[libc][math] Implement double precision exp2 function correctly round…

…ed for all rounding modes. Implement double precision exp2 function correctly rounded for all rounding modes. Using the same algorithm as double precision exp function in https://reviews.llvm.org/D158551. Reviewed By: zimmermann6 Differential Revision: https://reviews.llvm.org/D158812
llvm · Aug 25, 2023 · 8ca614a · 8ca614a
1 parent e3373c6
commit 8ca614a
Show file tree

Hide file tree

Showing 19 changed files with 844 additions and 196 deletions.
diff --git a/libc/config/darwin/arm/entrypoints.txt b/libc/config/darwin/arm/entrypoints.txt
@@ -132,6 +132,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.exp
     libc.src.math.expf
     libc.src.math.exp10f
+    libc.src.math.exp2
     libc.src.math.exp2f
     libc.src.math.expm1f
     libc.src.math.fabs

diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
@@ -246,6 +246,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.exp
     libc.src.math.expf
     libc.src.math.exp10f
+    libc.src.math.exp2
     libc.src.math.exp2f
     libc.src.math.expm1f
     libc.src.math.fabs

diff --git a/libc/config/linux/riscv64/entrypoints.txt b/libc/config/linux/riscv64/entrypoints.txt
@@ -255,6 +255,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.exp
     libc.src.math.expf
     libc.src.math.exp10f
+    libc.src.math.exp2
     libc.src.math.exp2f
     libc.src.math.expm1f
     libc.src.math.fabs

diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
@@ -259,6 +259,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.exp
     libc.src.math.expf
     libc.src.math.exp10f
+    libc.src.math.exp2
     libc.src.math.exp2f
     libc.src.math.expm1f
     libc.src.math.fabs

diff --git a/libc/config/windows/entrypoints.txt b/libc/config/windows/entrypoints.txt
@@ -131,6 +131,7 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.exp
     libc.src.math.expf
     libc.src.math.exp10f
+    libc.src.math.exp2
     libc.src.math.exp2f
     libc.src.math.expm1f
     libc.src.math.fabs

diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
@@ -364,7 +364,7 @@ Higher Math Functions
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | exp10l     |         |         |         |         |         |         |         |         |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
-| exp2       |         |         |         |         |         |         |         |         |         |         |         |         |
+| exp2       | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | exp2f      | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
@@ -485,7 +485,7 @@ cosh           |check|
 erf            |check|
 exp            |check|          |check|
 exp10          |check|
-exp2           |check|
+exp2           |check|          |check|
 expm1          |check|
 fma            |check|          |check|
 hypot          |check|          |check|

diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
@@ -437,6 +437,7 @@ def StdC : StandardSpec<"stdc"> {
           FunctionSpec<"exp", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"expf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
 
+          FunctionSpec<"exp2", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"exp2f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
           FunctionSpec<"expm1f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
 

diff --git a/libc/src/__support/FPUtil/CMakeLists.txt b/libc/src/__support/FPUtil/CMakeLists.txt
@@ -227,6 +227,12 @@ add_header_library(
     .multiply_add
 )
 
+add_header_library(
+  triple_double
+  HDRS
+    triple_double.h
+)
+
 add_header_library(
   dyadic_float
   HDRS

diff --git a/libc/src/__support/FPUtil/triple_double.h b/libc/src/__support/FPUtil/triple_double.h
@@ -0,0 +1,22 @@
+//===-- Utilities for triple-double data type. ------------------*- 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_FPUTIL_TRIPLEDOUBLE_H
+#define LLVM_LIBC_SRC_SUPPORT_FPUTIL_TRIPLEDOUBLE_H
+
+namespace __llvm_libc::fputil {
+
+struct TripleDouble {
+  double lo = 0.0;
+  double mid = 0.0;
+  double hi = 0.0;
+};
+
+} // namespace __llvm_libc::fputil
+
+#endif // LLVM_LIBC_SRC_SUPPORT_FPUTIL_TRIPLEDOUBLE_H
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
@@ -82,6 +82,7 @@ add_math_entrypoint_object(erff)
 add_math_entrypoint_object(exp)
 add_math_entrypoint_object(expf)
 
+add_math_entrypoint_object(exp2)
 add_math_entrypoint_object(exp2f)
 
 add_math_entrypoint_object(exp10f)

diff --git a/libc/src/math/exp2.h b/libc/src/math/exp2.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for exp2 --------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_MATH_EXP2_H
+#define LLVM_LIBC_SRC_MATH_EXP2_H
+
+namespace __llvm_libc {
+
+double exp2(double x);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_MATH_EXP2_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
@@ -556,6 +556,7 @@ add_entrypoint_object(
     ../exp.h
   DEPENDS
     .common_constants
+    .explogxf
     libc.src.__support.CPP.bit
     libc.src.__support.CPP.optional
     libc.src.__support.FPUtil.dyadic_float
@@ -565,6 +566,7 @@ add_entrypoint_object(
     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.macros.optimization
     libc.include.errno
     libc.src.errno.errno
@@ -596,6 +598,33 @@ add_entrypoint_object(
     -O3
 )
 
+add_entrypoint_object(
+  exp2
+  SRCS
+    exp2.cpp
+  HDRS
+    ../exp2.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.macros.optimization
+    libc.include.errno
+    libc.src.errno.errno
+    libc.include.math
+  COMPILE_OPTIONS
+    -O3
+)
+
 add_entrypoint_object(
   exp2f
   SRCS
@@ -816,6 +845,7 @@ add_object_library(
     common_constants.cpp
   DEPENDS
     libc.src.__support.number_pair
+    libc.src.__support.FPUtil.triple_double
 )
 
 add_header_library(
@@ -1363,6 +1393,9 @@ 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

diff --git a/libc/src/math/generic/common_constants.cpp b/libc/src/math/generic/common_constants.cpp
@@ -7,6 +7,7 @@
 //===----------------------------------------------------------------------===//
 
 #include "common_constants.h"
+#include "src/__support/FPUtil/triple_double.h"
 #include "src/__support/number_pair.h"
 
 namespace __llvm_libc {
@@ -561,4 +562,160 @@ 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, "},");
+//   };
+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, "},");
+//   };
+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 __llvm_libc
diff --git a/libc/src/math/generic/common_constants.h b/libc/src/math/generic/common_constants.h
@@ -9,6 +9,7 @@
 #ifndef LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H
 #define LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H
 
+#include "src/__support/FPUtil/triple_double.h"
 #include "src/__support/number_pair.h"
 
 namespace __llvm_libc {
@@ -65,6 +66,12 @@ 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 __llvm_libc
 
 #endif // LLVM_LIBC_SRC_MATH_GENERIC_COMMON_CONSTANTS_H