double
log1p(double x)
{
static const double zero=0.0, negone= -1.0, one=1.0,
half=1.0/2.0, small=1.0E-20; /* 1+small == 1 */
double z,s,t,c;
int k;
#if !defined(__vax__)&&!defined(tahoe)
if(x!=x) return(x); /* x is NaN */
#endif /* !defined(__vax__)&&!defined(tahoe) */
if(finite(x)) {
if( x > negone ) {
/* argument reduction */
if(copysign(x,one)<small) return(x);
k=logb(one+x); z=scalb(x,-k); t=scalb(one,-k);
if(z+t >= sqrt2 )
{ k += 1 ; z *= half; t *= half; }
t += negone; x = z + t;
c = (t-x)+z ; /* correction term for x */
/* compute log(1+x) */
s = x/(2+x); t = x*x*half;
c += (k*ln2lo-c*x);
z = c+s*(t+__log__L(s*s));
x += (z - t) ;
return(k*ln2hi+x);
}
/* end of if (x > negone) */
else {
#if defined(__vax__)||defined(tahoe)
if ( x == negone )
return (infnan(-ERANGE)); /* -INF */
else
return (infnan(EDOM)); /* NaN */
#else /* defined(__vax__)||defined(tahoe) */
/* x = -1, return -INF with signal */
if ( x == negone ) return( negone/zero );
/* negative argument for log, return NaN with signal */
else return ( zero / zero );
#endif /* defined(__vax__)||defined(tahoe) */
}
}
/* end of if (finite(x)) */
/* log(-INF) is NaN */
else if(x<0)
return(zero/zero);
/* log(+INF) is INF */
else return(x);
}
double cosh
(
double x /* value to compute the hyperbolic cosine of */
)
{
static double half=1.0/2.0,one=1.0, small=1.0E-18; /* fl(1+small)==1 */
double scalb(),copysign(),exp(),exp__E(),t;
#if !defined(vax)&&!defined(tahoe)
if(x!=x) return(x); /* x is NaN */
#endif /* !defined(vax)&&!defined(tahoe) */
if((x=copysign(x,one)) <= 22)
if(x<0.3465)
if(x<small) return(one+x);
else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
else /* for x lies in [0.3465,22] */
{ t=exp(x); return((t+one/t)*half); }
if( lnovfl <= x && x <= (lnovfl+0.7))
/* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
* and return 2^max*exp(x) to avoid unnecessary overflow
*/
return(scalb(exp((x-mln2hi)-mln2lo), max));
else
return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */
}
int main() {
double x = 1.0;
double y = 1.0;
int i = 1;
acosh(x);
asinh(x);
atanh(x);
cbrt(x);
expm1(x);
erf(x);
erfc(x);
isnan(x);
j0(x);
j1(x);
jn(i,x);
ilogb(x);
logb(x);
log1p(x);
rint(x);
y0(x);
y1(x);
yn(i,x);
# ifdef _THREAD_SAFE
gamma_r(x,&i);
lgamma_r(x,&i);
# else
gamma(x);
lgamma(x);
# endif
hypot(x,y);
nextafter(x,y);
remainder(x,y);
scalb(x,y);
return 0;
}
double ldexp ( double value, int exp )
{
if ( exp > SHRT_MAX )
exp = SHRT_MAX;
else if ( exp < -SHRT_MAX )
exp = -SHRT_MAX;
return scalb ( value, exp );
}
double
__exp__D(double x, double c)
{
double z, hi, lo;
int k;
if (isnan(x)) /* x is NaN */
return(x);
if ( x <= lnhuge ) {
if ( x >= lntiny ) {
/* argument reduction : x --> x - k*ln2 */
z = invln2*x;
k = z + copysign(.5, x);
/* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
hi=(x-k*ln2hi); /* Exact. */
x= hi - (lo = k*ln2lo-c);
/* return 2^k*[1+x+x*c/(2+c)] */
z=x*x;
c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
c = (x*c)/(2.0-c);
