[libc][math] Implement double precision exp10 function correctly rounded for all rounding modes.

[lntue]

Summary

Implement double precision exp10 function correctly rounded for all
rounding modes. Using the same algorithm as double precision exp
(https://reviews.llvm.org/D158551) and exp2 (https://reviews.llvm.org/D158812)
functions.

[lntue]

Remove debugging stuff.

[zimmermann6]

a small typo in the summary: fucntions should be functions.

The performance is quite good, nice work!

zimmerma@biscotte:~/svn/core-math$ LIBM=/localdisk/zimmerma/llvm-project/build/projects/libc/lib/libm.a CORE_MATH_PERF_MODE=rdtsc ./perf.sh exp10
GNU libc version: 2.37
GNU libc release: stable
[####################] 100 %
Ntrial = 20 ; Min = 33.623 + 0.357 clc/call; Median-Min = 0.334 clc/call; Max = 34.216 clc/call;
[####################] 100 %
Ntrial = 20 ; Min = 37.281 + 0.352 clc/call; Median-Min = 0.326 clc/call; Max = 39.768 clc/call;
[####################] 100 %
Ntrial = 20 ; Min = 18.802 + 0.174 clc/call; Median-Min = 0.028 clc/call; Max = 20.781 clc/call;

and for the latency:

zimmerma@biscotte:~/svn/core-math$ LIBM=/localdisk/zimmerma/llvm-project/build/projects/libc/lib/libm.a CORE_MATH_PERF_MODE=rdtsc PERF_ARGS=--latency ./perf.sh exp10
GNU libc version: 2.37
GNU libc release: stable
[####################] 100 %
Ntrial = 20 ; Min = 73.058 + 0.361 clc/call; Median-Min = 0.342 clc/call; Max = 73.720 clc/call;
[####################] 100 %
Ntrial = 20 ; Min = 72.787 + 0.393 clc/call; Median-Min = 0.337 clc/call; Max = 73.469 clc/call;
[####################] 100 %
Ntrial = 20 ; Min = 55.295 + 0.349 clc/call; Median-Min = 0.291 clc/call; Max = 55.876 clc/call;

libc/config/darwin/arm/entrypoints.txt

set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.ceil
     libc.src.math.ceilf
     libc.src.math.ceill
     libc.src.math.coshf
     libc.src.math.cosf
     libc.src.math.erff
     libc.src.math.exp
     libc.src.math.expf
+    libc.src.math.exp10
     libc.src.math.exp10f
     libc.src.math.exp2
     libc.src.math.exp2f
     libc.src.math.expm1f
     libc.src.math.fabs
     libc.src.math.fabsf
     libc.src.math.fabsl
     libc.src.math.fdim

libc/config/linux/aarch64/entrypoints.txt

set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.ceil
     libc.src.math.ceilf
     libc.src.math.ceill
     libc.src.math.coshf
     libc.src.math.cosf
     libc.src.math.erff
     libc.src.math.exp
     libc.src.math.expf
+    libc.src.math.exp10
     libc.src.math.exp10f
     libc.src.math.exp2
     libc.src.math.exp2f
     libc.src.math.expm1f
     libc.src.math.fabs
     libc.src.math.fabsf
     libc.src.math.fabsl
     libc.src.math.fdim

libc/config/linux/riscv64/entrypoints.txt

set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.ceil
     libc.src.math.ceilf
     libc.src.math.ceill
     libc.src.math.coshf
     libc.src.math.cosf
     libc.src.math.erff
     libc.src.math.exp
     libc.src.math.expf
+    libc.src.math.exp10
     libc.src.math.exp10f
     libc.src.math.exp2
     libc.src.math.exp2f
     libc.src.math.expm1f
     libc.src.math.fabs
     libc.src.math.fabsf
     libc.src.math.fabsl
     libc.src.math.fdim

libc/config/linux/x86_64/entrypoints.txt

set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.ceilf
     libc.src.math.ceill
     libc.src.math.cos
     libc.src.math.coshf
     libc.src.math.cosf
     libc.src.math.erff
     libc.src.math.exp
     libc.src.math.expf
+    libc.src.math.exp10
     libc.src.math.exp10f
     libc.src.math.exp2
     libc.src.math.exp2f
     libc.src.math.expm1f
     libc.src.math.fabs
     libc.src.math.fabsf
     libc.src.math.fabsl
     libc.src.math.fdim

libc/config/windows/entrypoints.txt

set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.ceilf
     libc.src.math.ceill
     libc.src.math.cos
     libc.src.math.cosf
     libc.src.math.coshf
     libc.src.math.erff
     libc.src.math.exp
     libc.src.math.expf
+    libc.src.math.exp10
     libc.src.math.exp10f
     libc.src.math.exp2
     libc.src.math.exp2f
     libc.src.math.expm1f
     libc.src.math.fabs
     libc.src.math.fabsf
     libc.src.math.fabsl
     libc.src.math.fdim

