ldcomplex
clogl(ldcomplex z) {
ldcomplex ans;
long double x, y, t, ax, ay;
int n, ix, iy, hx, hy;
x = LD_RE(z);
y = LD_IM(z);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
ay = fabsl(y);
ax = fabsl(x);
LD_IM(ans) = atan2l(y, x);
if (ix < iy || (ix == iy && ix < 0x7fff0000 && ax < ay)) {
/* swap x and y to force ax>=ay */
t = ax;
ax = ay;
ay = t;
n = ix, ix = iy;
iy = n;
}
n = (ix - iy) >> 16;
if (ix >= 0x7fff0000) { /* x or y is Inf or NaN */
if (isinfl(ax))
LD_RE(ans) = ax;
else if (isinfl(ay))
LD_RE(ans) = ay;
else
LD_RE(ans) = ax + ay;
} else if (ay == zero)
LD_RE(ans) = logl(ax);
else if (((0x3fffffff - ix) ^ (ix - 0x3ffe0000)) >= 0) {
/* 0.5 <= x < 2 */
if (ix >= 0x3fff0000) {
if (ax == one)
LD_RE(ans) = half * log1pl(ay * ay);
else if (n >= SIGP7)
LD_RE(ans) = logl(ax);
else
LD_RE(ans) = half * (log1pl(ay * ay + (ax -
one) * (ax + one)));
} else if (n >= SIGP7)
LD_RE(ans) = logl(ax);
else
LD_RE(ans) = __k_clog_rl(x, y, &t);
} else if (n >= HSIGP7)
LD_RE(ans) = logl(ax);
else if (ix < 0x5f3f0000 && iy >= 0x20bf0000)
/* 2**-8000 < y < x < 2**8000 */
LD_RE(ans) = half * logl(ax * ax + ay * ay);
else {
t = ay / ax;
LD_RE(ans) = logl(ax) + half * log1pl(t * t);
}
return (ans);
}
int
bugfun(long double x, long double y)
{
int result;
if (isinfl(x))
result = isinfl(y);
else
{
int kx, ky;
kx = ky = 1;
result = (kx == ky);
}
return (result);
}
ldcomplex
casinl(ldcomplex z) {
long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
int ix, iy, hx, hy;
ldcomplex ans;
x = LD_RE(z);
y = LD_IM(z);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
x = fabsl(x);
y = fabsl(y);
/* special cases */
/* x is inf or NaN */
if (ix >= 0x7fff0000) { /* x is inf or NaN */
if (isinfl(x)) { /* x is INF */
LD_IM(ans) = x;
if (iy >= 0x7fff0000) {
if (isinfl(y))
/* casin(inf + i inf) = pi/4 + i inf */
LD_RE(ans) = pi_4 + pi_4_l;
else /* casin(inf + i NaN) = NaN + i inf */
LD_RE(ans) = y + y;
} else /* casin(inf + iy) = pi/2 + i inf */
LD_RE(ans) = pi_2 + pi_2_l;
} else { /* x is NaN */
if (iy >= 0x7fff0000) {
/* INDENT OFF */
/*
* casin(NaN + i inf) = NaN + i inf
* casin(NaN + i NaN) = NaN + i NaN
*/
/* INDENT ON */
LD_IM(ans) = y + y;
LD_RE(ans) = x + x;
} else {
/* INDENT OFF */
/* casin(NaN + i y ) = NaN + i NaN */
/* INDENT ON */
LD_IM(ans) = LD_RE(ans) = x + y;
}
}
if (hx < 0)
LD_RE(ans) = -LD_RE(ans);
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
/* casin(+0 + i 0) = 0 + i 0. */
if (x == zero && y == zero)
return (z);
if (iy >= 0x7fff0000) { /* y is inf or NaN */
if (isinfl(y)) { /* casin( x + i inf ) = 0 + i inf */
LD_IM(ans) = y;
LD_RE(ans) = zero;
} else { /* casin( x + i NaN ) = NaN + i NaN */
LD_IM(ans) = x + y;
if (x == zero)
LD_RE(ans) = x;
else
LD_RE(ans) = y;
}
if (hx < 0)
LD_RE(ans) = -LD_RE(ans);
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
if (y == zero) { /* region 1: y=0 */
if (ix < 0x3fff0000) { /* |x| < 1 */
LD_RE(ans) = asinl(x);
LD_IM(ans) = zero;
} else {
