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authorDave Burke <daveburke@google.com>2012-04-17 09:51:45 -0700
committerDave Burke <daveburke@google.com>2012-04-17 23:04:43 -0700
commit9bf37cc9712506b2483650c82d3c41152337ef7e (patch)
tree77db44e2bae06e3d144b255628be2b7a55c581d3 /libFDK/src/fixpoint_math.cpp
parenta37315fe10ee143d6d0b28c19d41a476a23e63ea (diff)
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Fraunhofer AAC codec.
License boilerplate update to follow. Change-Id: I2810460c11a58b6d148d84673cc031f3685e79b5
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+/*************************** Fraunhofer IIS FDK Tools **********************
+
+ (C) Copyright Fraunhofer IIS (1999)
+ All Rights Reserved
+
+ Please be advised that this software and/or program delivery is
+ Confidential Information of Fraunhofer and subject to and covered by the
+
+ Fraunhofer IIS Software Evaluation Agreement
+ between Google Inc. and Fraunhofer
+ effective and in full force since March 1, 2012.
+
+ You may use this software and/or program only under the terms and
+ conditions described in the above mentioned Fraunhofer IIS Software
+ Evaluation Agreement. Any other and/or further use requires a separate agreement.
+
+
+ $Id$
+ Author(s): M. Gayer
+ Description: Fixed point specific mathematical functions
+
+ This software and/or program is protected by copyright law and international
+ treaties. Any reproduction or distribution of this software and/or program,
+ or any portion of it, may result in severe civil and criminal penalties, and
+ will be prosecuted to the maximum extent possible under law.
+
+******************************************************************************/
+
+#include "fixpoint_math.h"
+
+
+#define MAX_LD_PRECISION 10
+#define LD_PRECISION 10
+
+/* Taylor series coeffcients for ln(1-x), centered at 0 (MacLaurin polinomial). */
+#ifndef LDCOEFF_16BIT
+LNK_SECTION_CONSTDATA_L1
+static const FIXP_DBL ldCoeff[MAX_LD_PRECISION] = {
+ FL2FXCONST_DBL(-1.0),
+ FL2FXCONST_DBL(-1.0/2.0),
+ FL2FXCONST_DBL(-1.0/3.0),
+ FL2FXCONST_DBL(-1.0/4.0),
+ FL2FXCONST_DBL(-1.0/5.0),
+ FL2FXCONST_DBL(-1.0/6.0),
+ FL2FXCONST_DBL(-1.0/7.0),
+ FL2FXCONST_DBL(-1.0/8.0),
+ FL2FXCONST_DBL(-1.0/9.0),
+ FL2FXCONST_DBL(-1.0/10.0)
+};
+#else
+LNK_SECTION_CONSTDATA_L1
+static const FIXP_SGL ldCoeff[MAX_LD_PRECISION] = {
+ FL2FXCONST_SGL(-1.0),
+ FL2FXCONST_SGL(-1.0/2.0),
+ FL2FXCONST_SGL(-1.0/3.0),
+ FL2FXCONST_SGL(-1.0/4.0),
+ FL2FXCONST_SGL(-1.0/5.0),
+ FL2FXCONST_SGL(-1.0/6.0),
+ FL2FXCONST_SGL(-1.0/7.0),
+ FL2FXCONST_SGL(-1.0/8.0),
+ FL2FXCONST_SGL(-1.0/9.0),
+ FL2FXCONST_SGL(-1.0/10.0)
+};
+#endif
+
+/*****************************************************************************
+
+ functionname: CalcLdData
+ description: Delivers the Logarithm Dualis ld(op)/LD_DATA_SCALING with polynomial approximation.
+ input: Input op is assumed to be double precision fractional 0 < op < 1.0
+ This function does not accept negative values.
+ output: For op == 0, the result is saturated to -1.0
+ This function does not return positive values since input values are treated as fractional values.
+ It does not make sense to input an integer value into this function (and expect a positive output value)
+ since input values are treated as fractional values.
+
+*****************************************************************************/
+
+LNK_SECTION_CODE_L1
+FIXP_DBL CalcLdData(FIXP_DBL op)
+{
+ return fLog2(op, 0);
+}
+
+
+/*****************************************************************************
+ functionname: LdDataVector
+*****************************************************************************/
+LNK_SECTION_CODE_L1
+void LdDataVector( FIXP_DBL *srcVector,
+ FIXP_DBL *destVector,
+ INT n)
+{
+ INT i;
+ for ( i=0; i<n; i++) {
+ destVector[i] = CalcLdData(srcVector[i]);
+ }
+}
+
+
+
+#define MAX_POW2_PRECISION 8
+#ifndef SINETABLE_16BIT
+ #define POW2_PRECISION MAX_POW2_PRECISION
+#else
+ #define POW2_PRECISION 5
+#endif
+
+/*
+ Taylor series coefficients of the function x^2. The first coefficient is
+ ommited (equal to 1.0).
+
+ pow2Coeff[i-1] = (1/i!) d^i(2^x)/dx^i, i=1..MAX_POW2_PRECISION
+ To evaluate the taylor series around x = 0, the coefficients are: 1/!i * ln(2)^i
+ */
+#ifndef POW2COEFF_16BIT
+LNK_SECTION_CONSTDATA_L1
+static const FIXP_DBL pow2Coeff[MAX_POW2_PRECISION] = {
+ FL2FXCONST_DBL(0.693147180559945309417232121458177), /* ln(2)^1 /1! */
+ FL2FXCONST_DBL(0.240226506959100712333551263163332), /* ln(2)^2 /2! */
+ FL2FXCONST_DBL(0.0555041086648215799531422637686218), /* ln(2)^3 /3! */
+ FL2FXCONST_DBL(0.00961812910762847716197907157365887), /* ln(2)^4 /4! */
+ FL2FXCONST_DBL(0.00133335581464284434234122219879962), /* ln(2)^5 /5! */
+ FL2FXCONST_DBL(1.54035303933816099544370973327423e-4), /* ln(2)^6 /6! */
+ FL2FXCONST_DBL(1.52527338040598402800254390120096e-5), /* ln(2)^7 /7! */
+ FL2FXCONST_DBL(1.32154867901443094884037582282884e-6) /* ln(2)^8 /8! */
+};
+#else
+LNK_SECTION_CONSTDATA_L1
+static const FIXP_SGL pow2Coeff[MAX_POW2_PRECISION] = {
+ FL2FXCONST_SGL(0.693147180559945309417232121458177), /* ln(2)^1 /1! */
+ FL2FXCONST_SGL(0.240226506959100712333551263163332), /* ln(2)^2 /2! */
+ FL2FXCONST_SGL(0.0555041086648215799531422637686218), /* ln(2)^3 /3! */
+ FL2FXCONST_SGL(0.00961812910762847716197907157365887), /* ln(2)^4 /4! */
+ FL2FXCONST_SGL(0.00133335581464284434234122219879962), /* ln(2)^5 /5! */
+ FL2FXCONST_SGL(1.54035303933816099544370973327423e-4), /* ln(2)^6 /6! */
+ FL2FXCONST_SGL(1.52527338040598402800254390120096e-5), /* ln(2)^7 /7! */
+ FL2FXCONST_SGL(1.32154867901443094884037582282884e-6) /* ln(2)^8 /8! */
+};
+#endif
+
+
+
+/*****************************************************************************
+
+ functionname: mul_dbl_sgl_rnd
+ description: Multiply with round.
