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/*-----------------------------------------------------------------*-C-*---
* File: handc/runtime/longint.c
*
* Copyright (C)1997 Donovan Kolbly <d.kolbly@rscheme.org>
* as part of the RScheme project, licensed for free use.
* See <http://www.rscheme.org/> for the latest information.
*
* File version: 1.8
* File mod date: 1997.11.29 23:10:50
* System build: v0.7.2, 97.12.21
*
*------------------------------------------------------------------------*/
#include <rscheme/obj.h>
#include <rscheme/smemory.h>
#include <rscheme/scheme.h>
#include <math.h>
void printit( char *name, INT_64 val )
{
char buf[70];
printf( "%-5s %04x %04x %04x %04x (%g) (%s)\n",
name,
val.digits[0], val.digits[1], val.digits[2], val.digits[3],
int_64_to_float(val),
(name[0] == '*') ? "--"
: int_64_to_string(buf+25,val,10));
}
#ifndef UNIT_TEST
rs_bool LONG_INT_P( obj thing )
{
return OBJ_ISA_PTR_OF_CLASS(thing,long_int_class);
}
obj make_long_int( INT_64 a )
{
obj longint = make_bvec( long_int_class, sizeof(INT_64) );
*((INT_64 *)PTR_TO_DATAPTR(longint)) = a;
return longint;
}
obj int_64_compact( INT_64 a )
{
if (int_64_fit_in_30_q(a))
return int2fx( int_64_to_int_32(a) );
else
{
obj longint = make_bvec( long_int_class, sizeof(INT_64) );
*((INT_64 *)PTR_TO_DATAPTR(longint)) = a;
return longint;
}
}
#endif
#ifdef UNIT_TEST
_rs_volatile void scheme_error( const char *msg, unsigned num_args, ... );
void printit( char *name, INT_64 val );
#endif
INT_64 INT_64_zero = { { 0, 0, 0, 0 } };
INT_64 INT_64_one = { { 0, 0, 0, 1 } };
INT_64 INT_64_two = { { 0, 0, 0, 2 } };
INT_64 INT_64_neg_one = { { 0xFFFF, 0xFFFF, 0xFFFF, 0xFFFF } };
INT_64 int_32_to_int_64( INT_32 x )
{
INT_64 r;
r.digits[3] = x;
r.digits[2] = x >> 16;
r.digits[1] = r.digits[0] = (x & 0x80000000) ? 0xFFFF : 0;
return r;
}
INT_64 int_64_add( INT_64 a, INT_64 b )
{
int i, c = 0;
INT_32 t;
INT_64 r;
for (i=4; i>0;)
{
i--;
t = a.digits[i] + b.digits[i] + c;
r.digits[i] = t;
c = t >> 16;
}
return r;
}
rs_bool int_64_neg_q( INT_64 a )
{
return (a.digits[0] & 0x8000) ? YES : NO;
}
rs_bool int_64_zero_q( INT_64 a )
{
return (a.digits[0] || a.digits[1] || a.digits[2] || a.digits[3])
? NO
: YES;
}
#define CHECK_DIGIT(k,otherwise) \
if (a.digits[k] < b.digits[k]) \
return -1; \
else if (a.digits[k] > b.digits[k]) \
return 1; \
else { otherwise }
int int_64_cmp( INT_64 a, INT_64 b )
{
CHECK_DIGIT(0,CHECK_DIGIT(1,CHECK_DIGIT(2,CHECK_DIGIT(3,return 0;))))
}
rs_bool int_64_eq( INT_64 a, INT_64 b )
{
return ((a.digits[3] == b.digits[3])
&& (a.digits[2] == b.digits[2])
&& (a.digits[1] == b.digits[1])
&& (a.digits[0] == b.digits[0])) ? YES : NO;
