[libc] [llvm] [libc][math] Refactor exp implementation to header-only in src/__support/math folder. (PR #148761)
Muhammad Bassiouni via llvm-commits
llvm-commits at lists.llvm.org
Tue Jul 15 08:31:26 PDT 2025
https://github.com/bassiounix updated https://github.com/llvm/llvm-project/pull/148761
>From ab40515ce346d183b4d06173a4bc5f4d9616f5c1 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Fri, 11 Jul 2025 03:12:38 +0300
Subject: [PATCH 1/3] [libc][math] Refactor exp implementation to header-only
in src/__support/math folder.
---
libc/shared/math.h | 1 +
libc/shared/math/exp.h | 23 +
libc/src/__support/math/CMakeLists.txt | 39 ++
libc/src/__support/math/exp.h | 448 ++++++++++++++++++
libc/src/__support/math/exp_constants.h | 174 +++++++
libc/src/__support/math/exp_utils.h | 72 +++
libc/src/math/generic/CMakeLists.txt | 22 +-
libc/src/math/generic/common_constants.cpp | 157 ------
libc/src/math/generic/common_constants.h | 7 +-
libc/src/math/generic/exp.cpp | 429 +----------------
libc/src/math/generic/explogxf.h | 57 +--
.../llvm-project-overlay/libc/BUILD.bazel | 57 ++-
12 files changed, 809 insertions(+), 677 deletions(-)
create mode 100644 libc/shared/math/exp.h
create mode 100644 libc/src/__support/math/exp.h
create mode 100644 libc/src/__support/math/exp_constants.h
create mode 100644 libc/src/__support/math/exp_utils.h
diff --git a/libc/shared/math.h b/libc/shared/math.h
index b2f1a03e0940d..3012cbb938816 100644
--- a/libc/shared/math.h
+++ b/libc/shared/math.h
@@ -11,6 +11,7 @@
#include "libc_common.h"
+#include "math/exp.h"
#include "math/expf.h"
#include "math/expf16.h"
#include "math/frexpf.h"
diff --git a/libc/shared/math/exp.h b/libc/shared/math/exp.h
new file mode 100644
index 0000000000000..7cdd6331e613a
--- /dev/null
+++ b/libc/shared/math/exp.h
@@ -0,0 +1,23 @@
+//===-- Shared exp 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_EXP_H
+#define LLVM_LIBC_SHARED_MATH_EXP_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/exp.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::exp;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_EXP_H
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index 900c0ab04d3a3..f7ef9e7694fe6 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -110,3 +110,42 @@ add_header_library(
DEPENDS
libc.src.__support.FPUtil.manipulation_functions
)
+
+add_header_library(
+ exp_constants
+ HDRS
+ exp_constants.h
+ DEPENDS
+ libc.src.__support.FPUtil.triple_double
+)
+
+add_header_library(
+ exp_utils
+ HDRS
+ exp_utils.h
+ DEPENDS
+ libc.src.__support.CPP.optional
+ libc.src.__support.CPP.bit
+ libc.src.__support.FPUtil.fp_bits
+)
+
+add_header_library(
+ exp
+ HDRS
+ exp.h
+ DEPENDS
+ .exp_constants
+ .exp_utils
+ libc.src.__support.CPP.bit
+ libc.src.__support.CPP.optional
+ 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.nearest_integer
+ 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
+)
diff --git a/libc/src/__support/math/exp.h b/libc/src/__support/math/exp.h
new file mode 100644
index 0000000000000..a538df1e825dc
--- /dev/null
+++ b/libc/src/__support/math/exp.h
@@ -0,0 +1,448 @@
+//===-- Implementation header for exp ---------------------------*- 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_EXP_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP_H
+
+#include "exp_constants.h"
+#include "exp_utils.h"
+#include "src/__support/CPP/bit.h"
+#include "src/__support/CPP/optional.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/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 {
+
+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.
+static constexpr double ERR_D = 0x1.8p-63;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+// Errors when using double-double precision.
+static constexpr double ERR_DD = 0x1.0p-99;
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+// -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;
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+static constexpr double MLOG_2_EXP2_M12_MID_30 = 0x1.718432ap-47;
+static constexpr double MLOG_2_EXP2_M12_LO = 0x1.b0e2633fe0685p-79;
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+namespace {
+
+// 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.
+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;
+}
+
+#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+// Polynomial approximation with double-double precision:
+// Return exp(dx) ~ 1 + dx + dx^2 / 2 + ... + dx^6 / 720
+// For |dx| < 2^-13 + 2^-30:
+// | output - exp(dx) | < 2^-101
+static DoubleDouble poly_approx_dd(const DoubleDouble &dx) {
+ // Taylor polynomial.
+ constexpr DoubleDouble COEFFS[] = {
+ {0, 0x1p0}, // 1
+ {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
+ };
+
+ 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 + dx^2 / 2 + ... + dx^7 / 5040
+// For |dx| < 2^-13 + 2^-30:
+// | output - exp(dx) | < 2^-126.
+static Float128 poly_approx_f128(const Float128 &dx) {
+ constexpr Float128 COEFFS_128[]{
+ {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
+ {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], COEFFS_128[7]);
+ return p;
+}
+
+// Compute exp(x) using 128-bit precision.
+// TODO(lntue): investigate triple-double precision implementation for this
+// step.
+static Float128 exp_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);
+
+ Float128 p = poly_approx_f128(dx);
+
+ Float128 r = fputil::quick_mul(exp_mid, p);
+
+ r.exponent += static_cast<int>(kd) >> 12;
+
+ return r;
+}
+
+// Compute exp(x) with double-double precision.
+static DoubleDouble exp_double_double(double x, double kd,
+ const DoubleDouble &exp_mid) {
+ // 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::quick_mult(exp_mid, p);
+
+ return r;
+}
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+
+// Check for exceptional cases when
+// |x| <= 2^-53 or x < log(2^-1075) or x >= 0x1.6232bdd7abcd3p+9
+static 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) {
+ // exp(x) ~ 1 + x
+ return 1 + x;
+ }
+
+ // x <= log(2^-1075) || x >= 0x1.6232bdd7abcd3p+9 or inf/nan.
+
+ // x <= log(2^-1075) or -inf/nan
+ if (x_u >= 0xc087'4910'd52d'3052ULL) {
+ // exp(-Inf) = 0
+ if (xbits.is_inf())
+ return 0.0;
+
+ // exp(nan) = nan
+ if (xbits.is_nan())
+ return x;
+
+ if (fputil::quick_get_round() == FE_UPWARD)
+ return FPBits::min_subnormal().get_val();
+ fputil::set_errno_if_required(ERANGE);
+ fputil::raise_except_if_required(FE_UNDERFLOW);
+ return 0.0;
+ }
+
+ // 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
+
+namespace math {
+
+static double exp(double x) {
+ using FPBits = typename fputil::FPBits<double>;
+ FPBits xbits(x);
+
+ 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: min denormal number / 2 = 2^-1075
+ // > round(log(2^-1075), D, RN) = -0x1.74910d52d3052p9
+
+ // Another lower bound: min normal number = 2^-1022
+ // > round(log(2^-1022), D, RN) = -0x1.6232bdd7abcd2p9
+
+ // x < log(2^-1075) or x >= 0x1.6232bdd7abcd3p+9 or |x| < 2^-53.
+ if (LIBC_UNLIKELY(x_u >= 0xc0874910d52d3052 ||
+ (x_u < 0xbca0000000000000 && x_u >= 0x40862e42fefa39f0) ||
+ x_u < 0x3ca0000000000000)) {
+ return set_exceptional(x);
+ }
+
+ // Now log(2^-1075) <= 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;
+
+ bool denorm = (hi <= -1022);
+
+ 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);
+
+ // |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.