libc/docs/math/index.rst

 | erfcl      |         |         |         |         |         |         |         |         |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | exp        | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | expf       | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | expl       |         |         |         |         |         |         |         |         |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
-| exp10      |         |         |         |         |         |         |         |         |         |         |         |         |
+| exp10      | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | exp10f     | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | exp10l     |         |         |         |         |         |         |         |         |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | exp2       | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | exp2f      | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |

libc/spec/gnu_ext.td

HeaderSpec Math = HeaderSpec<
       [], // Types
       [], // Enumerations
       [
         FunctionSpec<
             "sincosf",
             RetValSpec<VoidType>,
             [ArgSpec<FloatType>, ArgSpec<FloatPtr>, ArgSpec<FloatPtr>]
         >,
+        FunctionSpec<"exp10", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
         FunctionSpec<"exp10f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
       ]
   >;
 
   HeaderSpec Sched = HeaderSpec<
       "sched.h",
       [], // Macros
       [PidT, SizeTType, CpuSetT], // Types

libc/src/math/CMakeLists.txt

 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(exp10)
 add_math_entrypoint_object(exp10f)
 
 add_math_entrypoint_object(expm1f)
 
 add_math_entrypoint_object(fabs)
 add_math_entrypoint_object(fabsf)
 add_math_entrypoint_object(fabsl)
 

libc/src/math/exp10.h

+//===-- Implementation header for exp10 -------------------------*- 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_EXP10_H
+#define LLVM_LIBC_SRC_MATH_EXP10_H
+
+namespace __llvm_libc {
+
+double exp10(double x);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_MATH_EXP10_H

libc/src/math/generic/CMakeLists.txt

DEPENDS
     libc.include.errno
     libc.src.errno.errno
     libc.include.math
   COMPILE_OPTIONS
     -O3
 )
 
 add_entrypoint_object(
+  exp10
+  SRCS
+    exp10.cpp
+  HDRS
+    ../exp10.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(
   exp10f
   SRCS
     exp10f.cpp
   HDRS
     ../exp10f.h
   DEPENDS
     .explogxf
     libc.src.__support.FPUtil.fenv_impl

libc/src/math/generic/exp10.cpp

-//===-- Double-precision 2^x function -------------------------------------===//
+//===-- Double-precision 10^x function ------------------------------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 
-#include "src/math/exp2.h"
+#include "src/math/exp10.h"
 #include "common_constants.h" // Lookup tables EXP2_MID1 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/macros/optimization.h" // LIBC_UNLIKELY
 
 #include <errno.h>
 
 namespace __llvm_libc {
 
 using fputil::DoubleDouble;
 using fputil::TripleDouble;
 using Float128 = typename fputil::DyadicFloat<128>;
 
+// log2(10)
+constexpr double LOG2_10 = 0x1.a934f0979a371p+1;
+
+// -2^-12 * log10(2)
+// > a = -2^-12 * log10(2);
+// > b = round(a, 32, RN);
+// > c = round(a - b, 32, RN);
+// > d = round(a - b - c, D, RN);
+// Errors < 1.5 * 2^-144
+constexpr double MLOG10_2_EXP2_M12_HI = -0x1.3441350ap-14;
+constexpr double MLOG10_2_EXP2_M12_MID = 0x1.0c0219dc1da99p-51;
+constexpr double MLOG10_2_EXP2_M12_MID_32 = 0x1.0c0219dcp-51;
+constexpr double MLOG10_2_EXP2_M12_LO = 0x1.da994fd20dba2p-87;
+
 // Error bounds:
 // Errors when using double precision.
-#ifdef LIBC_TARGET_CPU_HAS_FMA
-constexpr double ERR_D = 0x1.0p-63;
-#else
 constexpr double ERR_D = 0x1.8p-63;
-#endif // LIBC_TARGET_CPU_HAS_FMA
 
 // Errors when using double-double precision.
-constexpr double ERR_DD = 0x1.0p-100;
+constexpr double ERR_DD = 0x1.8p-99;
 
 // Polynomial approximations with double precision.  Generated by Sollya with:
-// > P = fpminimax((2^x - 1)/x, 3, [|D...|], [-2^-13 - 2^-30, 2^-13 + 2^-30]);
+// > P = fpminimax((10^x - 1)/x, 3, [|D...|], [-2^-14, 2^-14]);
 // > P;
 // Error bounds:
-//   | output - (2^dx - 1) / dx | < 1.5 * 2^-52.
+//   | output - (10^dx - 1) / dx | < 2^-52.
 LIBC_INLINE double poly_approx_d(double dx) {
   // dx^2
   double dx2 = dx * dx;
   double c0 =
-      fputil::multiply_add(dx, 0x1.ebfbdff82c58ep-3, 0x1.62e42fefa39efp-1);
+      fputil::multiply_add(dx, 0x1.53524c73cea6ap+1, 0x1.26bb1bbb55516p+1);
   double c1 =
-      fputil::multiply_add(dx, 0x1.3b2aba7a95a89p-7, 0x1.c6b08e8fc0c0ep-5);
+      fputil::multiply_add(dx, 0x1.2bd75cc6afc65p+0, 0x1.0470587aa264cp+1);
   double p = fputil::multiply_add(dx2, c1, c0);
   return p;
 }
 
