162 changes: 162 additions & 0 deletions libc/src/math/generic/range_reduction_double_common.h
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//===-- Range reduction for double precision sin/cos/tan -*- 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_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_COMMON_H
#define LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_COMMON_H

#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/double_double.h"
#include "src/__support/FPUtil/dyadic_float.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/common.h"
#include "src/__support/integer_literals.h"

namespace LIBC_NAMESPACE {

namespace generic {

using LIBC_NAMESPACE::fputil::DoubleDouble;
using Float128 = LIBC_NAMESPACE::fputil::DyadicFloat<128>;

LIBC_INLINE constexpr Float128 PI_OVER_128_F128 = {
Sign::POS, -133, 0xc90f'daa2'2168'c234'c4c6'628b'80dc'1cd1_u128};

// Note: The look-up tables ONE_TWENTY_EIGHT_OVER_PI is selected to be either
// from fma:: or nofma:: namespace.

// For large range |x| >= 2^32, we use the exponent of x to find 3 double-chunks
// of 128/pi c_hi, c_mid, c_lo such that:
// 1) ulp(round(x * c_hi, D, RN)) >= 256,
// 2) If x * c_hi = ph_hi + ph_lo and x * c_mid = pm_hi + pm_lo, then
// min(ulp(ph_lo), ulp(pm_hi)) >= 2^-53.
// 3) ulp(round(x * c_lo, D, RN)) <= 2^-7x.
// This will allow us to do quick computations as:
// (x * 256/pi) ~ x * (c_hi + c_mid + c_lo) (mod 256)
// ~ ph_lo + pm_hi + pm_lo + (x * c_lo)
// Then,
// round(x * 128/pi) = round(ph_lo + pm_hi) (mod 256)
// And the high part of fractional part of (x * 128/pi) can simply be:
// {x * 128/pi}_hi = {ph_lo + pm_hi}.
// To prevent overflow when x is very large, we simply scale up
// (c_hi, c_mid, c_lo) by a fixed power of 2 (based on the index) and scale down
// x by the same amount.

template <bool NO_FMA> struct LargeRangeReduction {
// Calculate the high part of the range reduction exactly.
LIBC_INLINE unsigned compute_high_part(double x) {
using FPBits = typename fputil::FPBits<double>;
FPBits xbits(x);

// TODO: The extra exponent gap of 62 below can be reduced a bit for non-FMA
// with a more careful analysis, which in turn will reduce the error bound
// for non-FMA
int x_e_m62 = xbits.get_biased_exponent() - (FPBits::EXP_BIAS + 62);
idx = static_cast<unsigned>((x_e_m62 >> 4) + 3);
// Scale x down by 2^(-(16 * (idx - 3))
xbits.set_biased_exponent((x_e_m62 & 15) + FPBits::EXP_BIAS + 62);
// 2^62 <= |x_reduced| < 2^(62 + 16) = 2^78
x_reduced = xbits.get_val();
// x * c_hi = ph.hi + ph.lo exactly.
DoubleDouble ph =
fputil::exact_mult<NO_FMA>(x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][0]);
// x * c_mid = pm.hi + pm.lo exactly.
DoubleDouble pm =
fputil::exact_mult<NO_FMA>(x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][1]);
// Extract integral parts and fractional parts of (ph.lo + pm.hi).
double kh = fputil::nearest_integer(ph.lo);
double ph_lo_frac = ph.lo - kh; // Exact
double km = fputil::nearest_integer(pm.hi + ph_lo_frac);
double pm_hi_frac = pm.hi - km; // Exact
// x * 128/pi mod 1 ~ y_hi + y_lo
y_hi = ph_lo_frac + pm_hi_frac; // Exact
pm_lo = pm.lo;
return static_cast<unsigned>(static_cast<int64_t>(kh) +
static_cast<int64_t>(km));
}

LIBC_INLINE DoubleDouble fast() const {
// y_lo = x * c_lo + pm.lo
double y_lo = fputil::multiply_add(x_reduced,
ONE_TWENTY_EIGHT_OVER_PI[idx][2], pm_lo);
DoubleDouble y = fputil::exact_add(y_hi, y_lo);

// Digits of pi/128, generated by Sollya with:
// > a = round(pi/128, D, RN);
// > b = round(pi/128 - a, D, RN);
constexpr DoubleDouble PI_OVER_128_DD = {0x1.1a62633145c07p-60,
0x1.921fb54442d18p-6};