+
+ 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, exp_mid.lo);
+
+#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+ if (LIBC_UNLIKELY(denorm)) {
+ return ziv_test_denorm</*SKIP_ZIV_TEST=*/true>(hi, exp_mid.hi, lo, ERR_D)
+ .value();
+ } else {
+ // 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>(exp_mid.hi + lo));
+ return r;
+ }
+#else
+ if (LIBC_UNLIKELY(denorm)) {
+ if (auto r = ziv_test_denorm(hi, exp_mid.hi, lo, ERR_D);
+ LIBC_LIKELY(r.has_value()))
+ return r.value();
+ } else {
+ double upper = exp_mid.hi + (lo + ERR_D);
+ double lower = exp_mid.hi + (lo - ERR_D);
+
+ 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);
+
+ if (LIBC_UNLIKELY(denorm)) {
+ if (auto r = ziv_test_denorm(hi, r_dd.hi, r_dd.lo, ERR_DD);
+ LIBC_LIKELY(r.has_value()))
+ return r.value();
+ } else {
+ 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 = exp_f128(x, kd, idx1, idx2);
+
+ return static_cast<double>(r_f128);
+#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP_H
diff --git a/libc/src/__support/math/exp_constants.h b/libc/src/__support/math/exp_constants.h
new file mode 100644
index 0000000000000..32976a86a01ad
--- /dev/null
+++ b/libc/src/__support/math/exp_constants.h
@@ -0,0 +1,174 @@
+//===-- Constants for exp 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_SRC___SUPPORT_MATH_EXP_CONSTANTS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP_CONSTANTS_H
+
+#include "src/__support/FPUtil/triple_double.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Lookup table for 2^(k * 2^-6) with k = 0..63.
+// Generated by Sollya with:
+// > display=hexadecimal;
+// > prec = 500;
+// > for i from 0 to 63 do {
+// a = 2^(i * 2^-6);
+// b = round(a, D, RN);
+// c = round(a - b, D, RN);
+// d = round(a - b - c, D, RN);
+// print("{", d, ",", c, ",", b, "},");
+// };
+alignas(16) static constexpr fputil::TripleDouble EXP2_MID1[64] = {
+ {0, 0, 0x1p0},
+ {-0x1.9085b0a3d74d5p-110, -0x1.19083535b085dp-56, 0x1.02c9a3e778061p0},
+ {0x1.05ff94f8d257ep-110, 0x1.d73e2a475b465p-55, 0x1.059b0d3158574p0},
+ {0x1.15820d96b414fp-111, 0x1.186be4bb284ffp-57, 0x1.0874518759bc8p0},
+ {-0x1.67c9bd6ebf74cp-108, 0x1.8a62e4adc610bp-54, 0x1.0b5586cf9890fp0},
+ {-0x1.5aa76994e9ddbp-113, 0x1.03a1727c57b53p-59, 0x1.0e3ec32d3d1a2p0},
+ {0x1.9d58b988f562dp-109, -0x1.6c51039449b3ap-54, 0x1.11301d0125b51p0},
+ {-0x1.2fe7bb4c76416p-108, -0x1.32fbf9af1369ep-54, 0x1.1429aaea92dep0},
+ {0x1.4f2406aa13ffp-109, -0x1.19041b9d78a76p-55, 0x1.172b83c7d517bp0},
+ {0x1.ad36183926ae8p-111, 0x1.e5b4c7b4968e4p-55, 0x1.1a35beb6fcb75p0},
+ {0x1.ea62d0881b918p-110, 0x1.e016e00a2643cp-54, 0x1.1d4873168b9aap0},
+ {-0x1.781dbc16f1ea4p-111, 0x1.dc775814a8495p-55, 0x1.2063b88628cd6p0},
+ {-0x1.4d89f9af532ep-109, 0x1.9b07eb6c70573p-54, 0x1.2387a6e756238p0},
+ {0x1.277393a461b77p-110, 0x1.2bd339940e9d9p-55, 0x1.26b4565e27cddp0},
+ {0x1.de5448560469p-111, 0x1.612e8afad1255p-55, 0x1.29e9df51fdee1p0},
+ {-0x1.ee9d8f8cb9307p-110, 0x1.0024754db41d5p-54, 0x1.2d285a6e4030bp0},
+ {0x1.7b7b2f09cd0d9p-110, 0x1.6f46ad23182e4p-55, 0x1.306fe0a31b715p0},
+ {-0x1.406a2ea6cfc6bp-108, 0x1.32721843659a6p-54, 0x1.33c08b26416ffp0},
+ {0x1.87e3e12516bfap-108, -0x1.63aeabf42eae2p-54, 0x1.371a7373aa9cbp0},
+ {0x1.9b0b1ff17c296p-111, -0x1.5e436d661f5e3p-56, 0x1.3a7db34e59ff7p0},
+ {-0x1.808ba68fa8fb7p-109, 0x1.ada0911f09ebcp-55, 0x1.3dea64c123422p0},
+ {-0x1.32b43eafc6518p-114, -0x1.ef3691c309278p-58, 0x1.4160a21f72e2ap0},
+ {-0x1.0ac312de3d922p-114, 0x1.89b7a04ef80dp-59, 0x1.44e086061892dp0},
+ {0x1.e1eebae743acp-111, 0x1.3c1a3b69062fp-56, 0x1.486a2b5c13cdp0},
+ {0x1.c06c7745c2b39p-113, 0x1.d4397afec42e2p-56, 0x1.4bfdad5362a27p0},
+ {-0x1.1aa1fd7b685cdp-112, -0x1.4b309d25957e3p-54, 0x1.4f9b2769d2ca7p0},
+ {0x1.fa733951f214cp-111, -0x1.07abe1db13cadp-55, 0x1.5342b569d4f82p0},
+ {-0x1.ff86852a613ffp-111, 0x1.9bb2c011d93adp-54, 0x1.56f4736b527dap0},
+ {-0x1.744ee506fdafep-109, 0x1.6324c054647adp-54, 0x1.5ab07dd485429p0},
+ {-0x1.95f9ab75fa7d6p-108, 0x1.ba6f93080e65ep-54, 0x1.5e76f15ad2148p0},
+ {0x1.5d8e757cfb991p-111, -0x1.383c17e40b497p-54, 0x1.6247eb03a5585p0},
+ {0x1.4a337f4dc0a3bp-108, -0x1.bb60987591c34p-54, 0x1.6623882552225p0},
+ {0x1.57d3e3adec175p-108, -0x1.bdd3413b26456p-54, 0x1.6a09e667f3bcdp0},
+ {0x1.a59f88abbe778p-115, -0x1.bbe3a683c88abp-57, 0x1.6dfb23c651a2fp0},
+ {-0x1.269796953a4c3p-109, -0x1.16e4786887a99p-55, 0x1.71f75e8ec5f74p0},
+ {-0x1.8f8e7fa19e5e8p-108, -0x1.0245957316dd3p-54, 0x1.75feb564267c9p0},
+ {-0x1.4217a932d10d4p-113, -0x1.41577ee04992fp-55, 0x1.7a11473eb0187p0},
+ {0x1.70a1427f8fcdfp-112, 0x1.05d02ba15797ep-56, 0x1.7e2f336cf4e62p0},
+ {0x1.0f6ad65cbbac1p-112, -0x1.d4c1dd41532d8p-54, 0x1.82589994cce13p0},
+ {-0x1.f16f65181d921p-109, -0x1.fc6f89bd4f6bap-54, 0x1.868d99b4492edp0},
+ {-0x1.30644a7836333p-110, 0x1.6e9f156864b27p-54, 0x1.8ace5422aa0dbp0},
+ {0x1.3bf26d2b85163p-114, 0x1.5cc13a2e3976cp-55, 0x1.8f1ae99157736p0},
+ {0x1.697e257ac0db2p-111, -0x1.75fc781b57ebcp-57, 0x1.93737b0cdc5e5p0},
+ {0x1.7edb9d7144b6fp-108, -0x1.d185b7c1b85d1p-54, 0x1.97d829fde4e5p0},
+ {0x1.6376b7943085cp-110, 0x1.c7c46b071f2bep-56, 0x1.9c49182a3f09p0},
+ {0x1.354084551b4fbp-109, -0x1.359495d1cd533p-54, 0x1.a0c667b5de565p0},
+ {-0x1.bfd7adfd63f48p-111, -0x1.d2f6edb8d41e1p-54, 0x1.a5503b23e255dp0},
+ {0x1.8b16ae39e8cb9p-109, 0x1.0fac90ef7fd31p-54, 0x1.a9e6b5579fdbfp0},
+ {0x1.a7fbc3ae675eap-108, 0x1.7a1cd345dcc81p-54, 0x1.ae89f995ad3adp0},
+ {0x1.2babc0edda4d9p-111, -0x1.2805e3084d708p-57, 0x1.b33a2b84f15fbp0},
+ {0x1.aa64481e1ab72p-111, -0x1.5584f7e54ac3bp-56, 0x1.b7f76f2fb5e47p0},
+ {0x1.9a164050e1258p-109, 0x1.23dd07a2d9e84p-55, 0x1.bcc1e904bc1d2p0},
+ {0x1.99e51125928dap-110, 0x1.11065895048ddp-55, 0x1.c199bdd85529cp0},
+ {-0x1.fc44c329d5cb2p-109, 0x1.2884dff483cadp-54, 0x1.c67f12e57d14bp0},
+ {0x1.d8765566b032ep-110, 0x1.503cbd1e949dbp-56, 0x1.cb720dcef9069p0},
+ {-0x1.e7044039da0f6p-108, -0x1.cbc3743797a9cp-54, 0x1.d072d4a07897cp0},
+ {-0x1.ab053b05531fcp-111, 0x1.2ed02d75b3707p-55, 0x1.d5818dcfba487p0},
+ {0x1.7f6246f0ec615p-108, 0x1.c2300696db532p-54, 0x1.da9e603db3285p0},
+ {0x1.b7225a944efd6p-108, -0x1.1a5cd4f184b5cp-54, 0x1.dfc97337b9b5fp0},
+ {0x1.1e92cb3c2d278p-109, 0x1.39e8980a9cc8fp-55, 0x1.e502ee78b3ff6p0},
+ {-0x1.fc0f242bbf3dep-109, -0x1.e9c23179c2893p-54, 0x1.ea4afa2a490dap0},
+ {0x1.f6dd5d229ff69p-108, 0x1.dc7f486a4b6bp-54, 0x1.efa1bee615a27p0},
+ {-0x1.4019bffc80ef3p-110, 0x1.9d3e12dd8a18bp-54, 0x1.f50765b6e454p0},
+ {0x1.dc060c36f7651p-112, 0x1.74853f3a5931ep-55, 0x1.fa7c1819e90d8p0},
+};
+
+// Lookup table for 2^(k * 2^-12) with k = 0..63.
