[libc-commits] [libc] [libc][math] Implement double precision cos correctly rounded to all rounding modes. (PR #96591)

[via libc-commits]

================
@@ -0,0 +1,197 @@
+//===-- Double-precision cos 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/cos.h"
+#include "hdr/errno_macros.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/dyadic_float.h"
+#include "src/__support/FPUtil/except_value_utils.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
+#include "src/math/generic/sincos_eval.h"
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+#include "range_reduction_double_fma.h"
+
+using LIBC_NAMESPACE::fma::FAST_PASS_EXPONENT;
+using LIBC_NAMESPACE::fma::ONE_TWENTY_EIGHT_OVER_PI;
+using LIBC_NAMESPACE::fma::range_reduction_small;
+using LIBC_NAMESPACE::fma::SIN_K_PI_OVER_128;
+
+LIBC_INLINE constexpr bool NO_FMA = false;
+#else
+#include "range_reduction_double_nofma.h"
+
+using LIBC_NAMESPACE::nofma::FAST_PASS_EXPONENT;
+using LIBC_NAMESPACE::nofma::ONE_TWENTY_EIGHT_OVER_PI;
+using LIBC_NAMESPACE::nofma::range_reduction_small;
+using LIBC_NAMESPACE::nofma::SIN_K_PI_OVER_128;
+
+LIBC_INLINE constexpr bool NO_FMA = true;
+#endif // LIBC_TARGET_CPU_HAS_FMA
+
+// TODO: We might be able to improve the performance of large range reduction of
+// non-FMA targets further by operating directly on 25-bit chunks of 128/pi and
+// pre-split SIN_K_PI_OVER_128, but that might double the memory footprint of
+// those lookup table.
+#include "range_reduction_double_common.h"
+
+#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0)
+#define LIBC_MATH_COS_SKIP_ACCURATE_PASS
+#endif
+
+namespace LIBC_NAMESPACE {
+
+using DoubleDouble = fputil::DoubleDouble;
+using Float128 = typename fputil::DyadicFloat<128>;
+
+LLVM_LIBC_FUNCTION(double, cos, (double x)) {
+  using FPBits = typename fputil::FPBits<double>;
+  FPBits xbits(x);
+
+  uint16_t x_e = xbits.get_biased_exponent();
+
+  DoubleDouble y;
+  unsigned k;
+  generic::LargeRangeReduction<NO_FMA> range_reduction_large;
+
+  // |x| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA)
+  if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
+    // |x| < 2^-27
+    if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) {
+      // Signed zeros.
+      if (LIBC_UNLIKELY(x == 0.0))
+        return 1.0;
+
+      // For |x| < 2^-27, |cos(x) - 1| < |x|^2/2 < 2^-54 = ulp(1 - 2^-53)/2.
+      return fputil::round_result_slightly_down(1.0);
+    }
+
+    // // Small range reduction.
+    k = range_reduction_small(x, y);
+  } else {
+    // Inf or NaN
+    if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
+      // sin(+-Inf) = NaN
+      if (xbits.get_mantissa() == 0) {
+        fputil::set_errno_if_required(EDOM);
+        fputil::raise_except_if_required(FE_INVALID);
+      }
+      return x + FPBits::quiet_nan().get_val();
+    }
+
+    // Large range reduction.
+    k = range_reduction_large.compute_high_part(x);
+    y = range_reduction_large.fast();
+  }
+
+  DoubleDouble sin_y, cos_y;
+
+  generic::sincos_eval(y, sin_y, cos_y);
+
+  // Look up sin(k * pi/128) and cos(k * pi/128)
+  // Memory saving versions:
+
+  // Use 128-entry table instead:
+  // DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 127];
+  // uint64_t sin_s = static_cast<uint64_t>((k + 128) & 128) << (63 - 7);
+  // sin_k.hi = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
+  // sin_k.lo = FPBits(FPBits(sin_k.hi).uintval() ^ sin_s).get_val();
+  // DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 127];
+  // uint64_t cos_s = static_cast<uint64_t>((k + 64) & 128) << (63 - 7);
+  // cos_k.hi = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
+  // cos_k.lo = FPBits(FPBits(cos_k.hi).uintval() ^ cos_s).get_val();
+
+  // Use 64-entry table instead:
+  // auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
+  //   unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
+  //   DoubleDouble ans = SIN_K_PI_OVER_128[idx];
+  //   if (kk & 128) {
+  //     ans.hi = -ans.hi;
+  //     ans.lo = -ans.lo;
+  //   }
+  //   return ans;
+  // };
+  // DoubleDouble sin_k = get_idx_dd(k + 128);
+  // DoubleDouble cos_k = get_idx_dd(k + 64);
+
+  // Fast look up version, but needs 256-entry table.
+  // -sin(k * pi/128) = sin((k + 128) * pi/128)
+  // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
+  DoubleDouble msin_k = SIN_K_PI_OVER_128[(k + 128) & 255];
+  DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
----------------
lntue wrote:

`SIN_K_PI_OVER_128` is defined in `range_reduction_fma.h` and `range_reduction_nofma.h`, and both definitions are of size 256.  `SIN_K_PI_OVER_128_F128` is 65 elements, and it's only accessed in `Float128` pass, not in `DoubleDouble` pass.

https://github.com/llvm/llvm-project/pull/96591