297 lines
8.1 KiB
C
297 lines
8.1 KiB
C
/*******************************************************************
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** m a t h 6 4 . c
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** Forth Inspired Command Language - 64 bit math support routines
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** Author: John Sadler (john_sadler@alum.mit.edu)
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** Created: 25 January 1998
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**
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*******************************************************************/
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#include "ficl.h"
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#include "math64.h"
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/**************************************************************************
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m 6 4 A b s
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** Returns the absolute value of an INT64
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**************************************************************************/
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INT64 m64Abs(INT64 x)
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{
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if (m64IsNegative(x))
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x = m64Negate(x);
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return x;
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}
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/**************************************************************************
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m 6 4 F l o o r e d D i v I
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**
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** FROM THE FORTH ANS...
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** Floored division is integer division in which the remainder carries
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** the sign of the divisor or is zero, and the quotient is rounded to
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** its arithmetic floor. Symmetric division is integer division in which
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** the remainder carries the sign of the dividend or is zero and the
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** quotient is the mathematical quotient rounded towards zero or
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** truncated. Examples of each are shown in tables 3.3 and 3.4.
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**
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** Table 3.3 - Floored Division Example
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** Dividend Divisor Remainder Quotient
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** -------- ------- --------- --------
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** 10 7 3 1
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** -10 7 4 -2
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** 10 -7 -4 -2
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** -10 -7 -3 1
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**
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**
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** Table 3.4 - Symmetric Division Example
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** Dividend Divisor Remainder Quotient
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** -------- ------- --------- --------
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** 10 7 3 1
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** -10 7 -3 -1
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** 10 -7 3 -1
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** -10 -7 -3 1
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**************************************************************************/
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INTQR m64FlooredDivI(INT64 num, INT32 den)
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{
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INTQR qr;
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UNSQR uqr;
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int signRem = 1;
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int signQuot = 1;
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if (m64IsNegative(num))
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{
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num = m64Negate(num);
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signQuot = -signQuot;
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}
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if (den < 0)
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{
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den = -den;
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signRem = -signRem;
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signQuot = -signQuot;
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}
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uqr = ficlLongDiv(m64CastIU(num), (UNS32)den);
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qr = m64CastQRUI(uqr);
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if (signQuot < 0)
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{
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qr.quot = -qr.quot;
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if (qr.rem != 0)
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{
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qr.quot--;
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qr.rem = den - qr.rem;
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}
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}
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if (signRem < 0)
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qr.rem = -qr.rem;
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return qr;
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}
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/**************************************************************************
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m 6 4 I s N e g a t i v e
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** Returns TRUE if the specified INT64 has its sign bit set.
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**************************************************************************/
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int m64IsNegative(INT64 x)
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{
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return (x.hi < 0);
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}
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/**************************************************************************
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m 6 4 M a c
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** Mixed precision multiply and accumulate primitive for number building.
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** Multiplies UNS64 u by UNS32 mul and adds UNS32 add. Mul is typically
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** the numeric base, and add represents a digit to be appended to the
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** growing number.
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** Returns the result of the operation
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**************************************************************************/
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UNS64 m64Mac(UNS64 u, UNS32 mul, UNS32 add)
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{
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UNS64 resultLo = ficlLongMul(u.lo, mul);
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UNS64 resultHi = ficlLongMul(u.hi, mul);
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resultLo.hi += resultHi.lo;
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resultHi.lo = resultLo.lo + add;
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if (resultHi.lo < resultLo.lo)
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resultLo.hi++;
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resultLo.lo = resultHi.lo;
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return resultLo;
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}
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/**************************************************************************
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m 6 4 M u l I
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** Multiplies a pair of INT32s and returns an INT64 result.
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**************************************************************************/
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INT64 m64MulI(INT32 x, INT32 y)
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{
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UNS64 prod;
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int sign = 1;
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if (x < 0)
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{
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sign = -sign;
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x = -x;
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}
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if (y < 0)
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{
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sign = -sign;
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y = -y;
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}
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prod = ficlLongMul(x, y);
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if (sign > 0)
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return m64CastUI(prod);
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else
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return m64Negate(m64CastUI(prod));
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}
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/**************************************************************************
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m 6 4 N e g a t e
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** Negates an INT64 by complementing and incrementing.