+// Generated by Sollya with:
+// > display=hexadecimal;
+// > prec = 500;
+// > for i from 0 to 63 do {
+// a = 2^(i * 2^-12);
+// b = round(a, D, RN);
+// c = round(a - b, D, RN);
+// d = round(a - b - c, D, RN);
+// print("{", d, ",", c, ",", b, "},");
+// };
+alignas(16) static constexpr fputil::TripleDouble EXP2_MID2[64] = {
+ {0, 0, 0x1p0},
+ {0x1.39726694630e3p-108, 0x1.ae8e38c59c72ap-54, 0x1.000b175effdc7p0},
+ {0x1.e5e06ddd31156p-112, -0x1.7b5d0d58ea8f4p-58, 0x1.00162f3904052p0},
+ {0x1.5a0768b51f609p-111, 0x1.4115cb6b16a8ep-54, 0x1.0021478e11ce6p0},
+ {0x1.d008403605217p-111, -0x1.d7c96f201bb2fp-55, 0x1.002c605e2e8cfp0},
+ {0x1.89bc16f765708p-109, 0x1.84711d4c35e9fp-54, 0x1.003779a95f959p0},
+ {-0x1.4535b7f8c1e2dp-109, -0x1.0484245243777p-55, 0x1.0042936faa3d8p0},
+ {-0x1.8ba92f6b25456p-108, -0x1.4b237da2025f9p-54, 0x1.004dadb113dap0},
+ {-0x1.30c72e81f4294p-113, -0x1.5e00e62d6b30dp-56, 0x1.0058c86da1c0ap0},
+ {-0x1.34a5384e6f0b9p-110, 0x1.a1d6cedbb9481p-54, 0x1.0063e3a559473p0},
+ {0x1.f8d0580865d2ep-108, -0x1.4acf197a00142p-54, 0x1.006eff583fc3dp0},
+ {-0x1.002bcb3ae9a99p-111, -0x1.eaf2ea42391a5p-57, 0x1.007a1b865a8cap0},
+ {0x1.c3c5aedee9851p-111, 0x1.da93f90835f75p-56, 0x1.0085382faef83p0},
+ {0x1.7217851d1ec6ep-109, -0x1.6a79084ab093cp-55, 0x1.00905554425d4p0},
+ {-0x1.80cbca335a7c3p-110, 0x1.86364f8fbe8f8p-54, 0x1.009b72f41a12bp0},
+ {-0x1.706bd4eb22595p-110, -0x1.82e8e14e3110ep-55, 0x1.00a6910f3b6fdp0},
+ {-0x1.b55dd523f3c08p-111, -0x1.4f6b2a7609f71p-55, 0x1.00b1afa5abcbfp0},
+ {0x1.90a1e207cced1p-110, -0x1.e1a258ea8f71bp-56, 0x1.00bcceb7707ecp0},
+ {0x1.78d0472db37c5p-110, 0x1.4362ca5bc26f1p-56, 0x1.00c7ee448ee02p0},
+ {-0x1.bcd4db3cb52fep-109, 0x1.095a56c919d02p-54, 0x1.00d30e4d0c483p0},
+ {-0x1.cf1b131575ec2p-112, -0x1.406ac4e81a645p-57, 0x1.00de2ed0ee0f5p0},
+ {-0x1.6aaa1fa7ff913p-112, 0x1.b5a6902767e09p-54, 0x1.00e94fd0398ep0},
+ {0x1.68f236dff3218p-110, -0x1.91b2060859321p-54, 0x1.00f4714af41d3p0},
+ {-0x1.e8bb58067e60ap-109, 0x1.427068ab22306p-55, 0x1.00ff93412315cp0},
+ {0x1.d4cd5e1d71fdfp-108, 0x1.c1d0660524e08p-54, 0x1.010ab5b2cbd11p0},
+ {0x1.e4ecf350ebe88p-108, -0x1.e7bdfb3204be8p-54, 0x1.0115d89ff3a8bp0},
+ {0x1.6a2aa2c89c4f8p-109, 0x1.843aa8b9cbbc6p-55, 0x1.0120fc089ff63p0},
+ {0x1.1ca368a20ed05p-110, -0x1.34104ee7edae9p-56, 0x1.012c1fecd613bp0},
+ {0x1.edb1095d925cfp-114, -0x1.2b6aeb6176892p-56, 0x1.0137444c9b5b5p0},
+ {-0x1.488c78eded75fp-111, 0x1.a8cd33b8a1bb3p-56, 0x1.01426927f5278p0},
+ {-0x1.7480f5ea1b3c9p-113, 0x1.2edc08e5da99ap-56, 0x1.014d8e7ee8d2fp0},
+ {-0x1.ae45989a04dd5p-111, 0x1.57ba2dc7e0c73p-55, 0x1.0158b4517bb88p0},
+ {0x1.bf48007d80987p-109, 0x1.b61299ab8cdb7p-54, 0x1.0163da9fb3335p0},
+ {0x1.1aa91a059292cp-109, -0x1.90565902c5f44p-54, 0x1.016f0169949edp0},
+ {0x1.b6663292855f5p-110, 0x1.70fc41c5c2d53p-55, 0x1.017a28af25567p0},
+ {0x1.e7fbca6793d94p-108, 0x1.4b9a6e145d76cp-54, 0x1.018550706ab62p0},
+ {-0x1.5b9f5c7de3b93p-110, -0x1.008eff5142bf9p-56, 0x1.019078ad6a19fp0},
+ {0x1.4638bf2f6acabp-110, -0x1.77669f033c7dep-54, 0x1.019ba16628de2p0},
+ {-0x1.ab237b9a069c5p-109, -0x1.09bb78eeead0ap-54, 0x1.01a6ca9aac5f3p0},
+ {0x1.3ab358be97cefp-108, 0x1.371231477ece5p-54, 0x1.01b1f44af9f9ep0},
+ {-0x1.4027b2294bb64p-110, 0x1.5e7626621eb5bp-56, 0x1.01bd1e77170b4p0},
+ {0x1.656394426c99p-111, -0x1.bc72b100828a5p-54, 0x1.01c8491f08f08p0},
+ {0x1.bf9785189bdd8p-111, -0x1.ce39cbbab8bbep-57, 0x1.01d37442d507p0},
+ {0x1.7c12f86114fe3p-109, 0x1.16996709da2e2p-55, 0x1.01de9fe280ac8p0},
+ {-0x1.653d5d24b5d28p-109, -0x1.c11f5239bf535p-55, 0x1.01e9cbfe113efp0},
+ {0x1.04a0cdc1d86d7p-109, 0x1.e1d4eb5edc6b3p-55, 0x1.01f4f8958c1c6p0},
+ {0x1.c678c46149782p-109, -0x1.afb99946ee3fp-54, 0x1.020025a8f6a35p0},
+ {0x1.48524e1e9df7p-108, -0x1.8f06d8a148a32p-54, 0x1.020b533856324p0},
+ {0x1.9953ea727ff0bp-109, -0x1.2bf310fc54eb6p-55, 0x1.02168143b0281p0},
+ {-0x1.ccfbbec22d28ep-108, -0x1.c95a035eb4175p-54, 0x1.0221afcb09e3ep0},
+ {0x1.9e2bb6e181de1p-108, -0x1.491793e46834dp-54, 0x1.022cdece68c4fp0},
+ {0x1.f17609ae29308p-110, -0x1.3e8d0d9c49091p-56, 0x1.02380e4dd22adp0},
+ {-0x1.c7dc2c476bfb8p-110, -0x1.314aa16278aa3p-54, 0x1.02433e494b755p0},
+ {-0x1.fab994971d4a3p-109, 0x1.48daf888e9651p-55, 0x1.024e6ec0da046p0},
+ {0x1.848b62cbdd0afp-109, 0x1.56dc8046821f4p-55, 0x1.02599fb483385p0},
+ {-0x1.bf603ba715d0cp-109, 0x1.45b42356b9d47p-54, 0x1.0264d1244c719p0},
+ {0x1.89434e751e1aap-110, -0x1.082ef51b61d7ep-56, 0x1.027003103b10ep0},
+ {-0x1.03b54fd64e8acp-110, 0x1.2106ed0920a34p-56, 0x1.027b357854772p0},
+ {0x1.7785ea0acc486p-109, -0x1.fd4cf26ea5d0fp-54, 0x1.0286685c9e059p0},
+ {-0x1.ce447fdb35ff9p-109, -0x1.09f8775e78084p-54, 0x1.02919bbd1d1d8p0},
+ {0x1.5b884aab5642ap-112, 0x1.64cbba902ca27p-58, 0x1.029ccf99d720ap0},
