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[libc][math] Refactor expm1 implementation to header-only in src/__support/math folder. (#162127)

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Part of #147386

in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
This commit is contained in:
Muhammad Bassiouni
2025-12-04 16:51:43 +02:00
committed by GitHub
parent 4f0eee3c46
commit e8defb503d
9 changed files with 586 additions and 511 deletions
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1
libc/shared/math.h
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@@ -54,6 +54,7 @@
#include "math/exp2m1f16.h"
#include "math/expf.h"
#include "math/expf16.h"
#include "math/expm1.h"
#include "math/frexpf.h"
#include "math/frexpf128.h"
#include "math/frexpf16.h"

23
libc/shared/math/expm1.h Normal file
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@@ -0,0 +1,23 @@
//===-- Shared expm1 function -----------------------------------*- 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_SHARED_MATH_EXPM1_H
#define LLVM_LIBC_SHARED_MATH_EXPM1_H
#include "shared/libc_common.h"
#include "src/__support/math/expm1.h"
namespace LIBC_NAMESPACE_DECL {
namespace shared {
using math::expm1;
} // namespace shared
} // namespace LIBC_NAMESPACE_DECL
#endif // LLVM_LIBC_SHARED_MATH_EXPM1_H

20
libc/src/__support/math/CMakeLists.txt
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@@ -871,6 +871,26 @@ add_header_library(
libc.src.__support.macros.properties.cpu_features
)
add_header_library(
expm1
HDRS
expm1.h
DEPENDS
.common_constants
.exp_constants
libc.src.__support.CPP.bit
libc.src.__support.FPUtil.dyadic_float
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.FPUtil.triple_double
libc.src.__support.integer_literals
libc.src.__support.macros.optimization
libc.src.errno.errno
)
add_header_library(
range_reduction_double
HDRS

518
libc/src/__support/math/expm1.h Normal file
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@@ -0,0 +1,518 @@
//===-- Implementation header for expm1 -------------------------*- 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___SUPPORT_MATH_EXPM1_H
#define LLVM_LIBC_SRC___SUPPORT_MATH_EXPM1_H
#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
#include "exp_constants.h"
#include "src/__support/CPP/bit.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/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/FPUtil/triple_double.h"
#include "src/__support/common.h"
#include "src/__support/integer_literals.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
namespace LIBC_NAMESPACE_DECL {
namespace math {
namespace expm1_internal {
#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0)
#define LIBC_MATH_EXPM1_SKIP_ACCURATE_PASS
#endif
using fputil::DoubleDouble;
using fputil::TripleDouble;
using Float128 = typename fputil::DyadicFloat<128>;
using LIBC_NAMESPACE::operator""_u128;
// log2(e)
static constexpr double LOG2_E = 0x1.71547652b82fep+0;
// Error bounds:
// Errors when using double precision.
// 0x1.8p-63;
static constexpr uint64_t ERR_D = 0x3c08000000000000;
// Errors when using double-double precision.
// 0x1.0p-99
[[maybe_unused]] static constexpr uint64_t ERR_DD = 0x39c0000000000000;
// -2^-12 * log(2)
// > a = -2^-12 * log(2);
// > b = round(a, 30, RN);
// > c = round(a - b, 30, RN);
// > d = round(a - b - c, D, RN);
// Errors < 1.5 * 2^-133
static constexpr double MLOG_2_EXP2_M12_HI = -0x1.62e42ffp-13;
static constexpr double MLOG_2_EXP2_M12_MID = 0x1.718432a1b0e26p-47;
static constexpr double MLOG_2_EXP2_M12_MID_30 = 0x1.718432ap-47;
static constexpr double MLOG_2_EXP2_M12_LO = 0x1.b0e2633fe0685p-79;
using namespace common_constants_internal;
// Polynomial approximations with double precision:
// Return expm1(dx) / x ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24.
// For |dx| < 2^-13 + 2^-30:
// | output - expm1(dx) / dx | < 2^-51.
LIBC_INLINE static double poly_approx_d(double dx) {
// dx^2
double dx2 = dx * dx;
// c0 = 1 + dx / 2
double c0 = fputil::multiply_add(dx, 0.5, 1.0);
// c1 = 1/6 + dx / 24
double c1 =
fputil::multiply_add(dx, 0x1.5555555555555p-5, 0x1.5555555555555p-3);
// p = dx^2 * c1 + c0 = 1 + dx / 2 + dx^2 / 6 + dx^3 / 24
double p = fputil::multiply_add(dx2, c1, c0);
return p;
}
// Polynomial approximation with double-double precision:
// Return expm1(dx) / dx ~ 1 + dx / 2 + dx^2 / 6 + ... + dx^6 / 5040
// For |dx| < 2^-13 + 2^-30:
// | output - expm1(dx) | < 2^-101
LIBC_INLINE static constexpr DoubleDouble
poly_approx_dd(const DoubleDouble &dx) {
// Taylor polynomial.
constexpr DoubleDouble COEFFS[] = {
{0, 0x1p0}, // 1
{0, 0x1p-1}, // 1/2
{0x1.5555555555555p-57, 0x1.5555555555555p-3}, // 1/6
{0x1.5555555555555p-59, 0x1.5555555555555p-5}, // 1/24
{0x1.1111111111111p-63, 0x1.1111111111111p-7}, // 1/120
{-0x1.f49f49f49f49fp-65, 0x1.6c16c16c16c17p-10}, // 1/720
{0x1.a01a01a01a01ap-73, 0x1.a01a01a01a01ap-13}, // 1/5040
};
DoubleDouble p = fputil::polyeval(dx, COEFFS[0], COEFFS[1], COEFFS[2],
COEFFS[3], COEFFS[4], COEFFS[5], COEFFS[6]);
return p;
}
// Polynomial approximation with 128-bit precision:
// Return (exp(dx) - 1)/dx ~ 1 + dx / 2 + dx^2 / 6 + ... + dx^6 / 5040
// For |dx| < 2^-13 + 2^-30:
// | output - exp(dx) | < 2^-126.