 // Polynomial approximation with double-double precision.  Generated by Solya
 // with:
-// > P = fpminimax((2^x - 1)/x, 5, [|DD...|], [-2^-13 - 2^-30, 2^-13 + 2^-30]);
+// > P = fpminimax((10^x - 1)/x, 5, [|DD...|], [-2^-14, 2^-14]);
 // Error bounds:
-//   | output - 2^(dx) | < 2^-101
+//   | output - 10^(dx) | < 2^-101
 DoubleDouble poly_approx_dd(const DoubleDouble &dx) {
   // Taylor polynomial.
   constexpr DoubleDouble COEFFS[] = {
       {0, 0x1p0},
-      {0x1.abc9e3b39824p-56, 0x1.62e42fefa39efp-1},
-      {-0x1.5e43a53e4527bp-57, 0x1.ebfbdff82c58fp-3},
-      {-0x1.d37963a9444eep-59, 0x1.c6b08d704a0cp-5},
-      {0x1.4eda1a81133dap-62, 0x1.3b2ab6fba4e77p-7},
-      {-0x1.c53fd1ba85d14p-64, 0x1.5d87fe7a265a5p-10},
-      {0x1.d89250b013eb8p-70, 0x1.430912f86cb8ep-13},
+      {-0x1.f48ad494e927bp-53, 0x1.26bb1bbb55516p1},
+      {-0x1.e2bfab3191cd2p-53, 0x1.53524c73cea69p1},
+      {0x1.80fb65ec3b503p-53, 0x1.0470591de2ca4p1},
+      {0x1.338fc05e21e55p-54, 0x1.2bd7609fd98c4p0},
+      {0x1.d4ea116818fbp-56, 0x1.1429ffd519865p-1},
+      {-0x1.872a8ff352077p-57, 0x1.a7ed70847c8b3p-3},
+
   };
 
   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 + a0 * dx + a1 * dx^2 + ... + a6 * dx^7
-// For |dx| < 2^-13 + 2^-30:
-//   | output - exp(dx) | < 2^-126.
+// For |dx| < 2^-14:
+//   | output - 10^dx | < 1.5 * 2^-124.
 Float128 poly_approx_f128(const Float128 &dx) {
   using MType = typename Float128::MantissaType;
 
   constexpr Float128 COEFFS_128[]{
       {false, -127, MType({0, 0x8000000000000000})}, // 1.0
-      {false, -128, MType({0xc9e3b39803f2f6af, 0xb17217f7d1cf79ab})},
-      {false, -128, MType({0xde2d60dd9c9a1d9f, 0x3d7f7bff058b1d50})},
-      {false, -132, MType({0x9d3b15d9e7fb6897, 0xe35846b82505fc59})},
-      {false, -134, MType({0x184462f6bcd2b9e7, 0x9d955b7dd273b94e})},
-      {false, -137, MType({0x39ea1bb964c51a89, 0xaec3ff3c53398883})},
-      {false, -138, MType({0x842c53418fa8ae61, 0x2861225f345c396a})},
-      {false, -144, MType({0x7abeb5abd5ad2079, 0xffe5fe2d109a319d})},
+      {false, -126, MType({0xea56d62b82d30a2d, 0x935d8dddaaa8ac16})},
+      {false, -126, MType({0x80a99ce75f4d5bdb, 0xa9a92639e753443a})},
+      {false, -126, MType({0x6a4f9d7dbf6c9635, 0x82382c8ef1652304})},
+      {false, -124, MType({0x345787019216c7af, 0x12bd7609fd98c44c})},
+      {false, -127, MType({0xcc41ed7e0d27aee5, 0x450a7ff47535d889})},
+      {false, -130, MType({0x8326bb91a6e7601d, 0xd3f6b844702d636b})},
+      {false, -130, MType({0xfa7b46df314112a9, 0x45b937f0d05bb1cd})},
   };
 
   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.
+// Compute 10^(x) using 128-bit precision.
 // TODO(lntue): investigate triple-double precision implementation for this
 // step.
-Float128 exp2_f128(double x, int hi, int idx1, int idx2) {
-  Float128 dx = Float128(x);
+Float128 exp10_f128(double x, double kd, int idx1, int idx2) {
+  double t1 = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
+  double t2 = kd * MLOG10_2_EXP2_M12_MID_32;                     // exact
+  double t3 = kd * MLOG10_2_EXP2_M12_LO; // Error < 2^-144
+
+  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 += hi;
+  r.exponent += static_cast<int>(kd) >> 12;
 
   return r;
 }
 
-// Compute 2^x with double-double precision.
-DoubleDouble exp2_double_double(double x, const DoubleDouble &exp_mid) {
-  DoubleDouble dx({0, x});
+// Compute 10^x with double-double precision.
+DoubleDouble exp10_double_double(double x, double kd,
+                                 const DoubleDouble &exp_mid) {
+  // Recalculate dx:
+  //   dx = x - k * 2^-12 * log10(2)
+  double t1 = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
+  double t2 = kd * MLOG10_2_EXP2_M12_MID_32;                     // exact
+  double t3 = kd * MLOG10_2_EXP2_M12_LO; // Error < 2^-140
+
+  DoubleDouble dx = fputil::exact_add(t1, t2);
+  dx.lo += t3;
 