+ {-0x1.cfb3e46d7c1cp-108, 0x1.4383ef231d207p-54, 0x1.02a803f2d170dp0},
+ {-0x1.0d40cee4b81afp-112, 0x1.4a47a505b3a47p-54, 0x1.02b338c811703p0},
+ {0x1.6ae7d36d7c1f7p-109, 0x1.e47120223467fp-54, 0x1.02be6e199c811p0},
+};
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP_CONSTANTS_H
diff --git a/libc/src/__support/math/exp_utils.h b/libc/src/__support/math/exp_utils.h
new file mode 100644
index 0000000000000..fc9ab10d76cc4
--- /dev/null
+++ b/libc/src/__support/math/exp_utils.h
@@ -0,0 +1,72 @@
+//===-- Common utils for exp 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_SRC___SUPPORT_MATH_EXP_UTILS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP_UTILS_H
+
+#include "src/__support/CPP/bit.h"
+#include "src/__support/CPP/optional.h"
+#include "src/__support/FPUtil/FPBits.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+// Rounding tests for 2^hi * (mid + lo) when the output might be denormal. We
+// assume further that 1 <= mid < 2, mid + lo < 2, and |lo| << mid.
+// Notice that, if 0 < x < 2^-1022,
+// double(2^-1022 + x) - 2^-1022 = double(x).
+// So if we scale x up by 2^1022, we can use
+// double(1.0 + 2^1022 * x) - 1.0 to test how x is rounded in denormal range.
+template <bool SKIP_ZIV_TEST = false>
+static constexpr cpp::optional<double> ziv_test_denorm(int hi, double mid,
+ double lo, double err) {
+ using FPBits = typename fputil::FPBits<double>;
+
+ // Scaling factor = 1/(min normal number) = 2^1022
+ int64_t exp_hi = static_cast<int64_t>(hi + 1022) << FPBits::FRACTION_LEN;
+ double mid_hi = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(mid));
+ double lo_scaled =
+ (lo != 0.0) ? cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(lo))
+ : 0.0;
+
+ double extra_factor = 0.0;
+ uint64_t scale_down = 0x3FE0'0000'0000'0000; // 1022 in the exponent field.
+
+ // Result is denormal if (mid_hi + lo_scale < 1.0).
+ if ((1.0 - mid_hi) > lo_scaled) {
+ // Extra rounding step is needed, which adds more rounding errors.
+ err += 0x1.0p-52;
+ extra_factor = 1.0;
+ scale_down = 0x3FF0'0000'0000'0000; // 1023 in the exponent field.
+ }
+
+ // By adding 1.0, the results will have similar rounding points as denormal
+ // outputs.
+ if constexpr (SKIP_ZIV_TEST) {
+ double r = extra_factor + (mid_hi + lo_scaled);
+ return cpp::bit_cast<double>(cpp::bit_cast<uint64_t>(r) - scale_down);
+ } else {
+ double err_scaled =
+ cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(err));
+
+ double lo_u = lo_scaled + err_scaled;
+ double lo_l = lo_scaled - err_scaled;
+
+ double upper = extra_factor + (mid_hi + lo_u);
+ double lower = extra_factor + (mid_hi + lo_l);
+
+ if (LIBC_LIKELY(upper == lower)) {
+ return cpp::bit_cast<double>(cpp::bit_cast<uint64_t>(upper) - scale_down);
+ }
+
+ return cpp::nullopt;
+ }
+}
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP_UTILS_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index a9237741788ae..b59beacd94143 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -1312,20 +1312,7 @@ add_entrypoint_object(
HDRS
../exp.h
DEPENDS
- .common_constants
- .explogxf
- libc.src.__support.CPP.bit
- libc.src.__support.CPP.optional
- 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.nearest_integer
- 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.exp
libc.src.errno.errno
)
@@ -1953,8 +1940,8 @@ add_object_library(
SRCS
common_constants.cpp
DEPENDS
+ libc.src.__support.math.exp_constants
libc.src.__support.number_pair
- libc.src.__support.FPUtil.triple_double
)
add_header_library(
@@ -3818,16 +3805,13 @@ add_object_library(
explogxf.cpp
DEPENDS
.common_constants
- libc.src.__support.CPP.bit
- libc.src.__support.CPP.optional
- libc.src.__support.FPUtil.basic_operations
libc.src.__support.FPUtil.basic_operations
libc.src.__support.FPUtil.fenv_impl
- libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.multiply_add
libc.src.__support.FPUtil.nearest_integer
libc.src.__support.FPUtil.polyeval
libc.src.__support.common
+ libc.src.__support.math.exp_utils
libc.src.errno.errno
)
diff --git a/libc/src/math/generic/common_constants.cpp b/libc/src/math/generic/common_constants.cpp
index b2c1293c6326d..4dcf84d00ad50 100644
--- a/libc/src/math/generic/common_constants.cpp
+++ b/libc/src/math/generic/common_constants.cpp
@@ -7,7 +7,6 @@
//===----------------------------------------------------------------------===//
#include "common_constants.h"
-#include "src/__support/FPUtil/triple_double.h"
#include "src/__support/macros/config.h"
#include "src/__support/number_pair.h"
@@ -728,160 +727,4 @@ const double EXP_M2[128] = {
0x1.568bb722dd593p1, 0x1.593b7d72305bbp1,
};
-// Lookup table for 2^(k * 2^-6) with k = 0..63.
