[libc-commits] [libc] [libc][math][c23] Implemented sinpif function correctly rounded for all rounding modes. (PR #97149)

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+//===-- Single-precision sinpif 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/sinpif.h"
+#include "sincosf_utils.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(float, sinpif, (float x)) {
+  using FPBits = typename fputil::FPBits<float>;
+  FPBits xbits(x);
+
+  uint32_t x_u = xbits.uintval();
+  uint32_t x_abs = x_u & 0x7fff'ffffU;
+  double xd = static_cast<double>(x);
+
+  // Range reduction:
+  // For |x| > pi/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
+  // For small range (|x| < 2^45 when FMA instructions are available, 2^22
+  // otherwise), 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 sine of sum
+  // formula:
+  //   sin(x * pi) = sin((k + y)*pi/32)
+  //          = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
+  // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 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.
+
+  // |x| <= 1/16
+  if (LIBC_UNLIKELY(x_abs <= 0x3d80'0000U)) {
+
+    if (LIBC_UNLIKELY(x_abs < 0x33CD'01D7U)) {
+      if (LIBC_UNLIKELY(x_abs == 0U)) {
+        // For signed zeros.
+        return x;
+      }
+
+      // For very small values we can approximate sinpi(x) with x * pi
+      // An exhaustive test shows that this is accurate for |x| < 9.546391 ×
+      // 10-8
+      double xdpi = xd * 0x1.921fb54442d18p1;
+      return static_cast<float>(xdpi);
+    }
+
+    // |x| < 1/16.
+    double xsq = xd * xd;
+
+    // Degree-9 polynomial approximation:
+    //   sinpi(x) ~ x + a_3 x^3 + a_5 x^5 + a_7 x^7 + a_9 x^9
+    //          = x (1 + a_3 x^2 + ... + a_9 x^8)
+    //          = x * P(x^2)
+    // generated by Sollya with the following commands:
+    // > display = hexadecimal;
+    // > Q = fpminimax(sin(pi * x)/x, [|0, 2, 4, 6, 8|], [|D...|], [0, 1/16]);
+    double result = fputil::polyeval(
+        xsq, 0x1.921fb54442d18p1, -0x1.4abbce625bbf2p2, 0x1.466bc675e116ap1,
+        -0x1.32d2c0b62d41cp-1, 0x1.501ec4497cb7dp-4);
+    return static_cast<float>(xd * result);
+  }
+
+  if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
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lntue wrote:

I think we can speed thing up a bit by doing quick return for `|x| >= 2^23`, since it will then always be an integer.

https://github.com/llvm/llvm-project/pull/97149