// Error bound: with {a} denote the fractional part of a, i.e.:
// {a} = a - round(a)
// Then,
// | {x * 128/pi} - (y_hi + y_lo) | < 2 * ulp(x_reduced *
// * ONE_TWENTY_EIGHT_OVER_PI[idx][2])
// For FMA:
// | {x * 128/pi} - (y_hi + y_lo) | <= 2 * 2^77 * 2^-103 * 2^-52
// = 2^-77.
// | {x mod pi/128} - (u.hi + u.lo) | < 2 * 2^-6 * 2^-77.
// = 2^-82.
// For non-FMA:
// | {x * 128/pi} - (y_hi + y_lo) | <= 2 * 2^77 * 2^-99 * 2^-52
// = 2^-73.
// | {x mod pi/128} - (u.hi + u.lo) | < 2 * 2^-6 * 2^-73.
// = 2^-78.
return fputil::quick_mult<NO_FMA>(y, PI_OVER_128_DD);
}

LIBC_INLINE Float128 accurate() const {
// y_lo = x * c_lo + pm.lo
Float128 y_lo_0(x_reduced * ONE_TWENTY_EIGHT_OVER_PI[idx][3]);
Float128 y_lo_1 = fputil::quick_mul(
Float128(x_reduced), Float128(ONE_TWENTY_EIGHT_OVER_PI[idx][2]));
Float128 y_lo_2(pm_lo);
Float128 y_hi_f128(y_hi);

Float128 y = fputil::quick_add(
y_hi_f128,
fputil::quick_add(y_lo_2, fputil::quick_add(y_lo_1, y_lo_0)));

return fputil::quick_mul(y, PI_OVER_128_F128);
}

private:
// Index of x in the look-up table ONE_TWENTY_EIGHT_OVER_PI.
unsigned idx;
// x scaled down by 2^(-16 *(idx - 3))).
double x_reduced;
// High part of (x * 128/pi) mod 1.
double y_hi;
// Low part of x * ONE_TWENTY_EIGHT_OVER_PI[idx][1].
double pm_lo;
};

LIBC_INLINE Float128 range_reduction_small_f128(double x) {
double prod_hi = x * ONE_TWENTY_EIGHT_OVER_PI[3][0];
double kd = fputil::nearest_integer(prod_hi);

Float128 mk_f128(-kd);
Float128 x_f128(x);
Float128 p_hi =
fputil::quick_mul(x_f128, Float128(ONE_TWENTY_EIGHT_OVER_PI[3][0]));
Float128 p_mid =
fputil::quick_mul(x_f128, Float128(ONE_TWENTY_EIGHT_OVER_PI[3][1]));
Float128 p_lo =
fputil::quick_mul(x_f128, Float128(ONE_TWENTY_EIGHT_OVER_PI[3][2]));
Float128 s_hi = fputil::quick_add(p_hi, mk_f128);
Float128 s_lo = fputil::quick_add(p_mid, p_lo);
Float128 y = fputil::quick_add(s_hi, s_lo);

return fputil::quick_mul(y, PI_OVER_128_F128);
}

} // namespace generic

} // namespace LIBC_NAMESPACE

#endif // LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_COMMON_H
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315 changes: 315 additions & 0 deletions libc/src/math/generic/sin.cpp
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//===-- Double-precision sin 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 "src/math/sin.h"
#include "hdr/errno_macros.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/double_double.h"
#include "src/__support/FPUtil/dyadic_float.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/common.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
#include "src/math/generic/sincos_eval.h"

#ifdef LIBC_TARGET_CPU_HAS_FMA
#include "range_reduction_double_fma.h"

using LIBC_NAMESPACE::fma::FAST_PASS_EXPONENT;
using LIBC_NAMESPACE::fma::ONE_TWENTY_EIGHT_OVER_PI;
using LIBC_NAMESPACE::fma::range_reduction_small;
using LIBC_NAMESPACE::fma::SIN_K_PI_OVER_128;

LIBC_INLINE constexpr bool NO_FMA = false;
#else
#include "range_reduction_double_nofma.h"

using LIBC_NAMESPACE::nofma::FAST_PASS_EXPONENT;
using LIBC_NAMESPACE::nofma::ONE_TWENTY_EIGHT_OVER_PI;
using LIBC_NAMESPACE::nofma::range_reduction_small;
using LIBC_NAMESPACE::nofma::SIN_K_PI_OVER_128;

LIBC_INLINE constexpr bool NO_FMA = true;
#endif // LIBC_TARGET_CPU_HAS_FMA

// TODO: We might be able to improve the performance of large range reduction of
// non-FMA targets further by operating directly on 25-bit chunks of 128/pi and
// pre-split SIN_K_PI_OVER_128, but that might double the memory footprint of
// those lookup table.
#include "range_reduction_double_common.h"