-// Generated by Sollya with:
-// > display=hexadecimal;
-// > prec = 500;
-// > for i from 0 to 63 do {
-// a = 2^(i * 2^-6);
-// b = round(a, D, RN);
-// c = round(a - b, D, RN);
-// d = round(a - b - c, D, RN);
-// print("{", d, ",", c, ",", b, "},");
-// };
-alignas(16) const fputil::TripleDouble EXP2_MID1[64] = {
- {0, 0, 0x1p0},
- {-0x1.9085b0a3d74d5p-110, -0x1.19083535b085dp-56, 0x1.02c9a3e778061p0},
- {0x1.05ff94f8d257ep-110, 0x1.d73e2a475b465p-55, 0x1.059b0d3158574p0},
- {0x1.15820d96b414fp-111, 0x1.186be4bb284ffp-57, 0x1.0874518759bc8p0},
- {-0x1.67c9bd6ebf74cp-108, 0x1.8a62e4adc610bp-54, 0x1.0b5586cf9890fp0},
- {-0x1.5aa76994e9ddbp-113, 0x1.03a1727c57b53p-59, 0x1.0e3ec32d3d1a2p0},
- {0x1.9d58b988f562dp-109, -0x1.6c51039449b3ap-54, 0x1.11301d0125b51p0},
- {-0x1.2fe7bb4c76416p-108, -0x1.32fbf9af1369ep-54, 0x1.1429aaea92dep0},
- {0x1.4f2406aa13ffp-109, -0x1.19041b9d78a76p-55, 0x1.172b83c7d517bp0},
- {0x1.ad36183926ae8p-111, 0x1.e5b4c7b4968e4p-55, 0x1.1a35beb6fcb75p0},
- {0x1.ea62d0881b918p-110, 0x1.e016e00a2643cp-54, 0x1.1d4873168b9aap0},
- {-0x1.781dbc16f1ea4p-111, 0x1.dc775814a8495p-55, 0x1.2063b88628cd6p0},
- {-0x1.4d89f9af532ep-109, 0x1.9b07eb6c70573p-54, 0x1.2387a6e756238p0},
- {0x1.277393a461b77p-110, 0x1.2bd339940e9d9p-55, 0x1.26b4565e27cddp0},
- {0x1.de5448560469p-111, 0x1.612e8afad1255p-55, 0x1.29e9df51fdee1p0},
- {-0x1.ee9d8f8cb9307p-110, 0x1.0024754db41d5p-54, 0x1.2d285a6e4030bp0},
- {0x1.7b7b2f09cd0d9p-110, 0x1.6f46ad23182e4p-55, 0x1.306fe0a31b715p0},
- {-0x1.406a2ea6cfc6bp-108, 0x1.32721843659a6p-54, 0x1.33c08b26416ffp0},
- {0x1.87e3e12516bfap-108, -0x1.63aeabf42eae2p-54, 0x1.371a7373aa9cbp0},
- {0x1.9b0b1ff17c296p-111, -0x1.5e436d661f5e3p-56, 0x1.3a7db34e59ff7p0},
- {-0x1.808ba68fa8fb7p-109, 0x1.ada0911f09ebcp-55, 0x1.3dea64c123422p0},
- {-0x1.32b43eafc6518p-114, -0x1.ef3691c309278p-58, 0x1.4160a21f72e2ap0},
- {-0x1.0ac312de3d922p-114, 0x1.89b7a04ef80dp-59, 0x1.44e086061892dp0},
- {0x1.e1eebae743acp-111, 0x1.3c1a3b69062fp-56, 0x1.486a2b5c13cdp0},
- {0x1.c06c7745c2b39p-113, 0x1.d4397afec42e2p-56, 0x1.4bfdad5362a27p0},
- {-0x1.1aa1fd7b685cdp-112, -0x1.4b309d25957e3p-54, 0x1.4f9b2769d2ca7p0},
- {0x1.fa733951f214cp-111, -0x1.07abe1db13cadp-55, 0x1.5342b569d4f82p0},
- {-0x1.ff86852a613ffp-111, 0x1.9bb2c011d93adp-54, 0x1.56f4736b527dap0},
- {-0x1.744ee506fdafep-109, 0x1.6324c054647adp-54, 0x1.5ab07dd485429p0},
- {-0x1.95f9ab75fa7d6p-108, 0x1.ba6f93080e65ep-54, 0x1.5e76f15ad2148p0},
- {0x1.5d8e757cfb991p-111, -0x1.383c17e40b497p-54, 0x1.6247eb03a5585p0},
- {0x1.4a337f4dc0a3bp-108, -0x1.bb60987591c34p-54, 0x1.6623882552225p0},
- {0x1.57d3e3adec175p-108, -0x1.bdd3413b26456p-54, 0x1.6a09e667f3bcdp0},
- {0x1.a59f88abbe778p-115, -0x1.bbe3a683c88abp-57, 0x1.6dfb23c651a2fp0},
- {-0x1.269796953a4c3p-109, -0x1.16e4786887a99p-55, 0x1.71f75e8ec5f74p0},
- {-0x1.8f8e7fa19e5e8p-108, -0x1.0245957316dd3p-54, 0x1.75feb564267c9p0},
- {-0x1.4217a932d10d4p-113, -0x1.41577ee04992fp-55, 0x1.7a11473eb0187p0},
- {0x1.70a1427f8fcdfp-112, 0x1.05d02ba15797ep-56, 0x1.7e2f336cf4e62p0},
- {0x1.0f6ad65cbbac1p-112, -0x1.d4c1dd41532d8p-54, 0x1.82589994cce13p0},
- {-0x1.f16f65181d921p-109, -0x1.fc6f89bd4f6bap-54, 0x1.868d99b4492edp0},
- {-0x1.30644a7836333p-110, 0x1.6e9f156864b27p-54, 0x1.8ace5422aa0dbp0},
- {0x1.3bf26d2b85163p-114, 0x1.5cc13a2e3976cp-55, 0x1.8f1ae99157736p0},
- {0x1.697e257ac0db2p-111, -0x1.75fc781b57ebcp-57, 0x1.93737b0cdc5e5p0},
- {0x1.7edb9d7144b6fp-108, -0x1.d185b7c1b85d1p-54, 0x1.97d829fde4e5p0},
- {0x1.6376b7943085cp-110, 0x1.c7c46b071f2bep-56, 0x1.9c49182a3f09p0},
- {0x1.354084551b4fbp-109, -0x1.359495d1cd533p-54, 0x1.a0c667b5de565p0},
- {-0x1.bfd7adfd63f48p-111, -0x1.d2f6edb8d41e1p-54, 0x1.a5503b23e255dp0},
- {0x1.8b16ae39e8cb9p-109, 0x1.0fac90ef7fd31p-54, 0x1.a9e6b5579fdbfp0},
- {0x1.a7fbc3ae675eap-108, 0x1.7a1cd345dcc81p-54, 0x1.ae89f995ad3adp0},
- {0x1.2babc0edda4d9p-111, -0x1.2805e3084d708p-57, 0x1.b33a2b84f15fbp0},
- {0x1.aa64481e1ab72p-111, -0x1.5584f7e54ac3bp-56, 0x1.b7f76f2fb5e47p0},
- {0x1.9a164050e1258p-109, 0x1.23dd07a2d9e84p-55, 0x1.bcc1e904bc1d2p0},
- {0x1.99e51125928dap-110, 0x1.11065895048ddp-55, 0x1.c199bdd85529cp0},
- {-0x1.fc44c329d5cb2p-109, 0x1.2884dff483cadp-54, 0x1.c67f12e57d14bp0},
- {0x1.d8765566b032ep-110, 0x1.503cbd1e949dbp-56, 0x1.cb720dcef9069p0},
- {-0x1.e7044039da0f6p-108, -0x1.cbc3743797a9cp-54, 0x1.d072d4a07897cp0},
- {-0x1.ab053b05531fcp-111, 0x1.2ed02d75b3707p-55, 0x1.d5818dcfba487p0},
- {0x1.7f6246f0ec615p-108, 0x1.c2300696db532p-54, 0x1.da9e603db3285p0},
- {0x1.b7225a944efd6p-108, -0x1.1a5cd4f184b5cp-54, 0x1.dfc97337b9b5fp0},
- {0x1.1e92cb3c2d278p-109, 0x1.39e8980a9cc8fp-55, 0x1.e502ee78b3ff6p0},
- {-0x1.fc0f242bbf3dep-109, -0x1.e9c23179c2893p-54, 0x1.ea4afa2a490dap0},
- {0x1.f6dd5d229ff69p-108, 0x1.dc7f486a4b6bp-54, 0x1.efa1bee615a27p0},
- {-0x1.4019bffc80ef3p-110, 0x1.9d3e12dd8a18bp-54, 0x1.f50765b6e454p0},
- {0x1.dc060c36f7651p-112, 0x1.74853f3a5931ep-55, 0x1.fa7c1819e90d8p0},
-};
-
-// Lookup table for 2^(k * 2^-12) with k = 0..63.