+*****************************************************************************/
+
+/* for rounding a dfract to fract */
+/* static LONG accu_r = (int64)((INT64(1)<<(DFRACT_BITS-1))>>FRACT_BITS); */
+//LNK_SECTION_CONSTDATA
+//static const LONG accu_r = 0x00008000;
+#define ACCU_R (LONG) 0x00008000
+
+LNK_SECTION_CODE_L1
+FIXP_DBL mul_dbl_sgl_rnd (const FIXP_DBL op1, const FIXP_SGL op2)
+{
+ FIXP_DBL prod;
+ LONG v = (LONG)(op1);
+ SHORT u = (SHORT)(op2);
+
+ LONG low = u*(v&SGL_MASK);
+ low = (low+(ACCU_R>>1)) >> (FRACT_BITS-1); /* round */
+ LONG high = u * ((v>>FRACT_BITS)<<1);
+
+ prod = (LONG)(high+low);
+
+ return((FIXP_DBL)prod);
+}
+
+
+/*****************************************************************************
+
+ functionname: CalcInvLdData
+ description: Delivers the inverse of function CalcLdData().
+ Delivers 2^(op*LD_DATA_SCALING)
+ input: Input op is assumed to be fractional -1.0 < op < 1.0
+ output: For op == 0, the result is MAXVAL_DBL (almost 1.0).
+ For negative input values the output should be treated as a positive fractional value.
+ For positive input values the output should be treated as a positive integer value.
+ This function does not output negative values.
+
+*****************************************************************************/
+LNK_SECTION_CODE_L1
+FIXP_DBL CalcInvLdData(FIXP_DBL op)
+{
+ FIXP_DBL result_m;
+
+ if ( op == FL2FXCONST_DBL(0.0f) ) {
+ result_m = (FIXP_DBL)MAXVAL_DBL;
+ }
+ else if ( op < FL2FXCONST_DBL(0.0f) ) {
+ result_m = f2Pow(op, LD_DATA_SHIFT);
+ }
+ else {
+ int result_e;
+
+ result_m = f2Pow(op, LD_DATA_SHIFT, &result_e);
+ result_e = fixMin(fixMax(result_e+1-(DFRACT_BITS-1), -(DFRACT_BITS-1)), (DFRACT_BITS-1)); /* rounding and saturation */
+
+ if ( (result_e>0) && ( result_m > (((FIXP_DBL)MAXVAL_DBL)>>result_e) ) ) {
+ result_m = (FIXP_DBL)MAXVAL_DBL; /* saturate to max representable value */
+ }
+ else {
+ result_m = (scaleValue(result_m, result_e)+(FIXP_DBL)1)>>1; /* descale result + rounding */
+ }
+ }
+ return result_m;
+}
+
+
+
+
+
+/*****************************************************************************
+ functionname: InitLdInt and CalcLdInt
+ description: Create and access table with integer LdData (0 to 193)
+*****************************************************************************/
+
+
+ LNK_SECTION_CONSTDATA_L1
+ static const FIXP_DBL ldIntCoeff[] = {
+ 0x80000001, 0x00000000, 0x02000000, 0x032b8034, 0x04000000, 0x04a4d3c2, 0x052b8034, 0x059d5da0,
+ 0x06000000, 0x06570069, 0x06a4d3c2, 0x06eb3a9f, 0x072b8034, 0x0766a009, 0x079d5da0, 0x07d053f7,
+ 0x08000000, 0x082cc7ee, 0x08570069, 0x087ef05b, 0x08a4d3c2, 0x08c8ddd4, 0x08eb3a9f, 0x090c1050,
+ 0x092b8034, 0x0949a785, 0x0966a009, 0x0982809d, 0x099d5da0, 0x09b74949, 0x09d053f7, 0x09e88c6b,
+ 0x0a000000, 0x0a16bad3, 0x0a2cc7ee, 0x0a423162, 0x0a570069, 0x0a6b3d79, 0x0a7ef05b, 0x0a92203d,
+ 0x0aa4d3c2, 0x0ab7110e, 0x0ac8ddd4, 0x0ada3f60, 0x0aeb3a9f, 0x0afbd42b, 0x0b0c1050, 0x0b1bf312,
+ 0x0b2b8034, 0x0b3abb40, 0x0b49a785, 0x0b584822, 0x0b66a009, 0x0b74b1fd, 0x0b82809d, 0x0b900e61,
+ 0x0b9d5da0, 0x0baa708f, 0x0bb74949, 0x0bc3e9ca, 0x0bd053f7, 0x0bdc899b, 0x0be88c6b, 0x0bf45e09,
+ 0x0c000000, 0x0c0b73cb, 0x0c16bad3, 0x0c21d671, 0x0c2cc7ee, 0x0c379085, 0x0c423162, 0x0c4caba8,
+ 0x0c570069, 0x0c6130af, 0x0c6b3d79, 0x0c7527b9, 0x0c7ef05b, 0x0c88983f, 0x0c92203d, 0x0c9b8926,
+ 0x0ca4d3c2, 0x0cae00d2, 0x0cb7110e, 0x0cc0052b, 0x0cc8ddd4, 0x0cd19bb0, 0x0cda3f60, 0x0ce2c97d,
+ 0x0ceb3a9f, 0x0cf39355, 0x0cfbd42b, 0x0d03fda9, 0x0d0c1050, 0x0d140ca0, 0x0d1bf312, 0x0d23c41d,
+ 0x0d2b8034, 0x0d3327c7, 0x0d3abb40, 0x0d423b08, 0x0d49a785, 0x0d510118, 0x0d584822, 0x0d5f7cff,
+ 0x0d66a009, 0x0d6db197, 0x0d74b1fd, 0x0d7ba190, 0x0d82809d, 0x0d894f75, 0x0d900e61, 0x0d96bdad,
+ 0x0d9d5da0, 0x0da3ee7f, 0x0daa708f, 0x0db0e412, 0x0db74949, 0x0dbda072, 0x0dc3e9ca, 0x0dca258e,
+ 0x0dd053f7, 0x0dd6753e, 0x0ddc899b, 0x0de29143, 0x0de88c6b, 0x0dee7b47, 0x0df45e09, 0x0dfa34e1,
+ 0x0e000000, 0x0e05bf94, 0x0e0b73cb, 0x0e111cd2, 0x0e16bad3, 0x0e1c4dfb, 0x0e21d671, 0x0e275460,
+ 0x0e2cc7ee, 0x0e323143, 0x0e379085, 0x0e3ce5d8, 0x0e423162, 0x0e477346, 0x0e4caba8, 0x0e51daa8,
+ 0x0e570069, 0x0e5c1d0b, 0x0e6130af, 0x0e663b74, 0x0e6b3d79, 0x0e7036db, 0x0e7527b9, 0x0e7a1030,
+ 0x0e7ef05b, 0x0e83c857, 0x0e88983f, 0x0e8d602e, 0x0e92203d, 0x0e96d888, 0x0e9b8926, 0x0ea03232,
+ 0x0ea4d3c2, 0x0ea96df0, 0x0eae00d2, 0x0eb28c7f, 0x0eb7110e, 0x0ebb8e96, 0x0ec0052b, 0x0ec474e4,
+ 0x0ec8ddd4, 0x0ecd4012, 0x0ed19bb0, 0x0ed5f0c4, 0x0eda3f60, 0x0ede8797, 0x0ee2c97d, 0x0ee70525,
+ 0x0eeb3a9f, 0x0eef69ff, 0x0ef39355, 0x0ef7b6b4, 0x0efbd42b, 0x0effebcd, 0x0f03fda9, 0x0f0809cf,
+ 0x0f0c1050, 0x0f10113b, 0x0f140ca0, 0x0f18028d, 0x0f1bf312, 0x0f1fde3d, 0x0f23c41d, 0x0f27a4c0,
