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/*******************************************************************
** m a t h 6 4 . c
** Forth Inspired Command Language - 64 bit math support routines
** Author: John Sadler (john_sadler@alum.mit.edu)
** Created: 25 January 1998
** Rev 2.03: Support for 128 bit DP math. This file really ouught to
** be renamed!
** $Id: math64.c,v 1.9 2001/12/05 07:21:34 jsadler Exp $
*******************************************************************/
/*
** Copyright (c) 1997-2001 John Sadler (john_sadler@alum.mit.edu)
** All rights reserved.
**
** Get the latest Ficl release at http://ficl.sourceforge.net
**
** I am interested in hearing from anyone who uses ficl. If you have
** a problem, a success story, a defect, an enhancement request, or
** if you would like to contribute to the ficl release, please
** contact me by email at the address above.
**
** L I C E N S E and D I S C L A I M E R
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
** 1. Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
** 2. Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in the
** documentation and/or other materials provided with the distribution.
**
** THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
** ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
** IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
** ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
** FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
** DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
** OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
** HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
** OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
** SUCH DAMAGE.
*/
/* $FreeBSD: release/9.1.0/sys/boot/ficl/math64.c 94290 2002-04-09 17:45:28Z dcs $ */
#include "ficl.h"
#include "math64.h"
/**************************************************************************
m 6 4 A b s
** Returns the absolute value of an DPINT
**************************************************************************/
DPINT m64Abs(DPINT x)
{
if (m64IsNegative(x))
x = m64Negate(x);
return x;
}
/**************************************************************************
m 6 4 F l o o r e d D i v I
**
** FROM THE FORTH ANS...
** Floored division is integer division in which the remainder carries
** the sign of the divisor or is zero, and the quotient is rounded to
** its arithmetic floor. Symmetric division is integer division in which
** the remainder carries the sign of the dividend or is zero and the
** quotient is the mathematical quotient rounded towards zero or
** truncated. Examples of each are shown in tables 3.3 and 3.4.
**
** Table 3.3 - Floored Division Example
** Dividend Divisor Remainder Quotient
** -------- ------- --------- --------
** 10 7 3 1
** -10 7 4 -2
** 10 -7 -4 -2
** -10 -7 -3 1
**
**
** Table 3.4 - Symmetric Division Example
** Dividend Divisor Remainder Quotient
** -------- ------- --------- --------
** 10 7 3 1
** -10 7 -3 -1
** 10 -7 3 -1
** -10 -7 -3 1
**************************************************************************/
INTQR m64FlooredDivI(DPINT num, FICL_INT den)
{
INTQR qr;
UNSQR uqr;
int signRem = 1;
int signQuot = 1;
if (m64IsNegative(num))
{
num = m64Negate(num);
signQuot = -signQuot;
}
if (den < 0)
{
den = -den;
signRem = -signRem;
signQuot = -signQuot;
}
uqr = ficlLongDiv(m64CastIU(num), (FICL_UNS)den);
qr = m64CastQRUI(uqr);
if (signQuot < 0)
{
qr.quot = -qr.quot;
if (qr.rem != 0)
{
qr.quot--;
qr.rem = den - qr.rem;
}
}
if (signRem < 0)
qr.rem = -qr.rem;
return qr;
}
/**************************************************************************
m 6 4 I s N e g a t i v e
** Returns TRUE if the specified DPINT has its sign bit set.
**************************************************************************/
int m64IsNegative(DPINT x)
{
return (x.hi < 0);
}
/**************************************************************************
m 6 4 M a c
** Mixed precision multiply and accumulate primitive for number building.
** Multiplies DPUNS u by FICL_UNS mul and adds FICL_UNS add. Mul is typically
** the numeric base, and add represents a digit to be appended to the
** growing number.
** Returns the result of the operation
**************************************************************************/
DPUNS m64Mac(DPUNS u, FICL_UNS mul, FICL_UNS add)
{
DPUNS resultLo = ficlLongMul(u.lo, mul);
DPUNS resultHi = ficlLongMul(u.hi, mul);
resultLo.hi += resultHi.lo;
resultHi.lo = resultLo.lo + add;
if (resultHi.lo < resultLo.lo)
resultLo.hi++;
resultLo.lo = resultHi.lo;
return resultLo;