LD_RE(ans) = pi_2 + pi_2_l;
if (ix >= ip1) /* |x| >= i386 ? 2**65 : 2**114 */
LD_IM(ans) = ln2 + logl(x);
else if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
one)));
else {
xm1 = x - one;
LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
one)));
}
}
} else if (y <= E * fabsl(x - one)) { /* region 2: y < tiny*|x-1| */
if (ix < 0x3fff0000) { /* x < 1 */
LD_RE(ans) = asinl(x);
LD_IM(ans) = y / sqrtl((one + x) * (one - x));
} else {
LD_RE(ans) = pi_2 + pi_2_l;
if (ix >= ip1) /* i386 ? 2**65 : 2**114 */
LD_IM(ans) = ln2 + logl(x);
else if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
one)));
else
LD_IM(ans) = log1pl((x - one) + sqrtl((x -
one) * (x + one)));
}
} else if (y < Foursqrtu) { /* region 3 */
t = sqrtl(y);
LD_RE(ans) = pi_2 - (t - pi_2_l);
LD_IM(ans) = t;
} else if (E * y - one >= x) { /* region 4 */
LD_RE(ans) = x / y; /* need to fix underflow cases */
LD_IM(ans) = ln2 + logl(y);
} else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
/* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
t = x / y;
LD_RE(ans) = atanl(t);
LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
} else if (x < Foursqrtu) {
/* region 6: x is very small, < 4sqrt(min) */
A = sqrtl(one + y * y);
LD_RE(ans) = x / A; /* may underflow */
if (iy >= 0x3fff8000) /* if y > Acrossover */
LD_IM(ans) = logl(y + A);
else
LD_IM(ans) = half * log1pl((y + y) * (y + A));
} else { /* safe region */
y2 = y * y;
xp1 = x + one;
xm1 = x - one;
R = sqrtl(xp1 * xp1 + y2);
S = sqrtl(xm1 * xm1 + y2);
A = half * (R + S);
B = x / A;
if (B <= Bcrossover)
LD_RE(ans) = asinl(B);
else { /* use atan and an accurate approx to a-x */
Apx = A + x;
if (x <= one)
LD_RE(ans) = atanl(x / sqrtl(half * Apx * (y2 /
(R + xp1) + (S - xm1))));
else
LD_RE(ans) = atanl(x / (y * sqrtl(half * (Apx /
(R + xp1) + Apx / (S + xm1)))));
}
if (A <= Acrossover) {
/* use log1p and an accurate approx to A-1 */
if (x < one)
Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
else
Am1 = half * (y2 / (R + xp1) + (S + xm1));
LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
} else {
LD_IM(ans) = logl(A + sqrtl(A * A - one));
}
}
if (hx < 0)
LD_RE(ans) = -LD_RE(ans);
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
ldcomplex
catanl(ldcomplex z) {
ldcomplex ans;
long double x, y, t1, ax, ay, t;
int hx, hy, ix, iy;
x = LD_RE(z);
y = LD_IM(z);
ax = fabsl(x);
ay = fabsl(y);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
/* x is inf or NaN */
if (ix >= 0x7fff0000) {
if (isinfl(x)) {
LD_RE(ans) = pi_2;
LD_IM(ans) = zero;
} else {
LD_RE(ans) = x + x;
if (iszerol(y) || (isinfl(y)))
LD_IM(ans) = zero;
else
LD_IM(ans) = (fabsl(y) - ay) / (fabsl(y) - ay);
}
} else if (iy >= 0x7fff0000) {
/* y is inf or NaN */
if (isinfl(y)) {
LD_RE(ans) = pi_2;
LD_IM(ans) = zero;
} else {
LD_RE(ans) = (fabsl(x) - ax) / (fabsl(x) - ax);
LD_IM(ans) = y;
}
} else if (iszerol(x)) {
/* INDENT OFF */
/*
* x = 0
* 1 1
* A = --- * atan2(2x, 1-x*x-y*y) = --- atan2(0,1-|y|)
