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|
/***************************************************************
__ST_EXP.C
This file contains source code of functions for
EXP constants operations.
PART OF : MPU - library .
USAGE : Internal only .
NOTE : NONE .
Copyright (C) 2000 - 2024 by Andrew V.Kosteltsev.
All Rights Reserved.
***************************************************************/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <errno.h> /* errno(3) */
#include <string.h> /* strcpy(3) */
#include <strings.h> /* bzero(3) */
#include <stdlib.h>
#include <libmpu.h>
#include <mpu-context.h>
#include <mpu-emutype.h>
#include <mpu-integer.h>
#include <mpu-real.h>
#include <mpu-floatp.h>
#include <mpu-char.h>
#include <mpu-symbols.h>
#include <mpu-math-errno.h>
#include <mpu-mtherr.h>
/***************************************************************
Кодировка имен файлов:
Трехзначное десятичное число, представляющее количество
128-и битных слов, из которых состоят вещественные числа
размещенные в массивах:
размер чисел в битах кодировка
-------------------- ---------
128 001
256 002
512 004
1024 008
2048 016
4096 032
8192 064
16384 128
32768 256
65536 512 (это предел);
ПРИМЕРЫ:
-------
ei_exp_001_emu32lsb.dfn - 128-бит,
ei_exp_512_emu32lsb.dfn - 65536-бит.
***************************************************************/
#if MPU_MATH_FN_LIMIT >= 128
#if MPU_WORD_ORDER_BIG_ENDIAN == 0
#include <math/exp/emu00128/ei_exp_001_emu32lsb.dfn>
#else
#include <math/exp/emu00128/ei_exp_001_emu32msb.dfn>
#endif
#endif /* MPU_MATH_FN_LIMIT >= 128 */
#if MPU_MATH_FN_LIMIT >= 256
#if MPU_WORD_ORDER_BIG_ENDIAN == 0
#include <math/exp/emu00256/ei_exp_002_emu32lsb.dfn>
#else
#include <math/exp/emu00256/ei_exp_002_emu32msb.dfn>
#endif
#endif /* MPU_MATH_FN_LIMIT >= 256 */
#if MPU_MATH_FN_LIMIT >= 512
#if MPU_WORD_ORDER_BIG_ENDIAN == 0
#include <math/exp/emu00512/ei_exp_004_emu32lsb.dfn>
#else
#include <math/exp/emu00512/ei_exp_004_emu32msb.dfn>
#endif
#endif /* MPU_MATH_FN_LIMIT >= 512 */
#if MPU_MATH_FN_LIMIT >= 1024
#if MPU_WORD_ORDER_BIG_ENDIAN == 0
#include <math/exp/emu01024/ei_exp_008_emu32lsb.dfn>
#else
#include <math/exp/emu01024/ei_exp_008_emu32msb.dfn>
#endif
#endif /* MPU_MATH_FN_LIMIT >= 1024 */
#if MPU_MATH_FN_LIMIT >= 2048
#if MPU_WORD_ORDER_BIG_ENDIAN == 0
#include <math/exp/emu02048/ei_exp_016_emu32lsb.dfn>
#else
#include <math/exp/emu02048/ei_exp_016_emu32msb.dfn>
#endif
#endif /* MPU_MATH_FN_LIMIT >= 2048 */
#if MPU_MATH_FN_LIMIT >= 4096
#if MPU_WORD_ORDER_BIG_ENDIAN == 0
#include <math/exp/emu04096/ei_exp_032_emu32lsb.dfn>
#else
#include <math/exp/emu04096/ei_exp_032_emu32msb.dfn>
#endif
#endif /* MPU_MATH_FN_LIMIT >= 4096 */
#if MPU_MATH_FN_LIMIT >= 8192
#if MPU_WORD_ORDER_BIG_ENDIAN == 0
#include <math/exp/emu08192/ei_exp_064_emu32lsb.dfn>
#else
#include <math/exp/emu08192/ei_exp_064_emu32msb.dfn>
#endif
#endif /* MPU_MATH_FN_LIMIT >= 8192 */
#if MPU_MATH_FN_LIMIT >= 16384
#if MPU_WORD_ORDER_BIG_ENDIAN == 0
#include <math/exp/emu16384/ei_exp_128_emu32lsb.dfn>
#else
#include <math/exp/emu16384/ei_exp_128_emu32msb.dfn>
#endif
#endif /* MPU_MATH_FN_LIMIT >= 16384 */