+ 0x0f2b8034
+ };
+
+
+ LNK_SECTION_INITCODE
+ void InitLdInt()
+ {
+ /* nothing to do! Use preinitialized logarithm table */
+ }
+
+
+
+LNK_SECTION_CODE_L1
+FIXP_DBL CalcLdInt(INT i)
+{
+ /* calculates ld(op)/LD_DATA_SCALING */
+ /* op is assumed to be an integer value between 1 and 193 */
+
+ FDK_ASSERT((193>0) && ((FIXP_DBL)ldIntCoeff[0]==(FIXP_DBL)0x80000001)); /* tab has to be initialized */
+
+ if ((i>0)&&(i<193))
+ return ldIntCoeff[i];
+ else
+ {
+ return (0);
+ }
+}
+
+
+/*****************************************************************************
+
+ functionname: invSqrtNorm2
+ description: delivers 1/sqrt(op) normalized to .5...1 and the shift value of the OUTPUT
+
+*****************************************************************************/
+#define SQRT_BITS 7
+#define SQRT_VALUES 128
+#define SQRT_BITS_MASK 0x7f
+
+LNK_SECTION_CONSTDATA_L1
+static const FIXP_DBL invSqrtTab[SQRT_VALUES] = {
+ 0x5a827999, 0x5a287e03, 0x59cf8cbb, 0x5977a0ab, 0x5920b4de, 0x58cac480, 0x5875cade, 0x5821c364,
+ 0x57cea99c, 0x577c792f, 0x572b2ddf, 0x56dac38d, 0x568b3631, 0x563c81df, 0x55eea2c3, 0x55a19521,
+ 0x55555555, 0x5509dfd0, 0x54bf311a, 0x547545d0, 0x542c1aa3, 0x53e3ac5a, 0x539bf7cc, 0x5354f9e6,
+ 0x530eafa4, 0x52c91617, 0x52842a5e, 0x523fe9ab, 0x51fc513f, 0x51b95e6b, 0x51770e8e, 0x51355f19,
+ 0x50f44d88, 0x50b3d768, 0x5073fa4f, 0x5034b3e6, 0x4ff601df, 0x4fb7e1f9, 0x4f7a5201, 0x4f3d4fce,
+ 0x4f00d943, 0x4ec4ec4e, 0x4e8986e9, 0x4e4ea718, 0x4e144ae8, 0x4dda7072, 0x4da115d9, 0x4d683948,
+ 0x4d2fd8f4, 0x4cf7f31b, 0x4cc08604, 0x4c898fff, 0x4c530f64, 0x4c1d0293, 0x4be767f5, 0x4bb23df9,
+ 0x4b7d8317, 0x4b4935ce, 0x4b1554a6, 0x4ae1de2a, 0x4aaed0f0, 0x4a7c2b92, 0x4a49ecb3, 0x4a1812fa,
+ 0x49e69d16, 0x49b589bb, 0x4984d7a4, 0x49548591, 0x49249249, 0x48f4fc96, 0x48c5c34a, 0x4896e53c,
+ 0x48686147, 0x483a364c, 0x480c6331, 0x47dee6e0, 0x47b1c049, 0x4784ee5f, 0x4758701c, 0x472c447c,
+ 0x47006a80, 0x46d4e130, 0x46a9a793, 0x467ebcb9, 0x46541fb3, 0x4629cf98, 0x45ffcb80, 0x45d61289,
+ 0x45aca3d5, 0x45837e88, 0x455aa1ca, 0x45320cc8, 0x4509beb0, 0x44e1b6b4, 0x44b9f40b, 0x449275ec,
+ 0x446b3b95, 0x44444444, 0x441d8f3b, 0x43f71bbe, 0x43d0e917, 0x43aaf68e, 0x43854373, 0x435fcf14,
+ 0x433a98c5, 0x43159fdb, 0x42f0e3ae, 0x42cc6397, 0x42a81ef5, 0x42841527, 0x4260458d, 0x423caf8c,
+ 0x4219528b, 0x41f62df1, 0x41d3412a, 0x41b08ba1, 0x418e0cc7, 0x416bc40d, 0x4149b0e4, 0x4127d2c3,
+ 0x41062920, 0x40e4b374, 0x40c3713a, 0x40a261ef, 0x40818511, 0x4060da21, 0x404060a1, 0x40201814
+};
+
+LNK_SECTION_INITCODE
+void InitInvSqrtTab()
+{
+ /* nothing to do !
+ use preinitialized square root table
+ */
+}
+
+
+
+#if !defined(FUNCTION_invSqrtNorm2)
+/*****************************************************************************
+ delivers 1/sqrt(op) normalized to .5...1 and the shift value of the OUTPUT,
+ i.e. the denormalized result is 1/sqrt(op) = invSqrtNorm(op) * 2^(shift)
+ uses Newton-iteration for approximation
+ Q(n+1) = Q(n) + Q(n) * (0.5 - 2 * V * Q(n)^2)
+ with Q = 0.5* V ^-0.5; 0.5 <= V < 1.0
+*****************************************************************************/
+FIXP_DBL invSqrtNorm2(FIXP_DBL op, INT *shift)
+{
+
+ FIXP_DBL val = op ;
+ FIXP_DBL reg1, reg2, regtmp ;
+
+ if (val == FL2FXCONST_DBL(0.0)) {
+ *shift = 1 ;
+ return((LONG)1); /* minimum positive value */
+ }
+
+
+ /* normalize input, calculate shift value */
+ FDK_ASSERT(val > FL2FXCONST_DBL(0.0));
+ *shift = fNormz(val) - 1; /* CountLeadingBits() is not necessary here since test value is always > 0 */
+ val <<=*shift ; /* normalized input V */
+ *shift+=2 ; /* bias for exponent */
+
+ /* Newton iteration of 1/sqrt(V) */
+ reg1 = invSqrtTab[ (INT)(val>>(DFRACT_BITS-1-(SQRT_BITS+1))) & SQRT_BITS_MASK ];
+ reg2 = FL2FXCONST_DBL(0.0625f); /* 0.5 >> 3 */
+
+ regtmp= fPow2Div2(reg1); /* a = Q^2 */
+ regtmp= reg2 - fMultDiv2(regtmp, val); /* b = 0.5 - 2 * V * Q^2 */
+ reg1 += (fMultDiv2(regtmp, reg1)<<4); /* Q = Q + Q*b */
+
+ /* calculate the output exponent = input exp/2 */
+ if (*shift & 0x00000001) { /* odd shift values ? */
+ reg2 = FL2FXCONST_DBL(0.707106781186547524400844362104849f); /* 1/sqrt(2); */
+ reg1 = fMultDiv2(reg1, reg2) << 2;
+ }
+
+ *shift = *shift>>1;
+
+ return(reg1);
+}
+#endif /* !defined(FUNCTION_invSqrtNorm2) */
+
+/*****************************************************************************
+
+ functionname: sqrtFixp
+ description: delivers sqrt(op)
+
+*****************************************************************************/
+FIXP_DBL sqrtFixp(FIXP_DBL op)
+{
+ INT tmp_exp = 0;
+ FIXP_DBL tmp_inv = invSqrtNorm2(op, &tmp_exp);
+
+ FDK_ASSERT(tmp_exp > 0) ;
+ return( (FIXP_DBL) ( fMultDiv2( (op<<(tmp_exp-1)), tmp_inv ) << 2 ));