* 2 2
*
* 1 [ (y+1)*(y+1) ] 1 2 1 2y
* B = - log [ ----------- ] = - log (1+ ---) or - log(1+ ----)
* 4 [ (y-1)*(y-1) ] 2 y-1 2 1-y
*/
/* INDENT ON */
t = one - ay;
if (ay == one) {
/* y=1: catan(0,1)=(0,+inf) with 1/0 signal */
LD_IM(ans) = ay / ax;
LD_RE(ans) = zero;
} else if (ay > one) { /* y>1 */
LD_IM(ans) = half * log1pl(two / (-t));
LD_RE(ans) = pi_2;
} else { /* y<1 */
LD_IM(ans) = half * log1pl((ay + ay) / t);
LD_RE(ans) = zero;
}
} else if (ay < E * (one + ax)) {
/* INDENT OFF */
/*
* Tiny y (relative to 1+|x|)
* |y| < E*(1+|x|)
* where E=2**-29, -35, -60 for double, extended, quad precision
*
* 1 [x<=1: atan(x)
* A = - * atan2(2x,1-x*x-y*y) ~ [ 1 1+x
* 2 [x>=1: - atan2(2,(1-x)*(-----))
* 2 x
*
* y/x
* B ~ t*(1-2t), where t = ----------------- is tiny
* x + (y-1)*(y-1)/x
*
* y
* (when x < 2**-60, t = ----------- )
* (y-1)*(y-1)
*/
/* INDENT ON */
if (ay == zero)
LD_IM(ans) = ay;
else {
t1 = ay - one;
if (ix < 0x3fc30000)
t = ay / (t1 * t1);
else if (ix > 0x403b0000)
t = (ay / ax) / ax;
else
t = ay / (ax * ax + t1 * t1);
LD_IM(ans) = t * (one - two * t);
}
if (ix < 0x3fff0000)
LD_RE(ans) = atanl(ax);
else
LD_RE(ans) = half * atan2l(two, (one - ax) * (one +
one / ax));
} else if (ay > Einv * (one + ax)) {
/* INDENT OFF */
/*
* Huge y relative to 1+|x|
* |y| > Einv*(1+|x|), where Einv~2**(prec/2+3),
* 1
* A ~ --- * atan2(2x, -y*y) ~ pi/2
* 2
* y
* B ~ t*(1-2t), where t = --------------- is tiny
* (y-1)*(y-1)
*/
/* INDENT ON */
LD_RE(ans) = pi_2;
t = (ay / (ay - one)) / (ay - one);
LD_IM(ans) = t * (one - (t + t));
} else if (ay == one) {
/* INDENT OFF */
/*
* y=1
* 1 1
* A = - * atan2(2x, -x*x) = --- atan2(2,-x)
* 2 2
*
* 1 [ x*x+4] 1 4 [ 0.5(log2-logx) if
* B = - log [ -----] = - log (1+ ---) = [ |x|<E, else 0.25*
* 4 [ x*x ] 4 x*x [ log1p((2/x)*(2/x))
*/
/* INDENT ON */
LD_RE(ans) = half * atan2l(two, -ax);
if (ax < E)
LD_IM(ans) = half * (ln2 - logl(ax));
else {
t = two / ax;
LD_IM(ans) = 0.25L * log1pl(t * t);
}
} else if (ax > Einv * Einv) {
/* INDENT OFF */
/*
* Huge x:
* when |x| > 1/E^2,
* 1 pi
* A ~ --- * atan2(2x, -x*x-y*y) ~ ---
* 2 2
* y y/x
* B ~ t*(1-2t), where t = --------------- = (-------------- )/x
* x*x+(y-1)*(y-1) 1+((y-1)/x)^2
*/
/* INDENT ON */
LD_RE(ans) = pi_2;
t = ((ay / ax) / (one + ((ay - one) / ax) * ((ay - one) /
ax))) / ax;
LD_IM(ans) = t * (one - (t + t));
} else if (ax < E * E * E * E) {
/* INDENT OFF */
/*
* Tiny x:
* when |x| < E^4, (note that y != 1)
* 1 1
* A = --- * atan2(2x, 1-x*x-y*y) ~ --- * atan2(2x,1-y*y)
* 2 2
*
* 1 [ (y+1)*(y+1) ] 1 2 1 2y
* B = - log [ ----------- ] = - log (1+ ---) or - log(1+ ----)
* 4 [ (y-1)*(y-1) ] 2 y-1 2 1-y
*/
/* INDENT ON */
LD_RE(ans) = half * atan2l(ax + ax, (one - ay) * (one + ay));
if (ay > one) /* y>1 */
LD_IM(ans) = half * log1pl(two / (ay - one));
else /* y<1 */
LD_IM(ans) = half * log1pl((ay + ay) / (one - ay));
} else {
/* INDENT OFF */
/*
* normal x,y
* 1
* A = --- * atan2(2x, 1-x*x-y*y)
* 2
*
* 1 [ x*x+(y+1)*(y+1) ] 1 4y