[[maybe_unused]] LIBC_INLINE static constexpr Float128
poly_approx_f128(const Float128 &dx) {
constexpr Float128 COEFFS_128[]{
{Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
{Sign::POS, -128, 0x80000000'00000000'00000000'00000000_u128}, // 0.5
{Sign::POS, -130, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/6
{Sign::POS, -132, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/24
{Sign::POS, -134, 0x88888888'88888888'88888888'88888889_u128}, // 1/120
{Sign::POS, -137, 0xb60b60b6'0b60b60b'60b60b60'b60b60b6_u128}, // 1/720
{Sign::POS, -140, 0xd00d00d0'0d00d00d'00d00d00'd00d00d0_u128}, // 1/5040
};
Float128 p = fputil::polyeval(dx, COEFFS_128[0], COEFFS_128[1], COEFFS_128[2],
COEFFS_128[3], COEFFS_128[4], COEFFS_128[5],
COEFFS_128[6]);
return p;
}
#ifdef DEBUGDEBUG
std::ostream &operator<<(std::ostream &OS, const Float128 &r) {
OS << (r.sign == Sign::NEG ? "-(" : "(") << r.mantissa.val[0] << " + "
<< r.mantissa.val[1] << " * 2^64) * 2^" << r.exponent << "\n";
return OS;
}
std::ostream &operator<<(std::ostream &OS, const DoubleDouble &r) {
OS << std::hexfloat << "(" << r.hi << " + " << r.lo << ")"
<< std::defaultfloat << "\n";
return OS;
}
#endif
// Compute exp(x) - 1 using 128-bit precision.
// TODO(lntue): investigate triple-double precision implementation for this
// step.
[[maybe_unused]] LIBC_INLINE static Float128 expm1_f128(double x, double kd,
int idx1, int idx2) {
// Recalculate dx:
double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
double t2 = kd * MLOG_2_EXP2_M12_MID_30; // exact
double t3 = kd * MLOG_2_EXP2_M12_LO; // Error < 2^-133
Float128 dx = fputil::quick_add(
Float128(t1), fputil::quick_add(Float128(t2), Float128(t3)));
// TODO: Skip recalculating exp_mid1 and exp_mid2.
Float128 exp_mid1 =
fputil::quick_add(Float128(EXP2_MID1[idx1].hi),
fputil::quick_add(Float128(EXP2_MID1[idx1].mid),
Float128(EXP2_MID1[idx1].lo)));
Float128 exp_mid2 =
fputil::quick_add(Float128(EXP2_MID2[idx2].hi),
fputil::quick_add(Float128(EXP2_MID2[idx2].mid),
Float128(EXP2_MID2[idx2].lo)));
Float128 exp_mid = fputil::quick_mul(exp_mid1, exp_mid2);
int hi = static_cast<int>(kd) >> 12;
Float128 minus_one{Sign::NEG, -127 - hi,
0x80000000'00000000'00000000'00000000_u128};
Float128 exp_mid_m1 = fputil::quick_add(exp_mid, minus_one);
Float128 p = poly_approx_f128(dx);
// r = exp_mid * (1 + dx * P) - 1
// = (exp_mid - 1) + (dx * exp_mid) * P
Float128 r =
fputil::multiply_add(fputil::quick_mul(exp_mid, dx), p, exp_mid_m1);
r.exponent += hi;
#ifdef DEBUGDEBUG
std::cout << "=== VERY SLOW PASS ===\n"
<< " kd: " << kd << "\n"
<< " hi: " << hi << "\n"
<< " minus_one: " << minus_one << " dx: " << dx
<< "exp_mid_m1: " << exp_mid_m1 << " exp_mid: " << exp_mid
<< " p: " << p << " r: " << r << std::endl;
#endif
return r;
}
// Compute exp(x) - 1 with double-double precision.
LIBC_INLINE static DoubleDouble exp_double_double(double x, double kd,
const DoubleDouble &exp_mid,
const DoubleDouble &hi_part) {
// Recalculate dx:
// dx = x - k * 2^-12 * log(2)
double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
double t2 = kd * MLOG_2_EXP2_M12_MID_30; // exact
double t3 = kd * MLOG_2_EXP2_M12_LO; // Error < 2^-130
DoubleDouble dx = fputil::exact_add(t1, t2);
dx.lo += t3;
// Degree-6 Taylor polynomial approximation in double-double precision.
// | p - exp(x) | < 2^-100.
DoubleDouble p = poly_approx_dd(dx);
// Error bounds: 2^-99.
DoubleDouble r =
fputil::multiply_add(fputil::quick_mult(exp_mid, dx), p, hi_part);
#ifdef DEBUGDEBUG
std::cout << "=== SLOW PASS ===\n"
<< " dx: " << dx << " p: " << p << " r: " << r << std::endl;
#endif
return r;
}
// Check for exceptional cases when
// |x| <= 2^-53 or x < log(2^-54) or x >= 0x1.6232bdd7abcd3p+9
LIBC_INLINE static constexpr double set_exceptional(double x) {
using FPBits = typename fputil::FPBits<double>;
FPBits xbits(x);
uint64_t x_u = xbits.uintval();
uint64_t x_abs = xbits.abs().uintval();
// |x| <= 2^-53.
if (x_abs <= 0x3ca0'0000'0000'0000ULL) {
// expm1(x) ~ x.
if (LIBC_UNLIKELY(x_abs <= 0x0370'0000'0000'0000ULL)) {
if (LIBC_UNLIKELY(x_abs == 0))
return x;
// |x| <= 2^-968, need to scale up a bit before rounding, then scale it
// back down.
return 0x1.0p-200 * fputil::multiply_add(x, 0x1.0p+200, 0x1.0p-1022);
}
// 2^-968 < |x| <= 2^-53.
return fputil::round_result_slightly_up(x);
}
// x < log(2^-54) || x >= 0x1.6232bdd7abcd3p+9 or inf/nan.
