src/third_party/opus/celt/mathops.c - cobalt - Git at Google

 /* 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
	/* 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+n0.4096419668459485).
	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 = xrr-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 += ry(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((rn)-1.Q15)
	= r((rn)+(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