[libc-commits] [libc] [libc][math] Add shared functions to check exceptions for exp* functions. (PR #202503)

[Hubert Tong via libc-commits]

================
@@ -0,0 +1,84 @@
+//===-- Check exceptions for exp functions ----------------------*- 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_CHECK_EXP_EXCEPTIONS_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_CHECK_EXP_EXCEPTIONS_H
+
+#include "hdr/fenv_macros.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+namespace check {
+
+namespace exp_internal {
+
+template <typename T> struct Bounds;
+
+template <> struct Bounds<float> {
+  // Smallest value that will cause overflow, generated from Sollya:
+  // > float_max = 2^127 * (2 - 2^-23);
+  // > upper = round(log(float_max), SG, RU);
+  // > printfloat(upper);
+  static constexpr float UPPER = 0x1.62e43p6f;
+  static constexpr uint32_t UPPER_BITS = 0x42b1'7218;
+  // Largest value that will cause underflow, generated from Sollya:
+  // > float_min = 2^-126;
+  // > lower = round(log(float_min), SG, RD);
+  // > printfloat(lower);
+  static constexpr float LOWER = -0x1.5d58ap6f;
+  static constexpr uint32_t LOWER_BITS = 0xc2ae'ac50;
+};
+
+template <> struct Bounds<double> {
+  // Smallest value that will cause overflow, generated from Sollya:
+  // > double_max = 2^1023 * (2 - 2^-52);
+  // > upper = round(log(double_max), D, RU);
+  // > printdouble(upper);
+  static constexpr double UPPER = 0x1.62e42fefa39fp9;
+  static constexpr uint64_t UPPER_BITS = 0x4086'2e42'fefa'39f0;
+  // Largest value that will cause underflow, generated from Sollya:
+  // > double_min = 2^-1022;
+  // > lower = round(log(double_min), D, RD);
+  // > printfloat(lower);
+  static constexpr double LOWER = -0x1.6232bdd7abcd3p9;
+  static constexpr uint64_t LOWER_BITS = 0xc086'232b'dd7a'bcd3;
+};
+
+} // namespace exp_internal
+
+template <typename T> LIBC_INLINE int exp_exceptions(T x, int rounding_mode) {
+  using FPBits = typename fputil::FPBits<T>;
+  using StorageType = typename FPBits::StorageType;
+
+  FPBits x_bits(x);
+  if (x_bits.is_signaling_nan())
+    return FE_INVALID;
+  if (x_bits.is_inf_or_nan() || x_bits.is_zero())
+    return 0;
+  StorageType x_u = x_bits.uintval();
+  if (x_u >= exp_internal::Bounds<T>::UPPER_BITS && x_bits.is_pos())
+    return (rounding_mode == FE_TONEAREST || rounding_mode == FE_UPWARD)
----------------
hubert-reinterpretcast wrote:

> In this example, the result is overflow with `FE_UPWARD` but not overflow with `FE_TONEAREST` because one is resulted in Inf, and the other is finite?

That is completely consistent with what I have been saying though.

Where infinity is an option, if a large result rounds to a finite value under `FE_TONEAREST`, then (by definition) the error between the finite result value and the true value is at most 0.5ulp of the true value.

Rounding from a finite true value to infinity has an error greater than 0.5ulp.

https://github.com/llvm/llvm-project/pull/202503