ref: e5f0c0798b44ffaa03772477138ff0ae4df4763b
dir: /math64.c/
/*******************************************************************
** 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
**
*******************************************************************/
#include "ficl.h"
#include "math64.h"
/**************************************************************************
m 6 4 A b s
** Returns the absolute value of an INT64
**************************************************************************/
INT64 m64Abs(INT64 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(INT64 num, INT32 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), (UNS32)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 INT64 has its sign bit set.
**************************************************************************/
int m64IsNegative(INT64 x)
{
return (x.hi < 0);
}
/**************************************************************************
m 6 4 M a c
** Mixed precision multiply and accumulate primitive for number building.
** Multiplies UNS64 u by UNS32 mul and adds UNS32 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
**************************************************************************/
UNS64 m64Mac(UNS64 u, UNS32 mul, UNS32 add)
{
UNS64 resultLo = ficlLongMul(u.lo, mul);
UNS64 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 INT32s and returns an INT64 result.
**************************************************************************/
INT64 m64MulI(INT32 x, INT32 y)
{
UNS64 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 INT64 by complementing and incrementing.
**************************************************************************/
INT64 m64Negate(INT64 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 INT64 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, INT64 i64)
{
stackPushINT32(pStack, i64.lo);
stackPushINT32(pStack, i64.hi);
return;
}
void u64Push(FICL_STACK *pStack, UNS64 u64)
{
stackPushINT32(pStack, u64.lo);
stackPushINT32(pStack, u64.hi);
return;
}
/**************************************************************************
m 6 4 P o p
** Pops an INT64 off the stack in the order required by ANS Forth
** (most significant cell on top)
** These should probably be macros...
**************************************************************************/
INT64 i64Pop(FICL_STACK *pStack)
{
INT64 ret;
ret.hi = stackPopINT32(pStack);
ret.lo = stackPopINT32(pStack);
return ret;
}
UNS64 u64Pop(FICL_STACK *pStack)
{
UNS64 ret;
ret.hi = stackPopINT32(pStack);
ret.lo = stackPopINT32(pStack);
return ret;
}
/**************************************************************************
m 6 4 S y m m e t r i c D i v
** Divide an INT64 by an INT32 and return an INT32 quotient and an INT32
** 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(INT64 num, INT32 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), (UNS32)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 an UNS64 by base (an UNS16) and returns an UNS16 remainder.
** Writes the quotient back to the original UNS64 as a side effect.
** This operation is typically used to convert an UNS64 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 UNS32 by an
** UNS16 and get an UNS32 quotient (ldiv is closest, but it's signed,
** unfortunately), so I've used ficlLongDiv.
**************************************************************************/
UNS16 m64UMod(UNS64 *pUD, UNS16 base)
{
UNS64 ud;
UNSQR qr;
UNS64 result;
result.hi = result.lo = 0;
ud.hi = 0;
ud.lo = pUD->hi >> 16;
qr = ficlLongDiv(ud, (UNS32)base);
result.hi = qr.quot << 16;
ud.lo = (qr.rem << 16) | (pUD->hi & 0x0000ffff);
qr = ficlLongDiv(ud, (UNS32)base);
result.hi |= qr.quot & 0x0000ffff;
ud.lo = (qr.rem << 16) | (pUD->lo >> 16);
qr = ficlLongDiv(ud, (UNS32)base);
result.lo = qr.quot << 16;
ud.lo = (qr.rem << 16) | (pUD->lo & 0x0000ffff);
qr = ficlLongDiv(ud, (UNS32)base);
result.lo |= qr.quot & 0x0000ffff;
*pUD = result;
return (UNS16)(qr.rem);
}