[libc-commits] [libc] Add sinf16 function (PR #116674)

[via libc-commits]

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@@ -0,0 +1,106 @@
+//===-- Half-precision sin(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/sinf16.h"
+#include "hdr/errno_macros.h"
+#include "hdr/fenv_macros.h"
+#include "sincosf16_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+constexpr size_t N_EXCEPTS = 4;
+
+constexpr fputil::ExceptValues<float16, N_EXCEPTS> SINF16_EXCEPTS{{
+    // (input, RZ output, RU offset, RD offset, RN offset)
+    {0x2b45, 0x2b43, 1, 0, 1},
+    {0x585c, 0x3ba3, 1, 0, 1},
+    {0x5cb0, 0xbbff, 0, 1, 0},
+    {0x51f5, 0xb80f, 0, 1, 0},
+}};
+
+LLVM_LIBC_FUNCTION(float16, sinf16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits xbits(x);
+
+  uint16_t x_u = xbits.uintval();
+  uint16_t x_abs = x_u & 0x7fff;
+  float xf = x;
+
+  // Range reduction:
+  // For |x| > pi/32, we perform range reduction as follows:
+  // Find k and y such that:
+  //   x = (k + y) * pi/32
+  //   k is an integer, |y| < 0.5
+  //
+  // This is done by performing:
+  //   k = round(x * 32/pi)
+  //   y = x * 32/pi - k
+  //
+  // Once k and y are computed, we then deduce the answer by the sine of sum
+  // formula:
+  //   sin(x) = sin((k + y) * pi/32)
+  //   	      = sin(k * pi/32) * cos(y * pi/32) +
+  //   	        sin(y * pi/32) * cos(k * pi/32)
+
+  // Handle exceptional values
+  if (LIBC_UNLIKELY(x_abs == 0x585c || x_abs == 0x5cb0 || x_abs == 0x51f5 ||
+                    x_abs == 0x2b45)) {
+    bool x_sign = x_u >> 15;
+    if (auto r = SINF16_EXCEPTS.lookup_odd(x_abs, x_sign);
+        LIBC_UNLIKELY(r.has_value()))
+      return r.value();
+  }
+
+  // Exhaustive tests show that for |x| <= 0x13d0, 1ULP rounding errors occur.
+  // To fix this, the following apply:
+  // - When x >= 0, and rounding upward, sin(x) == x.
+  // - When x < 0, and rounding downward, sin(x) == x.
+  // - When x < 0, and rounding upward, sin(x) == (x - 1ULP)
----------------
overmighty wrote:

Nit: I think writing what `0x13d0` corresponds to in hex float notation would be more helpful, and each "When ..., sin(x) = ..." comment should be put right above the corresponding `if` statement.

https://github.com/llvm/llvm-project/pull/116674