}
rs_bool int_64_gt( INT_64 a, INT_64 b )
{
return (int_64_cmp(a,b) > 0) ? YES : NO;
}
rs_bool int_64_ge( INT_64 a, INT_64 b )
{
return (int_64_cmp(a,b) >= 0) ? YES : NO;
}
INT_32 int_64_to_int_32( INT_64 a )
{
return (a.digits[2] << 16) | a.digits[3];
}
INT_64 int_64_neg( INT_64 a )
{
a.digits[0] ^= 0xFFFF;
a.digits[1] ^= 0xFFFF;
a.digits[2] ^= 0xFFFF;
a.digits[3] ^= 0xFFFF;
return int_64_add( a, INT_64_one );
}
INT_64 int_64_add_u32( INT_64 a, UINT_32 b, int shift )
{
int i, c = 0;
INT_32 t;
for (i=4-shift; i>0;)
{
i--;
t = a.digits[i] + (b & 0xFFFF) + c;
a.digits[i] = t;
c = t >> 16;
b >>= 16;
}
return a;
}
INT_64 int_64_sub( INT_64 a, INT_64 b )
{
return int_64_add( a, int_64_neg(b) );
}
static INT_64 int_64_umul( INT_64 a, INT_64 b )
{
INT_64 r = INT_64_zero;
UINT_32 pp;
int i, j;
for (i=4; i>0;)
{
i--;
for (j=4; j>0;)
{
j--;
pp = a.digits[i] * b.digits[j];
/*printf( " (%d,%d) => %08x\n", i, j, pp );*/
r = int_64_add_u32( r, pp, (3-i)+(3-j) );
}
}
return r;
}
INT_64 int_64_mul( INT_64 a, INT_64 b )
{
rs_bool a_neg = int_64_neg_q(a);
rs_bool b_neg = int_64_neg_q(b);
if (a_neg)
a = int_64_neg(a);
if (b_neg)
b = int_64_neg(b);
a = int_64_umul( a, b );
if (a_neg != b_neg)
return int_64_neg(a);
else
return a;
}
rs_bool int_64_fit_in_32_q( INT_64 a )
{
if (a.digits[0] == 0
&& a.digits[1] == 0
&& (a.digits[2] & 0x8000) == 0)
return YES;
else if (a.digits[0] == 0xFFFF
&& a.digits[1] == 0xFFFF
&& (a.digits[2] & 0x8000))
return YES;
else
return NO;
}
rs_bool int_64_fit_in_30_q( INT_64 a )
{
if (a.digits[0] == 0
&& a.digits[1] == 0
&& (a.digits[2] & 0xE000) == 0)
return YES;
else if (a.digits[0] == 0xFFFF
&& a.digits[1] == 0xFFFF
&& (a.digits[2] & 0xE000) == 0xE000)
return YES;
else
return NO;
}
struct INT_64_div2 {
INT_64 quotient;
INT_64 remainder;
};
static struct INT_64_div2 int_64_divu( INT_64 a, INT_64 b )
{
UINT_32 quot_hi, quot_lo, a_hi, a_lo, b_hi, b_lo, temp_hi, temp_lo;
struct INT_64_div2 r;
int i;
quot_hi = quot_lo = 0;
b_hi = (b.digits[0] << 16) + b.digits[1];
b_lo = (b.digits[2] << 16) + b.digits[3];
temp_hi = temp_lo = 0;
a_hi = (a.digits[0] << 16) + a.digits[1];
a_lo = (a.digits[2] << 16) + a.digits[3];
/*
printf( "a = %08x_%08x\n", a_hi, a_lo );
printf( "b = %08x_%08x\n", b_hi, b_lo );
*/
for (i=0; i<64; i++)
{
/*
printf( "i[%d] quot %08x_%08x t %08x_%08x a %08x_%08x\n",
i, quot_hi, quot_lo, temp_hi, temp_lo,
a_hi, a_lo );
*/
quot_hi = (quot_hi << 1) + ((quot_lo & 0x80000000) ? 1 : 0);
quot_lo <<= 1;
temp_hi = (temp_hi << 1) + ((temp_lo & 0x80000000) ? 1 : 0);
temp_lo = (temp_lo << 1) + ((a_hi & 0x80000000) ? 1 : 0);
a_hi = (a_hi << 1) + ((a_lo & 0x80000000) ? 1 : 0);
a_lo <<= 1;
