utun2/lib/libopus/celt/mathops.c

/* Copyright (c) 2002-2008 Jean-Marc Valin
   Copyright (c) 2007-2008 CSIRO
   Copyright (c) 2007-2009 Xiph.Org Foundation
   Copyright (c) 2024 Arm Limited
   Written by Jean-Marc Valin */
/**
   @file mathops.h
   @brief Various math functions
*/
/*
   Redistribution and use in source and binary forms, with or without
   modification, are permitted provided that the following conditions
   are met:

   - Redistributions of source code must retain the above copyright
   notice, this list of conditions and the following disclaimer.

   - Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in the
   documentation and/or other materials provided with the distribution.

   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
   A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
   OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
   EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
   PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include "float_cast.h"
#include "mathops.h"

/*Compute floor(sqrt(_val)) with exact arithmetic.
  _val must be greater than 0.
  This has been tested on all possible 32-bit inputs greater than 0.*/
unsigned isqrt32(opus_uint32 _val){
  unsigned b;
  unsigned g;
  int      bshift;
  /*Uses the second method from
     http://www.azillionmonkeys.com/qed/sqroot.html
    The main idea is to search for the largest binary digit b such that
     (g+b)*(g+b) <= _val, and add it to the solution g.*/
  g=0;
  bshift=(EC_ILOG(_val)-1)>>1;
  b=1U<<bshift;
  do{
    opus_uint32 t;
    t=(((opus_uint32)g<<1)+b)<<bshift;
    if(t<=_val){
      g+=b;
      _val-=t;
    }
    b>>=1;
    bshift--;
  }
  while(bshift>=0);
  return g;
}

#ifdef FIXED_POINT

opus_val32 frac_div32_q29(opus_val32 a, opus_val32 b)
{
   opus_val16 rcp;
   opus_val32 result, rem;
   int shift = celt_ilog2(b)-29;
   a = VSHR32(a,shift);
   b = VSHR32(b,shift);
   /* 16-bit reciprocal */
   rcp = ROUND16(celt_rcp(ROUND16(b,16)),3);
   result = MULT16_32_Q15(rcp, a);
   rem = PSHR32(a,2)-MULT32_32_Q31(result, b);
   result = ADD32(result, SHL32(MULT16_32_Q15(rcp, rem),2));
   return result;
}

opus_val32 frac_div32(opus_val32 a, opus_val32 b) {
   opus_val32 result = frac_div32_q29(a,b);
   if (result >= 536870912)       /*  2^29 */
      return 2147483647;          /*  2^31 - 1 */
   else if (result <= -536870912) /* -2^29 */
      return -2147483647;         /* -2^31 */
   else
      return SHL32(result, 2);
}

/** Reciprocal sqrt approximation in the range [0.25,1) (Q16 in, Q14 out) */
opus_val16 celt_rsqrt_norm(opus_val32 x)
{
   opus_val16 n;
   opus_val16 r;
   opus_val16 r2;
   opus_val16 y;
   /* Range of n is [-16384,32767] ([-0.5,1) in Q15). */
   n = x-32768;
   /* Get a rough initial guess for the root.
      The optimal minimax quadratic approximation (using relative error) is
       r = 1.437799046117536+n*(-0.823394375837328+n*0.4096419668459485).
      Coefficients here, and the final result r, are Q14.*/
   r = ADD16(23557, MULT16_16_Q15(n, ADD16(-13490, MULT16_16_Q15(n, 6713))));
   /* We want y = x*r*r-1 in Q15, but x is 32-bit Q16 and r is Q14.
      We can compute the result from n and r using Q15 multiplies with some
       adjustment, carefully done to avoid overflow.
      Range of y is [-1564,1594]. */
   r2 = MULT16_16_Q15(r, r);
   y = SHL16(SUB16(ADD16(MULT16_16_Q15(r2, n), r2), 16384), 1);
   /* Apply a 2nd-order Householder iteration: r += r*y*(y*0.375-0.5).
      This yields the Q14 reciprocal square root of the Q16 x, with a maximum
       relative error of 1.04956E-4, a (relative) RMSE of 2.80979E-5, and a
       peak absolute error of 2.26591/16384. */
   return ADD16(r, MULT16_16_Q15(r, MULT16_16_Q15(y,
              SUB16(MULT16_16_Q15(y, 12288), 16384))));
}

