[libc-commits] [libc] [llvm] [libc][math] Add tgammabf16 math support for bfloat16. (PR #208689)

[via libc-commits]

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+//===-- Implementation header for tgammabf16 --------------------*- 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_TGAMMABF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_TGAMMABF16_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/bfloat16.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h"
+#include "src/__support/math/exp.h"
+#include "src/__support/math/log.h"
+#include "src/__support/math/sin.h"
+
+namespace LIBC_NAMESPACE_DECL {
+namespace math {
+
+namespace tgammabf16_internal {
+
+LIBC_INLINE_VAR constexpr double PI = 0x1.921fb54442d18p+1;
+LIBC_INLINE_VAR constexpr double LOG_SQRT_2_PI = 0x1.d67f1c864beb5p-1;
+
+// Paul Godfrey's exact Lanczos approximation coefficients (g=7, n=9)
+// Reference: "A note on the computation of the convergent Lanczos complex Gamma
+// approximation" by Paul Godfrey (2001).
+// Original:
+// https://web.archive.org/web/20060915161115/http://my.fit.edu/~gabdo/gamma.txt
+// Mirror: http://www.mrob.com/pub/ries/lanczos-gamma.html
+LIBC_INLINE_VAR constexpr double LANCZOS_COEFFS[9] = {
+    0x1.ffffffffff950p-1,  0x1.52429b6c30b05p+9,  -0x1.3ac8e8ed4171bp+10,
+    0x1.81a9661d3b4d8p+9,  -0x1.613ae51a32f5dp+7, 0x1.903c27f8b9c81p+3,
+    -0x1.1bcb2992b2855p-3, 0x1.4f0514e4e324fp-17, 0x1.435508f3faeefp-23};
+
+} // namespace tgammabf16_internal
+
+LIBC_INLINE bfloat16 tgammabf16(bfloat16 x) {
+  using FPBits = fputil::FPBits<bfloat16>;
+  using namespace tgammabf16_internal;
+
+  FPBits xbits(x);
+
+  if (LIBC_UNLIKELY(xbits.is_nan())) {
+    if (xbits.is_signaling_nan()) {
+      fputil::raise_except_if_required(FE_INVALID);
+      return FPBits::quiet_nan().get_val();
+    }
+    return x;
+  }
+
+  if (LIBC_UNLIKELY(xbits.is_inf())) {
+    if (xbits.is_pos())
+      return x;
+    fputil::set_errno_if_required(EDOM);
+    fputil::raise_except_if_required(FE_INVALID);
+    return FPBits::quiet_nan().get_val();
+  }
+
+  if (LIBC_UNLIKELY(xbits.is_zero())) {
+    fputil::set_errno_if_required(ERANGE);
+    fputil::raise_except_if_required(FE_DIVBYZERO);
+    return FPBits::inf(xbits.sign()).get_val();
+  }
+
+  if (LIBC_UNLIKELY(xbits.is_neg())) {
+    uint16_t x_abs = xbits.uintval() & 0x7fffU;
+    int biased_exp = x_abs >> FPBits::FRACTION_LEN;
+    if (biased_exp >= FPBits::EXP_BIAS) {
+      int e = biased_exp - FPBits::EXP_BIAS;
+      if (e >= FPBits::FRACTION_LEN ||
+          (xbits.get_mantissa() &
+           static_cast<uint16_t>((1U << (FPBits::FRACTION_LEN - e)) - 1U)) ==
+              0U) {
+        fputil::set_errno_if_required(EDOM);
+        fputil::raise_except_if_required(FE_INVALID);
+        return FPBits::quiet_nan().get_val();
+      }
+    }
+  }
+
+  float xf = static_cast<float>(x);
+
+  // Fast path for exact positive integers
+  if (xf > 0.0f && xf <= 35.0f) {
+    int n = static_cast<int>(xf);
+    if (xf == static_cast<float>(n)) {
+      double res = 1.0;
+      for (int i = 1; i < n; ++i)
+        res *= i;
+      return fputil::cast<bfloat16>(res);
+    }
+  }
+
+  bool reflection = xbits.is_neg();
+  bool divide_by_x = false;
+
+  double xd = static_cast<double>(xf);
+  double x_eval = xd;
+  double res;
+
+  // Fast path for tiny positive inputs to prevent exact-boundary overshoots
+  // For tiny x, Gamma(x) ~= 1/x - gamma
+  if (LIBC_UNLIKELY(xf > 0.0f && xf < 0x1.0p-8f)) {
+    res = (1.0 / xd) - 0x1.2788cfc6fb619p-1;
----------------
Sukumarsawant wrote:

```
    res = (1.0 / xd) - 0x1.2788cfc6fb619p-1;
```
Add how its generated .
Also Add some info or define what it is (as a variable), if possible for better understanding

https://github.com/llvm/llvm-project/pull/208689