src/math/generic/sincosf_utils.h

//===-- Collection of utils for cosf/sinf/sincosf ---------------*- 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_MATH_SINCOSF_UTILS_H
#define LLVM_LIBC_SRC_MATH_SINCOSF_UTILS_H

#include "math_utils.h"

#include <stdint.h>

namespace __llvm_libc {

// 2PI * 2^-64.
static const double pi63 = as_double(0x3c1921fb54442d18);
// PI / 4.
static const double pio4 = as_double(0x3fe921fb54442d18);

// The constants and polynomials for sine and cosine.
typedef struct {
  double sign[4];            // Sign of sine in quadrants 0..3.
  double hpi_inv;            // 2 / PI ( * 2^24 ).
  double hpi;                // PI / 2.
  double c0, c1, c2, c3, c4; // Cosine polynomial.
  double s1, s2, s3;         // Sine polynomial.
} sincos_t;

// Polynomial data (the cosine polynomial is negated in the 2nd entry).
extern const sincos_t __sincosf_table[2];

// Table with 4/PI to 192 bit precision.
extern const uint32_t __inv_pio4[];

// Top 12 bits of the float representation with the sign bit cleared.
static inline uint32_t abstop12(float x) {
  return (as_uint32_bits(x) >> 20) & 0x7ff;
}

// Compute the sine and cosine of inputs X and X2 (X squared), using the
// polynomial P and store the results in SINP and COSP. N is the quadrant,
// if odd the cosine and sine polynomials are swapped.
static inline void sincosf_poly(double x, double x2, const sincos_t *p, int n,
                                float *sinp, float *cosp) {
  double x3, x4, x5, x6, s, c, c1, c2, s1;

  x4 = x2 * x2;
  x3 = x2 * x;
  c2 = p->c3 + x2 * p->c4;
  s1 = p->s2 + x2 * p->s3;

  // Swap sin/cos result based on quadrant.
  float *tmp = (n & 1 ? cosp : sinp);
  cosp = (n & 1 ? sinp : cosp);
  sinp = tmp;

  c1 = p->c0 + x2 * p->c1;
  x5 = x3 * x2;
  x6 = x4 * x2;

  s = x + x3 * p->s1;
  c = c1 + x4 * p->c2;

  *sinp = s + x5 * s1;
  *cosp = c + x6 * c2;
}

// Return the sine of inputs X and X2 (X squared) using the polynomial P.
// N is the quadrant, and if odd the cosine polynomial is used.
static inline float sinf_poly(double x, double x2, const sincos_t *p, int n) {
  double x3, x4, x6, x7, s, c, c1, c2, s1;

  if ((n & 1) == 0) {
    x3 = x * x2;
    s1 = p->s2 + x2 * p->s3;

    x7 = x3 * x2;
    s = x + x3 * p->s1;

    return s + x7 * s1;
  } else {
    x4 = x2 * x2;
    c2 = p->c3 + x2 * p->c4;
    c1 = p->c0 + x2 * p->c1;

    x6 = x4 * x2;
    c = c1 + x4 * p->c2;

    return c + x6 * c2;
  }
}

// Fast range reduction using single multiply-subtract. Return the modulo of
// X as a value between -PI/4 and PI/4 and store the quadrant in NP.
// The values for PI/2 and 2/PI are accessed via P. Since PI/2 as a double
// is accurate to 55 bits and the worst-case cancellation happens at 6 * PI/4,
// the result is accurate for |X| <= 120.0.
static inline double reduce_fast(double x, const sincos_t *p, int *np) {
  double r;
  // Use scaled float to int conversion with explicit rounding.
  // hpi_inv is prescaled by 2^24 so the quadrant ends up in bits 24..31.
  // This avoids inaccuracies introduced by truncating negative values.
  r = x * p->hpi_inv;
  int n = ((int32_t)r + 0x800000) >> 24;
  *np = n;
  return x - n * p->hpi;
}

// Reduce the range of XI to a multiple of PI/2 using fast integer arithmetic.
// XI is a reinterpreted float and must be >= 2.0f (the sign bit is ignored).
// Return the modulo between -PI/4 and PI/4 and store the quadrant in NP.
// Reduction uses a table of 4/PI with 192 bits of precision. A 32x96->128 bit
// multiply computes the exact 2.62-bit fixed-point modulo. Since the result
// can have at most 29 leading zeros after the binary point, the double
// precision result is accurate to 33 bits.
static inline double reduce_large(uint32_t xi, int *np) {
  const uint32_t *arr = &__inv_pio4[(xi >> 26) & 15];
  int shift = (xi >> 23) & 7;
  uint64_t n, res0, res1, res2;

  xi = (xi & 0xffffff) | 0x800000;
  xi <<= shift;

  res0 = xi * arr[0];
  res1 = (uint64_t)xi * arr[4];
  res2 = (uint64_t)xi * arr[8];
  res0 = (res2 >> 32) | (res0 << 32);
  res0 += res1;

  n = (res0 + (1ULL << 61)) >> 62;
  res0 -= n << 62;
  double x = (int64_t)res0;
  *np = n;
  return x * pi63;
}

} // namespace __llvm_libc

#endif // LLVM_LIBC_SRC_MATH_SINCOSF_UTILS_H