[libc-commits] [libc] [libc][C23][math] Implement cospif function correctly rounded for all rounding modes (PR #97464)

[via libc-commits]

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+//===-- Single-precision cospi 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/cospif.h"
+#include "sincosf_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h"            // LIBC_UNLIKELY
+#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(float, cospif, (float x)) {
+  using FPBits = typename fputil::FPBits<float>;
+
+  FPBits xbits(x);
+  xbits.set_sign(Sign::POS);
+
+  uint32_t x_abs = xbits.uintval();
+  double xd = static_cast<double>(xbits.get_val());
+
+  // Range reduction:
+  // For |x| > 1/32, we perform range reduction as follows:
+  // Find k and y such that:
+  //   x = (k + y) * 1/32
+  //   k is an integer
+  //   |y| < 0.5
+  //
+  // This is done by performing:
+  //   k = round(x * 32)
+  //   y = x * 32 - k
+  //
+  // Once k and y are computed, we then deduce the answer by the cosine of sum
+  // formula:
+  //   cospi(x) = cos((k + y)*pi/32)
+  //          = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
+  // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..63 are precomputed
+  // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
+  // computed using degree-7 and degree-6 minimax polynomials generated by
+  // Sollya respectively.
+
+  // The exhautive test passes for smaller values
+  if (LIBC_UNLIKELY(x_abs < 0x38A2'F984U)) {
+
+#if defined(LIBC_TARGET_CPU_HAS_FMA)
+    return fputil::multiply_add(xbits.get_val(), -0x1.0p-25f, 1.0f);
+#else
+    return static_cast<float>(fputil::multiply_add(xd, -0x1.0p-25, 1.0));
+#endif // LIBC_TARGET_CPU_HAS_FMA
+  }
+
+  // Numbers greater or equal to 2^23 are always integers or NaN
+  if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {
+
+    if (LIBC_UNLIKELY(x_abs < 0x4B80'0000)) {
+      return (x_abs & 0x1) ? -1.0f : 1.0f;
+    }
+
+    // x is inf or nan.
+    if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
+      if (x_abs == 0x7f80'0000U) {
+        fputil::set_errno_if_required(EDOM);
+        fputil::raise_except_if_required(FE_INVALID);
+      }
+      return x + FPBits::quiet_nan().get_val();
+    }
+
+    return 1.0f;
+  }
+
+  // Combine the results with the sine of sum formula:
+  //   cos(pi * x) = cos((k + y)*pi/32)
+  //          = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
+  //          = (cosm1_y + 1) * cos_k - sin_y * sin_k
+  //          = (cosm1_y * cos_k + cos_k) - sin_y * sin_k
+  double sin_k, cos_k, sin_y, cosm1_y;
+
+  sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y);
+
----------------
lntue wrote:

Adding a similar test to your `sinpif` should fix the signed zero issue:
```
  if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0))
    return FPBits::zero(xbits.sign()).get_val();
```

https://github.com/llvm/llvm-project/pull/97464