// x < log(2^-54) or -inf/nan
if (x_u >= 0xc042'b708'8723'20e2ULL) {
// expm1(-Inf) = -1
if (xbits.is_inf())
return -1.0;
// exp(nan) = nan
if (xbits.is_nan())
return x;
return fputil::round_result_slightly_up(-1.0);
}
// x >= round(log(MAX_NORMAL), D, RU) = 0x1.62e42fefa39fp+9 or +inf/nan
// x is finite
if (x_u < 0x7ff0'0000'0000'0000ULL) {
int rounding = fputil::quick_get_round();
if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
return FPBits::max_normal().get_val();
fputil::set_errno_if_required(ERANGE);
fputil::raise_except_if_required(FE_OVERFLOW);
}
// x is +inf or nan
return x + FPBits::inf().get_val();
}
} // namespace expm1_internal
LIBC_INLINE static constexpr double expm1(double x) {
using namespace expm1_internal;
using FPBits = typename fputil::FPBits<double>;
FPBits xbits(x);
bool x_is_neg = xbits.is_neg();
uint64_t x_u = xbits.uintval();
// Upper bound: max normal number = 2^1023 * (2 - 2^-52)
// > round(log (2^1023 ( 2 - 2^-52 )), D, RU) = 0x1.62e42fefa39fp+9
// > round(log (2^1023 ( 2 - 2^-52 )), D, RD) = 0x1.62e42fefa39efp+9
// > round(log (2^1023 ( 2 - 2^-52 )), D, RN) = 0x1.62e42fefa39efp+9
// > round(exp(0x1.62e42fefa39fp+9), D, RN) = infty
// Lower bound: log(2^-54) = -0x1.2b708872320e2p5
// > round(log(2^-54), D, RN) = -0x1.2b708872320e2p5
// x < log(2^-54) or x >= 0x1.6232bdd7abcd3p+9 or |x| <= 2^-53.
if (LIBC_UNLIKELY(x_u >= 0xc042b708872320e2 ||
(x_u <= 0xbca0000000000000 && x_u >= 0x40862e42fefa39f0) ||
x_u <= 0x3ca0000000000000)) {
return set_exceptional(x);
}
// Now log(2^-54) <= x <= -2^-53 or 2^-53 <= x < log(2^1023 * (2 - 2^-52))
// Range reduction:
// Let x = log(2) * (hi + mid1 + mid2) + lo
// in which:
// hi is an integer
// mid1 * 2^6 is an integer
// mid2 * 2^12 is an integer
// then:
// exp(x) = 2^hi * 2^(mid1) * 2^(mid2) * exp(lo).
// With this formula:
// - multiplying by 2^hi is exact and cheap, simply by adding the exponent
// field.
// - 2^(mid1) and 2^(mid2) are stored in 2 x 64-element tables.
// - exp(lo) ~ 1 + lo + a0 * lo^2 + ...
//
// They can be defined by:
// hi + mid1 + mid2 = 2^(-12) * round(2^12 * log_2(e) * x)
// If we store L2E = round(log2(e), D, RN), then:
// log2(e) - L2E ~ 1.5 * 2^(-56)
// So the errors when computing in double precision is:
// | x * 2^12 * log_2(e) - D(x * 2^12 * L2E) | <=
// <= | x * 2^12 * log_2(e) - x * 2^12 * L2E | +
// + | x * 2^12 * L2E - D(x * 2^12 * L2E) |
// <= 2^12 * ( |x| * 1.5 * 2^-56 + eps(x)) for RN
// 2^12 * ( |x| * 1.5 * 2^-56 + 2*eps(x)) for other rounding modes.
// So if:
// hi + mid1 + mid2 = 2^(-12) * round(x * 2^12 * L2E) is computed entirely
// in double precision, the reduced argument:
// lo = x - log(2) * (hi + mid1 + mid2) is bounded by:
// |lo| <= 2^-13 + (|x| * 1.5 * 2^-56 + 2*eps(x))
// < 2^-13 + (1.5 * 2^9 * 1.5 * 2^-56 + 2*2^(9 - 52))
// < 2^-13 + 2^-41
//
// The following trick computes the round(x * L2E) more efficiently
// than using the rounding instructions, with the tradeoff for less accuracy,
// and hence a slightly larger range for the reduced argument `lo`.
//
// To be precise, since |x| < |log(2^-1075)| < 1.5 * 2^9,
// |x * 2^12 * L2E| < 1.5 * 2^9 * 1.5 < 2^23,
// So we can fit the rounded result round(x * 2^12 * L2E) in int32_t.
// Thus, the goal is to be able to use an additional addition and fixed width
// shift to get an int32_t representing round(x * 2^12 * L2E).
//
// Assuming int32_t using 2-complement representation, since the mantissa part
// of a double precision is unsigned with the leading bit hidden, if we add an
// extra constant C = 2^e1 + 2^e2 with e1 > e2 >= 2^25 to the product, the
// part that are < 2^e2 in resulted mantissa of (x*2^12*L2E + C) can be
// considered as a proper 2-complement representations of x*2^12*L2E.
//
// One small problem with this approach is that the sum (x*2^12*L2E + C) in
// double precision is rounded to the least significant bit of the dorminant
// factor C. In order to minimize the rounding errors from this addition, we
// want to minimize e1. Another constraint that we want is that after
// shifting the mantissa so that the least significant bit of int32_t
// corresponds to the unit bit of (x*2^12*L2E), the sign is correct without
// any adjustment. So combining these 2 requirements, we can choose
// C = 2^33 + 2^32, so that the sign bit corresponds to 2^31 bit, and hence
// after right shifting the mantissa, the resulting int32_t has correct sign.
// With this choice of C, the number of mantissa bits we need to shift to the
// right is: 52 - 33 = 19.
//
// Moreover, since the integer right shifts are equivalent to rounding down,
// we can add an extra 0.5 so that it will become round-to-nearest, tie-to-
// +infinity. So in particular, we can compute:
// hmm = x * 2^12 * L2E + C,
// where C = 2^33 + 2^32 + 2^-1, then if
// k = int32_t(lower 51 bits of double(x * 2^12 * L2E + C) >> 19),
// the reduced argument:
// lo = x - log(2) * 2^-12 * k is bounded by:
// |lo| <= 2^-13 + 2^-41 + 2^-12*2^-19
// = 2^-13 + 2^-31 + 2^-41.
