST_F(LlvmLibcCospif16Test, NegativeRange) {
for (uint16_t v = NEG_START; v <= NEG_STOP; ++v) {
float16 x = FPBits(v).get_val();
EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Cospi, x,
LIBC_NAMESPACE::cospif16(x), 0.5);
}
}
11 changes: 11 additions & 0 deletions libc/test/src/math/smoke/CMakeLists.txt
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Expand Up @@ -25,6 +25,17 @@ add_fp_unittest(
libc.src.__support.FPUtil.fp_bits
)

add_fp_unittest(
cospif16_test
SUITE
libc-math-smoke-tests
SRCS
cospif16_test.cpp
DEPENDS
libc.src.errno.errno
libc.src.math.cospif16
)

add_fp_unittest(
sinf_test
SUITE
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44 changes: 44 additions & 0 deletions libc/test/src/math/smoke/cospif16_test.cpp
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@@ -0,0 +1,44 @@
//===-- Unittests for cospif16 --------------------------------------------===//
//
// 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 "src/errno/libc_errno.h"
#include "src/math/cospif16.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"

using LlvmLibcCospif16Test = LIBC_NAMESPACE::testing::FPTest<float16>;

TEST_F(LlvmLibcCospif16Test, SpecialNumbers) {
LIBC_NAMESPACE::libc_errno = 0;

EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::cospif16(aNaN));
EXPECT_MATH_ERRNO(0);

EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::cospif16(zero));
EXPECT_MATH_ERRNO(0);

EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::cospif16(neg_zero));
EXPECT_MATH_ERRNO(0);

EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::cospif16(inf));
EXPECT_MATH_ERRNO(EDOM);

EXPECT_FP_EQ(aNaN, LIBC_NAMESPACE::cospif16(neg_inf));
EXPECT_MATH_ERRNO(EDOM);
}

TEST_F(LlvmLibcCospif16Test, Integers) {
EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::cospif16(-0x420));
EXPECT_FP_EQ(1.0f, LIBC_NAMESPACE::cospif16(-0x1.4p+14));
EXPECT_FP_EQ(-1.0f, LIBC_NAMESPACE::cospif16(0x421));
EXPECT_FP_EQ(-1.0f, LIBC_NAMESPACE::cospif16(0x333));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::cospif16(-0x1.28p4));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::cospif16(-0x1.ffcp9));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::cospif16(0x1.01p7));
EXPECT_FP_EQ(zero, LIBC_NAMESPACE::cospif16(0x1.f6cp9));
}
20 changes: 7 additions & 13 deletions libc/utils/MPFRWrapper/MPFRUtils.cpp
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Expand Up @@ -255,19 +255,13 @@ class MPFRNumber {
mpfr_cospi(result.value, value, mpfr_rounding);
return result;
#else
MPFRNumber value_frac(*this);
mpfr_frac(value_frac.value, value, MPFR_RNDN);

if (mpfr_cmp_si(value_frac.value, 0.0) == 0) {
mpz_t integer_part;
mpz_init(integer_part);
mpfr_get_z(integer_part, value, MPFR_RNDN);

if (mpz_tstbit(integer_part, 0)) {
mpfr_set_si(result.value, -1.0, MPFR_RNDN); // odd
} else {
mpfr_set_si(result.value, 1.0, MPFR_RNDN); // even
}
if (mpfr_integer_p(value)) {
mpz_t integer;
mpz_init(integer);
mpfr_get_z(integer, value, mpfr_rounding);

int d = mpz_tstbit(integer, 0);
mpfr_set_si(result.value, d ? -1 : 1, mpfr_rounding);
return result;
}

Expand Down