if (temp_hi > b_hi || ((temp_hi == b_hi) && (temp_lo >= b_lo)))
{
quot_lo |= 1;
if (temp_lo >= b_lo)
{
temp_lo -= b_lo;
temp_hi -= b_hi;
}
else
{
temp_lo -= b_lo;
temp_hi -= b_hi - 1;
}
}
}
r.quotient.digits[0] = quot_hi >> 16;
r.quotient.digits[1] = quot_hi;
r.quotient.digits[2] = quot_lo >> 16;
r.quotient.digits[3] = quot_lo;
r.remainder.digits[0] = temp_hi >> 16;
r.remainder.digits[1] = temp_hi;
r.remainder.digits[2] = temp_lo >> 16;
r.remainder.digits[3] = temp_lo;
return r;
}
/*
* these three (_16) functions can be made faster...
*/
INT_64 int_64_add_16( INT_64 a, INT_16 b )
{
INT_64 temp = int_32_to_int_64( b );
return int_64_add( a, temp );
}
static INT_64 int_64_umul_16( INT_64 a, UINT_16 b )
{
INT_64 temp = int_32_to_int_64( b );
return int_64_umul( a, temp );
}
static struct INT_64_div2 int_64_divu_16( INT_64 a, UINT_16 b )
{
INT_64 temp = int_32_to_int_64( b );
return int_64_divu( a, temp );
}
struct INT_64_div2 int_64_div( INT_64 a, INT_64 b )
{
struct INT_64_div2 r;
rs_bool a_neg = int_64_neg_q(a);
rs_bool b_neg = int_64_neg_q(b);
if (a_neg)
a = int_64_neg(a);
if (b_neg)
b = int_64_neg(b);
r = int_64_divu( a, b );
if (a_neg != b_neg)
r.quotient = int_64_neg( r.quotient );
if (a_neg)
r.remainder = int_64_neg( r.remainder );
return r;
}
INT_64 int_64_quotient( INT_64 a, INT_64 b )
{
struct INT_64_div2 r = int_64_div( a, b );
return r.quotient;
}
INT_64 int_64_remainder( INT_64 a, INT_64 b )
{
struct INT_64_div2 r = int_64_div( a, b );
return r.remainder;
}
INT_64 int_64_modulo( INT_64 a, INT_64 b )
{
struct INT_64_div2 r;
INT_64 abs_b;
rs_bool a_neg = int_64_neg_q(a);
rs_bool b_neg = int_64_neg_q(b);
/*
printit( "a", a );
printit( "b", b );
printf( "... a%s0 b%s0\n", a_neg ? "<" : ">=", b_neg ? "<" : ">=" );
*/
if (a_neg)
a = int_64_neg(a);
if (b_neg)
abs_b = int_64_neg(b);
else
abs_b = b;
/*
printit( "|a|", a );
printit( "|b|", abs_b );
*/
r = int_64_divu( a, abs_b );
/*
printit( "Q'", r.quotient );
printit( "R'", r.remainder );
*/
if (int_64_zero_q(r.remainder))
{
return r.remainder;
}
else
{
/*
*
* we've done |a|/|b| and gotten Q' and R'
* (ie, Q' = floor(|a|/|b|)
* and Q' * |b| + R' = |a|)
*
* if SGN(a) != SGN(b)
* then the quotient a/b is negative,
* and hence floor(a/b) = - (floor(|a|/|b|) + 1)
*
* (UNLESS |a|%|b| == 0, that is)
*
* therefore, since, R = a - Q b
* and Q' = floor(|a|/|b|)
* Q = - (Q' + 1)
*
* note R = a - Q b
* = a + (Q' + 1)b
* = a + Q'b + b
*
* but R' = |a| - Q' |b|
*
* assume a<0
* then |a| = -a, and |b| = b
* so R' = -a - Q'b
* = -(a + Q'b)
* since R = a + Q'b + b
* = -R' + b
* = b - R'
*
* on the other hand, assume b<0
* then |a| = a, and |b| = -b
* so R' = a + Q'b
* since R = a + Q'b + b