//
// Finally, notice that k only uses the mantissa of x * 2^12 * L2E, so the
// exponent 2^12 is not needed. So we can simply define
// C = 2^(33 - 12) + 2^(32 - 12) + 2^(-13 - 12), and
// k = int32_t(lower 51 bits of double(x * L2E + C) >> 19).
// Rounding errors <= 2^-31 + 2^-41.
double tmp = fputil::multiply_add(x, LOG2_E, 0x1.8000'0000'4p21);
int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19);
double kd = static_cast<double>(k);
uint32_t idx1 = (k >> 6) & 0x3f;
uint32_t idx2 = k & 0x3f;
int hi = k >> 12;
DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi};
DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi};
DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2);
// -2^(-hi)
double one_scaled =
FPBits::create_value(Sign::NEG, FPBits::EXP_BIAS - hi, 0).get_val();
// 2^(mid1 + mid2) - 2^(-hi)
DoubleDouble hi_part = x_is_neg ? fputil::exact_add(one_scaled, exp_mid.hi)
: fputil::exact_add(exp_mid.hi, one_scaled);
hi_part.lo += exp_mid.lo;
// |x - (hi + mid1 + mid2) * log(2) - dx| < 2^11 * eps(M_LOG_2_EXP2_M12.lo)
// = 2^11 * 2^-13 * 2^-52
// = 2^-54.
// |dx| < 2^-13 + 2^-30.
double lo_h = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
double dx = fputil::multiply_add(kd, MLOG_2_EXP2_M12_MID, lo_h);
// We use the degree-4 Taylor polynomial to approximate exp(lo):
// exp(lo) ~ 1 + lo + lo^2 / 2 + lo^3 / 6 + lo^4 / 24 = 1 + lo * P(lo)
// So that the errors are bounded by:
// |P(lo) - expm1(lo)/lo| < |lo|^4 / 64 < 2^(-13 * 4) / 64 = 2^-58
// Let P_ be an evaluation of P where all intermediate computations are in
// double precision. Using either Horner's or Estrin's schemes, the evaluated
// errors can be bounded by:
// |P_(dx) - P(dx)| < 2^-51
// => |dx * P_(dx) - expm1(lo) | < 1.5 * 2^-64
// => 2^(mid1 + mid2) * |dx * P_(dx) - expm1(lo)| < 1.5 * 2^-63.
// Since we approximate
// 2^(mid1 + mid2) ~ exp_mid.hi + exp_mid.lo,
// We use the expression:
// (exp_mid.hi + exp_mid.lo) * (1 + dx * P_(dx)) ~
// ~ exp_mid.hi + (exp_mid.hi * dx * P_(dx) + exp_mid.lo)
// with errors bounded by 1.5 * 2^-63.
// Finally, we have the following approximation formula:
// expm1(x) = 2^hi * 2^(mid1 + mid2) * exp(lo) - 1
// = 2^hi * ( 2^(mid1 + mid2) * exp(lo) - 2^(-hi) )
// ~ 2^hi * ( (exp_mid.hi - 2^-hi) +
// + (exp_mid.hi * dx * P_(dx) + exp_mid.lo))
double mid_lo = dx * exp_mid.hi;
// Approximate expm1(dx)/dx ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24.
double p = poly_approx_d(dx);
double lo = fputil::multiply_add(p, mid_lo, hi_part.lo);
// TODO: The following line leaks encoding abstraction. Use FPBits methods
// instead.
uint64_t err = x_is_neg ? (static_cast<uint64_t>(-hi) << 52) : 0;
double err_d = cpp::bit_cast<double>(ERR_D + err);
double upper = hi_part.hi + (lo + err_d);
double lower = hi_part.hi + (lo - err_d);
#ifdef DEBUGDEBUG
std::cout << "=== FAST PASS ===\n"
<< " x: " << std::hexfloat << x << std::defaultfloat << "\n"
<< " k: " << k << "\n"
<< " idx1: " << idx1 << "\n"
<< " idx2: " << idx2 << "\n"
<< " hi: " << hi << "\n"
<< " dx: " << std::hexfloat << dx << std::defaultfloat << "\n"
<< "exp_mid: " << exp_mid << "hi_part: " << hi_part
<< " mid_lo: " << std::hexfloat << mid_lo << std::defaultfloat
<< "\n"
<< " p: " << std::hexfloat << p << std::defaultfloat << "\n"
<< " lo: " << std::hexfloat << lo << std::defaultfloat << "\n"
<< " upper: " << std::hexfloat << upper << std::defaultfloat
<< "\n"
<< " lower: " << std::hexfloat << lower << std::defaultfloat
<< "\n"
<< std::endl;
#endif
if (LIBC_LIKELY(upper == lower)) {
// to multiply by 2^hi, a fast way is to simply add hi to the exponent
// field.