* B = - log [ --------------- ] = - log (1+ -----------------)
* 4 [ x*x+(y-1)*(y-1) ] 4 x*x + (y-1)*(y-1)
*/
/* INDENT ON */
t = one - ay;
if (iy >= 0x3ffe0000 && iy < 0x40000000) {
/* y close to 1 */
LD_RE(ans) = half * (atan2l((ax + ax), (t * (one +
ay) - ax * ax)));
} else if (ix >= 0x3ffe0000 && ix < 0x40000000) {
/* x close to 1 */
LD_RE(ans) = half * atan2l((ax + ax), ((one - ax) *
(one + ax) - ay * ay));
} else
LD_RE(ans) = half * atan2l((ax + ax), ((one - ax *
ax) - ay * ay));
LD_IM(ans) = 0.25L * log1pl((4.0L * ay) / (ax * ax + t * t));
}
if (hx < 0)
LD_RE(ans) = -LD_RE(ans);
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
ldcomplex
cacosl(ldcomplex z) {
long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
int ix, iy, hx, hy;
ldcomplex ans;
x = LD_RE(z);
y = LD_IM(z);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
/* x is 0 */
if (x == zero) {
if (y == zero || (iy >= 0x7fff0000)) {
LD_RE(ans) = pi_2 + pi_2_l;
LD_IM(ans) = -y;
return (ans);
}
}
/* |y| is inf or NaN */
if (iy >= 0x7fff0000) {
if (isinfl(y)) { /* cacos(x + i inf) = pi/2 - i inf */
LD_IM(ans) = -y;
if (ix < 0x7fff0000) {
LD_RE(ans) = pi_2 + pi_2_l;
} else if (isinfl(x)) {
if (hx >= 0)
LD_RE(ans) = pi_4 + pi_4_l;
else
LD_RE(ans) = pi3_4 + pi3_4_l;
} else {
LD_RE(ans) = x;
}
} else { /* cacos(x + i NaN) = NaN + i NaN */
LD_RE(ans) = y + x;
if (isinfl(x))
LD_IM(ans) = -fabsl(x);
else
LD_IM(ans) = y;
}
return (ans);
}
y = fabsl(y);
if (ix >= 0x7fff0000) { /* x is inf or NaN */
if (isinfl(x)) { /* x is INF */
LD_IM(ans) = -fabsl(x);
if (iy >= 0x7fff0000) {
if (isinfl(y)) {
/* INDENT OFF */
/* cacos(inf + i inf) = pi/4 - i inf */
/* cacos(-inf+ i inf) =3pi/4 - i inf */
/* INDENT ON */
if (hx >= 0)
LD_RE(ans) = pi_4 + pi_4_l;
else
LD_RE(ans) = pi3_4 + pi3_4_l;
} else
/* INDENT OFF */
/* cacos(inf + i NaN) = NaN - i inf */
/* INDENT ON */
LD_RE(ans) = y + y;
} else {
/* INDENT OFF */
/* cacos(inf + iy ) = 0 - i inf */
/* cacos(-inf+ iy ) = pi - i inf */
/* INDENT ON */
if (hx >= 0)
LD_RE(ans) = zero;
else
LD_RE(ans) = pi + pi_l;
}
} else { /* x is NaN */
/* INDENT OFF */
/*
* cacos(NaN + i inf) = NaN - i inf
* cacos(NaN + i y ) = NaN + i NaN
* cacos(NaN + i NaN) = NaN + i NaN
*/
/* INDENT ON */
LD_RE(ans) = x + y;
if (iy >= 0x7fff0000) {
LD_IM(ans) = -y;
} else {
LD_IM(ans) = x;
}
}
if (hy < 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
if (y == zero) { /* region 1: y=0 */
if (ix < 0x3fff0000) { /* |x| < 1 */
LD_RE(ans) = acosl(x);
LD_IM(ans) = zero;
} else {
LD_RE(ans) = zero;
x = fabsl(x);
if (ix >= ip1) /* i386 ? 2**65 : 2**114 */
LD_IM(ans) = ln2 + logl(x);
else if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
one)));
else {
xm1 = x - one;
LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
one)));
}
}
} else if (y <= E * fabsl(fabsl(x) - one)) {
/* region 2: y < tiny*||x|-1| */
if (ix < 0x3fff0000) { /* x < 1 */
LD_RE(ans) = acosl(x);
x = fabsl(x);
LD_IM(ans) = y / sqrtl((one + x) * (one - x));