   // Degree-6 polynomial approximation in double-double precision.
-  // | p - 2^x | < 2^-103.
+  // | p - 10^x | < 2^-103.
   DoubleDouble p = poly_approx_dd(dx);
 
   // Error bounds: 2^-102.
   DoubleDouble r = fputil::quick_mult(exp_mid, p);
 
   return r;
 }
 
 // When output is denormal.
-double exp2_denorm(double x) {
+double exp10_denorm(double x) {
   // Range reduction.
-  int k =
-      static_cast<int>(cpp::bit_cast<uint64_t>(x + 0x1.8000'0000'4p21) >> 19);
+  double tmp = fputil::multiply_add(x, LOG2_10, 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);
 
-  // |dx| < 2^-13 + 2^-30.
-  double dx = fputil::multiply_add(kd, -0x1.0p-12, x); // exact
+  // |dx| < 1.5 * 2^-15 + 2^-31 < 2^-14
+  double lo_h = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
+  double dx = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_MID, lo_h);
 
   double mid_lo = dx * exp_mid.hi;
 
-  // Approximate (2^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4.
+  // Approximate (10^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4.
   double p = poly_approx_d(dx);
 
   double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo);
 
   if (auto r = ziv_test_denorm(hi, exp_mid.hi, lo, ERR_D);
       LIBC_LIKELY(r.has_value()))
     return r.value();
 
   // Use double-double
-  DoubleDouble r_dd = exp2_double_double(dx, exp_mid);
+  DoubleDouble r_dd = exp10_double_double(x, kd, exp_mid);
 
   if (auto r = ziv_test_denorm(hi, r_dd.hi, r_dd.lo, ERR_DD);
       LIBC_LIKELY(r.has_value()))
     return r.value();
 
   // Use 128-bit precision
-  Float128 r_f128 = exp2_f128(dx, hi, idx1, idx2);
+  Float128 r_f128 = exp10_f128(x, kd, idx1, idx2);
 
   return static_cast<double>(r_f128);
 }
 
 // Check for exceptional cases when:
-//  * log2(1 - 2^-54) < x < log2(1 + 2^-53)
-//  * x >= 1024
-//  * x <= -1075
+//  * log10(1 - 2^-54) < x < log10(1 + 2^-53)
+//  * x >= log10(2^1024)
+//  * x <= log10(2^-1022)
 //  * x is inf or nan
 double set_exceptional(double x) {
   using FPBits = typename fputil::FPBits<double>;
   using FloatProp = typename fputil::FloatProperties<double>;
   FPBits xbits(x);
 
   uint64_t x_u = xbits.uintval();
   uint64_t x_abs = x_u & FloatProp::EXP_MANT_MASK;
 
-  // |x| < log2(1 + 2^-53)
-  if (x_abs <= 0x3ca71547652b82fd) {
-    // 2^(x) ~ 1 + x/2
+  // |x| < log10(1 + 2^-53)
+  if (x_abs <= 0x3c8bcb7b1526e50e) {
+    // 10^(x) ~ 1 + x/2
     return fputil::multiply_add(x, 0.5, 1.0);
   }
 
-  // x <= 2^-1075 || x >= 1024 or inf/nan.
-  if (x_u > 0xc08ff00000000000) {
-    // x <= 2^-1075 or -inf/nan
-    if (x_u >= 0xc090cc0000000000) {
+  // x <= log10(2^-1022) || x >= log10(2^1024) or inf/nan.
+  if (x_u >= 0xc0733a7146f72a42) {
+    // x <= log10(2^-1075) or -inf/nan
+    if (x_u > 0xc07439b746e36b52) {
       // 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 static_cast<double>(FPBits(FPBits::MIN_SUBNORMAL));
       fputil::set_errno_if_required(ERANGE);
       fputil::raise_except_if_required(FE_UNDERFLOW);
       return 0.0;
     }
 
-    return exp2_denorm(x);
+    return exp10_denorm(x);
   }
 
-  // x >= 1024 or +inf/nan
+  // x >= log10(2^1024) 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 static_cast<double>(FPBits(FPBits::MAX_NORMAL));
 
     fputil::set_errno_if_required(ERANGE);
     fputil::raise_except_if_required(FE_OVERFLOW);
   }
   // x is +inf or nan
   return x + static_cast<double>(FPBits::inf());
 }
 