int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper));
return r;
}
// Use double-double
DoubleDouble r_dd = exp_double_double(x, kd, exp_mid, hi_part);
#ifdef LIBC_MATH_EXPM1_SKIP_ACCURATE_PASS
int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
double r =
cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(r_dd.hi + r_dd.lo));
return r;
#else
double err_dd = cpp::bit_cast<double>(ERR_DD + err);
double upper_dd = r_dd.hi + (r_dd.lo + err_dd);
double lower_dd = r_dd.hi + (r_dd.lo - err_dd);
if (LIBC_LIKELY(upper_dd == lower_dd)) {
int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper_dd));
return r;
}
// Use 128-bit precision
Float128 r_f128 = expm1_f128(x, kd, idx1, idx2);
return static_cast<double>(r_f128);
#endif // LIBC_MATH_EXPM1_SKIP_ACCURATE_PASS
}
} // namespace math
} // namespace LIBC_NAMESPACE_DECL
#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPM1_H

13
libc/src/math/generic/CMakeLists.txt
View File

@@ -1561,18 +1561,7 @@ add_entrypoint_object(
HDRS
../expm1.h
DEPENDS
libc.src.__support.CPP.bit
libc.src.__support.FPUtil.dyadic_float
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.polyeval
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.FPUtil.triple_double
libc.src.__support.integer_literals
libc.src.__support.macros.optimization
libc.src.__support.math.common_constants
libc.src.errno.errno
libc.src.__support.math.expm1
)
add_entrypoint_object(

492
libc/src/math/generic/expm1.cpp
View File

@@ -7,498 +7,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/expm1.h"
#include "src/__support/CPP/bit.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/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/FPUtil/triple_double.h"
#include "src/__support/common.h"
#include "src/__support/integer_literals.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/__support/math/common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
#include "src/__support/math/exp_constants.h"
#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0)
#define LIBC_MATH_EXPM1_SKIP_ACCURATE_PASS
#endif
#include "src/__support/math/expm1.h"
namespace LIBC_NAMESPACE_DECL {
using fputil::DoubleDouble;
using fputil::TripleDouble;
using Float128 = typename fputil::DyadicFloat<128>;
using LIBC_NAMESPACE::operator""_u128;
// log2(e)
constexpr double LOG2_E = 0x1.71547652b82fep+0;
// Error bounds:
// Errors when using double precision.
// 0x1.8p-63;
constexpr uint64_t ERR_D = 0x3c08000000000000;
// Errors when using double-double precision.
// 0x1.0p-99
[[maybe_unused]] constexpr uint64_t ERR_DD = 0x39c0000000000000;
// -2^-12 * log(2)
// > a = -2^-12 * log(2);
// > b = round(a, 30, RN);
// > c = round(a - b, 30, RN);
// > d = round(a - b - c, D, RN);
// Errors < 1.5 * 2^-133
constexpr double MLOG_2_EXP2_M12_HI = -0x1.62e42ffp-13;
constexpr double MLOG_2_EXP2_M12_MID = 0x1.718432a1b0e26p-47;
constexpr double MLOG_2_EXP2_M12_MID_30 = 0x1.718432ap-47;
constexpr double MLOG_2_EXP2_M12_LO = 0x1.b0e2633fe0685p-79;
namespace {
using namespace common_constants_internal;
// Polynomial approximations with double precision:
// Return expm1(dx) / x ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24.
// For |dx| < 2^-13 + 2^-30:
// | output - expm1(dx) / dx | < 2^-51.
LIBC_INLINE double poly_approx_d(double dx) {
// dx^2
double dx2 = dx * dx;
// c0 = 1 + dx / 2
double c0 = fputil::multiply_add(dx, 0.5, 1.0);
// c1 = 1/6 + dx / 24
double c1 =
fputil::multiply_add(dx, 0x1.5555555555555p-5, 0x1.5555555555555p-3);
// p = dx^2 * c1 + c0 = 1 + dx / 2 + dx^2 / 6 + dx^3 / 24
double p = fputil::multiply_add(dx2, c1, c0);
return p;
}
// Polynomial approximation with double-double precision:
// Return expm1(dx) / dx ~ 1 + dx / 2 + dx^2 / 6 + ... + dx^6 / 5040
// For |dx| < 2^-13 + 2^-30:
// | output - expm1(dx) | < 2^-101
DoubleDouble poly_approx_dd(const DoubleDouble &dx) {
// Taylor polynomial.
constexpr DoubleDouble COEFFS[] = {
{0, 0x1p0}, // 1
{0, 0x1p-1}, // 1/2
{0x1.5555555555555p-57, 0x1.5555555555555p-3}, // 1/6
{0x1.5555555555555p-59, 0x1.5555555555555p-5}, // 1/24
{0x1.1111111111111p-63, 0x1.1111111111111p-7}, // 1/120
{-0x1.f49f49f49f49fp-65, 0x1.6c16c16c16c17p-10}, // 1/720
{0x1.a01a01a01a01ap-73, 0x1.a01a01a01a01ap-13}, // 1/5040
};
DoubleDouble p = fputil::polyeval(dx, COEFFS[0], COEFFS[1], COEFFS[2],
COEFFS[3], COEFFS[4], COEFFS[5], COEFFS[6]);
return p;
}
// Polynomial approximation with 128-bit precision:
// Return (exp(dx) - 1)/dx ~ 1 + dx / 2 + dx^2 / 6 + ... + dx^6 / 5040
// For |dx| < 2^-13 + 2^-30:
// | output - exp(dx) | < 2^-126.
[[maybe_unused]] Float128 poly_approx_f128(const Float128 &dx) {
constexpr Float128 COEFFS_128[]{
{Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
{Sign::POS, -128, 0x80000000'00000000'00000000'00000000_u128}, // 0.5
{Sign::POS, -130, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/6
{Sign::POS, -132, 0xaaaaaaaa'aaaaaaaa'aaaaaaaa'aaaaaaab_u128}, // 1/24
{Sign::POS, -134, 0x88888888'88888888'88888888'88888889_u128}, // 1/120
{Sign::POS, -137, 0xb60b60b6'0b60b60b'60b60b60'b60b60b6_u128}, // 1/720
{Sign::POS, -140, 0xd00d00d0'0d00d00d'00d00d00'd00d00d0_u128}, // 1/5040
};
Float128 p = fputil::polyeval(dx, COEFFS_128[0], COEFFS_128[1], COEFFS_128[2],
COEFFS_128[3], COEFFS_128[4], COEFFS_128[5],
COEFFS_128[6]);
return p;
}
#ifdef DEBUGDEBUG
std::ostream &operator<<(std::ostream &OS, const Float128 &r) {
OS << (r.sign == Sign::NEG ? "-(" : "(") << r.mantissa.val[0] << " + "
<< r.mantissa.val[1] << " * 2^64) * 2^" << r.exponent << "\n";
return OS;
}
std::ostream &operator<<(std::ostream &OS, const DoubleDouble &r) {
OS << std::hexfloat << "(" << r.hi << " + " << r.lo << ")"
<< std::defaultfloat << "\n";
return OS;
}
#endif
// Compute exp(x) - 1 using 128-bit precision.