} else if (ix >= ip1) { /* i386 ? 2**65 : 2**114 */
if (hx >= 0)
LD_RE(ans) = y / x;
else {
if (ix >= ip1 + 0x00040000)
LD_RE(ans) = pi + pi_l;
else {
t = pi_l + y / x;
LD_RE(ans) = pi + t;
}
}
LD_IM(ans) = ln2 + logl(fabsl(x));
} else {
x = fabsl(x);
t = sqrtl((x - one) * (x + one));
LD_RE(ans) = (hx >= 0)? y / t : pi - (y / t - pi_l);
if (ix >= 0x3fff8000) /* x > Acrossover */
LD_IM(ans) = logl(x + t);
else
LD_IM(ans) = log1pl(t - (one - x));
}
} else if (y < Foursqrtu) { /* region 3 */
t = sqrtl(y);
LD_RE(ans) = (hx >= 0)? t : pi + pi_l;
LD_IM(ans) = t;
} else if (E * y - one >= fabsl(x)) { /* region 4 */
LD_RE(ans) = pi_2 + pi_2_l;
LD_IM(ans) = ln2 + logl(y);
} else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
/* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
t = x / y;
LD_RE(ans) = atan2l(y, x);
LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
} else if (fabsl(x) < Foursqrtu) {
/* region 6: x is very small, < 4sqrt(min) */
LD_RE(ans) = pi_2 + pi_2_l;
A = sqrtl(one + y * y);
if (iy >= 0x3fff8000) /* if y > Acrossover */
LD_IM(ans) = logl(y + A);
else
LD_IM(ans) = half * log1pl((y + y) * (y + A));
} else { /* safe region */
t = fabsl(x);
y2 = y * y;
xp1 = t + one;
xm1 = t - one;
R = sqrtl(xp1 * xp1 + y2);
S = sqrtl(xm1 * xm1 + y2);
A = half * (R + S);
B = t / A;
if (B <= Bcrossover)
LD_RE(ans) = (hx >= 0)? acosl(B) : acosl(-B);
else { /* use atan and an accurate approx to a-x */
Apx = A + t;
if (t <= one)
LD_RE(ans) = atan2l(sqrtl(half * Apx * (y2 /
(R + xp1) + (S - xm1))), x);
else
LD_RE(ans) = atan2l((y * sqrtl(half * (Apx /
(R + xp1) + Apx / (S + xm1)))), x);
}
if (A <= Acrossover) {
/* use log1p and an accurate approx to A-1 */
if (ix < 0x3fff0000)
Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
else
Am1 = half * (y2 / (R + xp1) + (S + xm1));
LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
} else {
LD_IM(ans) = logl(A + sqrtl(A * A - one));
}
}
if (hy >= 0)
LD_IM(ans) = -LD_IM(ans);
return (ans);
}
ldcomplex
csqrtl(ldcomplex z) {
ldcomplex ans;
long double x, y, t, ax, ay;
int n, ix, iy, hx, hy;
x = LD_RE(z);
y = LD_IM(z);
hx = HI_XWORD(x);
hy = HI_XWORD(y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
ay = fabsl(y);
ax = fabsl(x);
if (ix >= 0x7fff0000 || iy >= 0x7fff0000) {
/* x or y is Inf or NaN */
if (isinfl(y))
LD_IM(ans) = LD_RE(ans) = ay;
else if (isinfl(x)) {
if (hx > 0) {
LD_RE(ans) = ax;
LD_IM(ans) = ay * zero;
} else {
LD_RE(ans) = ay * zero;
LD_IM(ans) = ax;
}
} else
LD_IM(ans) = LD_RE(ans) = ax + ay;
} else if (y == zero) {
if (hx >= 0) {
LD_RE(ans) = sqrtl(ax);
LD_IM(ans) = zero;
} else {
LD_IM(ans) = sqrtl(ax);
LD_RE(ans) = zero;
}
} else if (ix >= iy) {
n = (ix - iy) >> 16;
#if defined(__x86) /* 64 significant bits */
if (n >= 35)
#else /* 113 significant bits */
if (n >= 60)
#endif
t = sqrtl(ax);
else if (ix >= 0x5f3f0000) { /* x > 2**8000 */
ax *= twom9001;
y *= twom9001;
t = two4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