#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0)
#define LIBC_MATH_SIN_SKIP_ACCURATE_PASS
#endif

namespace LIBC_NAMESPACE {

using DoubleDouble = fputil::DoubleDouble;
using Float128 = typename fputil::DyadicFloat<128>;

namespace {

#ifndef LIBC_MATH_SIN_SKIP_ACCURATE_PASS
LIBC_INLINE constexpr Float128 SIN_K_PI_OVER_128_F128[65] = {
{Sign::POS, 0, 0},
{Sign::POS, -133, 0xc90a'afbd'1b33'efc9'c539'edcb'fda0'cf2c_u128},
{Sign::POS, -132, 0xc8fb'2f88'6ec0'9f37'6a17'954b'2b7c'5171_u128},
{Sign::POS, -131, 0x96a9'0496'70cf'ae65'f775'7409'4d3c'35c4_u128},
{Sign::POS, -131, 0xc8bd'35e1'4da1'5f0e'c739'6c89'4bbf'7389_u128},
{Sign::POS, -131, 0xfab2'72b5'4b98'71a2'7047'29ae'56d7'8a37_u128},
{Sign::POS, -130, 0x9640'8374'7309'd113'000a'89a1'1e07'c1fe_u128},
{Sign::POS, -130, 0xaf10'a224'59fe'32a6'3fee'f3bb'58b1'f10d_u128},
{Sign::POS, -130, 0xc7c5'c1e3'4d30'55b2'5cc8'c00e'4fcc'd850_u128},
{Sign::POS, -130, 0xe05c'1353'f27b'17e5'0ebc'61ad'e6ca'83cd_u128},
{Sign::POS, -130, 0xf8cf'cbd9'0af8'd57a'4221'dc4b'a772'598d_u128},
{Sign::POS, -129, 0x888e'9315'8fb3'bb04'9841'56f5'5334'4306_u128},
{Sign::POS, -129, 0x94a0'3176'acf8'2d45'ae4b'a773'da6b'f754_u128},
{Sign::POS, -129, 0xa09a'e4a0'bb30'0a19'2f89'5f44'a303'cc0b_u128},
{Sign::POS, -129, 0xac7c'd3ad'58fe'e7f0'811f'9539'84ef'f83e_u128},
{Sign::POS, -129, 0xb844'2987'd22c'f576'9cc3'ef36'746d'e3b8_u128},
{Sign::POS, -129, 0xc3ef'1535'754b'168d'3122'c2a5'9efd'dc37_u128},
{Sign::POS, -129, 0xcf7b'ca1d'476c'516d'a812'90bd'baad'62e4_u128},
{Sign::POS, -129, 0xdae8'804f'0ae6'015b'362c'b974'182e'3030_u128},
{Sign::POS, -129, 0xe633'74c9'8e22'f0b4'2872'ce1b'fc7a'd1cd_u128},
{Sign::POS, -129, 0xf15a'e9c0'37b1'd8f0'6c48'e9e3'420b'0f1e_u128},
{Sign::POS, -129, 0xfc5d'26df'c4d5'cfda'27c0'7c91'1290'b8d1_u128},
{Sign::POS, -128, 0x839c'3cc9'17ff'6cb4'bfd7'9717'f288'0abf_u128},
{Sign::POS, -128, 0x88f5'9aa0'da59'1421'b892'ca83'61d8'c84c_u128},
{Sign::POS, -128, 0x8e39'd9cd'7346'4364'bba4'cfec'bff5'4867_u128},
{Sign::POS, -128, 0x9368'2a66'e896'f544'b178'2191'1e71'c16e_u128},
{Sign::POS, -128, 0x987f'bfe7'0b81'a708'19ce'c845'ac87'a5c6_u128},
{Sign::POS, -128, 0x9d7f'd149'0285'c9e3'e25e'3954'9638'ae68_u128},
{Sign::POS, -128, 0xa267'9928'48ee'b0c0'3b51'67ee'359a'234e_u128},
{Sign::POS, -128, 0xa736'55df'1f2f'489e'149f'6e75'9934'68a3_u128},
{Sign::POS, -128, 0xabeb'49a4'6764'fd15'1bec'da80'89c1'a94c_u128},
{Sign::POS, -128, 0xb085'baa8'e966'f6da'e4ca'd00d'5c94'bcd2_u128},
{Sign::POS, -128, 0xb504'f333'f9de'6484'597d'89b3'754a'be9f_u128},
{Sign::POS, -128, 0xb968'41bf'7ffc'b21a'9de1'e3b2'2b8b'f4db_u128},
{Sign::POS, -128, 0xbdae'f913'557d'76f0'ac85'320f'528d'6d5d_u128},
{Sign::POS, -128, 0xc1d8'705f'fcbb'6e90'bdf0'715c'b8b2'0bd7_u128},
{Sign::POS, -128, 0xc5e4'0358'a8ba'05a7'43da'25d9'9267'326b_u128},
{Sign::POS, -128, 0xc9d1'124c'931f'da7a'8335'241b'e169'3225_u128},
{Sign::POS, -128, 0xcd9f'023f'9c3a'059e'23af'31db'7179'a4aa_u128},
{Sign::POS, -128, 0xd14d'3d02'313c'0eed'744f'ea20'e8ab'ef92_u128},
{Sign::POS, -128, 0xd4db'3148'750d'1819'f630'e8b6'dac8'3e69_u128},
{Sign::POS, -128, 0xd848'52c0'a80f'fcdb'24b9'fe00'6635'74a4_u128},
{Sign::POS, -128, 0xdb94'1a28'cb71'ec87'2c19'b632'53da'43fc_u128},
{Sign::POS, -128, 0xdebe'0563'7ca9'4cfb'4b19'aa71'fec3'ae6d_u128},
{Sign::POS, -128, 0xe1c5'978c'05ed'8691'f4e8'a837'2f8c'5810_u128},
{Sign::POS, -128, 0xe4aa'5909'a08f'a7b4'1227'85ae'67f5'515d_u128},
{Sign::POS, -128, 0xe76b'd7a1'e63b'9786'1251'2952'9d48'a92f_u128},
{Sign::POS, -128, 0xea09'a68a'6e49'cd62'15ad'45b4'a1b5'e823_u128},
{Sign::POS, -128, 0xec83'5e79'946a'3145'7e61'0231'ac1d'6181_u128},
{Sign::POS, -128, 0xeed8'9db6'6611'e307'86f8'c20f'b664'b01b_u128},
{Sign::POS, -128, 0xf109'0827'b437'25fd'6712'7db3'5b28'7316_u128},
{Sign::POS, -128, 0xf314'4762'4708'8f74'a548'6bdc'455d'56a2_u128},
{Sign::POS, -128, 0xf4fa'0ab6'316e'd2ec'163c'5c7f'03b7'18c5_u128},
{Sign::POS, -128, 0xf6ba'073b'424b'19e8'2c79'1f59'cc1f'fc23_u128},
{Sign::POS, -128, 0xf853'f7dc'9186'b952'c7ad'c6b4'9888'91bb_u128},
{Sign::POS, -128, 0xf9c7'9d63'272c'4628'4504'ae08'd19b'2980_u128},
{Sign::POS, -128, 0xfb14'be7f'bae5'8156'2172'a361'fd2a'722f_u128},
{Sign::POS, -128, 0xfc3b'27d3'8a5d'49ab'2567'78ff'cb5c'1769_u128},
{Sign::POS, -128, 0xfd3a'abf8'4528'b50b'eae6'bd95'1c1d'abbe_u128},
{Sign::POS, -128, 0xfe13'2387'0cfe'9a3d'90cd'1d95'9db6'74ef_u128},
{Sign::POS, -128, 0xfec4'6d1e'8929'2cf0'4139'0efd'c726'e9ef_u128},
{Sign::POS, -128, 0xff4e'6d68'0c41'd0a9'0f66'8633'f1ab'858a_u128},
{Sign::POS, -128, 0xffb1'0f1b'cb6b'ef1d'421e'8eda'af59'453e_u128},
{Sign::POS, -128, 0xffec'4304'2668'65d9'5657'5523'6696'1732_u128},
{Sign::POS, 0, 1},
};