-LLVM_LIBC_FUNCTION(double, exp2, (double x)) {
+LLVM_LIBC_FUNCTION(double, exp10, (double x)) {
   using FPBits = typename fputil::FPBits<double>;
   using FloatProp = typename fputil::FloatProperties<double>;
   FPBits xbits(x);
 
   uint64_t x_u = xbits.uintval();
 
-  // x < -1022 or x >= 1024 or log2(1 - 2^-54) < x < log2(1 + 2^-53).
-  if (LIBC_UNLIKELY(x_u > 0xc08ff00000000000 ||
-                    (x_u <= 0xbc971547652b82fe && x_u >= 0x4090000000000000) ||
-                    x_u <= 0x3ca71547652b82fd)) {
+  // x <= log10(2^-1022) or x >= log10(2^1024) or
+  // log10(1 - 2^-54) < x < log10(1 + 2^-53).
+  if (LIBC_UNLIKELY(x_u >= 0xc0733a7146f72a42 ||
+                    (x_u <= 0xbc7bcb7b1526e50e && x_u >= 0x40734413509f79ff) ||
+                    x_u < 0x3c8bcb7b1526e50e)) {
     return set_exceptional(x);
   }
 
-  // Now -1075 < x <= log2(1 - 2^-54) or log2(1 + 2^-53) < x < 1024
+  // Now log10(2^-1075) < x <= log10(1 - 2^-54) or
+  //     log10(1 + 2^-53) < x < log10(2^1024)
 
   // Range reduction:
-  // Let x = (hi + mid1 + mid2) + lo
+  // Let x = log10(2) * (hi + mid1 + mid2) + lo
   // in which:
   //   hi is an integer
   //   mid1 * 2^6 is an integer
   //   mid2 * 2^12 is an integer
   // then:
-  //   2^(x) = 2^hi * 2^(mid1) * 2^(mid2) * 2^(lo).
+  //   10^(x) = 2^hi * 2^(mid1) * 2^(mid2) * 10^(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.
-  //   - 2^(lo) ~ 1 + a0*lo + a1 * lo^2 + ...
+  //   - 10^(lo) ~ 1 + a0*lo + a1 * lo^2 + ...
   //
-  // We compute (hi + mid1 + mid2) together by perform the rounding on x * 2^12.
-  // Since |x| < |-1075)| < 2^11,
-  //   |x * 2^12| < 2^11 * 2^12 < 2^23,
+  // We compute (hi + mid1 + mid2) together by perform the rounding on
+  //   x * log2(10) * 2^12.
+  // Since |x| < |log10(2^-1075)| < 2^9,
+  //   |x * 2^12| < 2^9 * 2^12 < 2^21,
   // So we can fit the rounded result round(x * 2^12) 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).
   //
   // 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
+  // extra constant C = 2^e1 + 2^e2 with e1 > e2 >= 2^23 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.
   //
   // One small problem with this approach is that the sum (x*2^12 + 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 + C,
   // where C = 2^33 + 2^32 + 2^-1, then if
   //   k = int32_t(lower 51 bits of double(x * 2^12 + C) >> 19),
   // the reduced argument:
-  //   lo = x - 2^-12 * k is bounded by:
-  //   |lo| <= 2^-13 + 2^-12*2^-19
-  //         = 2^-13 + 2^-31.
+  //   lo = x - log10(2) * 2^-12 * k is bounded by:
+  //   |lo|  = |x - log10(2) * 2^-12 * k|
+  //         = log10(2) * 2^-12 * | x * log2(10) * 2^12 - k |
+  //        <= log10(2) * 2^-12 * (2^-1 + 2^-19)
+  //         < 1.5 * 2^-2 * (2^-13 + 2^-31)
+  //         = 1.5 * (2^-15 * 2^-31)
   //
   // Finally, notice that k only uses the mantissa of x * 2^12, 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 + C) >> 19).
 
   // Rounding errors <= 2^-31.
-  int k =
-      static_cast<int>(cpp::bit_cast<uint64_t>(x + 0x1.8000'0000'4p21) >> 19);
+  double tmp = fputil::multiply_add(x, LOG2_10, 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);
 
-  // |dx| < 2^-13 + 2^-30.
-  double dx = fputil::multiply_add(kd, -0x1.0p-12, x); // exact
-
-  // We use the degree-4 polynomial to approximate 2^(lo):
-  //   2^(lo) ~ 1 + a0 * lo + a1 * lo^2 + a2 * lo^3 + a3 * lo^4 = 1 + lo * P(lo)
+  // |dx| < 1.5 * 2^-15 + 2^-31 < 2^-14
+  double lo_h = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact
+  double dx = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_MID, lo_h);
+
+  // We use the degree-4 polynomial to approximate 10^(lo):
+  //   10^(lo) ~ 1 + a0 * lo + a1 * lo^2 + a2 * lo^3 + a3 * lo^4
+  //           = 1 + lo * P(lo)
   // So that the errors are bounded by:
-  //   |P(lo) - (2^lo - 1)/lo| < |lo|^4 / 64 < 2^(-13 * 4) / 64 = 2^-58
+  //   |P(lo) - (10^lo - 1)/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_(lo) - P(lo)| < 2^-51
-  //   => |lo * P_(lo) - (2^lo - 1) | < 2^-64
-  //   => 2^(mid1 + mid2) * |lo * P_(lo) - expm1(lo)| < 2^-63.
+  //   => |lo * P_(lo) - (2^lo - 1) | < 2^-65
+  //   => 2^(mid1 + mid2) * |lo * P_(lo) - expm1(lo)| < 2^-64.
   // 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 2^-63.
+  // with errors bounded by 2^-64.
 