} else if (iy <= 0x20bf0000) { /* y < 2**-8000 */
ax *= two8999;
y *= two8999;
t = twom4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
} else
t = sqrtl(half * (ax + sqrtl(ax * ax + y * y)));
if (hx >= 0) {
LD_RE(ans) = t;
LD_IM(ans) = ay / (t + t);
} else {
LD_IM(ans) = t;
LD_RE(ans) = ay / (t + t);
}
} else {
long double
hypotl(long double x, long double y) {
int n0, n1, n2, n3;
long double t1, t2, y1, y2, w;
int *px = (int *) &x, *py = (int *) &y;
int *pt1 = (int *) &t1, *py1 = (int *) &y1;
enum fp_direction_type rd;
int j, k, nx, ny, nz;
if ((*(int *) &one) != 0) { /* determine word ordering */
n0 = 0;
n1 = 1;
n2 = 2;
n3 = 3;
} else {
n0 = 3;
n1 = 2;
n2 = 1;
n3 = 0;
}
px[n0] &= 0x7fffffff; /* clear sign bit of x and y */
py[n0] &= 0x7fffffff;
k = 0x7fff0000;
nx = px[n0] & k; /* exponent of x and y */
ny = py[n0] & k;
if (ny > nx) {
w = x;
x = y;
y = w;
nz = ny;
ny = nx;
nx = nz;
} /* force x > y */
if ((nx - ny) >= 0x00730000)
return (x + y); /* x/y >= 2**116 */
if (nx < 0x5ff30000 && ny > 0x205b0000) { /* medium x,y */
/* save and set RD to Rounding to nearest */
rd = __swapRD(fp_nearest);
w = x - y;
if (w > y) {
pt1[n0] = px[n0];
pt1[n1] = px[n1];
pt1[n2] = pt1[n3] = 0;
t2 = x - t1;
x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1)));
} else {
x = x + x;
py1[n0] = py[n0];
py1[n1] = py[n1];
py1[n2] = py1[n3] = 0;
y2 = y - y1;
pt1[n0] = px[n0];
pt1[n1] = px[n1];
pt1[n2] = pt1[n3] = 0;
t2 = x - t1;
x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x)));
}
if (rd != fp_nearest)
(void) __swapRD(rd); /* restore rounding mode */
return (x);
} else {
if (nx == k || ny == k) { /* x or y is INF or NaN */
if (isinfl(x))
t2 = x;
else if (isinfl(y))
t2 = y;
else
t2 = x + y; /* invalid if x or y is sNaN */
return (t2);
}
if (ny == 0) {
if (y == zero || x == zero)
return (x + y);
t1 = scalbnl(one, 16381);
x *= t1;
y *= t1;
return (scalbnl(one, -16381) * hypotl(x, y));
}
j = nx - 0x3fff0000;
px[n0] -= j;
py[n0] -= j;
pt1[n0] = nx;
pt1[n1] = pt1[n2] = pt1[n3] = 0;
return (t1 * hypotl(x, y));
}
}
int test1l(long double x)
{
return isinfl(x);
}
static int
print_float (struct printf_info *pinfo, char *startp, char *endp, int *signp, snv_long_double n)
{
int prec, fmtch;
char *p, *t;
snv_long_double fract;
int expcnt, gformat = 0;
snv_long_double integer, tmp;
char expbuf[10];
prec = pinfo->prec;
fmtch = pinfo->spec;
t = startp;
*signp = 0;
/* Do the special cases: nans, infinities, zero, and negative numbers. */
if (isnanl (n))
{
/* Not-a-numbers are printed as a simple string. */
*t++ = fmtch < 'a' ? 'N' : 'n';
*t++ = fmtch < 'a' ? 'A' : 'a';
*t++ = fmtch < 'a' ? 'N' : 'n';
return t - startp;
}
/* Zero and infinity also can have a sign in front of them. */
if (copysignl (1.0, n) < 0.0)
{
n = -1.0 * n;
*signp = '-';
}
if (isinfl (n))
{
/* Infinities are printed as a simple string. */
*t++ = fmtch < 'a' ? 'I' : 'i';
*t++ = fmtch < 'a' ? 'N' : 'n';
*t++ = fmtch < 'a' ? 'F' : 'f';
