[libc][math] Refactor exp10f implementation to header-only in src/__support/math folder.

libc/shared/math.h

@@ -13,6 +13,7 @@
 
 #include "math/exp.h"
 #include "math/exp10.h"
+#include "math/exp10f.h"
 #include "math/expf.h"
 #include "math/expf16.h"
 #include "math/frexpf.h"

libc/shared/math/exp10f.h

@@ -0,0 +1,24 @@
+//===-- Shared exp10f 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_EXP10F_H
+#define LLVM_LIBC_SHARED_MATH_EXP10F_H
+
+#include "shared/libc_common.h"
+#include "src/__support/math/exp10f.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace shared {
+
+using math::exp10f;
+
+} // namespace shared
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SHARED_MATH_EXP10F_H

libc/src/__support/math/CMakeLists.txt

@@ -170,3 +170,31 @@ add_header_library(
     libc.src.__support.integer_literals
     libc.src.__support.macros.optimization
 )
+
+add_header_library(
+  exp10f_utils
+  HDRS
+    exp10f_utils.h
+  DEPENDS
+    libc.src.__support.FPUtil.basic_operations
+    libc.src.__support.FPUtil.fenv_impl
+    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
+)
+
+add_header_library(
+  exp10f
+  HDRS
+    exp10f.h
+  DEPENDS
+    .exp10f_utils
+    libc.src.__support.macros.config
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.rounding_mode
+    libc.src.__support.macros.optimization
+)

libc/src/math/generic/exp10f_impl.h → libc/src/__support/math/exp10f.h

@@ -1,27 +1,26 @@
-//===-- Single-precision 10^x function ------------------------------------===//
+//===-- Implementation header for exp10f ------------------------*- 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_GENERIC_EXP10F_IMPL_H
-#define LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_H
 
-#include "explogxf.h"
+#include "exp10f_utils.h"
 #include "src/__support/FPUtil/FEnvImpl.h"
 #include "src/__support/FPUtil/FPBits.h"
 #include "src/__support/FPUtil/multiply_add.h"
 #include "src/__support/FPUtil/rounding_mode.h"
-#include "src/__support/common.h"
 #include "src/__support/macros/config.h"
 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
 
 namespace LIBC_NAMESPACE_DECL {
-namespace generic {
+namespace math {
 
-LIBC_INLINE float exp10f(float x) {
+static constexpr float exp10f(float x) {
   using FPBits = typename fputil::FPBits<float>;
   FPBits xbits(x);
 
@@ -132,7 +131,7 @@ LIBC_INLINE float exp10f(float x) {
   return static_cast<float>(multiply_add(p, lo2 * rr.mh, c0 * rr.mh));
 }
 