#ifdef LIBC_TARGET_CPU_HAS_FMA
constexpr double ERR = 0x1.0p-70;
#else
// TODO: Improve non-FMA fast pass accuracy.
constexpr double ERR = 0x1.0p-66;
#endif // LIBC_TARGET_CPU_HAS_FMA

#endif // !LIBC_MATH_SIN_SKIP_ACCURATE_PASS

} // anonymous namespace

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

uint16_t x_e = xbits.get_biased_exponent();

DoubleDouble y;
unsigned k;
generic::LargeRangeReduction<NO_FMA> range_reduction_large;

// |x| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA)
if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
// |x| < 2^-26
if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 26)) {
// Signed zeros.
if (LIBC_UNLIKELY(x == 0.0))
return x;

// For |x| < 2^-26, |sin(x) - x| < ulp(x)/2.
#ifdef LIBC_TARGET_CPU_HAS_FMA
return fputil::multiply_add(x, -0x1.0p-54, x);
#else
if (LIBC_UNLIKELY(x_e < 4)) {
int rounding_mode = fputil::quick_get_round();
if (rounding_mode == FE_TOWARDZERO ||
(xbits.sign() == Sign::POS && rounding_mode == FE_DOWNWARD) ||
(xbits.sign() == Sign::NEG && rounding_mode == FE_UPWARD))
return FPBits(xbits.uintval() - 1).get_val();
}
return fputil::multiply_add(x, -0x1.0p-54, x);
#endif // LIBC_TARGET_CPU_HAS_FMA
}