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**************************************************************************/
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INT64 m64Negate(INT64 x)
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{
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x.hi = ~x.hi;
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x.lo = ~x.lo;
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x.lo ++;
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if (x.lo == 0)
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x.hi++;
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return x;
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}
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/**************************************************************************
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m 6 4 P u s h
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** Push an INT64 onto the specified stack in the order required
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** by ANS Forth (most significant cell on top)
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** These should probably be macros...
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**************************************************************************/
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void i64Push(FICL_STACK *pStack, INT64 i64)
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{
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stackPushINT32(pStack, i64.lo);
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stackPushINT32(pStack, i64.hi);
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return;
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}
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void u64Push(FICL_STACK *pStack, UNS64 u64)
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{
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stackPushINT32(pStack, u64.lo);
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stackPushINT32(pStack, u64.hi);
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return;
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}
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/**************************************************************************
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m 6 4 P o p
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** Pops an INT64 off the stack in the order required by ANS Forth
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** (most significant cell on top)
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** These should probably be macros...
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**************************************************************************/
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INT64 i64Pop(FICL_STACK *pStack)
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{
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INT64 ret;
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ret.hi = stackPopINT32(pStack);
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ret.lo = stackPopINT32(pStack);
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return ret;
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}
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UNS64 u64Pop(FICL_STACK *pStack)
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{
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UNS64 ret;
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ret.hi = stackPopINT32(pStack);
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ret.lo = stackPopINT32(pStack);
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return ret;
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}
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/**************************************************************************
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m 6 4 S y m m e t r i c D i v
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** Divide an INT64 by an INT32 and return an INT32 quotient and an INT32
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** remainder. The absolute values of quotient and remainder are not
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** affected by the signs of the numerator and denominator (the operation
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** is symmetric on the number line)
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**************************************************************************/
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INTQR m64SymmetricDivI(INT64 num, INT32 den)
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{
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INTQR qr;
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UNSQR uqr;
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int signRem = 1;
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int signQuot = 1;
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if (m64IsNegative(num))
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{
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num = m64Negate(num);
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signRem = -signRem;
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signQuot = -signQuot;
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}
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if (den < 0)
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{
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den = -den;
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signQuot = -signQuot;
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}
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uqr = ficlLongDiv(m64CastIU(num), (UNS32)den);
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qr = m64CastQRUI(uqr);
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if (signRem < 0)
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qr.rem = -qr.rem;
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if (signQuot < 0)
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qr.quot = -qr.quot;
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return qr;
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}
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/**************************************************************************
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m 6 4 U M o d
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** Divides an UNS64 by base (an UNS16) and returns an UNS16 remainder.
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** Writes the quotient back to the original UNS64 as a side effect.
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** This operation is typically used to convert an UNS64 to a text string
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** in any base. See words.c:numberSignS, for example.
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** Mechanics: performs 4 ficlLongDivs, each of which produces 16 bits
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** of the quotient. C does not provide a way to divide an UNS32 by an
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** UNS16 and get an UNS32 quotient (ldiv is closest, but it's signed,
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** unfortunately), so I've used ficlLongDiv.
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**************************************************************************/
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UNS16 m64UMod(UNS64 *pUD, UNS16 base)
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{
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UNS64 ud;
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UNSQR qr;
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UNS64 result;
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result.hi = result.lo = 0;
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ud.hi = 0;
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ud.lo = pUD->hi >> 16;
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qr = ficlLongDiv(ud, (UNS32)base);
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result.hi = qr.quot << 16;
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ud.lo = (qr.rem << 16) | (pUD->hi & 0x0000ffff);
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qr = ficlLongDiv(ud, (UNS32)base);
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result.hi |= qr.quot & 0x0000ffff;
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ud.lo = (qr.rem << 16) | (pUD->lo >> 16);
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qr = ficlLongDiv(ud, (UNS32)base);
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result.lo = qr.quot << 16;
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ud.lo = (qr.rem << 16) | (pUD->lo & 0x0000ffff);
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qr = ficlLongDiv(ud, (UNS32)base);
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result.lo |= qr.quot & 0x0000ffff;
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*pUD = result;
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return (UNS16)(qr.rem);
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}
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