/src/opus/celt/mathops.c

Source (jump to first uncovered line)
/* Copyright (c) 2002-2008 Jean-Marc Valin
   Copyright (c) 2007-2008 CSIRO
   Copyright (c) 2007-2009 Xiph.Org Foundation
   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 "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(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));
   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))));
}

/** Sqrt approximation (QX input, QX/2 output) */
opus_val32 celt_sqrt(opus_val32 x)
{
   int k;
   opus_val16 n;
   opus_val32 rt;
   static const opus_val16 C[5] = {23175, 11561, -3011, 1699, -664};
   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 = ADD16(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, (C[4])))))))));
   rt = VSHR32(rt,7-k);
   return rt;
}

#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;
   }
}

/** Reciprocal approximation (Q15 input, Q16 output) */
opus_val32 celt_rcp(opus_val32 x)
{
   int i;
   opus_val16 n;
   opus_val16 r;
   celt_sig_assert(x>0);
   i = celt_ilog2(x);
   /* n is Q15 with range [0,1). */
   n = VSHR32(x,i-15)-32768;
   /* 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, n));
   /* Perform two Newton iterations:
      r -= r*((r*n)-1.Q15)
         = r*((r*n)+(r-1.Q15)). */
   r = SUB16(r, MULT16_16_Q15(r,
             ADD16(MULT16_16_Q15(r, n), 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. */
   r = SUB16(r, ADD16(1, MULT16_16_Q15(r,
             ADD16(MULT16_16_Q15(r, n), ADD16(r, -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