+}
+
+
+#if !defined(FUNCTION_schur_div)
+/*****************************************************************************
+
+ functionname: schur_div
+ description: delivers op1/op2 with op3-bit accuracy
+
+*****************************************************************************/
+
+
+FIXP_DBL schur_div(FIXP_DBL num, FIXP_DBL denum, INT count)
+{
+ INT L_num = (LONG)num>>1;
+ INT L_denum = (LONG)denum>>1;
+ INT div = 0;
+ INT k = count;
+
+ FDK_ASSERT (num>=(FIXP_DBL)0);
+ FDK_ASSERT (denum>(FIXP_DBL)0);
+ FDK_ASSERT (num <= denum);
+
+ if (L_num != 0)
+ while (--k)
+ {
+ div <<= 1;
+ L_num <<= 1;
+ if (L_num >= L_denum)
+ {
+ L_num -= L_denum;
+ div++;
+ }
+ }
+ return (FIXP_DBL)(div << (DFRACT_BITS - count));
+}
+
+
+#endif /* !defined(FUNCTION_schur_div) */
+
+
+#ifndef FUNCTION_fMultNorm
+FIXP_DBL fMultNorm(FIXP_DBL f1, FIXP_DBL f2, INT *result_e)
+{
+ INT product = 0;
+ INT norm_f1, norm_f2;
+
+ if ( (f1 == (FIXP_DBL)0) || (f2 == (FIXP_DBL)0) ) {
+ *result_e = 0;
+ return (FIXP_DBL)0;
+ }
+ norm_f1 = CountLeadingBits(f1);
+ f1 = f1 << norm_f1;
+ norm_f2 = CountLeadingBits(f2);
+ f2 = f2 << norm_f2;
+
+ product = fMult(f1, f2);
+ *result_e = - (norm_f1 + norm_f2);
+
+ return (FIXP_DBL)product;
+}
+#endif
+
+#ifndef FUNCTION_fDivNorm
+FIXP_DBL fDivNorm(FIXP_DBL L_num, FIXP_DBL L_denum, INT *result_e)
+{
+ FIXP_DBL div;
+ INT norm_num, norm_den;
+
+ FDK_ASSERT (L_num >= (FIXP_DBL)0);
+ FDK_ASSERT (L_denum > (FIXP_DBL)0);
+
+ if(L_num == (FIXP_DBL)0)
+ {
+ *result_e = 0;
+ return ((FIXP_DBL)0);
+ }
+
+ norm_num = CountLeadingBits(L_num);
+ L_num = L_num << norm_num;
+ L_num = L_num >> 1;
+ *result_e = - norm_num + 1;
+
+ norm_den = CountLeadingBits(L_denum);
+ L_denum = L_denum << norm_den;
+ *result_e -= - norm_den;
+
+ div = schur_div(L_num, L_denum, FRACT_BITS);
+
+ return div;
+}
+#endif /* !FUNCTION_fDivNorm */
+
+#ifndef FUNCTION_fDivNorm
+FIXP_DBL fDivNorm(FIXP_DBL num, FIXP_DBL denom)
+{
+ INT e;
+ FIXP_DBL res;
+
+ FDK_ASSERT (denom >= num);
+
+ res = fDivNorm(num, denom, &e);
+
+ /* Avoid overflow since we must output a value with exponent 0
+ there is no other choice than saturating to almost 1.0f */
+ if(res == (FIXP_DBL)(1<<(DFRACT_BITS-2)) && e == 1)
+ {
+ res = (FIXP_DBL)MAXVAL_DBL;
+ }
+ else
+ {
+ res = scaleValue(res, e);
+ }
+
+ return res;
+}
+#endif /* !FUNCTION_fDivNorm */
+
+#ifndef FUNCTION_fDivNormHighPrec
+FIXP_DBL fDivNormHighPrec(FIXP_DBL num, FIXP_DBL denom, INT *result_e)
+{
+ FIXP_DBL div;
+ INT norm_num, norm_den;
+
+ FDK_ASSERT (num >= (FIXP_DBL)0);
+ FDK_ASSERT (denom > (FIXP_DBL)0);
+
+ if(num == (FIXP_DBL)0)
+ {
+ *result_e = 0;
+ return ((FIXP_DBL)0);
+ }
+
+ norm_num = CountLeadingBits(num);
+ num = num << norm_num;
+ num = num >> 1;
+ *result_e = - norm_num + 1;
+
+ norm_den = CountLeadingBits(denom);
+ denom = denom << norm_den;
+ *result_e -= - norm_den;
+
+ div = schur_div(num, denom, 31);
+ return div;
+}
+#endif /* !FUNCTION_fDivNormHighPrec */
+
+
+
+FIXP_DBL CalcLog2(FIXP_DBL base_m, INT base_e, INT *result_e)
+{
+ return fLog2(base_m, base_e, result_e);
+}
+
+FIXP_DBL f2Pow(
+ const FIXP_DBL exp_m, const INT exp_e,
+ INT *result_e
+ )
+{
+ FIXP_DBL frac_part, result_m;
+ INT int_part;
+
+ if (exp_e > 0)
+ {
+ INT exp_bits = DFRACT_BITS-1 - exp_e;
+ int_part = exp_m >> exp_bits;
+ frac_part = exp_m - (FIXP_DBL)(int_part << exp_bits);
+ frac_part = frac_part << exp_e;
+ }
+ else
+ {
+ int_part = 0;
+ frac_part = exp_m >> -exp_e;
+ }
+
+ /* Best accuracy is around 0, so try to get there with the fractional part. */
+ if( frac_part > FL2FXCONST_DBL(0.5f) )
+ {
+ int_part = int_part + 1;
+ frac_part = frac_part + FL2FXCONST_DBL(-1.0f);
+ }
+ if( frac_part < FL2FXCONST_DBL(-0.5f) )
+ {
+ int_part = int_part - 1;
+ frac_part = -(FL2FXCONST_DBL(-1.0f) - frac_part);
+ }
+
+ /* Evaluate taylor polynomial which approximates 2^x */
+ {
+ FIXP_DBL p;
+
+ /* result_m ~= 2^frac_part */
+ p = frac_part;
+ /* First taylor series coefficient a_0 = 1.0, scaled by 0.5 due to fMultDiv2(). */
+ result_m = FL2FXCONST_DBL(1.0f/2.0f);
+ for (INT i = 0; i < POW2_PRECISION; i++) {
+ /* next taylor series term: a_i * x^i, x=0 */
+ result_m = fMultAddDiv2(result_m, pow2Coeff[i], p);
+ p = fMult(p, frac_part);
+ }
+ }
+
+ /* "+ 1" compensates fMultAddDiv2() of the polynomial evaluation above. */
+ *result_e = int_part + 1;
+
+ return result_m;
+}
+
+FIXP_DBL f2Pow(
+ const FIXP_DBL exp_m, const INT exp_e
+ )
+{
+ FIXP_DBL result_m;
+ INT result_e;
+
+ result_m = f2Pow(exp_m, exp_e, &result_e);
+ result_e = fixMin(DFRACT_BITS-1,fixMax(-(DFRACT_BITS-1),result_e));
+
+ return scaleValue(result_m, result_e);
+}
+
+FIXP_DBL fPow(
+ FIXP_DBL base_m, INT base_e,
+ FIXP_DBL exp_m, INT exp_e,