return scalb(1.+(hi-(lo - c)), k);
}
/* end of x > lntiny */
else
/* exp(-big#) underflows to zero */
if(finite(x)) return(scalb(1.0,-5000));
/* exp(-INF) is zero */
else return(0.0);
}
/* end of x < lnhuge */
else
/* exp(INF) is INF, exp(+big#) overflows to INF */
return( finite(x) ? scalb(1.0,5000) : x);
}
double
sinh(double x)
{
static const double one=1.0, half=1.0/2.0 ;
double t, sign;
#if !defined(__vax__)&&!defined(tahoe)
if(x!=x) return(x); /* x is NaN */
#endif /* !defined(__vax__)&&!defined(tahoe) */
sign=copysign(one,x);
x=copysign(x,one);
if(x<lnovfl)
{t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
else if(x <= lnovfl+0.7)
/* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
to avoid unnecessary overflow */
return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
return( expm1(x)*sign );
}
double
significand(double x)
{
return scalb(x,(double) -ilogb(x));
}
static void
F(compile_test) (void)
{
TYPE a, b, c = 1.0;
complex TYPE d;
int i;
int saved_count;
long int j;
long long int k;
a = cos (cos (x));
b = acos (acos (a));
a = sin (sin (x));
b = asin (asin (a));
a = tan (tan (x));
b = atan (atan (a));
c = atan2 (atan2 (a, c), atan2 (b, x));
a = cosh (cosh (x));
b = acosh (acosh (a));
a = sinh (sinh (x));
b = asinh (asinh (a));
a = tanh (tanh (x));
b = atanh (atanh (a));
a = exp (exp (x));
b = log (log (a));
a = log10 (log10 (x));
b = ldexp (ldexp (a, 1), 5);
a = frexp (frexp (x, &i), &i);
b = expm1 (expm1 (a));
a = log1p (log1p (x));
b = logb (logb (a));
a = exp2 (exp2 (x));
b = log2 (log2 (a));
a = pow (pow (x, a), pow (c, b));
b = sqrt (sqrt (a));
a = hypot (hypot (x, b), hypot (c, a));
b = cbrt (cbrt (a));
a = ceil (ceil (x));
b = fabs (fabs (a));
a = floor (floor (x));
b = fmod (fmod (a, b), fmod (c, x));
a = nearbyint (nearbyint (x));
b = round (round (a));
a = trunc (trunc (x));
b = remquo (remquo (a, b, &i), remquo (c, x, &i), &i);
j = lrint (x) + lround (a);
k = llrint (b) + llround (c);
a = erf (erf (x));
b = erfc (erfc (a));
a = tgamma (tgamma (x));
b = lgamma (lgamma (a));
a = rint (rint (x));
b = nextafter (nextafter (a, b), nextafter (c, x));
a = nextdown (nextdown (a));
b = nexttoward (nexttoward (x, a), c);
a = nextup (nextup (a));
b = remainder (remainder (a, b), remainder (c, x));
a = scalb (scalb (x, a), (TYPE) (6));
k = scalbn (a, 7) + scalbln (c, 10l);
i = ilogb (x);
j = llogb (x);
a = fdim (fdim (x, a), fdim (c, b));
b = fmax (fmax (a, x), fmax (c, b));
a = fmin (fmin (x, a), fmin (c, b));
b = fma (sin (a), sin (x), sin (c));
a = totalorder (totalorder (x, b), totalorder (c, x));
b = totalordermag (totalordermag (x, a), totalordermag (c, x));
#ifdef TEST_INT
a = atan2 (i, b);
b = remquo (i, a, &i);
c = fma (i, b, i);
a = pow (i, c);
#endif
x = a + b + c + i + j + k;
saved_count = count;
if (ccount != 0)
ccount = -10000;
d = cos (cos (z));
z = acos (acos (d));
d = sin (sin (z));
z = asin (asin (d));
d = tan (tan (z));
z = atan (atan (d));
d = cosh (cosh (z));
z = acosh (acosh (d));