-// Generated by Sollya with:
-// > display=hexadecimal;
-// > prec = 500;
-// > for i from 0 to 63 do {
-// a = 2^(i * 2^-12);
-// b = round(a, D, RN);
-// c = round(a - b, D, RN);
-// d = round(a - b - c, D, RN);
-// print("{", d, ",", c, ",", b, "},");
-// };
-alignas(16) const fputil::TripleDouble EXP2_MID2[64] = {
- {0, 0, 0x1p0},
- {0x1.39726694630e3p-108, 0x1.ae8e38c59c72ap-54, 0x1.000b175effdc7p0},
- {0x1.e5e06ddd31156p-112, -0x1.7b5d0d58ea8f4p-58, 0x1.00162f3904052p0},
- {0x1.5a0768b51f609p-111, 0x1.4115cb6b16a8ep-54, 0x1.0021478e11ce6p0},
- {0x1.d008403605217p-111, -0x1.d7c96f201bb2fp-55, 0x1.002c605e2e8cfp0},
- {0x1.89bc16f765708p-109, 0x1.84711d4c35e9fp-54, 0x1.003779a95f959p0},
- {-0x1.4535b7f8c1e2dp-109, -0x1.0484245243777p-55, 0x1.0042936faa3d8p0},
- {-0x1.8ba92f6b25456p-108, -0x1.4b237da2025f9p-54, 0x1.004dadb113dap0},
- {-0x1.30c72e81f4294p-113, -0x1.5e00e62d6b30dp-56, 0x1.0058c86da1c0ap0},
- {-0x1.34a5384e6f0b9p-110, 0x1.a1d6cedbb9481p-54, 0x1.0063e3a559473p0},
- {0x1.f8d0580865d2ep-108, -0x1.4acf197a00142p-54, 0x1.006eff583fc3dp0},
- {-0x1.002bcb3ae9a99p-111, -0x1.eaf2ea42391a5p-57, 0x1.007a1b865a8cap0},
- {0x1.c3c5aedee9851p-111, 0x1.da93f90835f75p-56, 0x1.0085382faef83p0},
- {0x1.7217851d1ec6ep-109, -0x1.6a79084ab093cp-55, 0x1.00905554425d4p0},
- {-0x1.80cbca335a7c3p-110, 0x1.86364f8fbe8f8p-54, 0x1.009b72f41a12bp0},
- {-0x1.706bd4eb22595p-110, -0x1.82e8e14e3110ep-55, 0x1.00a6910f3b6fdp0},
- {-0x1.b55dd523f3c08p-111, -0x1.4f6b2a7609f71p-55, 0x1.00b1afa5abcbfp0},
- {0x1.90a1e207cced1p-110, -0x1.e1a258ea8f71bp-56, 0x1.00bcceb7707ecp0},
- {0x1.78d0472db37c5p-110, 0x1.4362ca5bc26f1p-56, 0x1.00c7ee448ee02p0},
- {-0x1.bcd4db3cb52fep-109, 0x1.095a56c919d02p-54, 0x1.00d30e4d0c483p0},
- {-0x1.cf1b131575ec2p-112, -0x1.406ac4e81a645p-57, 0x1.00de2ed0ee0f5p0},
- {-0x1.6aaa1fa7ff913p-112, 0x1.b5a6902767e09p-54, 0x1.00e94fd0398ep0},
- {0x1.68f236dff3218p-110, -0x1.91b2060859321p-54, 0x1.00f4714af41d3p0},
- {-0x1.e8bb58067e60ap-109, 0x1.427068ab22306p-55, 0x1.00ff93412315cp0},
- {0x1.d4cd5e1d71fdfp-108, 0x1.c1d0660524e08p-54, 0x1.010ab5b2cbd11p0},
- {0x1.e4ecf350ebe88p-108, -0x1.e7bdfb3204be8p-54, 0x1.0115d89ff3a8bp0},
- {0x1.6a2aa2c89c4f8p-109, 0x1.843aa8b9cbbc6p-55, 0x1.0120fc089ff63p0},
- {0x1.1ca368a20ed05p-110, -0x1.34104ee7edae9p-56, 0x1.012c1fecd613bp0},
- {0x1.edb1095d925cfp-114, -0x1.2b6aeb6176892p-56, 0x1.0137444c9b5b5p0},
- {-0x1.488c78eded75fp-111, 0x1.a8cd33b8a1bb3p-56, 0x1.01426927f5278p0},
- {-0x1.7480f5ea1b3c9p-113, 0x1.2edc08e5da99ap-56, 0x1.014d8e7ee8d2fp0},
- {-0x1.ae45989a04dd5p-111, 0x1.57ba2dc7e0c73p-55, 0x1.0158b4517bb88p0},
- {0x1.bf48007d80987p-109, 0x1.b61299ab8cdb7p-54, 0x1.0163da9fb3335p0},
- {0x1.1aa91a059292cp-109, -0x1.90565902c5f44p-54, 0x1.016f0169949edp0},
- {0x1.b6663292855f5p-110, 0x1.70fc41c5c2d53p-55, 0x1.017a28af25567p0},
- {0x1.e7fbca6793d94p-108, 0x1.4b9a6e145d76cp-54, 0x1.018550706ab62p0},
- {-0x1.5b9f5c7de3b93p-110, -0x1.008eff5142bf9p-56, 0x1.019078ad6a19fp0},
- {0x1.4638bf2f6acabp-110, -0x1.77669f033c7dep-54, 0x1.019ba16628de2p0},
- {-0x1.ab237b9a069c5p-109, -0x1.09bb78eeead0ap-54, 0x1.01a6ca9aac5f3p0},
- {0x1.3ab358be97cefp-108, 0x1.371231477ece5p-54, 0x1.01b1f44af9f9ep0},
- {-0x1.4027b2294bb64p-110, 0x1.5e7626621eb5bp-56, 0x1.01bd1e77170b4p0},
- {0x1.656394426c99p-111, -0x1.bc72b100828a5p-54, 0x1.01c8491f08f08p0},
- {0x1.bf9785189bdd8p-111, -0x1.ce39cbbab8bbep-57, 0x1.01d37442d507p0},
- {0x1.7c12f86114fe3p-109, 0x1.16996709da2e2p-55, 0x1.01de9fe280ac8p0},
- {-0x1.653d5d24b5d28p-109, -0x1.c11f5239bf535p-55, 0x1.01e9cbfe113efp0},
- {0x1.04a0cdc1d86d7p-109, 0x1.e1d4eb5edc6b3p-55, 0x1.01f4f8958c1c6p0},
- {0x1.c678c46149782p-109, -0x1.afb99946ee3fp-54, 0x1.020025a8f6a35p0},
- {0x1.48524e1e9df7p-108, -0x1.8f06d8a148a32p-54, 0x1.020b533856324p0},
- {0x1.9953ea727ff0bp-109, -0x1.2bf310fc54eb6p-55, 0x1.02168143b0281p0},
- {-0x1.ccfbbec22d28ep-108, -0x1.c95a035eb4175p-54, 0x1.0221afcb09e3ep0},
- {0x1.9e2bb6e181de1p-108, -0x1.491793e46834dp-54, 0x1.022cdece68c4fp0},
- {0x1.f17609ae29308p-110, -0x1.3e8d0d9c49091p-56, 0x1.02380e4dd22adp0},
- {-0x1.c7dc2c476bfb8p-110, -0x1.314aa16278aa3p-54, 0x1.02433e494b755p0},
- {-0x1.fab994971d4a3p-109, 0x1.48daf888e9651p-55, 0x1.024e6ec0da046p0},
- {0x1.848b62cbdd0afp-109, 0x1.56dc8046821f4p-55, 0x1.02599fb483385p0},
- {-0x1.bf603ba715d0cp-109, 0x1.45b42356b9d47p-54, 0x1.0264d1244c719p0},
- {0x1.89434e751e1aap-110, -0x1.082ef51b61d7ep-56, 0x1.027003103b10ep0},
- {-0x1.03b54fd64e8acp-110, 0x1.2106ed0920a34p-56, 0x1.027b357854772p0},
- {0x1.7785ea0acc486p-109, -0x1.fd4cf26ea5d0fp-54, 0x1.0286685c9e059p0},
- {-0x1.ce447fdb35ff9p-109, -0x1.09f8775e78084p-54, 0x1.02919bbd1d1d8p0},
- {0x1.5b884aab5642ap-112, 0x1.64cbba902ca27p-58, 0x1.029ccf99d720ap0},
- {-0x1.cfb3e46d7c1cp-108, 0x1.4383ef231d207p-54, 0x1.02a803f2d170dp0},
- {-0x1.0d40cee4b81afp-112, 0x1.4a47a505b3a47p-54, 0x1.02b338c811703p0},
- {0x1.6ae7d36d7c1f7p-109, 0x1.e47120223467fp-54, 0x1.02be6e199c811p0},
-};
-
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/common_constants.h b/libc/src/math/generic/common_constants.h
index e65f002845953..291816a7889ad 100644
--- a/libc/src/math/generic/common_constants.h
+++ b/libc/src/math/generic/common_constants.h
@@ -11,6 +11,7 @@
#include "src/__support/FPUtil/triple_double.h"
#include "src/__support/macros/config.h"
+#include "src/__support/math/exp_constants.h"
#include "src/__support/number_pair.h"
namespace LIBC_NAMESPACE_DECL {
@@ -80,12 +81,6 @@ extern const double EXP_M1[195];
// > for i from 0 to 127 do { D(exp(i / 128)); };
extern const double EXP_M2[128];
-// Lookup table for 2^(k * 2^-6) with k = 0..63.