// // Small range reduction.
k = range_reduction_small(x, y);
} else {
// Inf or NaN
if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
// sin(+-Inf) = NaN
if (xbits.get_mantissa() == 0) {
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_INVALID);
}
return x + FPBits::quiet_nan().get_val();
}

// Large range reduction.
k = range_reduction_large.compute_high_part(x);
y = range_reduction_large.fast();
}

DoubleDouble sin_y, cos_y;

sincos_eval(y, sin_y, cos_y);

// Look up sin(k * pi/128) and cos(k * pi/128)
// Memory saving versions:

// Use 128-entry table instead:
// DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 127];
// uint64_t sin_s = static_cast<uint64_t>(k & 128) << (63 - 7);
// sin_k.hi = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
// sin_k.lo = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
// DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 127];
// uint64_t cos_s = static_cast<uint64_t>((k + 64) & 128) << (63 - 7);
// cos_k.hi = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
// cos_k.lo = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();

// Use 64-entry table instead:
// auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
// unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
// DoubleDouble ans = SIN_K_PI_OVER_128[idx];
// if (kk & 128) {
// ans.hi = -ans.hi;
// ans.lo = -ans.lo;
// }
// return ans;
// };
// DoubleDouble sin_k = get_idx_dd(k);
// DoubleDouble cos_k = get_idx_dd(k + 64);

// Fast look up version, but needs 256-entry table.
// cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 255];
DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];

// After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
// So k is an integer and -pi / 256 <= y <= pi / 256.
// Then sin(x) = sin((k * pi/128 + y)
// = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128)
DoubleDouble sin_k_cos_y = fputil::quick_mult<NO_FMA>(cos_y, sin_k);
DoubleDouble cos_k_sin_y = fputil::quick_mult<NO_FMA>(sin_y, cos_k);

FPBits sk_cy(sin_k_cos_y.hi);
FPBits ck_sy(cos_k_sin_y.hi);
DoubleDouble rr = fputil::exact_add<false>(sin_k_cos_y.hi, cos_k_sin_y.hi);
rr.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;

#ifdef LIBC_MATH_SIN_SKIP_ACCURATE_PASS
return rr.hi + rr.lo;
#else
// Accurate test and pass for correctly rounded implementation.
double rlp = rr.lo + ERR;
double rlm = rr.lo - ERR;

double r_upper = rr.hi + rlp; // (rr.lo + ERR);
double r_lower = rr.hi + rlm; // (rr.lo - ERR);

// Ziv's rounding test.
if (LIBC_LIKELY(r_upper == r_lower))
return r_upper;

Float128 u_f128;
if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
u_f128 = generic::range_reduction_small_f128(x);
else
u_f128 = range_reduction_large.accurate();

Float128 u_sq = fputil::quick_mul(u_f128, u_f128);

// sin(u) ~ x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - x^11/11! + x^13/13!
constexpr Float128 SIN_COEFFS[] = {
{Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1
{Sign::NEG, -130, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // -1/3!
{Sign::POS, -134, 0x88888888'88888888'88888888'88888889_u128}, // 1/5!
{Sign::NEG, -140, 0xd00d00d0'0d00d00d'00d00d00'd00d00d0_u128}, // -1/7!
{Sign::POS, -146, 0xb8ef1d2a'b6399c7d'560e4472'800b8ef2_u128}, // 1/9!
{Sign::NEG, -153, 0xd7322b3f'aa271c7f'3a3f25c1'bee38f10_u128}, // -1/11!
{Sign::POS, -160, 0xb092309d'43684be5'1c198e91'd7b4269e_u128}, // 1/13!
};

// cos(u) ~ 1 - x^2/2 + x^4/4! - x^6/6! + x^8/8! - x^10/10! + x^12/12!
constexpr Float128 COS_COEFFS[] = {
{Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
{Sign::NEG, -128, 0x80000000'00000000'00000000'00000000_u128}, // 1/2
{Sign::POS, -132, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/4!
{Sign::NEG, -137, 0xb60b60b6'0b60b60b'60b60b60'b60b60b6_u128}, // 1/6!
{Sign::POS, -143, 0xd00d00d0'0d00d00d'00d00d00'd00d00d0_u128}, // 1/8!
{Sign::NEG, -149, 0x93f27dbb'c4fae397'780b69f5'333c725b_u128}, // 1/10!
{Sign::POS, -156, 0x8f76c77f'c6c4bdaa'26d4c3d6'7f425f60_u128}, // 1/12!
};

Float128 sin_u = fputil::quick_mul(
u_f128, fputil::polyeval(u_sq, SIN_COEFFS[0], SIN_COEFFS[1],
SIN_COEFFS[2], SIN_COEFFS[3], SIN_COEFFS[4],
SIN_COEFFS[5], SIN_COEFFS[6]));
Float128 cos_u = fputil::polyeval(u_sq, COS_COEFFS[0], COS_COEFFS[1],
COS_COEFFS[2], COS_COEFFS[3], COS_COEFFS[4],
COS_COEFFS[5], COS_COEFFS[6]);

auto get_sin_k = [](unsigned kk) -> Float128 {
unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
Float128 ans = SIN_K_PI_OVER_128_F128[idx];
if (kk & 128)
ans.sign = Sign::NEG;
return ans;
};

// cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
Float128 sin_k_f128 = get_sin_k(k);
Float128 cos_k_f128 = get_sin_k(k + 64);

// sin(x) = sin((k * pi/128 + u)
// = sin(u) * cos(k*pi/128) + cos(u) * sin(k*pi/128)
Float128 r = fputil::quick_add(fputil::quick_mul(sin_k_f128, cos_u),
fputil::quick_mul(cos_k_f128, sin_u));

// TODO: Add assertion if Ziv's accuracy tests fail in debug mode.
// https://github.com/llvm/llvm-project/issues/96452.

return static_cast<double>(r);
#endif // !LIBC_MATH_SIN_SKIP_ACCURATE_PASS
}

} // namespace LIBC_NAMESPACE
81 changes: 81 additions & 0 deletions libc/src/math/generic/sincos_eval.h
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Original file line number Diff line number Diff line change
@@ -0,0 +1,81 @@
//===-- Compute sin + cos for small angles ----------------------*- 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_MATH_GENERIC_SINCOS_EVAL_H
#define LLVM_LIBC_SRC_MATH_GENERIC_SINCOS_EVAL_H

#include "src/__support/FPUtil/double_double.h"
#include "src/__support/FPUtil/multiply_add.h"

namespace LIBC_NAMESPACE {

using fputil::DoubleDouble;

LIBC_INLINE void sincos_eval(const DoubleDouble &u, DoubleDouble &sin_u,
DoubleDouble &cos_u) {
// Evaluate sin(y) = sin(x - k * (pi/128))
// We use the degree-7 Taylor approximation:
// sin(y) ~ y - y^3/3! + y^5/5! - y^7/7!
// Then the error is bounded by:
// |sin(y) - (y - y^3/3! + y^5/5! - y^7/7!)| < |y|^9/9! < 2^-54/9! < 2^-72.
// For y ~ u_hi + u_lo, fully expanding the polynomial and drop any terms
// < ulp(u_hi^3) gives us:
// y - y^3/3! + y^5/5! - y^7/7! = ...
// ~ u_hi + u_hi^3 * (-1/6 + u_hi^2 * (1/120 - u_hi^2 * 1/5040)) +
// + u_lo (1 + u_hi^2 * (-1/2 + u_hi^2 / 24))
double u_hi_sq = u.hi * u.hi; // Error < ulp(u_hi^2) < 2^(-6 - 52) = 2^-58.
// p1 ~ 1/120 + u_hi^2 / 5040.
double p1 = fputil::multiply_add(u_hi_sq, -0x1.a01a01a01a01ap-13,
0x1.1111111111111p-7);
// q1 ~ -1/2 + u_hi^2 / 24.
double q1 = fputil::multiply_add(u_hi_sq, 0x1.5555555555555p-5, -0x1.0p-1);
double u_hi_3 = u_hi_sq * u.hi;
// p2 ~ -1/6 + u_hi^2 (1/120 - u_hi^2 * 1/5040)
double p2 = fputil::multiply_add(u_hi_sq, p1, -0x1.5555555555555p-3);
// q2 ~ 1 + u_hi^2 (-1/2 + u_hi^2 / 24)
double q2 = fputil::multiply_add(u_hi_sq, q1, 1.0);
double sin_lo = fputil::multiply_add(u_hi_3, p2, u.lo * q2);
// Overall, |sin(y) - (u_hi + sin_lo)| < 2*ulp(u_hi^3) < 2^-69.

// Evaluate cos(y) = cos(x - k * (pi/128))
// We use the degree-8 Taylor approximation:
// cos(y) ~ 1 - y^2/2 + y^4/4! - y^6/6! + y^8/8!
// Then the error is bounded by:
// |cos(y) - (...)| < |y|^10/10! < 2^-81
// For y ~ u_hi + u_lo, fully expanding the polynomial and drop any terms
// < ulp(u_hi^3) gives us:
// 1 - y^2/2 + y^4/4! - y^6/6! + y^8/8! = ...
// ~ 1 - u_hi^2/2 + u_hi^4(1/24 + u_hi^2 (-1/720 + u_hi^2/40320)) +
// + u_hi u_lo (-1 + u_hi^2/6)
// We compute 1 - u_hi^2 accurately:
// v_hi + v_lo ~ 1 - u_hi^2/2
double v_hi = fputil::multiply_add(u.hi, u.hi * (-0.5), 1.0);
double v_lo = 1.0 - v_hi; // Exact
v_lo = fputil::multiply_add(u.hi, u.hi * (-0.5), v_lo);