d = sinh (sinh (z));
z = asinh (asinh (d));
d = tanh (tanh (z));
z = atanh (atanh (d));
d = exp (exp (z));
z = log (log (d));
d = sqrt (sqrt (z));
z = conj (conj (d));
d = fabs (conj (a));
z = pow (pow (a, d), pow (b, z));
d = cproj (cproj (z));
z += fabs (cproj (a));
a = carg (carg (z));
b = creal (creal (d));
c = cimag (cimag (z));
x += a + b + c + i + j + k;
z += d;
if (saved_count != count)
count = -10000;
if (0)
{
a = cos (y);
a = acos (y);
a = sin (y);
a = asin (y);
a = tan (y);
a = atan (y);
a = atan2 (y, y);
a = cosh (y);
a = acosh (y);
a = sinh (y);
a = asinh (y);
a = tanh (y);
a = atanh (y);
a = exp (y);
a = log (y);
a = log10 (y);
a = ldexp (y, 5);
a = frexp (y, &i);
a = expm1 (y);
a = log1p (y);
a = logb (y);
a = exp2 (y);
a = log2 (y);
a = pow (y, y);
a = sqrt (y);
a = hypot (y, y);
a = cbrt (y);
a = ceil (y);
a = fabs (y);
a = floor (y);
a = fmod (y, y);
a = nearbyint (y);
a = round (y);
a = trunc (y);
a = remquo (y, y, &i);
j = lrint (y) + lround (y);
k = llrint (y) + llround (y);
a = erf (y);
a = erfc (y);
a = tgamma (y);
a = lgamma (y);
a = rint (y);
a = nextafter (y, y);
a = nexttoward (y, y);
a = remainder (y, y);
a = scalb (y, (const TYPE) (6));
k = scalbn (y, 7) + scalbln (y, 10l);
i = ilogb (y);
j = llogb (y);
a = fdim (y, y);
a = fmax (y, y);
a = fmin (y, y);
a = fma (y, y, y);
a = totalorder (y, y);
a = totalordermag (y, y);
#ifdef TEST_INT
a = atan2 (i, y);
a = remquo (i, y, &i);
a = fma (i, y, i);
a = pow (i, y);
#endif
d = cos ((const complex TYPE) z);
d = acos ((const complex TYPE) z);
d = sin ((const complex TYPE) z);
d = asin ((const complex TYPE) z);
d = tan ((const complex TYPE) z);
d = atan ((const complex TYPE) z);
d = cosh ((const complex TYPE) z);
d = acosh ((const complex TYPE) z);
d = sinh ((const complex TYPE) z);
d = asinh ((const complex TYPE) z);
d = tanh ((const complex TYPE) z);
d = atanh ((const complex TYPE) z);
d = exp ((const complex TYPE) z);
d = log ((const complex TYPE) z);
d = sqrt ((const complex TYPE) z);
d = pow ((const complex TYPE) z, (const complex TYPE) z);
d = fabs ((const complex TYPE) z);
d = carg ((const complex TYPE) z);
d = creal ((const complex TYPE) z);
d = cimag ((const complex TYPE) z);
d = conj ((const complex TYPE) z);
d = cproj ((const complex TYPE) z);
}
}
float scalbf (float x, float y)
{
return (float) scalb( (double)x, (double)y );
}
double
atan2(double y, double x)
{
static const double zero=0, one=1, small=1.0E-9, big=1.0E18;
double t,z,signy,signx,hi,lo;
int k,m;
#if !defined(__vax__)&&!defined(tahoe)
/* if x or y is NAN */
if(x!=x) return(x); if(y!=y) return(y);
#endif /* !defined(__vax__)&&!defined(tahoe) */
/* copy down the sign of y and x */
signy = copysign(one,y) ;
signx = copysign(one,x) ;
/* if x is 1.0, goto begin */
if(x==1) { y=copysign(y,one); t=y; if(finite(t)) goto begin;}
/* when y = 0 */
if(y==zero) return((signx==one)?y:copysign(PI,signy));
/* when x = 0 */
if(x==zero) return(copysign(PIo2,signy));
/* when x is INF */
if(!finite(x))