-extern const fputil::TripleDouble EXP2_MID1[64];
-
-// Lookup table for 2^(k * 2^-12) with k = 0..63.
-extern const fputil::TripleDouble EXP2_MID2[64];
-
} // namespace LIBC_NAMESPACE_DECL
#endif // LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H
diff --git a/libc/src/math/generic/exp.cpp b/libc/src/math/generic/exp.cpp
index 143800ca078a6..dc4d2ca480cb8 100644
--- a/libc/src/math/generic/exp.cpp
+++ b/libc/src/math/generic/exp.cpp
@@ -7,434 +7,9 @@
//===----------------------------------------------------------------------===//
#include "src/math/exp.h"
-#include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
-#include "explogxf.h" // ziv_test_denorm.
-#include "src/__support/CPP/bit.h"
-#include "src/__support/CPP/optional.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/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/exp.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.
-constexpr double ERR_D = 0x1.8p-63;
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-// Errors when using double-double precision.
-constexpr double ERR_DD = 0x1.0p-99;
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-// -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;
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-constexpr double MLOG_2_EXP2_M12_MID_30 = 0x1.718432ap-47;
-constexpr double MLOG_2_EXP2_M12_LO = 0x1.b0e2633fe0685p-79;
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-namespace {
-
-// 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;
-}
-
-#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-// Polynomial approximation with double-double precision:
-// Return exp(dx) ~ 1 + dx + dx^2 / 2 + ... + dx^6 / 720
-// For |dx| < 2^-13 + 2^-30:
-// | output - exp(dx) | < 2^-101
-DoubleDouble poly_approx_dd(const DoubleDouble &dx) {
- // Taylor polynomial.
- constexpr DoubleDouble COEFFS[] = {
- {0, 0x1p0}, // 1
- {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
- };
-
- 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 + dx^2 / 2 + ... + dx^7 / 5040
-// For |dx| < 2^-13 + 2^-30:
-// | output - exp(dx) | < 2^-126.
-Float128 poly_approx_f128(const Float128 &dx) {
- constexpr Float128 COEFFS_128[]{
- {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0
- {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], COEFFS_128[7]);
- return p;
-}
-
-// Compute exp(x) using 128-bit precision.
-// TODO(lntue): investigate triple-double precision implementation for this
-// step.
-Float128 exp_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);
-
- Float128 p = poly_approx_f128(dx);
-
- Float128 r = fputil::quick_mul(exp_mid, p);
-
- r.exponent += static_cast<int>(kd) >> 12;
-
- return r;
-}
-
-// Compute exp(x) with double-double precision.
-DoubleDouble exp_double_double(double x, double kd,
- const DoubleDouble &exp_mid) {
- // 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::quick_mult(exp_mid, p);
-
- return r;
-}
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-
-// Check for exceptional cases when
-// |x| <= 2^-53 or x < log(2^-1075) 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) {
- // exp(x) ~ 1 + x
- return 1 + x;
- }
-
- // x <= log(2^-1075) || x >= 0x1.6232bdd7abcd3p+9 or inf/nan.
-
- // x <= log(2^-1075) or -inf/nan
- if (x_u >= 0xc087'4910'd52d'3052ULL) {
- // exp(-Inf) = 0
- if (xbits.is_inf())
- return 0.0;
-
- // exp(nan) = nan
- if (xbits.is_nan())
- return x;
-
- if (fputil::quick_get_round() == FE_UPWARD)
- return FPBits::min_subnormal().get_val();
- fputil::set_errno_if_required(ERANGE);
- fputil::raise_except_if_required(FE_UNDERFLOW);
- return 0.0;
- }
-
- // 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, exp, (double x)) {
- using FPBits = typename fputil::FPBits<double>;
- FPBits xbits(x);
-
- 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: min denormal number / 2 = 2^-1075
- // > round(log(2^-1075), D, RN) = -0x1.74910d52d3052p9
-
- // Another lower bound: min normal number = 2^-1022
- // > round(log(2^-1022), D, RN) = -0x1.6232bdd7abcd2p9
-
- // x < log(2^-1075) or x >= 0x1.6232bdd7abcd3p+9 or |x| < 2^-53.
- if (LIBC_UNLIKELY(x_u >= 0xc0874910d52d3052 ||
- (x_u < 0xbca0000000000000 && x_u >= 0x40862e42fefa39f0) ||
- x_u < 0x3ca0000000000000)) {
- return set_exceptional(x);
- }
-
- // Now log(2^-1075) <= 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;
-
- bool denorm = (hi <= -1022);
-
- 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);
-
- // |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.
-
- 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, exp_mid.lo);
-
-#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
- if (LIBC_UNLIKELY(denorm)) {
- return ziv_test_denorm</*SKIP_ZIV_TEST=*/true>(hi, exp_mid.hi, lo, ERR_D)
- .value();
- } else {
- // 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>(exp_mid.hi + lo));
- return r;
- }
-#else
- if (LIBC_UNLIKELY(denorm)) {
- if (auto r = ziv_test_denorm(hi, exp_mid.hi, lo, ERR_D);
- LIBC_LIKELY(r.has_value()))
- return r.value();
- } else {
- double upper = exp_mid.hi + (lo + ERR_D);
- double lower = exp_mid.hi + (lo - ERR_D);
-
- 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);
-
- if (LIBC_UNLIKELY(denorm)) {
- if (auto r = ziv_test_denorm(hi, r_dd.hi, r_dd.lo, ERR_DD);
- LIBC_LIKELY(r.has_value()))
- return r.value();
- } else {
- 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 = exp_f128(x, kd, idx1, idx2);
-
- return static_cast<double>(r_f128);
-#endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS
-}
+LLVM_LIBC_FUNCTION(double, exp, (double x)) { return math::exp(x); }
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/src/math/generic/explogxf.h b/libc/src/math/generic/explogxf.h
index 212ede4758549..5ae1457ca780e 100644
--- a/libc/src/math/generic/explogxf.h
+++ b/libc/src/math/generic/explogxf.h
@@ -10,16 +10,15 @@
#define LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H
#include "common_constants.h"
-#include "src/__support/CPP/bit.h"
-#include "src/__support/CPP/optional.h"
#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/properties/cpu_features.h"
+#include "src/__support/math/exp_utils.h"
+
namespace LIBC_NAMESPACE_DECL {
struct ExpBase {
@@ -375,58 +374,6 @@ LIBC_INLINE static double log_eval(double x) {
return result;
}
-// Rounding tests for 2^hi * (mid + lo) when the output might be denormal. We
-// assume further that 1 <= mid < 2, mid + lo < 2, and |lo| << mid.
-// Notice that, if 0 < x < 2^-1022,
-// double(2^-1022 + x) - 2^-1022 = double(x).
-// So if we scale x up by 2^1022, we can use
-// double(1.0 + 2^1022 * x) - 1.0 to test how x is rounded in denormal range.
-template <bool SKIP_ZIV_TEST = false>
-LIBC_INLINE static cpp::optional<double>
-ziv_test_denorm(int hi, double mid, double lo, double err) {
- using FPBits = typename fputil::FPBits<double>;
-
- // Scaling factor = 1/(min normal number) = 2^1022
- int64_t exp_hi = static_cast<int64_t>(hi + 1022) << FPBits::FRACTION_LEN;
- double mid_hi = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(mid));
- double lo_scaled =
- (lo != 0.0) ? cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(lo))
- : 0.0;
-
- double extra_factor = 0.0;
- uint64_t scale_down = 0x3FE0'0000'0000'0000; // 1022 in the exponent field.
-
- // Result is denormal if (mid_hi + lo_scale < 1.0).
- if ((1.0 - mid_hi) > lo_scaled) {
- // Extra rounding step is needed, which adds more rounding errors.
- err += 0x1.0p-52;
- extra_factor = 1.0;
- scale_down = 0x3FF0'0000'0000'0000; // 1023 in the exponent field.
- }
-
- // By adding 1.0, the results will have similar rounding points as denormal
- // outputs.
