453 lines
18 KiB
C++
453 lines
18 KiB
C++
// Copyright (c) Microsoft Corporation. All rights reserved.
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// Licensed under the MIT License.
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#pragma once
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//-----------------------------------------------------------------------------
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// Package Title ratpak
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// File ratpak.h
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// Copyright (C) 1995-99 Microsoft
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// Date 01-16-95
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//
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//
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// Description
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//
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// Infinite precision math package header file, if you use ratpak.lib you
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// need to include this header.
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//
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//-----------------------------------------------------------------------------
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#include "CalcErr.h"
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static constexpr uint32_t BASEXPWR = 31L;// Internal log2(BASEX)
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static constexpr uint32_t BASEX = 0x80000000; // Internal radix used in calculations, hope to raise
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// this to 2^32 after solving scaling problems with
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// overflow detection esp. in mul
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typedef unsigned long MANTTYPE;
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typedef unsigned __int64 TWO_MANTTYPE;
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enum eNUMOBJ_FMT {
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FMT_FLOAT, // returns floating point, or exponential if number is too big
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FMT_SCIENTIFIC, // always returns scientific notation
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FMT_ENGINEERING // always returns engineering notation such that exponent is a multiple of 3
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};
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enum eANGLE_TYPE {
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ANGLE_DEG, // Calculate trig using 360 degrees per revolution
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ANGLE_RAD, // Calculate trig using 2 pi radians per revolution
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ANGLE_GRAD // Calculate trig using 400 gradients per revolution
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};
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typedef enum eNUMOBJ_FMT NUMOBJ_FMT;
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typedef enum eANGLE_TYPE ANGLE_TYPE;
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//-----------------------------------------------------------------------------
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//
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// NUMBER type is a representation of a generic sized generic radix number
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//
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//-----------------------------------------------------------------------------
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#pragma warning(push)
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#pragma warning(disable:4200) // nonstandard extension used : zero-sized array in struct/union
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typedef struct _number
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{
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long sign; // The sign of the mantissa, +1, or -1
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long cdigit; // The number of digits, or what passes for digits in the
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// radix being used.
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long exp; // The offset of digits from the radix point
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// (decimal point in radix 10)
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MANTTYPE mant[];
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// This is actually allocated as a continuation of the
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// NUMBER structure.
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} NUMBER, *PNUMBER, **PPNUMBER;
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#pragma warning(pop)
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//-----------------------------------------------------------------------------
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//
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// RAT type is a representation radix on 2 NUMBER types.
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// pp/pq, where pp and pq are pointers to integral NUMBER types.
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//
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//-----------------------------------------------------------------------------
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typedef struct _rat
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{
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PNUMBER pp;
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PNUMBER pq;
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} RAT, *PRAT;
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static constexpr uint32_t MAX_LONG_SIZE = 33; // Base 2 requires 32 'digits'
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//-----------------------------------------------------------------------------
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//
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// List of useful constants for evaluation, note this list needs to be
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// initialized.
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//
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//-----------------------------------------------------------------------------
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extern PNUMBER num_one;
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extern PNUMBER num_two;
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extern PNUMBER num_five;
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extern PNUMBER num_six;
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extern PNUMBER num_ten;
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extern PRAT ln_ten;
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extern PRAT ln_two;
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extern PRAT rat_zero;
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extern PRAT rat_neg_one;
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extern PRAT rat_one;
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extern PRAT rat_two;
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extern PRAT rat_six;
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extern PRAT rat_half;
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extern PRAT rat_ten;
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extern PRAT pt_eight_five;
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extern PRAT pi;
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extern PRAT pi_over_two;
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extern PRAT two_pi;
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extern PRAT one_pt_five_pi;
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extern PRAT e_to_one_half;
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extern PRAT rat_exp;
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extern PRAT rad_to_deg;
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extern PRAT rad_to_grad;
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extern PRAT rat_qword;