* = R' + b
* = b + R'
*/
if (a_neg)
if (b_neg)
{
/* a<0 & b<0 => Q>=0 & R=-R' */
return int_64_neg(r.remainder);
}
else
{
/*printit( "b-R'", int_64_sub( b, r.remainder ) ); */
/* a<0 & b>=0 => Q<0 & R = b - R' */
return int_64_sub( b, r.remainder );
}
else
if (b_neg)
{
/* a>=0 & b<0 => Q<0 & R = b + R' */
return int_64_add( b, r.remainder );
}
else
{
/* a>=0 & b>=0 => Q>=0 & R = R' */
return r.remainder;
}
}
}
IEEE_64 int_64_to_float( INT_64 a )
{
rs_bool neg = int_64_neg_q(a);
IEEE_64 f;
if (neg)
a = int_64_neg(a);
f = a.digits[0] * (65536.0 * 4294967296.0)
+ a.digits[1] * 4294967296.0
+ a.digits[2] * 65536.0
+ a.digits[3];
if (neg)
return -f;
else
return f;
}
INT_64 float_to_int_64( IEEE_64 a ) /* trunc */
{
INT_64 r;
IEEE_64 abs_a = fabs(a);
r.digits[0] = (int)(abs_a / (65536.0 * 4294967296.0));
r.digits[1] = (int)(abs_a / 4294967296.0);
r.digits[2] = (int)(abs_a / 65536.0);
r.digits[3] = (int)(abs_a);
if (a < 0)
return int_64_neg(r);
else
return r;
}
#ifdef UNIT_TEST
unsigned char digit_values[256] = {
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 99, 99, 99, 99, 99, 99,
99, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 99, 99, 99, 99, 99,
99, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 99, 99, 99, 99, 99,
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99 };
static char value_digits[37] = "0123456789abcdefghijklmnopqrstuvwxyz";
#else
extern unsigned char digit_values[256];
extern char value_digits[37];
#endif
#define digit_value(ch) digit_values[ch]
rs_bool string_to_int_64( char *str, unsigned len, unsigned radix, INT_64 *v )
{
INT_64 accum;
rs_bool neg = NO;
char *lim = str + len;
static INT_64 preq;
static UINT_16 prem;
static unsigned q_cache = 0;
if (q_cache != radix)
{
struct INT_64_div2 pre;
/* fill the pre-multiply cache */
accum = INT_64_zero;
accum.digits[0] = 0x8000;
pre = int_64_divu_16( accum, radix );
preq = pre.quotient;
prem = int_64_to_int_32( pre.remainder );
q_cache = radix;
}
if (*str == '-')
{
str++;
neg = YES;
}
else if (*str == '+')
{
str++;
}
if (str >= lim)
return NO; /* no digits */
accum = INT_64_zero;
while (str < lim)
{
unsigned i;
unsigned ch;
INT_64 n;
ch = *str++;
i = digit_value(ch);
if (i >= radix)
{
return NO;
}
/* make sure the accumulator has room for the multiply-add */
if (int_64_gt( accum, preq )
|| (int_64_eq( accum, preq )
&& ((i > prem) || ((i == prem) && !neg))))
{
/* overflow */
return NO;
}
n = int_64_add_16( int_64_umul_16( accum, radix ), i );
if (int_64_gt(accum,n))
{
/* must have overflowed! */
return NO;
}
accum = n;
}
if (neg)
*v = int_64_neg( accum );
else
*v = accum;
return YES;
}