#if MPU_MATH_FN_LIMIT >= 32768
#if MPU_WORD_ORDER_BIG_ENDIAN == 0
#include <math/exp/emu32768/ei_exp_256_emu32lsb.dfn>
#else
#include <math/exp/emu32768/ei_exp_256_emu32msb.dfn>
#endif
#endif /* MPU_MATH_FN_LIMIT >= 32768 */
#if MPU_MATH_FN_LIMIT >= 65536
#if MPU_WORD_ORDER_BIG_ENDIAN == 0
#include <math/exp/emu65536/ei_exp_512_emu32lsb.dfn>
#else
#include <math/exp/emu65536/ei_exp_512_emu32msb.dfn>
#endif
#endif /* MPU_MATH_FN_LIMIT >= 65536 */
static int _get_n_exp( int nb )
{
int rc = 0;
if( nb < NBR_32 || nb > MPU_MATH_FN_LIMIT )
{
/* error: Invalid size of operand(s) */
__real_error_no = __R_ESIZE__;
__STIND; /* Set REAL ind-produsing operation Flag */
return( rc );
}
switch( nb )
{
#if MPU_MATH_FN_LIMIT >= 128
case NBR_32 :
case NBR_64 :
case NBR_128 :
rc = N_EXP_E128;
break;
#endif /* MPU_MATH_FN_LIMIT >= 128 */
#if MPU_MATH_FN_LIMIT >= 256
case NBR_256 :
rc = N_EXP_E256;
break;
#endif /* MPU_MATH_FN_LIMIT >= 256 */
#if MPU_MATH_FN_LIMIT >= 512
case NBR_512 :
rc = N_EXP_E512;
break;
#endif /* MPU_MATH_FN_LIMIT >= 512 */
#if MPU_MATH_FN_LIMIT >= 1024
case NBR_1024 :
rc = N_EXP_E1024;
break;
#endif /* MPU_MATH_FN_LIMIT >= 1024 */
#if MPU_MATH_FN_LIMIT >= 2048
case NBR_2048 :
rc = N_EXP_E2048;
break;
#endif /* MPU_MATH_FN_LIMIT >= 2048 */
#if MPU_MATH_FN_LIMIT >= 4096
case NBR_4096 :
rc = N_EXP_E4096;
break;
#endif /* MPU_MATH_FN_LIMIT >= 4096 */
#if MPU_MATH_FN_LIMIT >= 8192
case NBR_8192 :
rc = N_EXP_E8192;
break;
#endif /* MPU_MATH_FN_LIMIT >= 8192 */
#if MPU_MATH_FN_LIMIT >= 16384
case NBR_16384:
rc = N_EXP_E16384;
break;
#endif /* MPU_MATH_FN_LIMIT >= 16384 */
default:
{
/* error: Invalid size of operand(s) */
__real_error_no = __R_ESIZE__;
__STIND; /* Set REAL ind-produsing operation Flag */
break;
}
} /* End of switch( nb ) */
return( rc );
} /* End of _get_n_exp() */
static EMUSHORT *_get_exp__E_ptr( int nb )
{
EMUSHORT *rc = (EMUSHORT *)NULL;
if( nb < NBR_32 || nb > MPU_MATH_FN_LIMIT )
{
/* error: Invalid size of operand(s) */
__real_error_no = __R_ESIZE__;
__STIND; /* Set REAL ind-produsing operation Flag */
return( rc );
}
switch( nb )
{
#if MPU_MATH_FN_LIMIT >= 128
case NBR_32 :
case NBR_64 :
case NBR_128 :
rc = (EMUSHORT *)&_ei_exp__E_128_[0][0];
break;
#endif /* MPU_MATH_FN_LIMIT >= 128 */
#if MPU_MATH_FN_LIMIT >= 256
case NBR_256 :
rc = (EMUSHORT *)&_ei_exp__E_256_[0][0];
break;
#endif /* MPU_MATH_FN_LIMIT >= 256 */
#if MPU_MATH_FN_LIMIT >= 512
case NBR_512 :
rc = (EMUSHORT *)&_ei_exp__E_512_[0][0];
break;
#endif /* MPU_MATH_FN_LIMIT >= 512 */
#if MPU_MATH_FN_LIMIT >= 1024
case NBR_1024 :
rc = (EMUSHORT *)&_ei_exp__E_1024_[0][0];
break;
#endif /* MPU_MATH_FN_LIMIT >= 1024 */
#if MPU_MATH_FN_LIMIT >= 2048
case NBR_2048 :
rc = (EMUSHORT *)&_ei_exp__E_2048_[0][0];
break;
#endif /* MPU_MATH_FN_LIMIT >= 2048 */
#if MPU_MATH_FN_LIMIT >= 4096
case NBR_4096 :
rc = (EMUSHORT *)&_ei_exp__E_4096_[0][0];
break;
#endif /* MPU_MATH_FN_LIMIT >= 4096 */
#if MPU_MATH_FN_LIMIT >= 8192
case NBR_8192 :
rc = (EMUSHORT *)&_ei_exp__E_8192_[0][0];
break;
#endif /* MPU_MATH_FN_LIMIT >= 8192 */
#if MPU_MATH_FN_LIMIT >= 16384
case NBR_16384:
rc = (EMUSHORT *)&_ei_exp__E_16384_[0][0];
break;