+ INT *result_e
+ )
+{
+ INT ans_lg2_e, baselg2_e;
+ FIXP_DBL base_lg2, ans_lg2, result;
+
+ /* Calc log2 of base */
+ base_lg2 = fLog2(base_m, base_e, &baselg2_e);
+
+ /* Prepare exp */
+ {
+ INT leadingBits;
+
+ leadingBits = CountLeadingBits(fAbs(exp_m));
+ exp_m = exp_m << leadingBits;
+ exp_e -= leadingBits;
+ }
+
+ /* Calc base pow exp */
+ ans_lg2 = fMult(base_lg2, exp_m);
+ ans_lg2_e = exp_e + baselg2_e;
+
+ /* Calc antilog */
+ result = f2Pow(ans_lg2, ans_lg2_e, result_e);
+
+ return result;
+}
+
+FIXP_DBL fLdPow(
+ FIXP_DBL baseLd_m,
+ INT baseLd_e,
+ FIXP_DBL exp_m, INT exp_e,
+ INT *result_e
+ )
+{
+ INT ans_lg2_e;
+ FIXP_DBL ans_lg2, result;
+
+ /* Prepare exp */
+ {
+ INT leadingBits;
+
+ leadingBits = CountLeadingBits(fAbs(exp_m));
+ exp_m = exp_m << leadingBits;
+ exp_e -= leadingBits;
+ }
+
+ /* Calc base pow exp */
+ ans_lg2 = fMult(baseLd_m, exp_m);
+ ans_lg2_e = exp_e + baseLd_e;
+
+ /* Calc antilog */
+ result = f2Pow(ans_lg2, ans_lg2_e, result_e);
+
+ return result;
+}
+
+FIXP_DBL fLdPow(
+ FIXP_DBL baseLd_m, INT baseLd_e,
+ FIXP_DBL exp_m, INT exp_e
+ )
+{
+ FIXP_DBL result_m;
+ int result_e;
+
+ result_m = fLdPow(baseLd_m, baseLd_e, exp_m, exp_e, &result_e);
+
+ return SATURATE_SHIFT(result_m, -result_e, DFRACT_BITS);
+}
+
+FIXP_DBL fPowInt(
+ FIXP_DBL base_m, INT base_e,
+ INT exp,
+ INT *pResult_e
+ )
+{
+ FIXP_DBL result;
+
+ if (exp != 0) {
+ INT result_e = 0;
+
+ if (base_m != (FIXP_DBL)0) {
+ {
+ INT leadingBits;
+ leadingBits = CountLeadingBits( base_m );
+ base_m <<= leadingBits;
+ base_e -= leadingBits;
+ }
+
+ result = base_m;
+
+ {
+ int i;
+ for (i = 1; i < fAbs(exp); i++) {
+ result = fMult(result, base_m);
+ }
+ }
+
+ if (exp < 0) {
+ /* 1.0 / ans */
+ result = fDivNorm( FL2FXCONST_DBL(0.5f), result, &result_e );
+ result_e++;
+ } else {
+ int ansScale = CountLeadingBits( result );
+ result <<= ansScale;
+ result_e -= ansScale;
+ }
+
+ result_e += exp * base_e;
+
+ } else {
+ result = (FIXP_DBL)0;
+ }
+ *pResult_e = result_e;
+ }
+ else {
+ result = FL2FXCONST_DBL(0.5f);
+ *pResult_e = 1;
+ }
+
+ return result;
+}
+
+FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e, INT *result_e)
+{
+ FIXP_DBL result_m;
+
+ /* Short cut for zero and negative numbers. */
+ if ( x_m <= FL2FXCONST_DBL(0.0f) ) {
+ *result_e = DFRACT_BITS-1;
+ return FL2FXCONST_DBL(-1.0f);
+ }
+
+ /* Calculate log2() */
+ {
+ FIXP_DBL px2_m, x2_m;
+
+ /* Move input value x_m * 2^x_e toward 1.0, where the taylor approximation
+ of the function log(1-x) centered at 0 is most accurate. */
+ {
+ INT b_norm;
+
+ b_norm = fNormz(x_m)-1;
+ x2_m = x_m << b_norm;
+ x_e = x_e - b_norm;
+ }
+
+ /* map x from log(x) domain to log(1-x) domain. */
+ x2_m = - (x2_m + FL2FXCONST_DBL(-1.0) );
+
+ /* Taylor polinomial approximation of ln(1-x) */
+ result_m = FL2FXCONST_DBL(0.0);
+ px2_m = x2_m;
+ for (int i=0; i<LD_PRECISION; i++) {
+ result_m = fMultAddDiv2(result_m, ldCoeff[i], px2_m);
+ px2_m = fMult(px2_m, x2_m);
+ }
+ /* Multiply result with 1/ln(2) = 1.0 + 0.442695040888 (get log2(x) from ln(x) result). */
+ result_m = fMultAddDiv2(result_m, result_m, FL2FXCONST_DBL(2.0*0.4426950408889634073599246810019));
+
+ /* Add exponent part. log2(x_m * 2^x_e) = log2(x_m) + x_e */
+ if (x_e != 0)
+ {
+ int enorm;
+
+ enorm = DFRACT_BITS - fNorm((FIXP_DBL)x_e);
+ /* The -1 in the right shift of result_m compensates the fMultDiv2() above in the taylor polinomial evaluation loop.*/
+ result_m = (result_m >> (enorm-1)) + ((FIXP_DBL)x_e << (DFRACT_BITS-1-enorm));
+
+ *result_e = enorm;
+ } else {
+ /* 1 compensates the fMultDiv2() above in the taylor polinomial evaluation loop.*/
+ *result_e = 1;
+ }
+ }
+
+ return result_m;
+}
+
+FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e)
+{
+ if ( x_m <= FL2FXCONST_DBL(0.0f) ) {
+ x_m = FL2FXCONST_DBL(-1.0f);
+ }
+ else {
+ INT result_e;
+ x_m = fLog2(x_m, x_e, &result_e);
+ x_m = scaleValue(x_m, result_e-LD_DATA_SHIFT);
+ }
+ return x_m;
+}
+
+
+
+
+#if TEST_ROUNDING
+#include <math.h>
+
+void writeToFile( FDKFILE *fh, float v) {
+ FDKfprintf(fh, "%22.16f\n", v );
+}
+FDKFILE* openAppend(CHAR* filNam)
+{
+ FDKFILE* fh = NULL;
+ fh = FDKfopen(filNam, "a");
+ if (!fh) {
+ FDKprintf("\nError at fio_open\n");
+ return NULL;
+ }
+ return fh;
+}
+
+// loop version, long duration, huge output data
+void checkRound()
+{
+ #define IN_INT 0 // all four rounding modes are bitexact for 0 and for 1
+
+ float inp;
+ FIXP_DBL f_inp;
+ float r, rnd;
+ FIXP_DBL f_trc,f_rnd;
+ float step;
+
+ //step=0.1f;
+ step=0.001f;
+ //step=0.0001f;
+ //step=0.00001f;
+ //step=0.0000001f; // BEWARE output data of test might get huge!
+ //step=0.00000000005f; // BEWARE output data of test might get huge!