/* fills up buffer right-to-left! buffer starts out pointing
to the END of the buffer! */
char *int_64_to_string( char *buffer, INT_64 value, unsigned radix )
{
rs_bool neg;
*--buffer = 0;
neg = int_64_neg_q(value);
if (neg)
value = int_64_neg(value);
if (int_64_zero_q(value))
*--buffer = '0';
else
{
while (!int_64_zero_q(value))
{
struct INT_64_div2 d = int_64_divu_16( value, radix );
/*printit( "*part", value );*/
*--buffer = value_digits[int_64_to_int_32(d.remainder)];
value = d.quotient;
}
if (neg)
*--buffer = '-';
}
return buffer;
}
#ifdef UNIT_TEST
_rs_volatile void scheme_error( const char *msg, unsigned num_args, ... )
{
printf( "error: %s\n", msg );
exit(1);
}
int main( int argc, const char **argv )
{
INT_64 a, b, c;
struct INT_64_div2 d;
int i;
unsigned r = 10;
for (i=1; i<argc; i++)
{
rs_bool ok;
if (argv[i][0] == '-' && argv[i][1] == 'r')
r = atoi( argv[i]+2 );
else
{
ok = string_to_int_64( (char *)argv[i], strlen(argv[i]), r, &a );
printf( "'%s' => ", argv[i] );
if (ok)
printit( "val", a );
else
printf( "**ERROR**\n" );
}
}
if (argc > 1)
return 0;
a = int_32_to_int_64( 999101 );
b = int_32_to_int_64( -200000 );
c = int_64_add( a, b );
printit( "a", a );
printit( "b", b );
printit( "c", c );
putchar( '\n' );
a = int_32_to_int_64( 0x3456789a );
b = int_32_to_int_64( 0x10000000 );
printit( "a", a );
printit( "b", b );
c = int_64_mul( a, b );
printit( "c", c );
c = int_64_add( c, INT_64_one );
d = int_64_divu( c, a );
printit( "c/a", d.quotient );
printit( "c%a", d.remainder );
putchar( '\n' );
c = int_32_to_int_64( 1234567890 );
a = int_32_to_int_64( 10 );
d = int_64_divu( c, a );
printit( "c", c );
printit( "a", a );
printit( "c/a", d.quotient );
printit( "c%a", d.remainder );
putchar( '\n' );
a = int_32_to_int_64( 731234512 );
b = int_32_to_int_64( 123456 );
c = int_32_to_int_64( 1234567890 );
printit( "(c/a)", c );
printit( "(c%a)", b );
c = int_64_add( b, int_64_mul( c, a ) );
printit( "c", c );
d = int_64_divu( c, a );
printit( "c/a", d.quotient );
printit( "c%a", d.remainder );
printf( "`remainder'\n" );
for (i=0; i<4; i++)
{
char temp[8];
sprintf( temp, "%c/%c", (i & 1) ? '-' : '+', (i & 2) ? '-' : '+' );
a = int_32_to_int_64( ((i & 1) ? -1 : 1) * 13 );
b = int_32_to_int_64( ((i & 2) ? -1 : 1) * 4 );
c = int_64_remainder( a, b );
printit( temp, c );
}
printf( "`modulo'\n" );
for (i=0; i<4; i++)
{
char temp[8];
sprintf( temp, "%c/%c", (i & 1) ? '-' : '+', (i & 2) ? '-' : '+' );
a = int_32_to_int_64( ((i & 1) ? -1 : 1) * 13 );
b = int_32_to_int_64( ((i & 2) ? -1 : 1) * 4 );
c = int_64_modulo( a, b );
/* printit( temp, d.quotient ); */
printit( temp, c );
}
}
#endif
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