// TODO(lntue): investigate triple-double precision implementation for this
// step.
[[maybe_unused]] Float128 expm1_f128(double x, double kd, int idx1, int idx2) {
// Recalculate dx:
double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
double t2 = kd * MLOG_2_EXP2_M12_MID_30; // exact
double t3 = kd * MLOG_2_EXP2_M12_LO; // Error < 2^-133
Float128 dx = fputil::quick_add(
Float128(t1), fputil::quick_add(Float128(t2), Float128(t3)));
// TODO: Skip recalculating exp_mid1 and exp_mid2.
Float128 exp_mid1 =
fputil::quick_add(Float128(EXP2_MID1[idx1].hi),
fputil::quick_add(Float128(EXP2_MID1[idx1].mid),
Float128(EXP2_MID1[idx1].lo)));
Float128 exp_mid2 =
fputil::quick_add(Float128(EXP2_MID2[idx2].hi),
fputil::quick_add(Float128(EXP2_MID2[idx2].mid),
Float128(EXP2_MID2[idx2].lo)));
Float128 exp_mid = fputil::quick_mul(exp_mid1, exp_mid2);
int hi = static_cast<int>(kd) >> 12;
Float128 minus_one{Sign::NEG, -127 - hi,
0x80000000'00000000'00000000'00000000_u128};
Float128 exp_mid_m1 = fputil::quick_add(exp_mid, minus_one);
Float128 p = poly_approx_f128(dx);
// r = exp_mid * (1 + dx * P) - 1
// = (exp_mid - 1) + (dx * exp_mid) * P
Float128 r =
fputil::multiply_add(fputil::quick_mul(exp_mid, dx), p, exp_mid_m1);
r.exponent += hi;
#ifdef DEBUGDEBUG
std::cout << "=== VERY SLOW PASS ===\n"
<< " kd: " << kd << "\n"
<< " hi: " << hi << "\n"
<< " minus_one: " << minus_one << " dx: " << dx
<< "exp_mid_m1: " << exp_mid_m1 << " exp_mid: " << exp_mid
<< " p: " << p << " r: " << r << std::endl;
#endif
return r;
}
// Compute exp(x) - 1 with double-double precision.
DoubleDouble exp_double_double(double x, double kd, const DoubleDouble &exp_mid,
const DoubleDouble &hi_part) {
// Recalculate dx:
// dx = x - k * 2^-12 * log(2)
double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
double t2 = kd * MLOG_2_EXP2_M12_MID_30; // exact
double t3 = kd * MLOG_2_EXP2_M12_LO; // Error < 2^-130
DoubleDouble dx = fputil::exact_add(t1, t2);
dx.lo += t3;
// Degree-6 Taylor polynomial approximation in double-double precision.
// | p - exp(x) | < 2^-100.
DoubleDouble p = poly_approx_dd(dx);
// Error bounds: 2^-99.
DoubleDouble r =
fputil::multiply_add(fputil::quick_mult(exp_mid, dx), p, hi_part);
#ifdef DEBUGDEBUG
std::cout << "=== SLOW PASS ===\n"
<< " dx: " << dx << " p: " << p << " r: " << r << std::endl;
#endif
return r;
}
// Check for exceptional cases when
// |x| <= 2^-53 or x < log(2^-54) or x >= 0x1.6232bdd7abcd3p+9
double set_exceptional(double x) {
using FPBits = typename fputil::FPBits<double>;
FPBits xbits(x);
uint64_t x_u = xbits.uintval();
uint64_t x_abs = xbits.abs().uintval();
// |x| <= 2^-53.
if (x_abs <= 0x3ca0'0000'0000'0000ULL) {
// expm1(x) ~ x.
if (LIBC_UNLIKELY(x_abs <= 0x0370'0000'0000'0000ULL)) {
if (LIBC_UNLIKELY(x_abs == 0))
return x;
// |x| <= 2^-968, need to scale up a bit before rounding, then scale it
// back down.
return 0x1.0p-200 * fputil::multiply_add(x, 0x1.0p+200, 0x1.0p-1022);
}
// 2^-968 < |x| <= 2^-53.
return fputil::round_result_slightly_up(x);
}
// x < log(2^-54) || x >= 0x1.6232bdd7abcd3p+9 or inf/nan.
// x < log(2^-54) or -inf/nan
if (x_u >= 0xc042'b708'8723'20e2ULL) {
// expm1(-Inf) = -1
if (xbits.is_inf())
return -1.0;
// exp(nan) = nan
if (xbits.is_nan())
return x;
return fputil::round_result_slightly_up(-1.0);
}
// x >= round(log(MAX_NORMAL), D, RU) = 0x1.62e42fefa39fp+9 or +inf/nan
// x is finite
if (x_u < 0x7ff0'0000'0000'0000ULL) {
int rounding = fputil::quick_get_round();
if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
return FPBits::max_normal().get_val();
fputil::set_errno_if_required(ERANGE);
fputil::raise_except_if_required(FE_OVERFLOW);
}
// x is +inf or nan
return x + FPBits::inf().get_val();
}
} // namespace
LLVM_LIBC_FUNCTION(double, expm1, (double x)) {
using FPBits = typename fputil::FPBits<double>;
FPBits xbits(x);
bool x_is_neg = xbits.is_neg();
uint64_t x_u = xbits.uintval();
// Upper bound: max normal number = 2^1023 * (2 - 2^-52)
// > round(log (2^1023 ( 2 - 2^-52 )), D, RU) = 0x1.62e42fefa39fp+9
// > round(log (2^1023 ( 2 - 2^-52 )), D, RD) = 0x1.62e42fefa39efp+9
// > round(log (2^1023 ( 2 - 2^-52 )), D, RN) = 0x1.62e42fefa39efp+9
// > round(exp(0x1.62e42fefa39fp+9), D, RN) = infty
// Lower bound: log(2^-54) = -0x1.2b708872320e2p5
// > round(log(2^-54), D, RN) = -0x1.2b708872320e2p5
// x < log(2^-54) or x >= 0x1.6232bdd7abcd3p+9 or |x| <= 2^-53.