}
/**************************************************************************
m 6 4 M u l I
** Multiplies a pair of FICL_INTs and returns an DPINT result.
**************************************************************************/
DPINT m64MulI(FICL_INT x, FICL_INT y)
{
DPUNS prod;
int sign = 1;
if (x < 0)
{
sign = -sign;
x = -x;
}
if (y < 0)
{
sign = -sign;
y = -y;
}
prod = ficlLongMul(x, y);
if (sign > 0)
return m64CastUI(prod);
else
return m64Negate(m64CastUI(prod));
}
/**************************************************************************
m 6 4 N e g a t e
** Negates an DPINT by complementing and incrementing.
**************************************************************************/
DPINT m64Negate(DPINT x)
{
x.hi = ~x.hi;
x.lo = ~x.lo;
x.lo ++;
if (x.lo == 0)
x.hi++;
return x;
}
/**************************************************************************
m 6 4 P u s h
** Push an DPINT onto the specified stack in the order required
** by ANS Forth (most significant cell on top)
** These should probably be macros...
**************************************************************************/
void i64Push(FICL_STACK *pStack, DPINT i64)
{
stackPushINT(pStack, i64.lo);
stackPushINT(pStack, i64.hi);
return;
}
void u64Push(FICL_STACK *pStack, DPUNS u64)
{
stackPushINT(pStack, u64.lo);
stackPushINT(pStack, u64.hi);
return;
}
/**************************************************************************
m 6 4 P o p
** Pops an DPINT off the stack in the order required by ANS Forth
** (most significant cell on top)
** These should probably be macros...
**************************************************************************/
DPINT i64Pop(FICL_STACK *pStack)
{
DPINT ret;
ret.hi = stackPopINT(pStack);
ret.lo = stackPopINT(pStack);
return ret;
}
DPUNS u64Pop(FICL_STACK *pStack)
{
DPUNS ret;
ret.hi = stackPopINT(pStack);
ret.lo = stackPopINT(pStack);
return ret;
}
/**************************************************************************
m 6 4 S y m m e t r i c D i v
** Divide an DPINT by a FICL_INT and return a FICL_INT quotient and a
** FICL_INT remainder. The absolute values of quotient and remainder are not
** affected by the signs of the numerator and denominator (the operation
** is symmetric on the number line)
**************************************************************************/
INTQR m64SymmetricDivI(DPINT num, FICL_INT den)
{
INTQR qr;
UNSQR uqr;
int signRem = 1;
int signQuot = 1;
if (m64IsNegative(num))
{
num = m64Negate(num);
signRem = -signRem;
signQuot = -signQuot;
}
if (den < 0)
{
den = -den;
signQuot = -signQuot;
}
uqr = ficlLongDiv(m64CastIU(num), (FICL_UNS)den);
qr = m64CastQRUI(uqr);
if (signRem < 0)
qr.rem = -qr.rem;
if (signQuot < 0)
qr.quot = -qr.quot;
return qr;