if(!finite(y))
return(copysign((signx==one)?PIo4:3*PIo4,signy));
else
return(copysign((signx==one)?zero:PI,signy));
/* when y is INF */
if(!finite(y)) return(copysign(PIo2,signy));
/* compute y/x */
x=copysign(x,one);
y=copysign(y,one);
if((m=(k=logb(y))-logb(x)) > 60) t=big+big;
else if(m < -80 ) t=y/x;
else { t = y/x ; y = scalb(y,-k); x=scalb(x,-k); }
/* begin argument reduction */
begin:
if (t < 2.4375) {
/* truncate 4(t+1/16) to integer for branching */
k = 4 * (t+0.0625);
switch (k) {
/* t is in [0,7/16] */
case 0:
case 1:
if (t < small)
{ big + small ; /* raise inexact flag */
return (copysign((signx>zero)?t:PI-t,signy)); }
hi = zero; lo = zero; break;
/* t is in [7/16,11/16] */
case 2:
hi = athfhi; lo = athflo;
z = x+x;
t = ( (y+y) - x ) / ( z + y ); break;
/* t is in [11/16,19/16] */
case 3:
case 4:
hi = PIo4; lo = zero;
t = ( y - x ) / ( x + y ); break;
/* t is in [19/16,39/16] */
default:
hi = at1fhi; lo = at1flo;
z = y-x; y=y+y+y; t = x+x;
t = ( (z+z)-x ) / ( t + y ); break;
}
}
/* end of if (t < 2.4375) */
else
{
hi = PIo2; lo = zero;
/* t is in [2.4375, big] */
if (t <= big) t = - x / y;
/* t is in [big, INF] */
else
{ big+small; /* raise inexact flag */
t = zero; }
}
/* end of argument reduction */
/* compute atan(t) for t in [-.4375, .4375] */
z = t*t;
#if defined(__vax__)||defined(tahoe)
z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+
z*(a9+z*(a10+z*(a11+z*a12))))))))))));
#else /* defined(__vax__)||defined(tahoe) */
z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+
z*(a9+z*(a10+z*a11)))))))))));
#endif /* defined(__vax__)||defined(tahoe) */
z = lo - z; z += t; z += hi;
return(copysign((signx>zero)?z:PI-z,signy));
}
static int
mainInt()
{
long int n = N, n8 = N8, m, i, j;
signed long vDotProduct, sDotProduct;
signed short *sx, *sy;
vector signed short *x, *y;
IntegerToVector *sX, *sY;
sx = (short *) getMemory( 4*(n+3) );
if (sx == nil)
return 0;
sy = (short *) getMemory( 4*(n+3) );
if (sy == nil)
return 0;
x = (vector signed short *) getMemory( n8*16 );
if ( x == nil)
return 0;
y = (vector signed short *) getMemory( n8*16 );
if ( y == nil)
return 0;
sX = (IntegerToVector *) getMemory( n8*16 );
if (sX == nil)
return 0;
sY = (IntegerToVector *) getMemory( n8*16 );
if (sY == nil)
return 0;
for ( i = 0; i < n; i++ )
{
sx[i] = ( signed short ) scalb(( M_PI * ( double ) ( i ) / ( double ) n ), 8) + 0.5;
sy[i] = ( signed short ) scalb(( M_PI * ( double ) ( n - i ) / ( double ) n ), 8) + 0.5;
}
m = n % 8;
if (m != 0)
for (i = n; i < n + 8 - m; i++)
{
sx[i] = 0.0;
sy[i] = 0.0;
}
for ( i = 0; i < n8; i++ )
for ( j = 0; j < 8; j++ )
{
sX[i].sInt[j] = sx[i*8+j];
sY[i].sInt[j] = sy[i*8+j];
}
for ( i = 0; i < n8; i++ )
{
x[i] = sX[i].vInt;
y[i] = sY[i].vInt;
}
vDotProduct = vIntDotProduct ( x, y, n8 );
printf ( "\nVector dot product = %10d\n", (int) vDotProduct );
return 0;
}
TEST(math, scalb) {
ASSERT_DOUBLE_EQ(12.0, scalb(3.0, 2.0));
}
TEST(math, scalb) {
ASSERT_FLOAT_EQ(12.0, scalb(3.0, 2.0));
}