/** Reciprocal sqrt approximation in the range [0.25,1) (Q31 in, Q29 out) */
opus_val32 celt_rsqrt_norm32(opus_val32 x)
{
   opus_int32 tmp;
   /* Use the first-order Newton-Raphson method to refine the root estimate.
    * r = r * (1.5 - 0.5*x*r*r) */
   opus_int32 r_q29 = SHL32(celt_rsqrt_norm(SHR32(x, 31-16)), 15);
   /* Split evaluation in steps to avoid exploding macro expansion. */
   tmp = MULT32_32_Q31(r_q29, r_q29);
   tmp = MULT32_32_Q31(1073741824 /* Q31 */, tmp);
   tmp = MULT32_32_Q31(x, tmp);
   return SHL32(MULT32_32_Q31(r_q29, SUB32(201326592 /* Q27 */, tmp)), 4);
}

/** Sqrt approximation (QX input, QX/2 output) */
opus_val32 celt_sqrt(opus_val32 x)
{
   int k;
   opus_val16 n;
   opus_val32 rt;
   /* These coeffs are optimized in fixed-point to minimize both RMS and max error
      of sqrt(x) over .25<x<1 without exceeding 32767.
      The RMS error is 3.4e-5 and the max is 8.2e-5. */
   static const opus_val16 C[6] = {23171, 11574, -2901, 1592, -1002, 336};
   if (x==0)
      return 0;
   else if (x>=1073741824)
      return 32767;
   k = (celt_ilog2(x)>>1)-7;
   x = VSHR32(x, 2*k);
   n = x-32768;
   rt = ADD32(C[0], MULT16_16_Q15(n, ADD16(C[1], MULT16_16_Q15(n, ADD16(C[2],
              MULT16_16_Q15(n, ADD16(C[3], MULT16_16_Q15(n, ADD16(C[4], MULT16_16_Q15(n, (C[5])))))))))));
   rt = VSHR32(rt,7-k);
   return rt;
}

/* Perform fixed-point arithmetic to approximate the square root. When the input
 * is in Qx format, the output will be in Q(x/2 + 16) format. */
opus_val32 celt_sqrt32(opus_val32 x)
{
   int k;
   opus_int32 x_frac;
   if (x==0)
      return 0;
   else if (x>=1073741824)
      return 2147483647; /* 2^31 -1 */
   k = (celt_ilog2(x)>>1);
   x_frac = VSHR32(x, 2*(k-14)-1);
   x_frac = MULT32_32_Q31(celt_rsqrt_norm32(x_frac), x_frac);
   if (k < 12) return PSHR32(x_frac, 12-k);
   else return SHL32(x_frac, k-12);
}

#define L1 32767
#define L2 -7651
#define L3 8277
#define L4 -626

static OPUS_INLINE opus_val16 _celt_cos_pi_2(opus_val16 x)
{
   opus_val16 x2;

   x2 = MULT16_16_P15(x,x);
   return ADD16(1,MIN16(32766,ADD32(SUB16(L1,x2), MULT16_16_P15(x2, ADD32(L2, MULT16_16_P15(x2, ADD32(L3, MULT16_16_P15(L4, x2
                                                                                ))))))));
}

#undef L1
#undef L2
#undef L3
#undef L4

opus_val16 celt_cos_norm(opus_val32 x)
{
   x = x&0x0001ffff;
   if (x>SHL32(EXTEND32(1), 16))
      x = SUB32(SHL32(EXTEND32(1), 17),x);
   if (x&0x00007fff)
   {
      if (x<SHL32(EXTEND32(1), 15))
      {
         return _celt_cos_pi_2(EXTRACT16(x));
      } else {
         return NEG16(_celt_cos_pi_2(EXTRACT16(65536-x)));
      }
   } else {
      if (x&0x0000ffff)
         return 0;
      else if (x&0x0001ffff)
         return -32767;
      else
         return 32767;
   }
}

/* Calculates the cosine of (PI*0.5*x) where the input x ranges from -1 to 1 and
 * is in Q30 format. The output will also be in Q31 format. */
opus_val32 celt_cos_norm32(opus_val32 x)
{
   static const opus_val32 COS_NORM_COEFF_A0 = 134217720;   /* Q27 */
   static const opus_val32 COS_NORM_COEFF_A1 = -662336704;  /* Q29 */
   static const opus_val32 COS_NORM_COEFF_A2 = 544710848;   /* Q31 */
   static const opus_val32 COS_NORM_COEFF_A3 = -178761936;  /* Q33 */
   static const opus_val32 COS_NORM_COEFF_A4 = 29487206;    /* Q35 */
   opus_int32 x_sq_q29, tmp;
   /* The expected x is in the range of [-1.0f, 1.0f] */
   celt_sig_assert((x >= -1073741824) && (x <= 1073741824));
   /* Make cos(+/- pi/2) exactly zero. */
   if (ABS32(x) == 1<<30) return 0;
   x_sq_q29 = MULT32_32_Q31(x, x);
   /* Split evaluation in steps to avoid exploding macro expansion. */
   tmp = ADD32(COS_NORM_COEFF_A3, MULT32_32_Q31(x_sq_q29, COS_NORM_COEFF_A4));
   tmp = ADD32(COS_NORM_COEFF_A2, MULT32_32_Q31(x_sq_q29, tmp));
   tmp = ADD32(COS_NORM_COEFF_A1, MULT32_32_Q31(x_sq_q29, tmp));
   return SHL32(ADD32(COS_NORM_COEFF_A0, MULT32_32_Q31(x_sq_q29, tmp)), 4);
}

