[libc] Use nearest_integer instructions to improve expf performance.

[lntue]

Summary

Use nearest_integer instructions to improve expf performance.

Performance tests with CORE-MATH's perf tool:

Before the patch:

$ ./perf.sh expf
LIBC-location: /home/lnt/experiment/llvm-project/build/projects/libc/lib/libllvmlibc.a
GNU libc version: 2.31
GNU libc release: stable
CORE-MATH reciprocal throughput   : 9.860
System LIBC reciprocal throughput : 7.728
LIBC reciprocal throughput        : 12.363

$ ./perf.sh expf --latency
LIBC-location: /home/lnt/experiment/llvm-project/build/projects/libc/lib/libllvmlibc.a
GNU libc version: 2.31
GNU libc release: stable
CORE-MATH latency   : 42.802
System LIBC latency : 35.941
LIBC latency        : 49.808

After the patch:

$ ./perf.sh expf
LIBC-location: /home/lnt/experiment/llvm/llvm-project/build/projects/libc/lib/libllvmlibc.a
GNU libc version: 2.31
GNU libc release: stable
CORE-MATH reciprocal throughput   : 9.441
System LIBC reciprocal throughput : 7.382
LIBC reciprocal throughput        : 8.843

$ ./perf.sh expf --latency
LIBC-location: /home/lnt/experiment/llvm/llvm-project/build/projects/libc/lib/libllvmlibc.a
GNU libc version: 2.31
GNU libc release: stable
CORE-MATH latency   : 44.192
System LIBC latency : 37.693
LIBC latency        : 44.145

[lntue]

Update math status page.

[michaelrj]

libc/src/math/generic/CMakeLists.txt

486

you should probably also explicitly include multiply add

[lntue]

Add multiply_add to dependency.

[zimmermann6]

I confirm it is still correctly rounded, and now faster than CORE-MATH. Nice work!

libc/docs/math.rst

 
 +--------------+-------------------------------+-------------------------------+-------------------------------------+---------------------------------------------------------------------+
 | <Func>       | Reciprocal throughput (ns)    | Latency (ns)                  | Testing ranges                      | Testing configuration                                               |
 |              +-----------+-------------------+-----------+-------------------+                                     +------------+-------------------------+--------------+---------------+
 |              | LLVM libc | Reference (glibc) | LLVM libc | Reference (glibc) |                                     | CPU        | OS                      | Compiler     | Special flags |
 +==============+===========+===================+===========+===================+=====================================+============+=========================+==============+===============+
 | cosf         |        37 |                32 |        73 |                72 | :math:`[0, 2\pi]`                   | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 |               |
 +--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| expf         |        14 |                 9 |        58 |                42 | :math:`[-10, 10]`                   | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA           |
+| expf         |         9 |                 7 |        44 |                38 | :math:`[-10, 10]`                   | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA           |
 +--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
 | exp2f        |        25 |                 8 |        81 |                37 | :math:`[-10, 10]`                   | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA           |
 +--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
 | expm1f       |        14 |                53 |        59 |               146 | :math:`[-10, 10]`                   | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA           |
 +--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
 | fmodf        |        73 |               263 |        -  |                 - | [MIN_NORMAL, MAX_NORMAL]            | i5 mobile  | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 |               |
 |              +-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
 |              |         9 |                11 |        -  |                 - | [0, MAX_SUBNORMAL]                  | i5 mobile  | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 |               |

libc/src/math/generic/CMakeLists.txt

add_entrypoint_object(
   expf
   SRCS
     expf.cpp
   HDRS
     ../expf.h
   DEPENDS
     .common_constants
     libc.src.__support.FPUtil.fputil
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.nearest_integer
     libc.src.__support.FPUtil.polyeval
     libc.include.math
   COMPILE_OPTIONS
     -O3
 )
 
 add_entrypoint_object(
   exp2f

libc/src/math/generic/expf.cpp

 //===-- Single-precision e^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/expf.h"
 #include "common_constants.h" // Lookup tables EXP_M1 and EXP_M2.
 #include "src/__support/FPUtil/BasicOperations.h"
 #include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FMA.h"
 #include "src/__support/FPUtil/FPBits.h"
 #include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/nearest_integer.h"
 #include "src/__support/common.h"
 
 #include <errno.h>
 
 namespace __llvm_libc {
 
 LLVM_LIBC_FUNCTION(float, expf, (float x)) {
   using FPBits = typename fputil::FPBits<float>;
LLVM_LIBC_FUNCTION(float, expf, (float x)) {
   //   hi + mid = round(x * 2^7) * 2^(-7).
   // Then,
   //   exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo).
   // We store exp(hi) and exp(mid) in the lookup tables EXP_M1 and EXP_M2
   // respectively.  exp(lo) is computed using a degree-4 minimax polynomial
   // generated by Sollya.
 
   // x_hi = (hi + mid) * 2^7 = round(x * 2^7).
-  // The default rounding mode for float-to-int conversion in C++ is
-  // round-toward-zero. To make it round-to-nearest, we add (-1)^sign(x) * 0.5
-  // before conversion.
-  int x_hi = static_cast<int>(x * 0x1.0p7f + (xbits.get_sign() ? -0.5f : 0.5f));
+  float kf = fputil::nearest_integer(x * 0x1.0p7f);
   // Subtract (hi + mid) from x to get lo.
-  x -= static_cast<float>(x_hi) * 0x1.0p-7f;
-  double xd = static_cast<double>(x);
+  double xd = static_cast<double>(fputil::multiply_add(kf, -0x1.0p-7f, x));
+  int x_hi = static_cast<int>(kf);
   x_hi += 104 << 7;
   // hi = x_hi >> 7
   double exp_hi = EXP_M1[x_hi >> 7];
   // mid * 2^7 = x_hi & 0x0000'007fU;
   double exp_mid = EXP_M2[x_hi & 0x7f];
   // Degree-4 minimax polynomial generated by Sollya with the following
   // commands:
   //   > display = hexadecimal;