// r1 ~ -1/720 + u_hi^2 / 40320
double r1 = fputil::multiply_add(u_hi_sq, 0x1.a01a01a01a01ap-16,
-0x1.6c16c16c16c17p-10);
// s1 ~ -1 + u_hi^2 / 6
double s1 = fputil::multiply_add(u_hi_sq, 0x1.5555555555555p-3, -1.0);
double u_hi_4 = u_hi_sq * u_hi_sq;
double u_hi_u_lo = u.hi * u.lo;
// r2 ~ 1/24 + u_hi^2 (-1/720 + u_hi^2 / 40320)
double r2 = fputil::multiply_add(u_hi_sq, r1, 0x1.5555555555555p-5);
// s2 ~ v_lo + u_hi * u_lo * (-1 + u_hi^2 / 6)
double s2 = fputil::multiply_add(u_hi_u_lo, s1, v_lo);
double cos_lo = fputil::multiply_add(u_hi_4, r2, s2);
// Overall, |cos(y) - (v_hi + cos_lo)| < 2*ulp(u_hi^4) < 2^-75.

sin_u = fputil::exact_add(u.hi, sin_lo);
cos_u = fputil::exact_add(v_hi, cos_lo);
}

} // namespace LIBC_NAMESPACE

#endif // LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF_EVAL_H
10 changes: 0 additions & 10 deletions libc/src/math/x86_64/CMakeLists.txt
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Original file line number Diff line number Diff line change
Expand Up @@ -8,16 +8,6 @@ add_entrypoint_object(
-O2
)

add_entrypoint_object(
sin
SRCS
sin.cpp
HDRS
../sin.h
COMPILE_OPTIONS
-O2
)

add_entrypoint_object(
tan
SRCS
Expand Down
19 changes: 0 additions & 19 deletions libc/src/math/x86_64/sin.cpp
View file

This file was deleted.

107 changes: 94 additions & 13 deletions libc/test/src/math/sin_test.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -12,22 +12,103 @@
#include "test/UnitTest/Test.h"
#include "utils/MPFRWrapper/MPFRUtils.h"

#include "hdr/math_macros.h"

using LlvmLibcSinTest = LIBC_NAMESPACE::testing::FPTest<double>;

namespace mpfr = LIBC_NAMESPACE::testing::mpfr;

TEST_F(LlvmLibcSinTest, Range) {
static constexpr double _2pi = 6.283185307179586;
constexpr StorageType COUNT = 100'000;
constexpr StorageType STEP = STORAGE_MAX / COUNT;
for (StorageType i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
double x = FPBits(v).get_val();
// TODO: Expand the range of testing after range reduction is implemented.
if (isnan(x) || isinf(x) || x > _2pi || x < -_2pi)
continue;

ASSERT_MPFR_MATCH(mpfr::Operation::Sin, x, LIBC_NAMESPACE::sin(x), 1.0);
using LIBC_NAMESPACE::testing::tlog;

TEST_F(LlvmLibcSinTest, TrickyInputs) {
constexpr double INPUTS[] = {
0x1.940c877fb7dacp-7, 0x1.fffffffffdb6p24, 0x1.fd4da4ef37075p29,
0x1.b951f1572eba5p+31, 0x1.55202aefde314p+31, 0x1.85fc0f04c0128p101,
0x1.7776c2343ba4ep101, 0x1.678309fa50d58p110, 0x1.fffffffffef4ep199,
-0x1.ab514bfc61c76p+7, -0x1.f7898d5a756ddp+2, -0x1.f42fb19b5b9b2p-6,
0x1.5f09cad750ab1p+3, -0x1.14823229799c2p+7, -0x1.0285070f9f1bcp-5,
0x1.23f40dccdef72p+0, 0x1.43cf16358c9d7p+0, 0x1.addf3b9722265p+0,
0x1.48ff1782ca91dp+8, 0x1.a211877de55dbp+4, 0x1.dcbfda0c7559ep+8,
0x1.1ffb509f3db15p+5, 0x1.2345d1e090529p+5, 0x1.ae945054939c2p+10,
0x1.2e566149bf5fdp+9, 0x1.be886d9c2324dp+6, -0x1.119471e9216cdp+10,
-0x1.aaf85537ea4c7p+3, 0x1.cb996c60f437ep+9, 0x1.c96e28eb679f8p+5,
-0x1.a5eece87e8606p+4, 0x1.e31b55306f22cp+2, 0x1.ae78d360afa15p+0,
0x1.1685973506319p+3, 0x1.4f2b874135d27p+4, 0x1.ae945054939c2p+10,
0x1.3eec5912ea7cdp+331, 0x1.dcbfda0c7559ep+8, 0x1.a65d441ea6dcep+4,
0x1.e639103a05997p+2, 0x1.13114266f9764p+4, -0x1.3eec5912ea7cdp+331,
0x1.08087e9aad90bp+887, 0x1.2b5fe88a9d8d5p+903, -0x1.a880417b7b119p+1023,
-0x1.6deb37da81129p+205, 0x1.08087e9aad90bp+887, 0x1.f6d7518808571p+1023,
-0x1.8bb5847d49973p+845, 0x1.f08b14e1c4d0fp+890, 0x1.6ac5b262ca1ffp+849,
0x1.e0000000001c2p-20,
};
constexpr int N = sizeof(INPUTS) / sizeof(INPUTS[0]);

