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The C Users' Group Library 1994 August
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wc-cdrom-cusersgrouplibrary-1994-08.iso
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vol_100
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107_01
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clogs.c
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1984-06-05
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/* CLOGS.C *****
A group of programs in C, using the BDS-C floating point package
as modified by LCC (FLOAT+44.*) and depending on the ability to
insert null characters in a string available in BDS-C V 1.44.
Four functions are handled:
log10, exp10, expe, pi
In addition, there is a service function exprange() which returns
a false (00) if the exponent of a floating point variable is reaching
near the end of the usable range.
These are discussed in detail in CLOGS.DOC
L. C. Calhoun
257 South Broadway
Lebanon, Ohio 45036 513 day 433 7510 nite 932 4541
*/
char *pi(result)
/* result is a standard character array char result[5]; in calling
program as used for floating point variables. The return is a pointer
to result, and the value of pi stored in the result array in floating
point */
char *result;
{
char *piconst, *fpasg();
piconst = "\171\356\207\144\2";
return (fpasg(result,piconst) );
}
char *expe(result,xin)
/* computes the base of the natural log "e" raised to the "x'th"
power. Checks are made for out of range values and result is
defaulted to 0, 1, or a large number as appropriate. There are
no error flags. The arguments are floating point character
arrays char result[5], x[5]; in calling program. Return is
a pointer to result, and "e to the x" stored in result.
*/
char *result, *xin;
{
char *zero, *one, *large, *coef[7], *eghty6, *meghty6;
char intres[5], xint[5], x[5];
char *fpmult(), *fpasg(), *fpdiv(), *fpchs();
int signx, index, bigexp, smallexp, zeroin;
int exprange();
bigexp = smallexp = zeroin = 0;
zero ="\0\0\0\0\0";
one = "\0\0\0\100\1";
large = "\0\0\0\100\175";
eghty6 = "\0\0\0\126\7";
meghty6 = "\0\0\0\252\7";
coef[0] = "\0\0\0\100\1";
coef[1] = "\140\326\377\177\376";
coef[2] = "\130\373\3\100\374";
coef[3] = "\200\1\352\124\370";
coef[4] = "\351\253\362\131\364";
coef[5] = "\21\213\32\133\357";
coef[6] = "\371\330\260\134\354";
/* preserve input datum */
fpasg(x,xin);
/* check for sign */
if (x[3] < 128) /* positive */
{signx = 1;
}
else
{signx = 0;
fpchs(x,x);
}
/* check for zero and out of range of fp var */
/* check for zero and very small numbers */
if ( ((x[4]>127) && (x[4]<226)) || ( (x[4]==0) &&
(x[3]==0) && (x[2]==0) && (x[1]==0) && (x[0]==0) ) )
zeroin = 1;
/* check for very small exponent */
if ( fpcomp(xin,meghty6) < 0)
smallexp = 1;
/* check for very large exponent */
if ( fpcomp(x,eghty6) > 0 )
bigexp = 1;
/* now if small number or zero, result is one */
/* now if big number and positive, result is large number */
/* now if big number and negative, result is zero */
if (zeroin) return (fpasg(result,one) );
if (smallexp) return (fpasg(result,zero) );
if (bigexp) return (fpasg(result,large) );
/* all exceptions taken care of, so evaluate rest */
fpasg(result,one);
fpasg(xint,x);
index = 1;
while ( (index<=6) && exprange(xint) )
{
fpmult(intres,coef[index],xint);
fpadd(result,result,intres);
fpmult(xint,xint,x);
index++;
}
/* now do the square square */
fpmult(result,result,result);
fpmult(result,result,result);
/* now treat sign appropriately */
if (signx) return (result);
else
{fpdiv(result,one,result);
return (result);
}
}
char *exp10(result,xin)
/* similar to expe, except result returned is 10 raised to the x
power the antilogarithm to base 10 */
char *result, *xin;
{
char *zero, *ten, *one, *large, *thty8;
char xint[5], *coef[7], intres[5], tenfac[5], x[5];
int index, bigexp, smallexp, signx, tenpower;
int exprange();
bigexp = smallexp = 0;
zero ="\0\0\0\0\0";
one = "\0\0\0\100\1";
large = "\0\0\0\100\175";
ten = "\0\0\0\120\4";
thty8 = "\0\0\0\114\6";
coef[1] = "\65\264\256\111\1";
coef[2] = "\0\14\330\124\0";
coef[3] = "\0\46\354\100\377";
coef[4] = "\24\140\107\115\375";
coef[5] = "\242\304\361\155\372";
coef[6] = "\361\143\246\134\371";
/* preserve input datum */
fpasg(x,xin);
/* check for sign */
if (x[3] < 128) /* positive */
signx = 1;
else /* negative */
{signx = 0;
fpchs(x,x);
}
/* check for very small or large numbers, check by exponent size */
/* check for zero or small */
if ( ((x[4]>127) && (x[4]<226)) || ( (x[4]==0) &&
(x[3]==0) && (x[2]==0) && (x[1]==0) && (x[0]==0) ) )
smallexp = 1;
/* check for big number */
if ( fpcomp(x,thty8) > 0)
bigexp = 1;
/* if value is small or zero, return 1 as with expe */
/* if value is large and positive, return a large number */
/* if value is large and negative, return zero */
if (smallexp) return (fpasg(result,one) );
if(bigexp && signx) return (fpasg(result,large) );
if(bigexp && !signx) return (fpasg(result,zero) );
/* now reduce range of x to between zero and one */
tenpower = ftoit(x);
itof(tenfac,tenpower);
fpsub(x,x,tenfac);
fpasg(tenfac,one);
while (tenpower)
{fpmult(tenfac,tenfac,ten);
tenpower--;
}
/* now evaluate series */
fpasg(result,one);
fpasg(xint,x);
index = 1;
while ( (index <= 6) && exprange(xint) )
{fpmult(intres,coef[index],xint);
fpadd(result,result,intres);
fpmult(xint,xint,x);
index += 1;
}
/* now square result (note error in referenced article) */
fpmult(result,result,result);
/* now check sign and make proper return */
fpmult(result,result,tenfac); /* scale back up */
if (signx) return (result);
else return ( fpdiv(result,one,result) );
}
char *log10(result,sign,xin)
/* computes briggsian logarithm of x which is a char[5]
floating point number. Return is logarithm in result[5],
and sign pointed to by sign. The logarithm is taken
of the magnitude, and sign information preserved
as required by sign.
