summaryrefslogtreecommitdiffstats
path: root/media/libopus/celt/mathops.c
diff options
context:
space:
mode:
Diffstat (limited to 'media/libopus/celt/mathops.c')
-rw-r--r--media/libopus/celt/mathops.c208
1 files changed, 208 insertions, 0 deletions
diff --git a/media/libopus/celt/mathops.c b/media/libopus/celt/mathops.c
new file mode 100644
index 000000000..21a01f52e
--- /dev/null
+++ b/media/libopus/celt/mathops.c
@@ -0,0 +1,208 @@
+/* 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.
+ This has been tested on all possible 32-bit inputs.*/
+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_assert2(x>0, "celt_rcp() only defined for positive values");
+ 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