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extern PRAT rat_dword;
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extern PRAT rat_word;
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extern PRAT rat_byte;
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extern PRAT rat_360;
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extern PRAT rat_400;
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extern PRAT rat_180;
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extern PRAT rat_200;
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extern PRAT rat_nRadix;
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extern PRAT rat_smallest;
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extern PRAT rat_negsmallest;
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extern PRAT rat_max_exp;
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extern PRAT rat_min_exp;
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extern PRAT rat_max_fact;
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extern PRAT rat_min_fact;
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extern PRAT rat_max_long;
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extern PRAT rat_min_long;
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// DUPNUM Duplicates a number taking care of allocation and internals
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#define DUPNUM(a,b) destroynum(a);createnum( a, (b)->cdigit );_dupnum(a, b);
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// DUPRAT Duplicates a rational taking care of allocation and internals
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#define DUPRAT(a,b) destroyrat(a);createrat(a);DUPNUM((a)->pp,(b)->pp);DUPNUM((a)->pq,(b)->pq);
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// LOG*RADIX calculates the integral portion of the log of a number in
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// the base currently being used, only accurate to within g_ratio
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#define LOGNUMRADIX(pnum) (((pnum)->cdigit+(pnum)->exp)*g_ratio)
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#define LOGRATRADIX(prat) (LOGNUMRADIX((prat)->pp)-LOGNUMRADIX((prat)->pq))
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// LOG*2 calculates the integral portion of the log of a number in
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// the internal base being used, only accurate to within g_ratio
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#define LOGNUM2(pnum) ((pnum)->cdigit+(pnum)->exp)
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#define LOGRAT2(prat) (LOGNUM2((prat)->pp)-LOGNUM2((prat)->pq))
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#if defined( DEBUG_RATPAK )
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//-----------------------------------------------------------------------------
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//
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// Debug versions of rational number creation and destruction routines.
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// used for debugging allocation errors.
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//
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//-----------------------------------------------------------------------------
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#define createrat(y) (y)=_createrat(); \
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{ \
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std::wstringstream outputString; \
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outputString << "createrat " << y << " " << # y << " file= " << __FILE__ << ", line= " << __LINE__ << "\n"; \
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OutputDebugString(outputString.str().c_str()); \
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}
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#define destroyrat(x) \
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{ \
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std::wstringstream outputString; \
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outputString << "destroyrat " << x << " file= " << __FILE__ << ", line= " << __LINE__ << "\n"; \
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OutputDebugString(outputString.str().c_str()); \
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} \
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_destroyrat(x),(x)=nullptr
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#define createnum(y,x) (y)=_createnum(x); \
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{ \
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std::wstringstream outputString; \
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outputString << "createnum " << y << " " << # y << " file= " << __FILE__ << ", line= " << __LINE__ << "\n"; \
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OutputDebugString(outputString.str().c_str()); \
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}
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#define destroynum(x) \
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{ \
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std::wstringstream outputString; \
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outputString << "destroynum " << x << " file= " << __FILE__ << ", line= " << __LINE__ << "\n"; \
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OutputDebugString(outputString.str().c_str()); \
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} \
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_destroynum(x),(x)=nullptr
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#else
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#define createrat(y) (y)=_createrat()
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#define destroyrat(x) _destroyrat(x),(x)=nullptr
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#define createnum(y,x) (y)=_createnum(x)
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#define destroynum(x) _destroynum(x),(x)=nullptr
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#endif
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//-----------------------------------------------------------------------------
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//
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// Defines for checking when to stop taylor series expansions due to
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// precision satisfaction.
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//
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//-----------------------------------------------------------------------------
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// RENORMALIZE, gets the exponents non-negative.
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#define RENORMALIZE(x) if ( (x)->pp->exp < 0 ) { \
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(x)->pq->exp -= (x)->pp->exp; \
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(x)->pp->exp = 0; \
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} \
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if ( (x)->pq->exp < 0 ) { \
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(x)->pp->exp -= (x)->pq->exp; \
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(x)->pq->exp = 0; \
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}
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// TRIMNUM ASSUMES the number is in radix form NOT INTERNAL BASEX!!!
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#define TRIMNUM(x, precision) if ( !g_ftrueinfinite ) { \
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long trim = (x)->cdigit - precision-g_ratio;\
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if ( trim > 1 ) \
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{ \
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memmove( (x)->mant, &((x)->mant[trim]), sizeof(MANTTYPE)*((x)->cdigit-trim) ); \
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(x)->cdigit -= trim; \
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(x)->exp += trim; \
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} \
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}
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// TRIMTOP ASSUMES the number is in INTERNAL BASEX!!!
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#define TRIMTOP(x, precision) if ( !g_ftrueinfinite ) { \
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long trim = (x)->pp->cdigit - (precision/g_ratio) - 2;\
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if ( trim > 1 ) \
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{ \
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memmove( (x)->pp->mant, &((x)->pp->mant[trim]), sizeof(MANTTYPE)*((x)->pp->cdigit-trim) ); \
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(x)->pp->cdigit -= trim; \
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(x)->pp->exp += trim; \
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} \
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trim = min((x)->pp->exp,(x)->pq->exp);\
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(x)->pp->exp -= trim;\
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(x)->pq->exp -= trim;\
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}
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#define SMALL_ENOUGH_RAT(a, precision) (zernum((a)->pp) || ( ( ( (a)->pq->cdigit + (a)->pq->exp ) - ( (a)->pp->cdigit + (a)->pp->exp ) - 1 ) * g_ratio > precision ) )
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//-----------------------------------------------------------------------------
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//
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// Defines for setting up taylor series expansions for infinite precision
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// functions.
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//
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//-----------------------------------------------------------------------------
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#define CREATETAYLOR() PRAT xx=nullptr;\
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PNUMBER n2=nullptr; \
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PRAT pret=nullptr; \
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PRAT thisterm=nullptr; \
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DUPRAT(xx,*px); \
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mulrat(&xx,*px, precision); \
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createrat(pret); \
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pret->pp=longtonum( 0L, BASEX ); \
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pret->pq=longtonum( 0L, BASEX );
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#define DESTROYTAYLOR() destroynum( n2 ); \
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destroyrat( xx );\
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destroyrat( thisterm );\
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destroyrat( *px );\
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trimit(&pret, precision);\
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*px=pret;
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// INC(a) is the rational equivalent of a++
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// Check to see if we can avoid doing this the hard way.
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#define INC(a) if ( (a)->mant[0] < BASEX - 1 ) \
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{ \
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(a)->mant[0]++; \
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} \
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else \
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{ \
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addnum( &(a), num_one, BASEX); \
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}
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#define MSD(x) ((x)->mant[(x)->cdigit-1])
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// MULNUM(b) is the rational equivalent of thisterm *= b where thisterm is
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// a rational and b is a number, NOTE this is a mixed type operation for
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// efficiency reasons.
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#define MULNUM(b) mulnumx( &(thisterm->pp), b);
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// DIVNUM(b) is the rational equivalent of thisterm /= b where thisterm is
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// a rational and b is a number, NOTE this is a mixed type operation for
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// efficiency reasons.
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#define DIVNUM(b) mulnumx( &(thisterm->pq), b);
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// NEXTTERM(p,d) is the rational equivalent of
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// thisterm *= p
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// d <d is usually an expansion of operations to get thisterm updated.>
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// pret += thisterm
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#define NEXTTERM(p,d,precision) mulrat(&thisterm,p,precision);d addrat( &pret, thisterm, precision )
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//-----------------------------------------------------------------------------
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//
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// External variables used in the math package.
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//
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//-----------------------------------------------------------------------------
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extern bool g_ftrueinfinite; // set to true to allow infinite precision
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// don't use unless you know what you are doing
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// used to help decide when to stop calculating.
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extern long g_ratio; // Internally calculated ratio of internal radix
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//-----------------------------------------------------------------------------
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//
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// External functions defined in the math package.
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//
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//-----------------------------------------------------------------------------
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// Call whenever decimal separator character changes.
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extern void SetDecimalSeparator(wchar_t decimalSeparator);
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// Call whenever either radix or precision changes, is smarter about recalculating constants.
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extern void ChangeConstants(uint32_t radix, int32_t precision);
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extern bool equnum(_In_ PNUMBER a, _In_ PNUMBER b ); // returns true of a == b
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extern bool lessnum(_In_ PNUMBER a, _In_ PNUMBER b ); // returns true of a < b
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extern bool zernum(_In_ PNUMBER a ); // returns true of a == 0
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extern bool zerrat(_In_ PRAT a ); // returns true if a == 0/q
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extern std::wstring NumberToString(_Inout_ PNUMBER& pnum, int format, uint32_t radix, int32_t precision);
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// returns a text representation of a PRAT
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extern std::wstring RatToString(_Inout_ PRAT& prat, int format, uint32_t radix, int32_t precision);
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extern long numtolong(_In_ PNUMBER pnum, uint32_t radix );
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extern long rattolong(_In_ PRAT prat, uint32_t radix, int32_t precision);
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ULONGLONG rattoUlonglong(_In_ PRAT prat, uint32_t radix, int32_t precision);
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extern PNUMBER _createnum(_In_ ULONG size ); // returns an empty number structure with size digits
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extern PNUMBER nRadixxtonum(_In_ PNUMBER a, uint32_t radix, int32_t precision);
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extern PNUMBER gcd(_In_ PNUMBER a, _In_ PNUMBER b );
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extern PNUMBER StringToNumber(std::wstring_view numberString, uint32_t radix, int32_t precision); // takes a text representation of a number and returns a number.
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// takes a text representation of a number as a mantissa with sign and an exponent with sign.
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extern PRAT StringToRat(bool mantissaIsNegative, std::wstring_view mantissa, bool exponentIsNegative, std::wstring_view exponent, uint32_t radix, int32_t precision);
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extern PNUMBER longfactnum(long inlong, uint32_t radix);
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extern PNUMBER longprodnum(long start, long stop, uint32_t radix);
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extern PNUMBER longtonum(long inlong, uint32_t radix);
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extern PNUMBER Ulongtonum(unsigned long inlong, uint32_t radix);
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extern PNUMBER numtonRadixx(PNUMBER a, uint32_t radix);
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// creates a empty/undefined rational representation (p/q)
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extern PRAT _createrat( void );
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// returns a new rat structure with the acos of x->p/x->q taking into account
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// angle type
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extern void acosanglerat( _Inout_ PRAT *px, ANGLE_TYPE angletype, uint32_t radix, int32_t precision);
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// returns a new rat structure with the acosh of x->p/x->q
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extern void acoshrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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// returns a new rat structure with the acos of x->p/x->q
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extern void acosrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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// returns a new rat structure with the asin of x->p/x->q taking into account
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// angle type
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extern void asinanglerat( _Inout_ PRAT *px, ANGLE_TYPE angletype, uint32_t radix, int32_t precision);
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extern void asinhrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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// returns a new rat structure with the asinh of x->p/x->q
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// returns a new rat structure with the asin of x->p/x->q
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extern void asinrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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// returns a new rat structure with the atan of x->p/x->q taking into account
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// angle type
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extern void atananglerat( _Inout_ PRAT *px, ANGLE_TYPE angletype, uint32_t radix, int32_t precision);
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// returns a new rat structure with the atanh of x->p/x->q
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extern void atanhrat( _Inout_ PRAT *px, int32_t precision);
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// returns a new rat structure with the atan of x->p/x->q
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extern void atanrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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// returns a new rat structure with the cosh of x->p/x->q
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extern void coshrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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// returns a new rat structure with the cos of x->p/x->q
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extern void cosrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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// returns a new rat structure with the cos of x->p/x->q taking into account
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// angle type
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extern void cosanglerat( _Inout_ PRAT *px, ANGLE_TYPE angletype, uint32_t radix, int32_t precision);
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// returns a new rat structure with the exp of x->p/x->q this should not be called explicitly.
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extern void _exprat( _Inout_ PRAT *px, int32_t precision);
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// returns a new rat structure with the exp of x->p/x->q
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extern void exprat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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// returns a new rat structure with the log base 10 of x->p/x->q
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extern void log10rat( _Inout_ PRAT *px, int32_t precision);
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// returns a new rat structure with the natural log of x->p/x->q
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extern void lograt( _Inout_ PRAT *px, int32_t precision);
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extern PRAT longtorat( long inlong );
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extern PRAT Ulongtorat( unsigned long inulong );
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extern PRAT numtorat( _In_ PNUMBER pin, uint32_t radix);
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extern void sinhrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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extern void sinrat( _Inout_ PRAT *px );
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// returns a new rat structure with the sin of x->p/x->q taking into account
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// angle type
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extern void sinanglerat( _Inout_ PRAT *px, ANGLE_TYPE angletype, uint32_t radix, int32_t precision);
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extern void tanhrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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extern void tanrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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// returns a new rat structure with the tan of x->p/x->q taking into account
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// angle type
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extern void tananglerat( _Inout_ PRAT *px, ANGLE_TYPE angletype, uint32_t radix, int32_t precision);
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extern void _dupnum(_In_ PNUMBER dest, _In_ PNUMBER src);
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extern void _destroynum( _In_ PNUMBER pnum );
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extern void _destroyrat( _In_ PRAT prat );
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extern void addnum( _Inout_ PNUMBER *pa, _In_ PNUMBER b, uint32_t radix);
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extern void addrat( _Inout_ PRAT *pa, _In_ PRAT b, int32_t precision);
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extern void andrat( _Inout_ PRAT *pa, _In_ PRAT b, uint32_t radix, int32_t precision);
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extern void divnum( _Inout_ PNUMBER *pa, _In_ PNUMBER b, uint32_t radix, int32_t precision);
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extern void divnumx( _Inout_ PNUMBER *pa, _In_ PNUMBER b, int32_t precision);
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extern void divrat( _Inout_ PRAT *pa, _In_ PRAT b, int32_t precision);
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extern void fracrat( _Inout_ PRAT *pa , uint32_t radix, int32_t precision);
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extern void factrat( _Inout_ PRAT *pa, uint32_t radix, int32_t precision);
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extern void modrat( _Inout_ PRAT *pa, _In_ PRAT b );
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extern void gcdrat( _Inout_ PRAT *pa, uint32_t radix, int32_t precision);
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extern void intrat( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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extern void mulnum( _Inout_ PNUMBER *pa, _In_ PNUMBER b, uint32_t radix);
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extern void mulnumx( _Inout_ PNUMBER *pa, _In_ PNUMBER b );
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extern void mulrat( _Inout_ PRAT *pa, _In_ PRAT b, int32_t precision);
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extern void numpowlong( _Inout_ PNUMBER *proot, long power, uint32_t radix, int32_t precision);
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extern void numpowlongx( _Inout_ PNUMBER *proot, long power );
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extern void orrat( _Inout_ PRAT *pa, _In_ PRAT b, uint32_t radix, int32_t precision);
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extern void powrat( _Inout_ PRAT *pa, _In_ PRAT b , uint32_t radix, int32_t precision);
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extern void powratNumeratorDenominator(_Inout_ PRAT *pa, _In_ PRAT b, uint32_t radix, int32_t precision);
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extern void powratcomp(_Inout_ PRAT *pa, _In_ PRAT b, uint32_t radix, int32_t precision);
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extern void ratpowlong( _Inout_ PRAT *proot, long power, int32_t precision);
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extern void remnum( _Inout_ PNUMBER *pa, _In_ PNUMBER b, uint32_t radix);
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extern void rootrat( _Inout_ PRAT *pa, _In_ PRAT b , uint32_t radix, int32_t precision);
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extern void scale2pi( _Inout_ PRAT *px, uint32_t radix, int32_t precision);
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extern void scale( _Inout_ PRAT *px, _In_ PRAT scalefact, uint32_t radix, int32_t precision);
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extern void subrat( _Inout_ PRAT *pa, _In_ PRAT b, int32_t precision);
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extern void xorrat( _Inout_ PRAT *pa, _In_ PRAT b, uint32_t radix, int32_t precision);
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extern void lshrat( _Inout_ PRAT *pa, _In_ PRAT b , uint32_t radix, int32_t precision);
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extern void rshrat( _Inout_ PRAT *pa, _In_ PRAT b, uint32_t radix, int32_t precision);
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extern bool rat_equ( _In_ PRAT a, _In_ PRAT b, int32_t precision);
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extern bool rat_neq( _In_ PRAT a, _In_ PRAT b, int32_t precision);
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extern bool rat_gt( _In_ PRAT a, _In_ PRAT b, int32_t precision);
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extern bool rat_ge( _In_ PRAT a, _In_ PRAT b, int32_t precision);
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extern bool rat_lt( _In_ PRAT a, _In_ PRAT b, int32_t precision);
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extern bool rat_le( _In_ PRAT a, _In_ PRAT b, int32_t precision);
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extern void inbetween( _In_ PRAT *px, _In_ PRAT range, int32_t precision);
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extern void trimit( _Inout_ PRAT *px, int32_t precision);
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extern void _dumprawrat(_In_ const wchar_t *varname, _In_ PRAT rat, std::wostream& out);
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extern void _dumprawnum(_In_ const wchar_t *varname, _In_ PNUMBER num, std::wostream& out);
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