   double mid_lo = dx * exp_mid.hi;
 
-  // Approximate (2^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4.
+  // Approximate (10^dx - 1)/dx ~ 1 + a0*dx + a1*dx^2 + a2*dx^3 + a3*dx^4.
   double p = poly_approx_d(dx);
 
   double lo = fputil::multiply_add(p, mid_lo, exp_mid.lo);
 
   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) << FloatProp::MANTISSA_WIDTH;
     double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper));
     return r;
   }
 
+  // Exact outputs when x = 1, 2, ..., 22 + hard to round with x = 23.
+  // Quick check mask: 0x800f'ffffU = ~(bits of 1.0 | ... | bits of 23.0)
+  if (LIBC_UNLIKELY((x_u & 0x8000'ffff'ffff'ffffULL) == 0ULL)) {
+    switch (x_u) {
+    case 0x3ff0000000000000: // x = 1.0
+      return 10.0;
+    case 0x4000000000000000: // x = 2.0
+      return 100.0;
+    case 0x4008000000000000: // x = 3.0
+      return 1'000.0;
+    case 0x4010000000000000: // x = 4.0
+      return 10'000.0;
+    case 0x4014000000000000: // x = 5.0
+      return 100'000.0;
+    case 0x4018000000000000: // x = 6.0
+      return 1'000'000.0;
+    case 0x401c000000000000: // x = 7.0
+      return 10'000'000.0;
+    case 0x4020000000000000: // x = 8.0
+      return 100'000'000.0;
+    case 0x4022000000000000: // x = 9.0
+      return 1'000'000'000.0;
+    case 0x4024000000000000: // x = 10.0
+      return 10'000'000'000.0;
+    case 0x4026000000000000: // x = 11.0
+      return 100'000'000'000.0;
+    case 0x4028000000000000: // x = 12.0
+      return 1'000'000'000'000.0;
+    case 0x402a000000000000: // x = 13.0
+      return 10'000'000'000'000.0;
+    case 0x402c000000000000: // x = 14.0
+      return 100'000'000'000'000.0;
+    case 0x402e000000000000: // x = 15.0
+      return 1'000'000'000'000'000.0;
+    case 0x4030000000000000: // x = 16.0
+      return 10'000'000'000'000'000.0;
+    case 0x4031000000000000: // x = 17.0
+      return 100'000'000'000'000'000.0;
+    case 0x4032000000000000: // x = 18.0
+      return 1'000'000'000'000'000'000.0;
+    case 0x4033000000000000: // x = 19.0
+      return 10'000'000'000'000'000'000.0;
+    case 0x4034000000000000: // x = 20.0
+      return 100'000'000'000'000'000'000.0;
+    case 0x4035000000000000: // x = 21.0
+      return 1'000'000'000'000'000'000'000.0;
+    case 0x4036000000000000: // x = 22.0
+      return 10'000'000'000'000'000'000'000.0;
+    case 0x4037000000000000: // x = 23.0
+      return 0x1.52d02c7e14af6p76 + x;
+    }
+  }
+
   // Use double-double
-  DoubleDouble r_dd = exp2_double_double(dx, exp_mid);
+  DoubleDouble r_dd = exp10_double_double(x, kd, exp_mid);
 
   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)) {
     // 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) << FloatProp::MANTISSA_WIDTH;
     double r = cpp::bit_cast<double>(exp_hi + cpp::bit_cast<int64_t>(upper_dd));
     return r;
   }
 
   // Use 128-bit precision
-  Float128 r_f128 = exp2_f128(dx, hi, idx1, idx2);
+  Float128 r_f128 = exp10_f128(x, kd, idx1, idx2);
 
   return static_cast<double>(r_f128);
 }
 
 } // namespace __llvm_libc

libc/src/math/generic/exp2.cpp

Float128 poly_approx_f128(const Float128 &dx) {
   };
 
   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.
+// Compute 2^(x) using 128-bit precision.
 // TODO(lntue): investigate triple-double precision implementation for this
 // step.
 Float128 exp2_f128(double x, int hi, int idx1, int idx2) {
   Float128 dx = Float128(x);
 