-} // namespace generic
+} // namespace math
 } // namespace LIBC_NAMESPACE_DECL
 
-#endif // LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_H

libc/src/__support/math/exp10f_utils.h

@@ -0,0 +1,171 @@
+//===-- Common utils for exp10f ---------------------------------*- 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_FLOAT_CONSTANTS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP_FLOAT_CONSTANTS_H
+
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+struct ExpBase {
+  // Base = e
+  static constexpr int MID_BITS = 5;
+  static constexpr int MID_MASK = (1 << MID_BITS) - 1;
+  // log2(e) * 2^5
+  static constexpr double LOG2_B = 0x1.71547652b82fep+0 * (1 << MID_BITS);
+  // High and low parts of -log(2) * 2^(-5)
+  static constexpr double M_LOGB_2_HI = -0x1.62e42fefa0000p-1 / (1 << MID_BITS);
+  static constexpr double M_LOGB_2_LO =
+      -0x1.cf79abc9e3b3ap-40 / (1 << MID_BITS);
+  // Look up table for bit fields of 2^(i/32) for i = 0..31, generated by Sollya
+  // with:
+  // > for i from 0 to 31 do printdouble(round(2^(i/32), D, RN));
+  static constexpr int64_t EXP_2_MID[1 << MID_BITS] = {
+      0x3ff0000000000000, 0x3ff059b0d3158574, 0x3ff0b5586cf9890f,
+      0x3ff11301d0125b51, 0x3ff172b83c7d517b, 0x3ff1d4873168b9aa,
+      0x3ff2387a6e756238, 0x3ff29e9df51fdee1, 0x3ff306fe0a31b715,
+      0x3ff371a7373aa9cb, 0x3ff3dea64c123422, 0x3ff44e086061892d,
+      0x3ff4bfdad5362a27, 0x3ff5342b569d4f82, 0x3ff5ab07dd485429,
+      0x3ff6247eb03a5585, 0x3ff6a09e667f3bcd, 0x3ff71f75e8ec5f74,
+      0x3ff7a11473eb0187, 0x3ff82589994cce13, 0x3ff8ace5422aa0db,
+      0x3ff93737b0cdc5e5, 0x3ff9c49182a3f090, 0x3ffa5503b23e255d,
+      0x3ffae89f995ad3ad, 0x3ffb7f76f2fb5e47, 0x3ffc199bdd85529c,
+      0x3ffcb720dcef9069, 0x3ffd5818dcfba487, 0x3ffdfc97337b9b5f,
+      0x3ffea4afa2a490da, 0x3fff50765b6e4540,
+  };
+
+  // Approximating e^dx with degree-5 minimax polynomial generated by Sollya:
+  // > Q = fpminimax(expm1(x)/x, 4, [|1, D...|], [-log(2)/64, log(2)/64]);
+  // Then:
+  //   e^dx ~ P(dx) = 1 + dx + COEFFS[0] * dx^2 + ... + COEFFS[3] * dx^5.
+  static constexpr double COEFFS[4] = {
+      0x1.ffffffffe5bc8p-2, 0x1.555555555cd67p-3, 0x1.5555c2a9b48b4p-5,
+      0x1.11112a0e34bdbp-7};
+
+  LIBC_INLINE static double powb_lo(double dx) {
+    using fputil::multiply_add;
+    double dx2 = dx * dx;
+    double c0 = 1.0 + dx;
+    // c1 = COEFFS[0] + COEFFS[1] * dx
+    double c1 = multiply_add(dx, ExpBase::COEFFS[1], ExpBase::COEFFS[0]);
+    // c2 = COEFFS[2] + COEFFS[3] * dx
+    double c2 = multiply_add(dx, ExpBase::COEFFS[3], ExpBase::COEFFS[2]);
+    // r = c4 + c5 * dx^4
+    //   = 1 + dx + COEFFS[0] * dx^2 + ... + COEFFS[5] * dx^7
+    return fputil::polyeval(dx2, c0, c1, c2);
+  }
+};
+
+struct Exp10Base : public ExpBase {
+  // log2(10) * 2^5
+  static constexpr double LOG2_B = 0x1.a934f0979a371p1 * (1 << MID_BITS);
+  // High and low parts of -log10(2) * 2^(-5).
+  // Notice that since |x * log2(10)| < 150:
+  //   |k| = |round(x * log2(10) * 2^5)| < 2^8 * 2^5 = 2^13
+  // So when the FMA instructions are not available, in order for the product
+  //   k * M_LOGB_2_HI
+  // to be exact, we only store the high part of log10(2) up to 38 bits
+  // (= 53 - 15) of precision.
+  // It is generated by Sollya with:
+  // > round(log10(2), 44, RN);
+  static constexpr double M_LOGB_2_HI = -0x1.34413509f8p-2 / (1 << MID_BITS);
+  // > round(log10(2) - 0x1.34413509f8p-2, D, RN);
+  static constexpr double M_LOGB_2_LO = 0x1.80433b83b532ap-44 / (1 << MID_BITS);
+