/* Computes a 16 bit approximate reciprocal (1/x) for a normalized Q15 input,
 * resulting in a Q15 output. */
opus_val16 celt_rcp_norm16(opus_val16 x)
{
   opus_val16 r;
   /* Start with a linear approximation:
      r = 1.8823529411764706-0.9411764705882353*n.
      The coefficients and the result are Q14 in the range [15420,30840].*/
   r = ADD16(30840, MULT16_16_Q15(-15420, x));
   /* Perform two Newton iterations:
      r -= r*((r*n)+(r-1.Q15))
         = r*((r*n)+(r-1.Q15)). */
   r = SUB16(r, MULT16_16_Q15(r,
             ADD16(MULT16_16_Q15(r, x), ADD16(r, -32768))));
   /* We subtract an extra 1 in the second iteration to avoid overflow; it also
       neatly compensates for truncation error in the rest of the process. */
   return SUB16(r, ADD16(1, MULT16_16_Q15(r,
                ADD16(MULT16_16_Q15(r, x), ADD16(r, -32768)))));
}

/* Computes a 32 bit approximated reciprocal (1/x) for a normalized Q31 input,
 * resulting in a Q30 output. The expected input range is [0.5f, 1.0f) in Q31
 * and the expected output range is [1.0f, 2.0f) in Q30. */
opus_val32 celt_rcp_norm32(opus_val32 x)
{
   opus_val32 r_q30;
   celt_sig_assert(x >= 1073741824);
   r_q30 = SHL32(EXTEND32(celt_rcp_norm16(SHR32(x, 15)-32768)), 16);
   /* Solving f(y) = a - 1/y using the Newton Method
    * Note: f(y)' = 1/y^2
    * r = r - f(r)/f(r)' = r - (x * r*r - r)
    *   = r - r*(r*x - 1)
    * where
    *   - r means 1/y's approximation.
    *   - x means a, the input of function.
    * Please note that:
    *   - It adds 1 to avoid overflow
    *   - -1.0f in Q30 is -1073741824. */
   return SUB32(r_q30, ADD32(SHL32(
                MULT32_32_Q31(ADD32(MULT32_32_Q31(r_q30, x), -1073741824),
                              r_q30), 1), 1));
}

/** Reciprocal approximation (Q15 input, Q16 output) */
opus_val32 celt_rcp(opus_val32 x)
{
   int i;
   opus_val16 r;
   celt_sig_assert(x>0);
   i = celt_ilog2(x);

   /* Compute the reciprocal of a Q15 number in the range [0, 1). */
   r = celt_rcp_norm16(VSHR32(x,i-15)-32768);

   /* r is now the Q15 solution to 2/(n+1), with a maximum relative error
       of 7.05346E-5, a (relative) RMSE of 2.14418E-5, and a peak absolute
       error of 1.24665/32768. */
   return VSHR32(EXTEND32(r),i-16);
}

#endif

#ifndef DISABLE_FLOAT_API

void celt_float2int16_c(const float * OPUS_RESTRICT in, short * OPUS_RESTRICT out, int cnt)
{
   int i;
   for (i = 0; i < cnt; i++)
   {
      out[i] = FLOAT2INT16(in[i]);
   }
}

int opus_limit2_checkwithin1_c(float * samples, int cnt)
{
   int i;
   if (cnt <= 0)
   {
      return 1;
   }

   for (i = 0; i < cnt; i++)
   {
      float clippedVal = samples[i];
      clippedVal = FMAX(-2.0f, clippedVal);
      clippedVal = FMIN(2.0f, clippedVal);
      samples[i] = clippedVal;
   }

   /* C implementation can't provide quick hint. Assume it might exceed -1/+1. */
   return 0;
}

#endif /* DISABLE_FLOAT_API */