   // TODO: Skip recalculating exp_mid1 and exp_mid2.
   Float128 exp_mid1 =
       fputil::quick_add(Float128(EXP2_MID1[idx1].hi),
double exp2_denorm(double x) {
   Float128 r_f128 = exp2_f128(dx, hi, idx1, idx2);
 
   return static_cast<double>(r_f128);
 }
 
 // Check for exceptional cases when:
 //  * log2(1 - 2^-54) < x < log2(1 + 2^-53)
 //  * x >= 1024
-//  * x <= -1075
+//  * x <= -1022
 //  * x is inf or nan
 double set_exceptional(double x) {
   using FPBits = typename fputil::FPBits<double>;
   using FloatProp = typename fputil::FloatProperties<double>;
   FPBits xbits(x);
 
   uint64_t x_u = xbits.uintval();
   uint64_t x_abs = x_u & FloatProp::EXP_MANT_MASK;
 
   // |x| < log2(1 + 2^-53)
   if (x_abs <= 0x3ca71547652b82fd) {
     // 2^(x) ~ 1 + x/2
     return fputil::multiply_add(x, 0.5, 1.0);
   }
 
-  // x <= 2^-1075 || x >= 1024 or inf/nan.
+  // x <= -1022 || x >= 1024 or inf/nan.
   if (x_u > 0xc08ff00000000000) {
-    // x <= 2^-1075 or -inf/nan
+    // x <= -1075 or -inf/nan
     if (x_u >= 0xc090cc0000000000) {
       // exp(-Inf) = 0
       if (xbits.is_inf())
         return 0.0;
 
       // exp(nan) = nan
       if (xbits.is_nan())
         return x;

libc/test/src/math/CMakeLists.txt

add_fp_unittest(
   DEPENDS
     libc.src.errno.errno
     libc.include.math
     libc.src.math.exp10f
     libc.src.__support.FPUtil.fp_bits
 )
 
 add_fp_unittest(
+ exp10_test
+ NEED_MPFR
+ SUITE
+   libc_math_unittests
+ SRCS
+   exp10_test.cpp
+ DEPENDS
+   libc.src.errno.errno
+   libc.include.math
+   libc.src.math.exp10
+   libc.src.__support.FPUtil.fp_bits
+)
+
+add_fp_unittest(
   copysign_test
   SUITE
     libc_math_unittests
   SRCS
     copysign_test.cpp
   HDRS
     CopySignTest.h
   DEPENDS