Coverage Report

Created: 2024-03-26 07:23

Line	Count	Source (jump to first uncovered line)
1		/* Copyright (c) 2002-2008 Jean-Marc Valin
2		Copyright (c) 2007-2008 CSIRO
3		Copyright (c) 2007-2009 Xiph.Org Foundation
4		Written by Jean-Marc Valin */
5		/**
6		@file mathops.h
7		@brief Various math functions
8		*/
9		/*
10		Redistribution and use in source and binary forms, with or without
11		modification, are permitted provided that the following conditions
12		are met:
13
14		- Redistributions of source code must retain the above copyright
15		notice, this list of conditions and the following disclaimer.
16
17		- Redistributions in binary form must reproduce the above copyright
18		notice, this list of conditions and the following disclaimer in the
19		documentation and/or other materials provided with the distribution.
20
21		THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
22		``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
23		LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
24		A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
25		OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
26		EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
27		PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
28		PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
29		LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
30		NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
31		SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
32		*/
33
34		#ifdef HAVE_CONFIG_H
35		#include "config.h"
36		#endif
37
38		#include "mathops.h"
39
40		/*Compute floor(sqrt(_val)) with exact arithmetic.
41		_val must be greater than 0.
42		This has been tested on all possible 32-bit inputs greater than 0.*/
43	0	unsigned isqrt32(opus_uint32 _val){
44	0	unsigned b;
45	0	unsigned g;
46	0	int bshift;
47		/*Uses the second method from
48		http://www.azillionmonkeys.com/qed/sqroot.html
49		The main idea is to search for the largest binary digit b such that
50		(g+b)(g+b) <= _val, and add it to the solution g./
51	0	g=0;
52	0	bshift=(EC_ILOG(_val)-1)>>1;
53	0	b=1U<<bshift;
54	0	do{
55	0	opus_uint32 t;
56	0	t=(((opus_uint32)g<<1)+b)<<bshift;
57	0	if(t<=_val){
58	0	g+=b;
59	0	_val-=t;
60	0	}
61	0	b>>=1;
62	0	bshift--;
63	0	}
64	0	while(bshift>=0);
65	0	return g;
66	0	}
67
68		#ifdef FIXED_POINT
69
70		opus_val32 frac_div32(opus_val32 a, opus_val32 b)
71	5.30M	{
72	5.30M	opus_val16 rcp;
73	5.30M	opus_val32 result, rem;
74	5.30M	int shift = celt_ilog2(b)-29;
75	5.30M	a = VSHR32(a,shift);
76	5.30M	b = VSHR32(b,shift);
77		/* 16-bit reciprocal */
78	5.30M	rcp = ROUND16(celt_rcp(ROUND16(b,16)),3);
79	5.30M	result = MULT16_32_Q15(rcp, a);
80	5.30M	rem = PSHR32(a,2)-MULT32_32_Q31(result, b);
81	5.30M	result = ADD32(result, SHL32(MULT16_32_Q15(rcp, rem),2));
82	5.30M	if (result >= 536870912) /* 2^29 */
83	156	return 2147483647; /* 2^31 - 1 */
84	5.30M	else if (result <= -536870912) /* -2^29 */
85	0	return -2147483647; /* -2^31 */
86	5.30M	else
87	5.30M	return SHL32(result, 2);
88	5.30M	}
89
90		/** Reciprocal sqrt approximation in the range [0.25,1) (Q16 in, Q14 out) */
91		opus_val16 celt_rsqrt_norm(opus_val32 x)
92	290M	{
93	290M	opus_val16 n;
94	290M	opus_val16 r;
95	290M	opus_val16 r2;
96	290M	opus_val16 y;
97		/* Range of n is [-16384,32767] ([-0.5,1) in Q15). */
98	290M	n = x-32768;
99		/* Get a rough initial guess for the root.
100		The optimal minimax quadratic approximation (using relative error) is
101		r = 1.437799046117536+n(-0.823394375837328+n0.4096419668459485).
102		Coefficients here, and the final result r, are Q14.*/
103	290M	r = ADD16(23557, MULT16_16_Q15(n, ADD16(-13490, MULT16_16_Q15(n, 6713))));
104		/* We want y = xrr-1 in Q15, but x is 32-bit Q16 and r is Q14.
105		We can compute the result from n and r using Q15 multiplies with some
106		adjustment, carefully done to avoid overflow.
107		Range of y is [-1564,1594]. */
108	290M	r2 = MULT16_16_Q15(r, r);
109	290M	y = SHL16(SUB16(ADD16(MULT16_16_Q15(r2, n), r2), 16384), 1);
110		/* Apply a 2nd-order Householder iteration: r += ry(y*0.375-0.5).
111		This yields the Q14 reciprocal square root of the Q16 x, with a maximum
112		relative error of 1.04956E-4, a (relative) RMSE of 2.80979E-5, and a
113		peak absolute error of 2.26591/16384. */
114	290M	return ADD16(r, MULT16_16_Q15(r, MULT16_16_Q15(y,
115	290M	SUB16(MULT16_16_Q15(y, 12288), 16384))));
116	290M	}
117
118		/** Sqrt approximation (QX input, QX/2 output) */
119		opus_val32 celt_sqrt(opus_val32 x)
120	1.05G	{
121	1.05G	int k;
122	1.05G	opus_val16 n;
123	1.05G	opus_val32 rt;
124	1.05G	static const opus_val16 C[5] = {23175, 11561, -3011, 1699, -664};
125	1.05G	if (x==0)
126	137M	return 0;
127	913M	else if (x>=1073741824)
128	69.6k	return 32767;
129	913M	k = (celt_ilog2(x)>>1)-7;
130	913M	x = VSHR32(x, 2*k);
131	913M	n = x-32768;
132	913M	rt = ADD16(C[0], MULT16_16_Q15(n, ADD16(C[1], MULT16_16_Q15(n, ADD16(C[2],
133	913M	MULT16_16_Q15(n, ADD16(C[3], MULT16_16_Q15(n, (C[4])))))))));
134	913M	rt = VSHR32(rt,7-k);
135	913M	return rt;
136	1.05G	}
137
138		#define L1 32767
139		#define L2 -7651
140		#define L3 8277
141		#define L4 -626
142
143		static OPUS_INLINE opus_val16 _celt_cos_pi_2(opus_val16 x)
144	29.7M	{
145	29.7M	opus_val16 x2;
146
147	29.7M	x2 = MULT16_16_P15(x,x);
148	29.7M	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
149	29.7M	))))))));
150	29.7M	}
151
152		#undef L1
153		#undef L2
154		#undef L3
155		#undef L4
156
157		opus_val16 celt_cos_norm(opus_val32 x)
158	29.7M	{
159	29.7M	x = x&0x0001ffff;
160	29.7M	if (x>SHL32(EXTEND32(1), 16))
161	0	x = SUB32(SHL32(EXTEND32(1), 17),x);
162	29.7M	if (x&0x00007fff)
163	29.7M	{
164	29.7M	if (x<SHL32(EXTEND32(1), 15))
165	29.7M	{
166	29.7M	return _celt_cos_pi_2(EXTRACT16(x));
167	29.7M	} else {
168	0	return NEG16(_celt_cos_pi_2(EXTRACT16(65536-x)));
169	0	}
170	29.7M	} else {
171	0	if (x&0x0000ffff)
172	0	return 0;
173	0	else if (x&0x0001ffff)
174	0	return -32767;
175	0	else
176	0	return 32767;
177	0	}
178	29.7M	}
179
180		/** Reciprocal approximation (Q15 input, Q16 output) */
181		opus_val32 celt_rcp(opus_val32 x)
182	1.29G	{
183	1.29G	int i;
184	1.29G	opus_val16 n;
185	1.29G	opus_val16 r;
186	1.29G	celt_sig_assert(x>0);
187	1.29G	i = celt_ilog2(x);
188		/* n is Q15 with range [0,1). */
189	1.29G	n = VSHR32(x,i-15)-32768;
190		/* Start with a linear approximation:
191		r = 1.8823529411764706-0.9411764705882353*n.
192		The coefficients and the result are Q14 in the range [15420,30840].*/
193	1.29G	r = ADD16(30840, MULT16_16_Q15(-15420, n));
194		/* Perform two Newton iterations:
195		r -= r((rn)-1.Q15)
196		= r((rn)+(r-1.Q15)). */
197	1.29G	r = SUB16(r, MULT16_16_Q15(r,
198	1.29G	ADD16(MULT16_16_Q15(r, n), ADD16(r, -32768))));
199		/* We subtract an extra 1 in the second iteration to avoid overflow; it also
200		neatly compensates for truncation error in the rest of the process. */
201	1.29G	r = SUB16(r, ADD16(1, MULT16_16_Q15(r,
202	1.29G	ADD16(MULT16_16_Q15(r, n), ADD16(r, -32768)))));
203		/* r is now the Q15 solution to 2/(n+1), with a maximum relative error
204		of 7.05346E-5, a (relative) RMSE of 2.14418E-5, and a peak absolute
205		error of 1.24665/32768. */
206	1.29G	return VSHR32(EXTEND32(r),i-16);
207	1.29G	}
208
209		#endif