*/
char *result, *xin;
int *sign;
{
char *zero, *ten, *one, *large;
char *sqrtten, x[5];
char gamma[5], gamnum[5], gamden[5], *coef[5];
char *half;
char intres[5], gamint[5];
int tenpower;
int index, bigexp, smallexp, signx;
int exprange();
bigexp = smallexp = 0;
zero ="\0\0\0\0\0";
one = "\0\0\0\100\1";
large = "\0\0\0\114\6";
ten = "\0\0\0\120\4";
half = "\0\0\0\100\0";
sqrtten = "\304\145\61\145\2";
coef[0] = "\362\6\56\157\0";
coef[1] = "\30\346\21\112\377";
coef[2] = "\100\55\344\132\376";
coef[3] = "\106\73\244\140\375";
coef[4] = "\174\5\367\141\376";
/* preserve input variable */
fpasg(x,xin);
/* check for sign */
if (x[3] < 128) /* positive */
signx = 1;
else /* negative */
{signx = -1;
fpchs(x,x);
}
/* check for very small or large numbers, check by exponent size */
/* check for zero or small */
if ( ((x[4]>127) && (x[4]<209)) || ( (x[4]==0) &&
(x[3]==0) && (x[2]==0) && (x[1]==0) && (x[0]==0) ) )
smallexp = 1;
/* check for big number */
if ( (x[4] >47) && (x[4] < 128) )
bigexp = 1;
/* if very small, return - a large number
if very large, return + a large number */
if (smallexp)
{*sign = signx;
return (fpchs(result,large) );
}
if (bigexp)
{*sign = signx;
return (fpasg(result,large) );
}
/* now bring into range 1 <= x < 10 */
tenpower = 0;
while ( fpcomp(x,ten) >= 0)
{tenpower++;
fpdiv(x,x,ten);
}
while ( fpcomp(x,one) < 0)
{tenpower--;
fpmult(x,x,ten);
}
/* now if exactly one, no need to evaluate */
fpsub(gamnum,x,one);
if (((gamnum[4]>127)&&(gamnum[4]<209)) || ((gamnum[0]==0) &&
(gamnum[1]==0) && (gamnum[2] == 0) && (gamnum[3] == 0) ) )
{*sign = signx;
itof(result,tenpower);
return (result);
}
/* now compute gamma for series */
fpsub(gamnum,x,sqrtten);
/* now check for size of numerator */
if (((gamnum[4]>127)&&(gamnum[4]<209)) || ((gamnum[0]==0) &&
(gamnum[1]==0) && (gamnum[2] == 0) && (gamnum[3] == 0) ) )
{itof(result,tenpower);
fpadd(result,result,half);
*sign = signx;
return (result);
}
fpadd(gamden,x,sqrtten);
fpdiv(gamma,gamnum,gamden);
/* now set up for series (use gamnum as gamma squared) */
fpmult(gamnum,gamma,gamma);
fpasg(gamint,gamma);
index = 0;
fpasg(result,half);
/* now do series evaluation */
while ( (index <= 4) && exprange(gamint) )
{fpmult(intres,coef[index],gamint);
fpadd(result,result,intres);
fpmult(gamint,gamint,gamnum);
index++;
}
/* now do correction for range reduction */
if (tenpower != 0)
{itof(intres,tenpower);
fpadd(result,result,intres);
}
/* now clean up and return */
*sign = signx;
return (result);
}
int exprange(x)
/* The input argument is a floating point function from BDS C which
consists of an array of 5 character data. The function returns
a 1 if the exponent is in the range of - 47 to + 47. Outside this
range a value of 0 (false) is returned. This is a range of ten to
plus or minus 14 power */
char *x;
{ if ( ((x[4]<128) && (x[4]>47) ) || ((x[4]>127) && (x[4] < 209) ) )
return (0);
else return (1);
}
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