}
/**************************************************************************
m 6 4 U M o d
** Divides a DPUNS by base (an UNS16) and returns an UNS16 remainder.
** Writes the quotient back to the original DPUNS as a side effect.
** This operation is typically used to convert an DPUNS to a text string
** in any base. See words.c:numberSignS, for example.
** Mechanics: performs 4 ficlLongDivs, each of which produces 16 bits
** of the quotient. C does not provide a way to divide an FICL_UNS by an
** UNS16 and get an FICL_UNS quotient (ldiv is closest, but it's signed,
** unfortunately), so I've used ficlLongDiv.
**************************************************************************/
#if (BITS_PER_CELL == 32)
#define UMOD_SHIFT 16
#define UMOD_MASK 0x0000ffff
#elif (BITS_PER_CELL == 64)
#define UMOD_SHIFT 32
#define UMOD_MASK 0x00000000ffffffff
#endif
UNS16 m64UMod(DPUNS *pUD, UNS16 base)
{
DPUNS ud;
UNSQR qr;
DPUNS result;
result.hi = result.lo = 0;
ud.hi = 0;
ud.lo = pUD->hi >> UMOD_SHIFT;
qr = ficlLongDiv(ud, (FICL_UNS)base);
result.hi = qr.quot << UMOD_SHIFT;
ud.lo = (qr.rem << UMOD_SHIFT) | (pUD->hi & UMOD_MASK);
qr = ficlLongDiv(ud, (FICL_UNS)base);
result.hi |= qr.quot & UMOD_MASK;
ud.lo = (qr.rem << UMOD_SHIFT) | (pUD->lo >> UMOD_SHIFT);
qr = ficlLongDiv(ud, (FICL_UNS)base);
result.lo = qr.quot << UMOD_SHIFT;
ud.lo = (qr.rem << UMOD_SHIFT) | (pUD->lo & UMOD_MASK);
qr = ficlLongDiv(ud, (FICL_UNS)base);
result.lo |= qr.quot & UMOD_MASK;
*pUD = result;
return (UNS16)(qr.rem);
}
/**************************************************************************
** Contributed by
** Michael A. Gauland gaulandm@mdhost.cse.tek.com
**************************************************************************/
#if PORTABLE_LONGMULDIV != 0
/**************************************************************************
m 6 4 A d d
**
**************************************************************************/
DPUNS m64Add(DPUNS x, DPUNS y)
{
DPUNS result;
int carry;
result.hi = x.hi + y.hi;
result.lo = x.lo + y.lo;
carry = ((x.lo | y.lo) & CELL_HI_BIT) && !(result.lo & CELL_HI_BIT);
carry |= ((x.lo & y.lo) & CELL_HI_BIT);
if (carry)
{
result.hi++;
}
return result;
}
/**************************************************************************
m 6 4 S u b
**
**************************************************************************/
DPUNS m64Sub(DPUNS x, DPUNS y)
{
DPUNS result;
result.hi = x.hi - y.hi;
result.lo = x.lo - y.lo;
if (x.lo < y.lo)
{
result.hi--;
}
return result;
}
/**************************************************************************
m 6 4 A S L
** 64 bit left shift
**************************************************************************/
DPUNS m64ASL( DPUNS x )
{
DPUNS result;
result.hi = x.hi << 1;
if (x.lo & CELL_HI_BIT)
{
result.hi++;
}
result.lo = x.lo << 1;
return result;
}
/**************************************************************************
m 6 4 A S R
** 64 bit right shift (unsigned - no sign extend)
**************************************************************************/
DPUNS m64ASR( DPUNS x )
{
DPUNS result;
result.lo = x.lo >> 1;
if (x.hi & 1)
{
result.lo |= CELL_HI_BIT;
}
result.hi = x.hi >> 1;
return result;
}
/**************************************************************************
m 6 4 O r
** 64 bit bitwise OR
**************************************************************************/
DPUNS m64Or( DPUNS x, DPUNS y )
{
DPUNS result;
result.hi = x.hi | y.hi;
result.lo = x.lo | y.lo;
return result;
}
/**************************************************************************
m 6 4 C o m p a r e
** Return -1 if x < y; 0 if x==y, and 1 if x > y.
**************************************************************************/
int m64Compare(DPUNS x, DPUNS y)
{
int result;
if (x.hi > y.hi)
{
result = +1;
}
else if (x.hi < y.hi)
{
result = -1;
}
else
{
/* High parts are equal */
if (x.lo > y.lo)
{
result = +1;
}
else if (x.lo < y.lo)
{
result = -1;
}
else
{
result = 0;
}
}
return result;
}
/**************************************************************************
f i c l L o n g M u l
** Portable versions of ficlLongMul and ficlLongDiv in C
** Contributed by:
** Michael A. Gauland gaulandm@mdhost.cse.tek.com
**************************************************************************/
DPUNS ficlLongMul(FICL_UNS x, FICL_UNS y)
{
DPUNS result = { 0, 0 };
DPUNS addend;
addend.lo = y;
addend.hi = 0; /* No sign extension--arguments are unsigned */
while (x != 0)
{
if ( x & 1)
{
result = m64Add(result, addend);
}
x >>= 1;
addend = m64ASL(addend);
}
return result;
}
/**************************************************************************
f i c l L o n g D i v
** Portable versions of ficlLongMul and ficlLongDiv in C
** Contributed by:
** Michael A. Gauland gaulandm@mdhost.cse.tek.com
**************************************************************************/
UNSQR ficlLongDiv(DPUNS q, FICL_UNS y)
{
UNSQR result;
DPUNS quotient;
DPUNS subtrahend;
DPUNS mask;
quotient.lo = 0;
quotient.hi = 0;
subtrahend.lo = y;
subtrahend.hi = 0;
mask.lo = 1;
mask.hi = 0;
while ((m64Compare(subtrahend, q) < 0) &&
(subtrahend.hi & CELL_HI_BIT) == 0)
{
mask = m64ASL(mask);
subtrahend = m64ASL(subtrahend);
}
while (mask.lo != 0 || mask.hi != 0)
{
if (m64Compare(subtrahend, q) <= 0)
{
q = m64Sub( q, subtrahend);
quotient = m64Or(quotient, mask);
}
mask = m64ASR(mask);
subtrahend = m64ASR(subtrahend);
}
result.quot = quotient.lo;
result.rem = q.lo;
return result;
}
#endif