+
+ double d_floor,d_ceil;
+ FIXP_DBL f_floor,f_ceil;
+ INT i,j,floorInt,ceilInt,roundInt,truncInt;
+
+ FDKFILE *fpF_a = NULL; FDKFILE *fpC_a = NULL;
+ FDKFILE *fpF_b = NULL; FDKFILE *fpC_b = NULL;
+ FDKFILE *fpF_c = NULL; FDKFILE *fpC_c = NULL;
+ FDKFILE *fpF_d = NULL; FDKFILE *fpC_d = NULL;
+ FDKFILE *fpF_e = NULL; FDKFILE *fpC_e = NULL;
+
+ fpF_a = openAppend("_FLT_a.txt"); fpC_a = openAppend("_FDK_a.txt");
+ fpF_b = openAppend("_FLT_b.txt"); fpC_b = openAppend("_FDK_b.txt");
+ fpF_c = openAppend("_FLT_c.txt"); fpC_c = openAppend("_FDK_c.txt");
+ fpF_d = openAppend("_FLT_d.txt"); fpC_d = openAppend("_FDK_d.txt");
+ fpF_e = openAppend("_FLT_e.txt"); fpC_e = openAppend("_FDK_e.txt");
+
+
+
+ #define INPUT_SF 3 // BEWARE at SF 0 !!! over/under-flow
+ #define INPUT_SCALE (float)(1<<INPUT_SF)
+
+ for (inp = -3.1f; inp < 2.1f; inp=inp+step)
+ //for (inp = -0.9f; inp < 0.9f; inp=inp+step)
+ //for (inp = -0.0000000001f; inp < 0.0000000001f; inp=inp+step)
+ //for (inp = -3.1f; inp < 2.1f; inp=inp+step)
+ { // # #
+ // --- write input
+ writeToFile(fpF_a,(float) inp);
+ f_inp = (FIXP_DBL)(inp / INPUT_SCALE); writeToFile(fpC_a,(float)f_inp * (float)FDKpow(2,INPUT_SF));
+
+
+ // --- floor
+ d_floor = FDKfloor(inp); writeToFile(fpF_b,(float) d_floor);
+ // --- floor fixedpoint
+ floorInt = fixp_floorToInt(f_inp,INPUT_SF);
+ f_floor = fixp_floor (f_inp,INPUT_SF);
+ #if IN_INT
+ writeToFile(fpC_b,(float) floorInt);
+ #else
+ writeToFile(fpC_b,(float) f_floor * (float)FDKpow(2,INPUT_SF));
+ #endif
+
+
+ // --- ceil
+ d_ceil = FDKceil(inp); writeToFile(fpF_c,(float) d_ceil );
+ // --- ceil fixedpoint
+ ceilInt = fixp_ceilToInt(f_inp,INPUT_SF);
+ f_ceil = fixp_ceil (f_inp,INPUT_SF);
+ #if IN_INT
+ writeToFile(fpC_c,(float) ceilInt);
+ #else
+ writeToFile(fpC_c,(float) f_ceil * (float)FDKpow(2,INPUT_SF));
+ #endif
+
+
+ // --- truncate
+ i = (INT)inp; writeToFile(fpF_d,(float) i);
+ // --- truncate fixedpoint
+ truncInt = fixp_truncateToInt(f_inp,INPUT_SF);
+ f_trc = fixp_truncate (f_inp,INPUT_SF);
+ #if IN_INT
+ writeToFile(fpC_d,(float) truncInt);
+ #else
+ writeToFile(fpC_d,(float) f_trc * (float)FDKpow(2,INPUT_SF));
+ #endif
+
+
+ // --- round
+ r = 0.5f;
+ if (inp > 0) rnd = inp + r;
+ if (inp < 0) rnd = -(-inp + r); // avoid offset; you might get offset with 'rnd = inp - r'
+ j = (INT)(rnd); writeToFile(fpF_e,(float) j);
+ // --- round fixedpoint
+ roundInt = fixp_roundToInt(f_inp,INPUT_SF);
+ f_rnd = fixp_round (f_inp,INPUT_SF);
+ #if IN_INT
+ writeToFile(fpC_e,(float) roundInt);
+ #else
+ writeToFile(fpC_e,(float) f_rnd * (float)FDKpow(2,INPUT_SF));
+ #endif
+ }
+
+ if (fpF_a) FDKfclose(fpF_a); if (fpC_a) FDKfclose(fpC_a);
+ if (fpF_b) FDKfclose(fpF_b); if (fpC_b) FDKfclose(fpC_b);
+ if (fpF_c) FDKfclose(fpF_c); if (fpC_c) FDKfclose(fpC_c);
+ if (fpF_d) FDKfclose(fpF_d); if (fpC_d) FDKfclose(fpC_d);
+ if (fpF_e) FDKfclose(fpF_e); if (fpC_e) FDKfclose(fpC_e);
+}
+
+
+// round only a few selected values (faster)
+void checkRound2()
+{
+ // set point
+ #define BLOD 24 // left bits (of dot): number of bits _left_ of decimal point ==> Q 24.8 format (incl. sign bit)
+ #define BROD 8 // right bits (of dot): number of bits _right_ of decimal point ==> Q 24.8 format
+ FDK_ASSERT((BROD+BLOD)==DFRACT_BITS);
+
+ // scale factors
+ #define FL_SF BLOD
+ #define FL_SCALE (1<<FL_SF)
+
+ #define FR_SF BROD
+ #define FR_SCALE (1<<FR_SF)
+
+ #define INL_SF 7 // bits at INput Left of dot
+ #define INL_SCALE (float)(1<<INL_SF)
+
+ #define INR_SF (DFRACT_BITS-1-INL_SF) // bits at INput Right of dot 32-1-7 = 24
+ #define INR_SCALE (float)(1<<INR_SF)
+
+
+ // testdata
+ #define X_MIN -128.0000f //
+ #define X0 -127.0000f //
+
+ #define X1 -5.0000f //
+//#define X1 -4.4999f // round
+//#define X1 4.4999f // round
+
+ #define X2 -4.9999f //
+ #define X3 -4.5000f //
+ #define X4 -0.1234f //
+ #define X_NULL 0.0f //
+ #define X5 0.1234f //
+ #define X6 4.5000f //
+ #define X7 4.9999f //
+ #define X8 5.0000f //
+ // subtract one LSB from 128.0f [this is needed AFTER hex values have been dumped --> this is needed to get a valid float reference for floor and trunc ]
+ #define X_MAX ((-0.0000000004656613f) + 128.0000f)
+
+
+ FIXP_DBL f_reg0, f_reg1, f_reg2, f_reg3, f_reg4, f_reg5, f_reg6, f_reg7, f_reg8, f_reg_min, f_reg_max, f_reg_null;
+ INT res0, res1, res2, res3, res4, res5, res6, res7, res8;
+ FIXP_DBL f_res0, f_res1, f_res2, f_res3, f_res4, f_res5, f_res6, f_res7, f_res8;
+
+ f_reg_min = (LONG)0x80000000 ; // data taken from above dump; cast to LONG needed because of
+ f_reg0 = (LONG)0x81000000 ; // fract-class needs a sign; 0x######## is of type unsigned int.