#endif /* MPU_MATH_FN_LIMIT >= 16384 */
default:
{
/* error: Invalid size of operand(s) */
__real_error_no = __R_ESIZE__;
__STIND; /* Set REAL ind-produsing operation Flag */
break;
}
} /* End of switch( nb ) */
return( rc );
} /* End of _get_exp__E_ptr() */
void ei_exp__E( EMUSHORT *eiy, EMUSHORT *eix, int nb )
/***************************************************************
Description : ei_exp__E() Работает с
internal e-type data struct.
Concepts : SEE: ei_exp() [polinom R].
ACCURACY : In the absence of rounding error,
the appriximation has absolute error
less than EPSILON [see: FLOATP.H].
NOTE : The coefficient L's are obtained by
a special Remez algorithm.
===============================================
В INTERNET я нашел следующие алгоритмы:
409 cacm 355 356 14 5 May 1971 e2 A60
------------------------------------------
H. Schmitt;
Discrete {Chebychev} Curve Fit
approximation;Chebyshev approximation;
Chebyshev curve fitting;
+Chebyshev polynomial;
curve approximation;curve fitting;
exchange algorithm;
+polynomial approximation;Remez algorithm;
501 toms 95 97 2 1 March 1976 e2 F K2
---------------------------------------------
J. C. Simpson;
{FORTRAN} Translation of Algorithm 409
Discrete {Chebyshev} Curve Fit
approximation;polynomial approximation;
exchange algorithm;
+Chebyshev approximation;
polynomial approximation;
R,toms,95,4,1,March,1978,F. Futrell;
последний из которых я перевел на "С", затем
на язык операций повышенной разрядности.
===============================================
Use Global Variable:
Use Functions : internal_np( nb ); | real.c
ei_copy( eiy, eix, nb ); | real.c
_gen_zero( eic, nb ); | real.c
ei_add( eic,eia,eib,nb ); | real.c
ei_mul( eic,eia,eib,nb ); | real.c
Parameters : EMUSHORT *eiy; - указатель на
internal e-type
data struct.
TARGET;
EMUSHORT *eix; - указатель на
internal e-type
data struct.
SOURCE;
int nb; - количество бит в
external e-type
data struct.
Return : [void]
***************************************************************/
{
EMUSHORT *x = NULL, *y = NULL;
EMUSHORT *p;
int np;
int i, n = _get_n_exp( nb );
np = internal_np( nb );
/*** Allocate memory for x, y . *****************************/
x = (EMUSHORT *)__mpu_sbrk( (int)(np*SIZE_OF_EMUSHORT) );
if( !x )
{
/* fatal error */
return;
}
y = (EMUSHORT *)__mpu_sbrk( (int)(np*SIZE_OF_EMUSHORT) );
if( !y )
{
/* fatal error */
/* FREE x *****************/
__mpu_sbrk( -(int)(np*SIZE_OF_EMUSHORT) );
/**************************/
return;
}
/************************************************************/
_gen_zero( y, nb );
ei_copy( x, eix, nb );
p = _get_exp__E_ptr( nb );
for( i = 0; i < n; i++ )
{
ei_add( y, y, p, nb );
ei_mul( y, y, x, nb );
p += np;
}
ei_copy( eiy, y, nb );
/* FREE x *****************/
/* FREE y *****************/
__mpu_sbrk( -(int)(2*np*SIZE_OF_EMUSHORT) );
/**************************/
} /* End of ei_exp__E() */
/***************************************************************
Hide internal symbols:
***************************************************************/
__mpu_hidden_decl(ei_exp__E);
/*
End of hide internal symbols.
***************************************************************/
|