if (LIBC_UNLIKELY(x_u >= 0xc042b708872320e2 ||
(x_u <= 0xbca0000000000000 && x_u >= 0x40862e42fefa39f0) ||
x_u <= 0x3ca0000000000000)) {
return set_exceptional(x);
}
// Now log(2^-54) <= x <= -2^-53 or 2^-53 <= x < log(2^1023 * (2 - 2^-52))
// Range reduction:
// Let x = log(2) * (hi + mid1 + mid2) + lo
// in which:
// hi is an integer
// mid1 * 2^6 is an integer
// mid2 * 2^12 is an integer
// then:
// exp(x) = 2^hi * 2^(mid1) * 2^(mid2) * exp(lo).
// With this formula:
// - multiplying by 2^hi is exact and cheap, simply by adding the exponent
// field.
// - 2^(mid1) and 2^(mid2) are stored in 2 x 64-element tables.
// - exp(lo) ~ 1 + lo + a0 * lo^2 + ...
//
// They can be defined by:
// hi + mid1 + mid2 = 2^(-12) * round(2^12 * log_2(e) * x)
// If we store L2E = round(log2(e), D, RN), then:
// log2(e) - L2E ~ 1.5 * 2^(-56)
// So the errors when computing in double precision is:
// | x * 2^12 * log_2(e) - D(x * 2^12 * L2E) | <=
// <= | x * 2^12 * log_2(e) - x * 2^12 * L2E | +
// + | x * 2^12 * L2E - D(x * 2^12 * L2E) |
// <= 2^12 * ( |x| * 1.5 * 2^-56 + eps(x)) for RN
// 2^12 * ( |x| * 1.5 * 2^-56 + 2*eps(x)) for other rounding modes.
// So if:
// hi + mid1 + mid2 = 2^(-12) * round(x * 2^12 * L2E) is computed entirely
// in double precision, the reduced argument:
// lo = x - log(2) * (hi + mid1 + mid2) is bounded by:
// |lo| <= 2^-13 + (|x| * 1.5 * 2^-56 + 2*eps(x))
// < 2^-13 + (1.5 * 2^9 * 1.5 * 2^-56 + 2*2^(9 - 52))
// < 2^-13 + 2^-41
//
// The following trick computes the round(x * L2E) more efficiently
// than using the rounding instructions, with the tradeoff for less accuracy,
// and hence a slightly larger range for the reduced argument `lo`.
//
// To be precise, since |x| < |log(2^-1075)| < 1.5 * 2^9,
// |x * 2^12 * L2E| < 1.5 * 2^9 * 1.5 < 2^23,
// So we can fit the rounded result round(x * 2^12 * L2E) in int32_t.
// Thus, the goal is to be able to use an additional addition and fixed width
// shift to get an int32_t representing round(x * 2^12 * L2E).
//
// Assuming int32_t using 2-complement representation, since the mantissa part
// of a double precision is unsigned with the leading bit hidden, if we add an
// extra constant C = 2^e1 + 2^e2 with e1 > e2 >= 2^25 to the product, the
// part that are < 2^e2 in resulted mantissa of (x*2^12*L2E + C) can be
// considered as a proper 2-complement representations of x*2^12*L2E.
//
// One small problem with this approach is that the sum (x*2^12*L2E + C) in
// double precision is rounded to the least significant bit of the dorminant
// factor C. In order to minimize the rounding errors from this addition, we
// want to minimize e1. Another constraint that we want is that after
// shifting the mantissa so that the least significant bit of int32_t
// corresponds to the unit bit of (x*2^12*L2E), the sign is correct without
// any adjustment. So combining these 2 requirements, we can choose
// C = 2^33 + 2^32, so that the sign bit corresponds to 2^31 bit, and hence
// after right shifting the mantissa, the resulting int32_t has correct sign.
// With this choice of C, the number of mantissa bits we need to shift to the
// right is: 52 - 33 = 19.
//
// Moreover, since the integer right shifts are equivalent to rounding down,
// we can add an extra 0.5 so that it will become round-to-nearest, tie-to-
// +infinity. So in particular, we can compute:
// hmm = x * 2^12 * L2E + C,
// where C = 2^33 + 2^32 + 2^-1, then if
// k = int32_t(lower 51 bits of double(x * 2^12 * L2E + C) >> 19),
// the reduced argument:
// lo = x - log(2) * 2^-12 * k is bounded by:
// |lo| <= 2^-13 + 2^-41 + 2^-12*2^-19
// = 2^-13 + 2^-31 + 2^-41.
//
// Finally, notice that k only uses the mantissa of x * 2^12 * L2E, so the
// exponent 2^12 is not needed. So we can simply define
// C = 2^(33 - 12) + 2^(32 - 12) + 2^(-13 - 12), and
// k = int32_t(lower 51 bits of double(x * L2E + C) >> 19).
// Rounding errors <= 2^-31 + 2^-41.
double tmp = fputil::multiply_add(x, LOG2_E, 0x1.8000'0000'4p21);
int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19);
double kd = static_cast<double>(k);
uint32_t idx1 = (k >> 6) & 0x3f;
uint32_t idx2 = k & 0x3f;
int hi = k >> 12;
DoubleDouble exp_mid1{EXP2_MID1[idx1].mid, EXP2_MID1[idx1].hi};
DoubleDouble exp_mid2{EXP2_MID2[idx2].mid, EXP2_MID2[idx2].hi};
DoubleDouble exp_mid = fputil::quick_mult(exp_mid1, exp_mid2);
// -2^(-hi)
double one_scaled =
FPBits::create_value(Sign::NEG, FPBits::EXP_BIAS - hi, 0).get_val();
// 2^(mid1 + mid2) - 2^(-hi)
DoubleDouble hi_part = x_is_neg ? fputil::exact_add(one_scaled, exp_mid.hi)
: fputil::exact_add(exp_mid.hi, one_scaled);
hi_part.lo += exp_mid.lo;
// |x - (hi + mid1 + mid2) * log(2) - dx| < 2^11 * eps(M_LOG_2_EXP2_M12.lo)
// = 2^11 * 2^-13 * 2^-52
// = 2^-54.