+  // Approximating 10^dx with degree-5 minimax polynomial generated by Sollya:
+  // > Q = fpminimax((10^x - 1)/x, 4, [|D...|], [-log10(2)/2^6, log10(2)/2^6]);
+  // Then:
+  //   10^dx ~ P(dx) = 1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5.
+  static constexpr double COEFFS[5] = {0x1.26bb1bbb55515p1, 0x1.53524c73bd3eap1,
+                                       0x1.0470591dff149p1, 0x1.2bd7c0a9fbc4dp0,
+                                       0x1.1429e74a98f43p-1};
+
+  static double powb_lo(double dx) {
+    using fputil::multiply_add;
+    double dx2 = dx * dx;
+    // c0 = 1 + COEFFS[0] * dx
+    double c0 = multiply_add(dx, Exp10Base::COEFFS[0], 1.0);
+    // c1 = COEFFS[1] + COEFFS[2] * dx
+    double c1 = multiply_add(dx, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);
+    // c2 = COEFFS[3] + COEFFS[4] * dx
+    double c2 = multiply_add(dx, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);
+    // r = c0 + dx^2 * (c1 + c2 * dx^2)
+    //   = c0 + c1 * dx^2 + c2 * dx^4
+    //   = 1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5.
+    return fputil::polyeval(dx2, c0, c1, c2);
+  }
+};
+
+constexpr int LOG_P1_BITS = 6;
+constexpr int LOG_P1_SIZE = 1 << LOG_P1_BITS;
+
+// N[Table[Log[2, 1 + x], {x, 0/64, 63/64, 1/64}], 40]
+extern const double LOG_P1_LOG2[LOG_P1_SIZE];
+
+// N[Table[1/(1 + x), {x, 0/64, 63/64, 1/64}], 40]
+extern const double LOG_P1_1_OVER[LOG_P1_SIZE];
+
+// Taylor series expansion for Log[2, 1 + x] splitted to EVEN AND ODD numbers
+// K_LOG2_ODD starts from x^3
+extern const double K_LOG2_ODD[4];
+extern const double K_LOG2_EVEN[4];
+
+// Output of range reduction for exp_b: (2^(mid + hi), lo)
+// where:
+//   b^x = 2^(mid + hi) * b^lo
+struct exp_b_reduc_t {
+  double mh; // 2^(mid + hi)
+  double lo;
+};
+
+// The function correctly calculates b^x value with at least float precision
+// in a limited range.
+// Range reduction:
+//   b^x = 2^(hi + mid) * b^lo
+// where:
+//   x = (hi + mid) * log_b(2) + lo
+//   hi is an integer,
+//   0 <= mid * 2^MID_BITS < 2^MID_BITS is an integer
+//   -2^(-MID_BITS - 1) <= lo * log2(b) <= 2^(-MID_BITS - 1)
+// Base class needs to provide the following constants:
+//   - MID_BITS    : number of bits after decimal points used for mid
+//   - MID_MASK    : 2^MID_BITS - 1, mask to extract mid bits
+//   - LOG2_B      : log2(b) * 2^MID_BITS for scaling
+//   - M_LOGB_2_HI : high part of -log_b(2) * 2^(-MID_BITS)
+//   - M_LOGB_2_LO : low part of -log_b(2) * 2^(-MID_BITS)
+//   - EXP_2_MID   : look up table for bit fields of 2^mid
+// Return:
+//   { 2^(hi + mid), lo }
+template <class Base>
+LIBC_INLINE static constexpr exp_b_reduc_t exp_b_range_reduc(float x) {
+  double xd = static_cast<double>(x);
+  // kd = round((hi + mid) * log2(b) * 2^MID_BITS)
+  double kd = fputil::nearest_integer(Base::LOG2_B * xd);
+  // k = round((hi + mid) * log2(b) * 2^MID_BITS)
+  int k = static_cast<int>(kd);
+  // hi = floor(kd * 2^(-MID_BITS))
+  // exp_hi = shift hi to the exponent field of double precision.
+  uint64_t exp_hi = static_cast<uint64_t>(k >> Base::MID_BITS)
+                    << fputil::FPBits<double>::FRACTION_LEN;
+  // mh = 2^hi * 2^mid
+  // mh_bits = bit field of mh
+  uint64_t mh_bits = Base::EXP_2_MID[k & Base::MID_MASK] + exp_hi;
+  double mh = fputil::FPBits<double>(mh_bits).get_val();
+  // dx = lo = x - (hi + mid) * log(2)
+  double dx = fputil::multiply_add(
+      kd, Base::M_LOGB_2_LO, fputil::multiply_add(kd, Base::M_LOGB_2_HI, xd));
+  return {mh, dx};
+}
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP_FLOAT_CONSTANTS_H