libc/test/src/math/exp10_test.cpp

+//===-- Unittests for 10^x ------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/errno/libc_errno.h"
+#include "src/math/exp10.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include "utils/MPFRWrapper/MPFRUtils.h"
+#include <math.h>
+
+#include <errno.h>
+#include <stdint.h>
+
+namespace mpfr = __llvm_libc::testing::mpfr;
+using __llvm_libc::testing::tlog;
+
+DECLARE_SPECIAL_CONSTANTS(double)
+
+TEST(LlvmLibcExp10Test, SpecialNumbers) {
+  EXPECT_FP_EQ(aNaN, __llvm_libc::exp10(aNaN));
+  EXPECT_FP_EQ(inf, __llvm_libc::exp10(inf));
+  EXPECT_FP_EQ_ALL_ROUNDING(zero, __llvm_libc::exp10(neg_inf));
+  EXPECT_FP_EQ_WITH_EXCEPTION(zero, __llvm_libc::exp10(-0x1.0p20),
+                              FE_UNDERFLOW);
+  EXPECT_FP_EQ_WITH_EXCEPTION(inf, __llvm_libc::exp10(0x1.0p20), FE_OVERFLOW);
+  EXPECT_FP_EQ_ALL_ROUNDING(1.0, __llvm_libc::exp10(0.0));
+  EXPECT_FP_EQ_ALL_ROUNDING(1.0, __llvm_libc::exp10(-0.0));
+}
+
+TEST(LlvmLibcExp10Test, TrickyInputs) {
+  constexpr int N = 41;
+  constexpr uint64_t INPUTS[N] = {
+      0x40033093317082F8, 0x3FD79289C6E6A5C0,
+      0x3FD05DE80A173EA0, // 0x1.05de80a173eap-2
+      0xbf1eb7a4cb841fcc, // -0x1.eb7a4cb841fccp-14
+      0xbf19a61fb925970d,
+      0x3fda7b764e2cf47a, // 0x1.a7b764e2cf47ap-2
+      0xc04757852a4b93aa, // -0x1.757852a4b93aap+5
+      0x4044c19e5712e377, // x=0x1.4c19e5712e377p+5
+      0xbf19a61fb925970d, // x=-0x1.9a61fb925970dp-14
+      0xc039a74cdab36c28, // x=-0x1.9a74cdab36c28p+4
+      0xc085b3e4e2e3bba9, // x=-0x1.5b3e4e2e3bba9p+9
+      0xc086960d591aec34, // x=-0x1.6960d591aec34p+9
+      0xc086232c09d58d91, // x=-0x1.6232c09d58d91p+9
+      0xc0874910d52d3051, // x=-0x1.74910d52d3051p9
+      0xc0867a172ceb0990, // x=-0x1.67a172ceb099p+9
+      0xc08ff80000000000, // x=-0x1.ff8p+9
+      0xbc971547652b82fe, // x=-0x1.71547652b82fep-54
+      0x0000000000000000, // x = 0
+      0x3ff0000000000000, // x = 1
+      0x4000000000000000, // x = 2
+      0x4008000000000000, // x = 3
+      0x4010000000000000, // x = 4
+      0x4014000000000000, // x = 5
+      0x4018000000000000, // x = 6
+      0x401c000000000000, // x = 7
+      0x4020000000000000, // x = 8
+      0x4022000000000000, // x = 9
+      0x4024000000000000, // x = 10
+      0x4026000000000000, // x = 11
+      0x4028000000000000, // x = 12
+      0x402a000000000000, // x = 13
+      0x402c000000000000, // x = 14
+      0x402e000000000000, // x = 15
+      0x4030000000000000, // x = 16
+      0x4031000000000000, // x = 17
+      0x4032000000000000, // x = 18
+      0x4033000000000000, // x = 19
+      0x4034000000000000, // x = 20
+      0x4035000000000000, // x = 21
+      0x4036000000000000, // x = 22
+      0x4037000000000000, // x = 23
+  };
+  for (int i = 0; i < N; ++i) {
+    double x = double(FPBits(INPUTS[i]));
+    EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Exp10, x,
+                                   __llvm_libc::exp10(x), 0.5);
+  }
+}
+
+TEST(LlvmLibcExp10Test, InDoubleRange) {
+  constexpr uint64_t COUNT = 1'231;
+  uint64_t START = __llvm_libc::fputil::FPBits<double>(0.25).uintval();
+  uint64_t STOP = __llvm_libc::fputil::FPBits<double>(4.0).uintval();
+  uint64_t STEP = (STOP - START) / COUNT;
+
+  auto test = [&](mpfr::RoundingMode rounding_mode) {
+    mpfr::ForceRoundingMode __r(rounding_mode);
+    if (!__r.success)
+      return;
+
+    uint64_t fails = 0;
+    uint64_t count = 0;
+    uint64_t cc = 0;
+    double mx, mr = 0.0;
+    double tol = 0.5;
+
+    for (uint64_t i = 0, v = START; i <= COUNT; ++i, v += STEP) {
+      double x = FPBits(v).get_val();
+      if (isnan(x) || isinf(x) || x < 0.0)
+        continue;
+      libc_errno = 0;
+      double result = __llvm_libc::exp10(x);
+      ++cc;
+      if (isnan(result) || isinf(result))
+        continue;
+
+      ++count;
+
+      if (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Exp10, x, result,
+                                             0.5, rounding_mode)) {
+        ++fails;
+        while (!TEST_MPFR_MATCH_ROUNDING_SILENTLY(mpfr::Operation::Exp10, x,
+                                                  result, tol, rounding_mode)) {
+          mx = x;
+          mr = result;
+
+          if (tol > 1000.0)
+            break;
+
+          tol *= 2.0;
+        }
+      }
+    }
+    tlog << " Exp10 failed: " << fails << "/" << count << "/" << cc
+         << " tests.\n";
+    tlog << "   Max ULPs is at most: " << static_cast<uint64_t>(tol) << ".\n";
+    if (fails) {
+      EXPECT_MPFR_MATCH(mpfr::Operation::Exp10, mx, mr, 0.5, rounding_mode);
+    }
+  };
+
+  tlog << " Test Rounding To Nearest...\n";
+  test(mpfr::RoundingMode::Nearest);
+
+  tlog << " Test Rounding Downward...\n";
+  test(mpfr::RoundingMode::Downward);
+
+  tlog << " Test Rounding Upward...\n";
+  test(mpfr::RoundingMode::Upward);
+
+  tlog << " Test Rounding Toward Zero...\n";
+  test(mpfr::RoundingMode::TowardZero);
+}

utils/bazel/llvm-project-overlay/libc/BUILD.bazel

additional_deps = [
         ":__support_fputil_polyeval",
         ":__support_fputil_rounding_mode",
         ":__support_macros_optimization",
         ":common_constants",
     ],
 )
 
 libc_math_function(
+    name = "exp10",
+    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_macros_optimization",
+        ":common_constants",
+        ":explogxf",
+    ],
+)
+
+libc_math_function(
     name = "exp10f",
     additional_deps = [
         ":__support_fputil_fma",
         ":__support_fputil_multiply_add",
         ":__support_fputil_nearest_integer",
         ":__support_fputil_polyeval",
         ":__support_fputil_rounding_mode",
         ":__support_macros_optimization",

utils/bazel/llvm-project-overlay/libc/test/src/math/BUILD.bazel

 math_test(
     name = "exp2",
     deps = [
         "//libc/utils/MPFRWrapper:mpfr_wrapper",
     ],
 )
 
 math_test(
+    name = "exp10",
+    deps = [
+        "//libc/utils/MPFRWrapper:mpfr_wrapper",
+    ],
+)
+
+math_test(
     name = "fmod",
     hdrs = ["FModTest.h"],
 )
 
 math_test(
     name = "fmodf",
     hdrs = ["FModTest.h"],
 )