for (int i = 0; i < N; ++i) {
double x = INPUTS[i];
ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Sin, x,
LIBC_NAMESPACE::sin(x), 0.5);
}
}

TEST_F(LlvmLibcSinTest, InDoubleRange) {
constexpr uint64_t COUNT = 1'234'51;
uint64_t START = LIBC_NAMESPACE::fputil::FPBits<double>(0x1.0p-50).uintval();
uint64_t STOP = LIBC_NAMESPACE::fputil::FPBits<double>(0x1.0p200).uintval();
uint64_t STEP = (STOP - START) / COUNT;

auto test = [&](mpfr::RoundingMode rounding_mode) {
mpfr::ForceRoundingMode __r(rounding_mode);
if (!__r.success)
return;

uint64_t fails = 0;
uint64_t count = 0;
uint64_t cc = 0;
double mx, mr = 0.0;
double tol = 0.5;

for (uint64_t i = 0, v = START; i <= COUNT; ++i, v += STEP) {
double x = FPBits(v).get_val();
if (isnan(x) || isinf(x))
continue;
LIBC_NAMESPACE::libc_errno = 0;
double result = LIBC_NAMESPACE::sin(x);
++cc;
if (isnan(result) || isinf(result))
continue;

++count;

if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Sin, x, result,
0.5, rounding_mode)) {
++fails;
while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Sin, x,
result, tol, rounding_mode)) {
mx = x;
mr = result;

if (tol > 1000.0)
break;

tol *= 2.0;
}
}
}
if (fails) {
tlog << " Sin failed: " << fails << "/" << count << "/" << cc
<< " tests.\n";
tlog << " Max ULPs is at most: " << static_cast<uint64_t>(tol) << ".\n";
EXPECT_MPFR_MATCH(mpfr::Operation::Sin, mx, mr, 0.5, rounding_mode);
}
};

tlog << " Test Rounding To Nearest...\n";
test(mpfr::RoundingMode::Nearest);

tlog << " Test Rounding Downward...\n";
test(mpfr::RoundingMode::Downward);

tlog << " Test Rounding Upward...\n";
test(mpfr::RoundingMode::Upward);

tlog << " Test Rounding Toward Zero...\n";
test(mpfr::RoundingMode::TowardZero);
}
10 changes: 10 additions & 0 deletions libc/test/src/math/smoke/CMakeLists.txt
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Original file line number Diff line number Diff line change
Expand Up @@ -3653,3 +3653,13 @@ add_fp_unittest(
DEPENDS
libc.src.math.f16sqrtf
)

add_fp_unittest(
sin_test
SUITE
libc-math-smoke-tests
SRCS
sin_test.cpp
DEPENDS
libc.src.math.sin
)
26 changes: 26 additions & 0 deletions libc/test/src/math/smoke/sin_test.cpp
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Original file line number Diff line number Diff line change
@@ -0,0 +1,26 @@
//===-- Unittests for sin -------------------------------------------------===//
//
// 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/sin.h"
#include "test/UnitTest/FPMatcher.h"
#include "test/UnitTest/Test.h"

using LlvmLibcSinTest = LIBC_NAMESPACE::testing::FPTest<double>;

using LIBC_NAMESPACE::testing::tlog;

TEST_F(LlvmLibcSinTest, SpecialNumbers) {
EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::sin(aNaN));
EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::sin(inf));
EXPECT_FP_EQ_ALL_ROUNDING(aNaN, LIBC_NAMESPACE::sin(neg_inf));
EXPECT_FP_EQ_ALL_ROUNDING(zero, LIBC_NAMESPACE::sin(zero));
EXPECT_FP_EQ_ALL_ROUNDING(neg_zero, LIBC_NAMESPACE::sin(neg_zero));
EXPECT_FP_EQ(0x1.0p-50, LIBC_NAMESPACE::sin(0x1.0p-50));
EXPECT_FP_EQ(min_normal, LIBC_NAMESPACE::sin(min_normal));
EXPECT_FP_EQ(min_denormal, LIBC_NAMESPACE::sin(min_denormal));
}