libc/src/math/generic/CMakeLists.txt

@@ -358,7 +358,6 @@ add_entrypoint_object(
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.except_value_utils
     libc.src.__support.FPUtil.fma
-    libc.src.__support.FPUtil.multiply_add
     libc.src.__support.FPUtil.polyeval
     libc.src.__support.macros.optimization
 )
@@ -448,7 +447,6 @@ add_entrypoint_object(
     libc.src.__support.FPUtil.fenv_impl
     libc.src.__support.FPUtil.fp_bits
     libc.src.__support.FPUtil.fma
-    libc.src.__support.FPUtil.multiply_add
     libc.src.__support.FPUtil.polyeval
     libc.src.__support.FPUtil.rounding_mode
     libc.src.__support.macros.optimization
@@ -1461,29 +1459,15 @@ add_entrypoint_object(
     libc.src.errno.errno
 )
 
-add_header_library(
-  exp10f_impl
-  HDRS
-    exp10f_impl.h
-  DEPENDS
-    .explogxf
-    libc.src.__support.FPUtil.fenv_impl
-    libc.src.__support.FPUtil.fp_bits
-    libc.src.__support.FPUtil.multiply_add
-    libc.src.__support.FPUtil.rounding_mode
-    libc.src.__support.macros.optimization
-    libc.src.__support.common
-    libc.src.errno.errno
-)
-
 add_entrypoint_object(
   exp10f
   SRCS
     exp10f.cpp
   HDRS
     ../exp10f.h
   DEPENDS
-    .exp10f_impl
+    libc.src.__support.math.exp10f
+    libc.src.errno.errno
 )
 
 add_entrypoint_object(
@@ -1620,17 +1604,15 @@ add_entrypoint_object(
     ../powf.h
   DEPENDS
     .common_constants
-    .exp10f_impl
     .exp2f_impl
     .explogxf
+    libc.src.__support.math.exp10f
     libc.src.__support.CPP.bit
-    libc.src.__support.CPP.optional
     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.sqrt
     libc.src.__support.FPUtil.triple_double
     libc.src.__support.macros.optimization
@@ -3792,13 +3774,9 @@ add_object_library(
     explogxf.cpp
   DEPENDS
     .common_constants
-    libc.src.__support.FPUtil.basic_operations
-    libc.src.__support.FPUtil.fenv_impl
-    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.__support.math.exp10f_utils
+    libc.src.__support.macros.properties.cpu_features
     libc.src.errno.errno
 )
 
@@ -3981,6 +3959,7 @@ add_entrypoint_object(
   DEPENDS
     .explogxf
     libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.fenv_impl
     libc.src.__support.macros.optimization
 )
 

libc/src/math/generic/atanhf.cpp

@@ -7,6 +7,7 @@
 //===----------------------------------------------------------------------===//
 
 #include "src/math/atanhf.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
 #include "src/__support/FPUtil/FPBits.h"
 #include "src/__support/macros/config.h"
 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY

libc/src/math/generic/coshf.cpp

@@ -7,8 +7,8 @@
 //===----------------------------------------------------------------------===//
 
 #include "src/math/coshf.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
 #include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/multiply_add.h"
 #include "src/__support/FPUtil/rounding_mode.h"
 #include "src/__support/macros/config.h"
 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY