161 lines
4.0 KiB
C++
161 lines
4.0 KiB
C++
// Copyright (c) Microsoft Corporation. All rights reserved.
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// Licensed under the MIT License.
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//-----------------------------------------------------------------------------
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// Package Title ratpak
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// File itransh.c
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// Copyright (C) 1995-97 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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// Contains inverse hyperbolic sin, cos, and tan functions.
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//
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// Special Information
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//
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//
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//-----------------------------------------------------------------------------
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#include "pch.h"
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#include "ratpak.h"
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: asinhrat
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//
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// ARGUMENTS: x PRAT representation of number to take the inverse
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// hyperbolic sine of
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// RETURN: asinh of x in PRAT form.
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//
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// EXPLANATION: This uses Taylor series
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//
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// n
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// ___ 2 2
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// \ ] -(2j+1) X
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// \ thisterm ; where thisterm = thisterm * ---------
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// / j j+1 j (2j+2)*(2j+3)
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// /__]
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// j=0
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//
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// thisterm = X ; and stop when thisterm < precision used.
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// 0 n
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//
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// For abs(x) < .85, and
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//
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// asinh(x) = log(x+sqrt(x^2+1))
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//
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// For abs(x) >= .85
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//
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//-----------------------------------------------------------------------------
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void asinhrat( PRAT *px, uint32_t radix, int32_t precision)
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{
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PRAT neg_pt_eight_five = nullptr;
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DUPRAT(neg_pt_eight_five,pt_eight_five);
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neg_pt_eight_five->pp->sign *= -1;
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if ( rat_gt( *px, pt_eight_five, precision) || rat_lt( *px, neg_pt_eight_five, precision) )
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{
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PRAT ptmp = nullptr;
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DUPRAT(ptmp,(*px));
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mulrat(&ptmp, *px, precision);
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addrat(&ptmp, rat_one, precision);
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rootrat(&ptmp, rat_two, radix, precision);
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addrat(px, ptmp, precision);
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lograt(px, precision);
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destroyrat(ptmp);
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}
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else
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{
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CREATETAYLOR();
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xx->pp->sign *= -1;
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DUPRAT(pret,(*px));
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DUPRAT(thisterm,(*px));
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DUPNUM(n2,num_one);
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do
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{
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NEXTTERM(xx,MULNUM(n2) MULNUM(n2)
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INC(n2) DIVNUM(n2) INC(n2) DIVNUM(n2), precision);
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}
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while ( !SMALL_ENOUGH_RAT( thisterm, precision) );
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DESTROYTAYLOR();
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}
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destroyrat(neg_pt_eight_five);
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: acoshrat
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//
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// ARGUMENTS: x PRAT representation of number to take the inverse
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// hyperbolic cose of
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// RETURN: acosh of x in PRAT form.
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//
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// EXPLANATION: This uses
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//
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// acosh(x)=ln(x+sqrt(x^2-1))
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//
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// For x >= 1
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//
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//-----------------------------------------------------------------------------
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void acoshrat( PRAT *px, uint32_t radix, int32_t precision)
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{
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if ( rat_lt( *px, rat_one, precision) )
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{
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throw CALC_E_DOMAIN;
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}
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else
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{
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PRAT ptmp = nullptr;
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DUPRAT(ptmp,(*px));
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mulrat(&ptmp, *px, precision);
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subrat(&ptmp, rat_one, precision);
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rootrat(&ptmp,rat_two, radix, precision);
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addrat(px, ptmp, precision);
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lograt(px, precision);
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destroyrat(ptmp);
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}
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}
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//-----------------------------------------------------------------------------
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//
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// FUNCTION: atanhrat
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//
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// ARGUMENTS: x PRAT representation of number to take the inverse
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// hyperbolic tangent of
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//
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// RETURN: atanh of x in PRAT form.
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//
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// EXPLANATION: This uses
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//
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// 1 x+1
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// atanh(x) = -*ln(----)
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// 2 x-1
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//
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//-----------------------------------------------------------------------------
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void atanhrat( PRAT *px, int32_t precision)
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{
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PRAT ptmp = nullptr;
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DUPRAT(ptmp,(*px));
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subrat(&ptmp, rat_one, precision);
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addrat(px, rat_one, precision);
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divrat(px, ptmp, precision);
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(*px)->pp->sign *= -1;
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lograt(px, precision);
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divrat(px, rat_two, precision);
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destroyrat(ptmp);
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}
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