- if constexpr (SKIP_ZIV_TEST) {
- double r = extra_factor + (mid_hi + lo_scaled);
- return cpp::bit_cast<double>(cpp::bit_cast<uint64_t>(r) - scale_down);
- } else {
- double err_scaled =
- cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(err));
-
- double lo_u = lo_scaled + err_scaled;
- double lo_l = lo_scaled - err_scaled;
-
- double upper = extra_factor + (mid_hi + lo_u);
- double lower = extra_factor + (mid_hi + lo_l);
-
- if (LIBC_LIKELY(upper == lower)) {
- return cpp::bit_cast<double>(cpp::bit_cast<uint64_t>(upper) - scale_down);
- }
-
- return cpp::nullopt;
- }
-}
-
} // namespace LIBC_NAMESPACE_DECL
#endif // LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H
diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
index cd608a1352a7a..4ab0126291276 100644
--- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel
@@ -1919,7 +1919,7 @@ libc_support_library(
srcs = ["src/math/generic/common_constants.cpp"],
hdrs = ["src/math/generic/common_constants.h"],
deps = [
- ":__support_fputil_triple_double",
+ ":__support_math_exp_constants",
":__support_number_pair",
],
)
@@ -2002,10 +2002,10 @@ libc_support_library(
":__support_common",
":__support_fputil_fenv_impl",
":__support_fputil_fma",
- ":__support_fputil_fp_bits",
":__support_fputil_multiply_add",
":__support_fputil_nearest_integer",
":__support_fputil_polyeval",
+ ":__support_math_exp_utils",
":common_constants",
],
)
@@ -2205,6 +2205,46 @@ libc_support_library(
],
)
+libc_support_library(
+ name = "__support_math_exp_constants",
+ hdrs = ["src/__support/math/exp_constants.h"],
+ deps = [
+ ":__support_fputil_triple_double",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_exp_utils",
+ hdrs = ["src/__support/math/exp_utils.h"],
+ deps = [
+ ":__support_cpp_optional",
+ ":__support_cpp_bit",
+ ":__support_fputil_fp_bits",
+ ],
+)
+
+libc_support_library(
+ name = "__support_math_exp",
+ hdrs = ["src/__support/math/exp.h"],
+ deps = [
+ ":__support_math_exp_constants",
+ ":__support_math_exp_utils",
+ ":__support_cpp_bit",
+ ":__support_cpp_optional",
+ ":__support_fputil_dyadic_float",
+ ":__support_fputil_fenv_impl",
+ ":__support_fputil_fp_bits",
+ ":__support_fputil_multiply_add",
+ ":__support_fputil_nearest_integer",
+ ":__support_fputil_polyeval",
+ ":__support_fputil_rounding_mode",
+ ":__support_fputil_triple_double",
+ ":__support_fputil_double_double",
+ ":__support_integer_literals",
+ ":__support_macros_optimization",
+ ],
+)
+
############################### complex targets ################################
libc_function(
@@ -2785,17 +2825,8 @@ libc_math_function(
libc_math_function(
name = "exp",
additional_deps = [
- ":__support_fputil_double_double",
- ":__support_fputil_dyadic_float",
- ":__support_fputil_multiply_add",
- ":__support_fputil_nearest_integer",
- ":__support_fputil_polyeval",
- ":__support_fputil_rounding_mode",
- ":__support_fputil_triple_double",
- ":__support_integer_literals",
- ":__support_macros_optimization",
- ":common_constants",
- ":explogxf",
+ ":__support_math_exp",
+ ":errno",
],
)
>From cff531dedd573e4a84778d7243d77af6ee340a01 Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Tue, 15 Jul 2025 06:03:56 +0300
Subject: [PATCH 2/3] remove alignas
---
libc/src/__support/math/exp_constants.h | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/libc/src/__support/math/exp_constants.h b/libc/src/__support/math/exp_constants.h
index 32976a86a01ad..1abb4479e0848 100644
--- a/libc/src/__support/math/exp_constants.h
+++ b/libc/src/__support/math/exp_constants.h
@@ -24,7 +24,7 @@ namespace LIBC_NAMESPACE_DECL {
// d = round(a - b - c, D, RN);
// print("{", d, ",", c, ",", b, "},");
// };
-alignas(16) static constexpr fputil::TripleDouble EXP2_MID1[64] = {
+static constexpr fputil::TripleDouble EXP2_MID1[64] = {
{0, 0, 0x1p0},
{-0x1.9085b0a3d74d5p-110, -0x1.19083535b085dp-56, 0x1.02c9a3e778061p0},
{0x1.05ff94f8d257ep-110, 0x1.d73e2a475b465p-55, 0x1.059b0d3158574p0},
@@ -102,7 +102,7 @@ alignas(16) static constexpr fputil::TripleDouble EXP2_MID1[64] = {
// d = round(a - b - c, D, RN);
// print("{", d, ",", c, ",", b, "},");
// };
-alignas(16) static constexpr fputil::TripleDouble EXP2_MID2[64] = {
+static constexpr fputil::TripleDouble EXP2_MID2[64] = {
{0, 0, 0x1p0},
{0x1.39726694630e3p-108, 0x1.ae8e38c59c72ap-54, 0x1.000b175effdc7p0},
{0x1.e5e06ddd31156p-112, -0x1.7b5d0d58ea8f4p-58, 0x1.00162f3904052p0},
>From a22b106cd0bd37f04c56340cb9cc4bb1e18b81ec Mon Sep 17 00:00:00 2001
From: bassiounix <muhammad.m.bassiouni at gmail.com>
Date: Tue, 15 Jul 2025 18:29:27 +0300
Subject: [PATCH 3/3] fix gcc problems
---
libc/src/__support/FPUtil/multiply_add.h | 2 +-
libc/src/__support/FPUtil/nearest_integer.h | 4 ++--
libc/src/__support/math/expf16_utils.h | 2 +-
3 files changed, 4 insertions(+), 4 deletions(-)
diff --git a/libc/src/__support/FPUtil/multiply_add.h b/libc/src/__support/FPUtil/multiply_add.h
index 8260702e2c9f4..1469326c9ba3e 100644
--- a/libc/src/__support/FPUtil/multiply_add.h
+++ b/libc/src/__support/FPUtil/multiply_add.h
@@ -29,7 +29,7 @@ multiply_add(const T &x, const T &y, const T &z) {
}
template <typename T>
-LIBC_INLINE cpp::enable_if_t<(sizeof(T) <= sizeof(void *)), T>
+LIBC_INLINE static constexpr cpp::enable_if_t<(sizeof(T) <= sizeof(void *)), T>
multiply_add(T x, T y, T z) {
return x * y + z;
}
diff --git a/libc/src/__support/FPUtil/nearest_integer.h b/libc/src/__support/FPUtil/nearest_integer.h
index 768f13414bd95..fabd309bd3520 100644
--- a/libc/src/__support/FPUtil/nearest_integer.h
+++ b/libc/src/__support/FPUtil/nearest_integer.h
@@ -40,7 +40,7 @@ namespace fputil {
// Notice that for AARCH64 and x86-64 with SSE4.2 support, we will use their
// corresponding rounding instruction instead. And in those cases, the results
// are rounded to the nearest integer, tie-to-even.
-LIBC_INLINE float nearest_integer(float x) {
+LIBC_INLINE static constexpr float nearest_integer(float x) {
if (x < 0x1p24f && x > -0x1p24f) {
float r = x < 0 ? (x - 0x1.0p23f) + 0x1.0p23f : (x + 0x1.0p23f) - 0x1.0p23f;
float diff = x - r;
@@ -56,7 +56,7 @@ LIBC_INLINE float nearest_integer(float x) {
return x;
}
-LIBC_INLINE double nearest_integer(double x) {
+LIBC_INLINE static constexpr double nearest_integer(double x) {
if (x < 0x1p53 && x > -0x1p53) {
double r = x < 0 ? (x - 0x1.0p52) + 0x1.0p52 : (x + 0x1.0p52) - 0x1.0p52;
double diff = x - r;
diff --git a/libc/src/__support/math/expf16_utils.h b/libc/src/__support/math/expf16_utils.h
index bebb72b09b886..8a2fc9415ab8e 100644
--- a/libc/src/__support/math/expf16_utils.h
+++ b/libc/src/__support/math/expf16_utils.h
@@ -47,7 +47,7 @@ struct ExpRangeReduction {
float exp_lo;
};
-static constexpr ExpRangeReduction exp_range_reduction(float16 x) {
+[[maybe_unused]] static ExpRangeReduction exp_range_reduction(float16 x) {
// For -18 < x < 12, to compute exp(x), we perform the following range
// reduction: find hi, mid, lo, such that:
// x = hi + mid + lo, in which
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