[llvm-branch-commits] [libc] [libc][math][c23] Add exp10m1f16 C23 math function (PR #105706)

[via llvm-branch-commits]

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@@ -0,0 +1,162 @@
+//===-- Half-precision 10^x - 1 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/exp10m1f16.h"
+#include "expxf16.h"
+#include "hdr/errno_macros.h"
+#include "hdr/fenv_macros.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/except_value_utils.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"
+#include "src/__support/macros/properties/cpu_features.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+static constexpr fputil::ExceptValues<float16, 3> EXP10M1F16_EXCEPTS_LO = {{
+    // (input, RZ output, RU offset, RD offset, RN offset)
+    // x = 0x1.5c4p-4, exp10m1f16(x) = 0x1.bacp-3 (RZ)
+    {0x2d71U, 0x32ebU, 1U, 0U, 0U},
+    // x = -0x1.5ep-13, exp10m1f16(x) = -0x1.92cp-12 (RZ)
+    {0x8978U, 0x8e4bU, 0U, 1U, 0U},
+    // x = -0x1.e2p-10, exp10m1f16(x) = -0x1.14cp-8 (RZ)
+    {0x9788U, 0x9c53U, 0U, 1U, 0U},
+}};
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+static constexpr size_t N_EXP10M1F16_EXCEPTS_HI = 3;
+#else
+static constexpr size_t N_EXP10M1F16_EXCEPTS_HI = 6;
+#endif
+
+static constexpr fputil::ExceptValues<float16, N_EXP10M1F16_EXCEPTS_HI>
+    EXP10M1F16_EXCEPTS_HI = {{
+        // (input, RZ output, RU offset, RD offset, RN offset)
+        // x = 0x1.8f4p-2, exp10m1f16(x) = 0x1.744p+0 (RZ)
+        {0x363dU, 0x3dd1U, 1U, 0U, 0U},
+        // x = 0x1.95cp-2, exp10m1f16(x) = 0x1.7d8p+0 (RZ)
+        {0x3657U, 0x3df6U, 1U, 0U, 0U},
+        // x = 0x1.d04p-2, exp10m1f16(x) = 0x1.d7p+0 (RZ)
+        {0x3741U, 0x3f5cU, 1U, 0U, 1U},
+#ifndef LIBC_TARGET_CPU_HAS_FMA
+        // x = 0x1.0cp+1, exp10m1f16(x) = 0x1.ec4p+6 (RZ)
+        {0x4030U, 0x57b1U, 1U, 0U, 1U},
+        // x = 0x1.1b8p+1, exp10m1f16(x) = 0x1.45cp+7 (RZ)
+        {0x406eU, 0x5917U, 1U, 0U, 1U},
+        // x = 0x1.2f4p+2, exp10m1f16(x) = 0x1.ab8p+15 (RZ)
+        {0x44bdU, 0x7aaeU, 1U, 0U, 1U},
+#endif
+    }};
+
+LLVM_LIBC_FUNCTION(float16, exp10m1f16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits x_bits(x);
+
+  uint16_t x_u = x_bits.uintval();
+  uint16_t x_abs = x_u & 0x7fffU;
+
+  // When |x| <= 2^(-3), or |x| >= 11 * log10(2), or x is NaN.
+  if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x429fU)) {
+    // exp10m1(NaN) = NaN
+    if (x_bits.is_nan()) {
+      if (x_bits.is_signaling_nan()) {
+        fputil::raise_except_if_required(FE_INVALID);
+        return FPBits::quiet_nan().get_val();
+      }
+
+      return x;
+    }
+
+    // When x >= 16 * log10(2).
+    if (x_u >= 0x44d1U && x_bits.is_pos()) {
+      // exp10m1(+inf) = +inf
+      if (x_bits.is_inf())
+        return FPBits::inf().get_val();
+
+      switch (fputil::quick_get_round()) {
+      case FE_TONEAREST:
+      case FE_UPWARD:
+        fputil::set_errno_if_required(ERANGE);
+        fputil::raise_except_if_required(FE_OVERFLOW | FE_INEXACT);
+        return FPBits::inf().get_val();
+      default:
+        return FPBits::max_normal().get_val();
+      }
+    }
+
+    // When x < -11 * log10(2).
+    if (x_u > 0xc29fU) {
+      // exp10m1(-inf) = -1
+      if (x_bits.is_inf())
+        return FPBits::one(Sign::NEG).get_val();
+
+      // When x >= -0x1.ce4p+1, round(10^x - 1, HP, RN) = -0x1.ffcp-1.
+      if (x_u <= 0xc339U) {
+        return fputil::round_result_slightly_down(
+            static_cast<float16>(-0x1.ffcp-1));
+      }
+
+      // When x < -0x1.ce4p+1, round(10^x - 1, HP, RN) = -1.
+      switch (fputil::quick_get_round()) {
+      case FE_TONEAREST:
+      case FE_DOWNWARD:
+        return FPBits::one(Sign::NEG).get_val();
+      default:
+        return static_cast<float16>(-0x1.ffcp-1);
+      }
+    }
+
+    // When |x| <= 2^(-3).
+    if (x_abs <= 0x3000U) {
+      if (auto r = EXP10M1F16_EXCEPTS_LO.lookup(x_u);
+          LIBC_UNLIKELY(r.has_value()))
+        return r.value();
+
+      float xf = x;
+      // Degree-5 minimax polynomial generated by Sollya with the following
+      // commands:
+      //   > display = hexadecimal;
+      //   > P = fpminimax((10^x - 1)/x, 4, [|SG...|], [-2^-3, 2^-3]);
+      //   > x * P;
+      return static_cast<float16>(
+          xf * fputil::polyeval(xf, 0x1.26bb1cp+1f, 0x1.5351c8p+1f,
+                                0x1.04704p+1f, 0x1.2ce084p+0f, 0x1.14a6bep-1f));
+    }
+  }
+
+  // When x is 1, 2, or 3. These are hard-to-round cases with exact results.
+  // 10^4 - 1 = 9'999 is not exactly representable as a float16, but luckily the
----------------
lntue wrote:

It's actually not luck, because the relative error of `9'999` to the nearest half-precision is:
```
> (9999 - round(9999, HP, RN)) / 9999;
0x1.a37...p-14
```
while the relative error of the relative errors from the approximation is:
```
> dirtyinfnorm(((10^x - 1) - x*P)/(10^x - 1), [-2^-3, 2^-3]);
0x1.9d5...p-23
```

https://github.com/llvm/llvm-project/pull/105706