+ f_reg1 = (LONG)0xfb000000 ;
+ f_reg2 = (LONG)0xfb000690 ;
+ f_reg3 = (LONG)0xfb800000 ;
+ f_reg4 = (LONG)0xffe068dc ;
+ f_reg_null = (LONG)0x00000000 ;
+ f_reg5 = (LONG)0x001f9724 ;
+ f_reg6 = (LONG)0x04800000 ;
+ f_reg7 = (LONG)0x04fff970 ;
+ f_reg8 = (LONG)0x05000000 ;
+ f_reg_max = (LONG)0x7fffffff ;
+
+
+ FDKprintf("---- input values ----\n");
+ FDKprintf("%f %f %f %f %f %f %f %f %f\n", X0
+ , X1
+ , X2
+ , X3
+ , X4
+ , X5
+ , X6
+ , X7
+ , X8
+ );
+ FDKprintf("%f %f %f %f %f %f %f %f %f\n", (float)f_reg0 * (float)FDKpow(2,INL_SF)
+ , (float)f_reg1 * (float)FDKpow(2,INL_SF)
+ , (float)f_reg2 * (float)FDKpow(2,INL_SF)
+ , (float)f_reg3 * (float)FDKpow(2,INL_SF)
+ , (float)f_reg4 * (float)FDKpow(2,INL_SF)
+ , (float)f_reg5 * (float)FDKpow(2,INL_SF)
+ , (float)f_reg6 * (float)FDKpow(2,INL_SF)
+ , (float)f_reg7 * (float)FDKpow(2,INL_SF)
+ , (float)f_reg8 * (float)FDKpow(2,INL_SF)
+ );
+ FDKprintf("---- min/max input values ----\n");
+ FDKprintf("%f %f %f\n", X_MIN
+ , X_NULL
+ , X_MAX
+ );
+ FDKprintf("%f %f %f\n", (float)f_reg_min * (float)FDKpow(2,INL_SF)
+ , (float)f_reg_null * (float)FDKpow(2,INL_SF)
+ , (float)f_reg_max * (float)FDKpow(2,INL_SF)
+ );
+ FDKprintf("\n");
+
+ FDKprintf("\n---- floor ----\n");
+ res0 = fixp_floorToInt(f_reg0, INL_SF); f_res0 = fixp_floor(f_reg0, INL_SF);
+ res1 = fixp_floorToInt(f_reg1, INL_SF); f_res1 = fixp_floor(f_reg1, INL_SF);
+ res2 = fixp_floorToInt(f_reg2, INL_SF); f_res2 = fixp_floor(f_reg2, INL_SF);
+ res3 = fixp_floorToInt(f_reg3, INL_SF); f_res3 = fixp_floor(f_reg3, INL_SF);
+ res4 = fixp_floorToInt(f_reg4, INL_SF); f_res4 = fixp_floor(f_reg4, INL_SF);
+ res5 = fixp_floorToInt(f_reg5, INL_SF); f_res5 = fixp_floor(f_reg5, INL_SF);
+ res6 = fixp_floorToInt(f_reg6, INL_SF); f_res6 = fixp_floor(f_reg6, INL_SF);
+ res7 = fixp_floorToInt(f_reg7, INL_SF); f_res7 = fixp_floor(f_reg7, INL_SF);
+ res8 = fixp_floorToInt(f_reg8, INL_SF); f_res8 = fixp_floor(f_reg8, INL_SF);
+ FDKprintf("reference %i %i %i %i %i %i %i %i %i\n", (int)floor(X0), (int)floor(X1), (int)floor(X2), (int)floor(X3), (int)floor(X4), (int)floor(X5), (int)floor(X6), (int)floor(X7), (int)floor(X8));
+ FDKprintf("fixp_floorToInt %i %i %i %i %i %i %i %i %i\n", res0, res1, res2, res3, res4, res5, res6, res7, res8);
+ FDKprintf("fixp_floor %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f\n", (float)f_res0*(float)FDKpow(2,INL_SF),
+ (float)f_res1*(float)FDKpow(2,INL_SF),
+ (float)f_res2*(float)FDKpow(2,INL_SF),
+ (float)f_res3*(float)FDKpow(2,INL_SF),
+ (float)f_res4*(float)FDKpow(2,INL_SF),
+ (float)f_res5*(float)FDKpow(2,INL_SF),
+ (float)f_res6*(float)FDKpow(2,INL_SF),
+ (float)f_res7*(float)FDKpow(2,INL_SF),
+ (float)f_res8*(float)FDKpow(2,INL_SF));
+
+ FDKprintf("\n---- min/max floor ----\n");
+ res1 = fixp_floorToInt(f_reg_min, INL_SF); f_res1 = fixp_floor(f_reg_min, INL_SF);
+ res2 = fixp_floorToInt(f_reg_null, INL_SF); f_res2 = fixp_floor(f_reg_null, INL_SF);
+ res3 = fixp_floorToInt(f_reg_max, INL_SF); f_res3 = fixp_floor(f_reg_max, INL_SF);
+ FDKprintf("reference %i %i %i\n", (int)floor(X_MIN), (int)floor(X_NULL), (int)floor(X_MAX));
+ FDKprintf("fixp_floorToInt %i %i %i\n", res1, res2, res3);
+ FDKprintf("fixp_floor %10.7f %10.7f %10.7f\n", (float)f_res1*(float)FDKpow(2,INL_SF),
+ (float)f_res2*(float)FDKpow(2,INL_SF),
+ (float)f_res3*(float)FDKpow(2,INL_SF));
+ FDKprintf("\n\n\n");
+
+
+ FDKprintf("---- ceil ----\n");
+ res0 = fixp_ceilToInt(f_reg0, INL_SF); f_res0 = fixp_ceil(f_reg0, INL_SF);
+ res1 = fixp_ceilToInt(f_reg1, INL_SF); f_res1 = fixp_ceil(f_reg1, INL_SF);
+ res2 = fixp_ceilToInt(f_reg2, INL_SF); f_res2 = fixp_ceil(f_reg2, INL_SF);
+ res3 = fixp_ceilToInt(f_reg3, INL_SF); f_res3 = fixp_ceil(f_reg3, INL_SF);
+ res4 = fixp_ceilToInt(f_reg4, INL_SF); f_res4 = fixp_ceil(f_reg4, INL_SF);
+ res5 = fixp_ceilToInt(f_reg5, INL_SF); f_res5 = fixp_ceil(f_reg5, INL_SF);
+ res6 = fixp_ceilToInt(f_reg6, INL_SF); f_res6 = fixp_ceil(f_reg6, INL_SF);
+ res7 = fixp_ceilToInt(f_reg7, INL_SF); f_res7 = fixp_ceil(f_reg7, INL_SF);
+ res8 = fixp_ceilToInt(f_reg8, INL_SF); f_res8 = fixp_ceil(f_reg8, INL_SF);
+ FDKprintf("reference %i %i %i %i %i %i %i %i %i\n", (int)ceil(X0), (int)ceil(X1), (int)ceil(X2), (int)ceil(X3), (int)ceil(X4), (int)ceil(X5), (int)ceil(X6), (int)ceil(X7), (int)ceil(X8));
+ FDKprintf("fixp_ceilToInt %i %i %i %i %i %i %i %i %i\n", res0, res1, res2, res3, res4, res5, res6, res7, res8);
+ FDKprintf("fixp_ceil %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f\n", (float)f_res0*(float)FDKpow(2,INL_SF),
+ (float)f_res1*(float)FDKpow(2,INL_SF),
+ (float)f_res2*(float)FDKpow(2,INL_SF),
+ (float)f_res3*(float)FDKpow(2,INL_SF),
+ (float)f_res4*(float)FDKpow(2,INL_SF),
+ (float)f_res5*(float)FDKpow(2,INL_SF),
+ (float)f_res6*(float)FDKpow(2,INL_SF),
+ (float)f_res7*(float)FDKpow(2,INL_SF),
+ (float)f_res8*(float)FDKpow(2,INL_SF));
+
+ FDKprintf("\n---- min/max ceil ----\n");
+ res1 = fixp_ceilToInt(f_reg_min, INL_SF);