// |dx| < 2^-13 + 2^-30.
double lo_h = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact
double dx = fputil::multiply_add(kd, MLOG_2_EXP2_M12_MID, lo_h);
// We use the degree-4 Taylor polynomial to approximate exp(lo):
// exp(lo) ~ 1 + lo + lo^2 / 2 + lo^3 / 6 + lo^4 / 24 = 1 + lo * P(lo)
// So that the errors are bounded by:
// |P(lo) - expm1(lo)/lo| < |lo|^4 / 64 < 2^(-13 * 4) / 64 = 2^-58
// Let P_ be an evaluation of P where all intermediate computations are in
// double precision. Using either Horner's or Estrin's schemes, the evaluated
// errors can be bounded by:
// |P_(dx) - P(dx)| < 2^-51
// => |dx * P_(dx) - expm1(lo) | < 1.5 * 2^-64
// => 2^(mid1 + mid2) * |dx * P_(dx) - expm1(lo)| < 1.5 * 2^-63.
// Since we approximate
// 2^(mid1 + mid2) ~ exp_mid.hi + exp_mid.lo,
// We use the expression:
// (exp_mid.hi + exp_mid.lo) * (1 + dx * P_(dx)) ~
// ~ exp_mid.hi + (exp_mid.hi * dx * P_(dx) + exp_mid.lo)
// with errors bounded by 1.5 * 2^-63.
// Finally, we have the following approximation formula:
// expm1(x) = 2^hi * 2^(mid1 + mid2) * exp(lo) - 1
// = 2^hi * ( 2^(mid1 + mid2) * exp(lo) - 2^(-hi) )
// ~ 2^hi * ( (exp_mid.hi - 2^-hi) +
// + (exp_mid.hi * dx * P_(dx) + exp_mid.lo))
double mid_lo = dx * exp_mid.hi;
// Approximate expm1(dx)/dx ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24.
double p = poly_approx_d(dx);
double lo = fputil::multiply_add(p, mid_lo, hi_part.lo);
// TODO: The following line leaks encoding abstraction. Use FPBits methods
// instead.
uint64_t err = x_is_neg ? (static_cast<uint64_t>(-hi) << 52) : 0;
double err_d = cpp::bit_cast<double>(ERR_D + err);
double upper = hi_part.hi + (lo + err_d);
double lower = hi_part.hi + (lo - err_d);
#ifdef DEBUGDEBUG
std::cout << "=== FAST PASS ===\n"
<< " x: " << std::hexfloat << x << std::defaultfloat << "\n"
<< " k: " << k << "\n"
<< " idx1: " << idx1 << "\n"
<< " idx2: " << idx2 << "\n"
<< " hi: " << hi << "\n"
<< " dx: " << std::hexfloat << dx << std::defaultfloat << "\n"
<< "exp_mid: " << exp_mid << "hi_part: " << hi_part
<< " mid_lo: " << std::hexfloat << mid_lo << std::defaultfloat
<< "\n"
<< " p: " << std::hexfloat << p << std::defaultfloat << "\n"
<< " lo: " << std::hexfloat << lo << std::defaultfloat << "\n"
<< " upper: " << std::hexfloat << upper << std::defaultfloat
<< "\n"
<< " lower: " << std::hexfloat << lower << std::defaultfloat
<< "\n"
<< std::endl;
#endif
if (LIBC_LIKELY(upper == lower)) {
// to multiply by 2^hi, a fast way is to simply add hi to the exponent
// field.
int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper));
return r;
}
// Use double-double
DoubleDouble r_dd = exp_double_double(x, kd, exp_mid, hi_part);
#ifdef LIBC_MATH_EXPM1_SKIP_ACCURATE_PASS
int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
double r =
cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(r_dd.hi + r_dd.lo));
return r;
#else
double err_dd = cpp::bit_cast<double>(ERR_DD + err);
double upper_dd = r_dd.hi + (r_dd.lo + err_dd);
double lower_dd = r_dd.hi + (r_dd.lo - err_dd);
if (LIBC_LIKELY(upper_dd == lower_dd)) {
int64_t exp_hi = static_cast<int64_t>(hi) << FPBits::FRACTION_LEN;
double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper_dd));
return r;
}
// Use 128-bit precision
Float128 r_f128 = expm1_f128(x, kd, idx1, idx2);
return static_cast<double>(r_f128);
#endif // LIBC_MATH_EXPM1_SKIP_ACCURATE_PASS
}
LLVM_LIBC_FUNCTION(double, expm1, (double x)) { return math::expm1(x); }
} // namespace LIBC_NAMESPACE_DECL

1
libc/test/shared/CMakeLists.txt
View File

@@ -45,6 +45,7 @@ add_fp_unittest(
libc.src.__support.math.exp2f16
libc.src.__support.math.exp2m1f
libc.src.__support.math.exp2m1f16
libc.src.__support.math.expm1
libc.src.__support.math.exp10
libc.src.__support.math.exp10f
libc.src.__support.math.exp10f16

1
libc/test/shared/shared_math_test.cpp
View File

@@ -87,6 +87,7 @@ TEST(LlvmLibcSharedMathTest, AllDouble) {
EXPECT_FP_EQ(0x1p+0, LIBC_NAMESPACE::shared::exp(0.0));
EXPECT_FP_EQ(0x1p+0, LIBC_NAMESPACE::shared::exp2(0.0));
EXPECT_FP_EQ(0x1p+0, LIBC_NAMESPACE::shared::exp10(0.0));
EXPECT_FP_EQ(0x0p+0, LIBC_NAMESPACE::shared::expm1(0.0));
}
#ifdef LIBC_TYPES_HAS_FLOAT128