ntypes.h

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//
//  ntypes.h
//
//  Authors: Nicolae Mihalache & François Vigneron
//
//  This software is released under BSD licence, with an attribution clause (see Licence file).
//  Please cite the reference below if you use or distribute this software.
//
//  • [1] R. Anton, N. Mihalache & F. Vigneron. Fast evaluation of real and complex polynomials. 2022.
//        https://hal.archives-ouvertes.fr/hal-03820369
//
//  Copyright 2022 Univ. Paris-Est Créteil & Univ. de Reims Champagne-Ardenne.
//
 
#ifndef ntypes_h
#define ntypes_h
 
#include <inttypes.h>
#include <stdint.h>
#include <math.h>
 
typedef uint8_t byte;
 
typedef uint16_t word;
 
typedef uint32_t uint;
 
typedef uint64_t ulong;
 
typedef byte bool;
 
#define true   1
 
#define false  0
 
#define PI (3.14159265358979323846264338327950288L)
 
// comment this line to use the fastest precise machine floating point numbers
// for polynomial evaluation (@c fp64 numbers)
// leave the line uncommented to use @c fp80 numbers on x86 machines, that occupy
// 16 bytes of memory, but only use 10 bytes for storing the numbers
// #define MACHINE_EXTRA_PREC
 
// Comment the previous line and uncomment this line to use 32-bit floats for coefficients
// #define MACHINE_LOW_PREC
 
#ifdef MACHINE_EXTRA_PREC
  typedef long double coeff_t;
  #define flog2 log2l
  #define fhypot hypotl
  #define ffloor floorl
  #define fpow powl
  #define fexp expl
  #define fsin sinl
  #define fcos cosl
  #define ftan tanl
  #define mpfr_getf mpfr_get_ld
  #define precf 64
  #define PRECF_STR "64"
  #define TYPEFP_STR "FP80"
  #define TYPEF_STR "long double"
  #define INF_M (-HUGE_VALL)
  #define INF_P HUGE_VALL
  #define FMT_COEFF "L"
#else
#ifndef MACHINE_LOW_PREC
  typedef double coeff_t;
  #define flog2 log2
  #define fhypot hypot
  #define ffloor floor
  #define fpow pow
  #define fexp exp
  #define fsin sin
  #define fcos cos
  #define ftan tan
  #define mpfr_getf mpfr_get_d
  #define precf 53
  #define PRECF_STR "53"
  #define TYPEFP_STR "FP64"
  #define TYPEF_STR "double"
  #define INF_M (-HUGE_VAL)
  #define INF_P HUGE_VAL
  #define FMT_COEFF "l"
#else
  typedef float coeff_t;
  #define flog2 log2f
  #define fhypot hypotf
  #define ffloor floorf
  #define fpow powf
  #define fexp expf
  #define fsin sinf
  #define fcos cosf
  #define ftan tanf
  #define mpfr_getf mpfr_get_f
  #define precf 24
  #define PRECF_STR "24"
  #define TYPEFP_STR "FP32"
  #define TYPEF_STR "float"
  #define INF_M (-HUGE_VALF)
  #define INF_P HUGE_VALF
  #define FMT_COEFF ""
#endif
#endif
 
#define MAX_EXP (sizeof(coeff_t) == 8 ? 960 : 16320)
 
 
// Comment this line to limit the degree of the polynomials to 2^32-2
// leave this line uncommented to use degrees up to 2^64-2
#define HUGE_DEGREES
 
#ifdef HUGE_DEGREES
  typedef ulong deg_t;
  #define MAX_DEG (UINT64_MAX - 1)
  #define FMT_DEG PRIu64
#else
  typedef uint deg_t;
  #define MAX_DEG (UINT32_MAX - 1)
  #define FMT_DEG PRIu32
#endif
 
 
// Comment this line to use the fastest precise machine floating point numbers
// for polynomial pre-condtionning; largely enough in 99+% usage cases
// leave the line uncommented to use @c fp80 numbers on x86 machines, that occupy
// 16 bytes of memory, but only use 10 bytes for storing the numbers
//#define INTERNAL_EXTRA_PREC
 
#ifdef INTERNAL_EXTRA_PREC
  typedef long double real_t;
  #define plog2 log2l
  #define pexp2 exp2l
  #define phypot hypotl
  #define pfloor floorl
  #define pceil ceill
  #define mpfr_getp mpfr_get_ld
  #define PEPS 1E-3000L
  #define PDEL 1E-15L
  #define pexp expl
  #define pcos cosl
  #define psin sinl
  #define ptan tanl
  #define pldexp ldexpl
  #define pfrexp frexpl
  #define FMT_REAL "L"
#else
  typedef double real_t;
  #define plog2 log2
  #define pexp2 exp2
  #define phypot hypot
  #define pfloor floor
  #define pceil ceil
  #define mpfr_getp mpfr_get_d
  #define PEPS 1E-200
  #define PDEL 1E-12
  #define pexp exp
  #define pcos cos
  #define psin sin
  #define ptan tan
  #define pldexp ldexp
  #define pfrexp frexp
  #define FMT_REAL "l"
#endif
 
 
// Comment this line to limit the precision of mpfr numbers to to 4 * 10^9
// leave this line uncommented to use up to 16 * 10^18 bits for each number
#define HUGE_PREC
 
#ifdef HUGE_PREC
  typedef ulong prec_t;
  #define MAX_PREC (16000000000000000000UL)
#else
  typedef uint prec_t;
  #define MAX_PREC (4000000000UL)
#endif
 
// Comment this line to limit the exponents of mpfr numbers to to +/- 2 * 10^9
// leave this line uncommented to use exponents in the range +/- 4 * 10^18
#define HUGE_MP_EXP
 
#ifdef HUGE_MP_EXP
  #define MAX_MP_EXP (4000000000000000000L)
#else
  #define MAX_MP_EXP (2000000000L)
#endif
 
#define NEWTON_CONV_BITS     5
#define NEWTON_ESCAPE_BITS   4
 
bool ntypes_check(void);
 
real_t bits_sum(real_t b1, real_t b2);
 
real_t nt_err(real_t vb, real_t evb, real_t db, real_t edb);
 
#endif /* ntypes_h */