+ res2 = fixp_ceilToInt(f_reg_null, INL_SF);
+ res3 = fixp_ceilToInt(f_reg_max, INL_SF);
+
+ f_res1 = fixp_ceil(f_reg_min, INL_SF);
+ f_res2 = fixp_ceil(f_reg_null, INL_SF);
+ f_res3 = fixp_ceil(f_reg_max, INL_SF);
+
+ FDKprintf("reference %i %i %i\n", (int)ceil(X_MIN), (int)ceil(X_NULL), (int)ceil(X_MAX));
+ FDKprintf("fixp_ceilToInt %i %i %i\n", res1, res2, res3);
+ FDKprintf("fixp_ceil %10.7f %10.7f %10.7f\n", (float)f_res1*(float)FDKpow(2,INL_SF),
+ (float)f_res2*(float)FDKpow(2,INL_SF),
+ (float)f_res3*(float)FDKpow(2,INL_SF));
+ FDKprintf("\n\n\n");
+
+
+ FDKprintf("---- trunc ----\n");
+ res0 = fixp_truncateToInt(f_reg0, INL_SF); f_res0 = fixp_truncate(f_reg0, INL_SF);
+ res1 = fixp_truncateToInt(f_reg1, INL_SF); f_res1 = fixp_truncate(f_reg1, INL_SF);
+ res2 = fixp_truncateToInt(f_reg2, INL_SF); f_res2 = fixp_truncate(f_reg2, INL_SF);
+ res3 = fixp_truncateToInt(f_reg3, INL_SF); f_res3 = fixp_truncate(f_reg3, INL_SF);
+ res4 = fixp_truncateToInt(f_reg4, INL_SF); f_res4 = fixp_truncate(f_reg4, INL_SF);
+ res5 = fixp_truncateToInt(f_reg5, INL_SF); f_res5 = fixp_truncate(f_reg5, INL_SF);
+ res6 = fixp_truncateToInt(f_reg6, INL_SF); f_res6 = fixp_truncate(f_reg6, INL_SF);
+ res7 = fixp_truncateToInt(f_reg7, INL_SF); f_res7 = fixp_truncate(f_reg7, INL_SF);
+ res8 = fixp_truncateToInt(f_reg8, INL_SF); f_res8 = fixp_truncate(f_reg8, INL_SF);
+ FDKprintf("reference %i %i %i %i %i %i %i %i %i\n", (int)(X0), (int)(X1), (int)(X2), (int)(X3), (int)(X4), (int)(X5), (int)(X6), (int)(X7), (int)(X8));
+ FDKprintf("fixp_truncateToInt %i %i %i %i %i %i %i %i %i\n", res0, res1, res2, res3, res4, res5, res6, res7, res8);
+ FDKprintf("fixp_truncate %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f\n", (float)f_res0*(float)FDKpow(2,INL_SF),
+ (float)f_res1*(float)FDKpow(2,INL_SF),
+ (float)f_res2*(float)FDKpow(2,INL_SF),
+ (float)f_res3*(float)FDKpow(2,INL_SF),
+ (float)f_res4*(float)FDKpow(2,INL_SF),
+ (float)f_res5*(float)FDKpow(2,INL_SF),
+ (float)f_res6*(float)FDKpow(2,INL_SF),
+ (float)f_res7*(float)FDKpow(2,INL_SF),
+ (float)f_res8*(float)FDKpow(2,INL_SF));
+
+ FDKprintf("\n---- min/max trunc ----\n");
+ res1 = fixp_truncateToInt(f_reg_min, INL_SF); f_res1 = fixp_truncate(f_reg_min, INL_SF);
+ res2 = fixp_truncateToInt(f_reg_null,INL_SF); f_res2 = fixp_truncate(f_reg_null,INL_SF);
+ res3 = fixp_truncateToInt(f_reg_max, INL_SF); f_res3 = fixp_truncate(f_reg_max, INL_SF);
+ FDKprintf("reference %i %i %i\n", (int)(X_MIN), (int)(X_NULL), (int)(X_MAX));
+ FDKprintf("fixp_truncateToInt %i %i %i\n", res1, res2, res3);
+ FDKprintf("fixp_truncate %10.7f %10.7f %10.7f\n", (float)f_res1*(float)FDKpow(2,INL_SF),
+ (float)f_res2*(float)FDKpow(2,INL_SF),
+ (float)f_res3*(float)FDKpow(2,INL_SF));
+ FDKprintf("\n\n\n");
+
+
+ FDKprintf("---- round ----\n");
+ res0 = fixp_roundToInt(f_reg0, INL_SF); f_res0 = fixp_round(f_reg0, INL_SF);
+ res1 = fixp_roundToInt(f_reg1, INL_SF); f_res1 = fixp_round(f_reg1, INL_SF);
+ res2 = fixp_roundToInt(f_reg2, INL_SF); f_res2 = fixp_round(f_reg2, INL_SF);
+ res3 = fixp_roundToInt(f_reg3, INL_SF); f_res3 = fixp_round(f_reg3, INL_SF);
+ res4 = fixp_roundToInt(f_reg4, INL_SF); f_res4 = fixp_round(f_reg4, INL_SF);
+ res5 = fixp_roundToInt(f_reg5, INL_SF); f_res5 = fixp_round(f_reg5, INL_SF);
+ res6 = fixp_roundToInt(f_reg6, INL_SF); f_res6 = fixp_round(f_reg6, INL_SF);
+ res7 = fixp_roundToInt(f_reg7, INL_SF); f_res7 = fixp_round(f_reg7, INL_SF);
+ res8 = fixp_roundToInt(f_reg8, INL_SF); f_res8 = fixp_round(f_reg8, INL_SF);
+ FDKprintf("reference %i %i %i %i %i %i %i %i %i\n", roundRef(X0),
+ roundRef(X1),
+ roundRef(X2),
+ roundRef(X3),
+ roundRef(X4),
+ roundRef(X5),
+ roundRef(X6),
+ roundRef(X7),
+ roundRef(X8));
+ FDKprintf("fixp_roundToInt %i %i %i %i %i %i %i %i %i\n", res0, res1, res2, res3, res4, res5, res6, res7, res8);
+ FDKprintf("fixp_round %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f %10.7f\n", (float)f_res0*(float)FDKpow(2,INL_SF),
+ (float)f_res1*(float)FDKpow(2,INL_SF),
+ (float)f_res2*(float)FDKpow(2,INL_SF),
+ (float)f_res3*(float)FDKpow(2,INL_SF),
+ (float)f_res4*(float)FDKpow(2,INL_SF),
+ (float)f_res5*(float)FDKpow(2,INL_SF),
+ (float)f_res6*(float)FDKpow(2,INL_SF),
+ (float)f_res7*(float)FDKpow(2,INL_SF),
+ (float)f_res8*(float)FDKpow(2,INL_SF));
+
+ FDKprintf("\n---- min/max round ----\n");
+ res1 = fixp_roundToInt(f_reg_min, INL_SF); f_res1 = fixp_round(f_reg_min, INL_SF);
+ res2 = fixp_roundToInt(f_reg_null,INL_SF); f_res2 = fixp_round(f_reg_null,INL_SF);
+ res3 = fixp_roundToInt(f_reg_max, INL_SF); f_res3 = fixp_round(f_reg_max, INL_SF);
+
+ FDKprintf("reference %i %i %i\n", roundRef(X_MIN),
+ roundRef(X_NULL),
+ roundRef(X_MAX));
+ FDKprintf("fixp_roundToInt %i %i %i\n", res1, res2, res3);
+ FDKprintf("fixp_round %10.7f %10.7f %10.7f\n", (float)f_res1*(float)FDKpow(2,INL_SF),
+ (float)f_res2*(float)FDKpow(2,INL_SF),
+ (float)f_res3*(float)FDKpow(2,INL_SF));
+ FDKprintf("\n\n\n");
+
+}
+#endif