goto set_signp;
}
expcnt = 0;
fract = modfl (n, &integer);
/* get an extra slot for rounding. */
*t++ = '0';
/* get integer portion of number; put into the end of the buffer; the
.01 is added for modfl (356.0 / 10, &integer) returning .59999999... */
for (p = endp - 1; p >= startp && integer; ++expcnt)
{
tmp = modfl (integer / 10, &integer);
*p-- = '0' + ((int) ((tmp + .01L) * 10));
}
switch (fmtch)
{
case 'g':
case 'G':
gformat = 1;
/* a precision of 0 is treated as a precision of 1. */
if (!prec)
pinfo->prec = ++prec;
/* ``The style used depends on the value converted; style e
will be used only if the exponent resulting from the
conversion is less than -4 or greater than the precision.''
-- ANSI X3J11 */
if (expcnt > prec || (!expcnt && fract && fract < .0001L))
{
/* g/G format counts "significant digits, not digits of
precision; for the e/E format, this just causes an
off-by-one problem, i.e. g/G considers the digit
before the decimal point significant and e/E doesn't
count it as precision. */
--prec;
fmtch -= 2; /* G->E, g->e */
goto eformat;
}
else
{
/* Decrement precision */
if (n != 0.0L)
prec -= (endp - p) - 1;
else
prec--;
goto fformat;
}
case 'f':
case 'F':
fformat:
/* reverse integer into beginning of buffer */
if (expcnt)
for (; ++p < endp; *t++ = *p);
else
*t++ = '0';
/* If precision required or alternate flag set, add in a
decimal point. */
if (pinfo->prec || pinfo->alt)
*t++ = '.';
/* if requires more precision and some fraction left */
if (fract)
{
if (prec)
{
/* For %g, if no integer part, don't count initial
zeros as significant digits. */
do
{
fract = modfl (fract * 10, &tmp);
*t++ = '0' + ((int) tmp);
}
while (!tmp && !expcnt && gformat);
while (--prec && fract)
{
fract = modfl (fract * 10, &tmp);
*t++ = '0' + ((int) tmp);
}
}
if (fract)
startp =
print_float_round (fract, (int *) NULL, startp, t - 1, (char) 0, signp);
}
break;
case 'e':
case 'E':
eformat:
if (expcnt)
{
*t++ = *++p;
if (pinfo->prec || pinfo->alt)
*t++ = '.';
/* if requires more precision and some integer left */
for (; prec && ++p < endp; --prec)
*t++ = *p;
/* if done precision and more of the integer component,
round using it; adjust fract so we don't re-round
later. */
if (!prec && ++p < endp)
{
fract = 0;
startp = print_float_round ((snv_long_double) 0, &expcnt, startp, t - 1, *p, signp);
}
/* adjust expcnt for digit in front of decimal */
--expcnt;
}
/* until first fractional digit, decrement exponent */
else if (fract)
{
/* adjust expcnt for digit in front of decimal */
for (expcnt = -1;; --expcnt)
{
fract = modfl (fract * 10, &tmp);
if (tmp)
break;
}
*t++ = '0' + ((int) tmp);
if (pinfo->prec || pinfo->alt)
*t++ = '.';
}
else
{
*t++ = '0';
if (pinfo->prec || pinfo->alt)
*t++ = '.';
}
/* if requires more precision and some fraction left */
if (fract)
{
if (prec)
do
{
fract = modfl (fract * 10, &tmp);
*t++ = '0' + ((int) tmp);
}
while (--prec && fract);
if (fract)
startp = print_float_round (fract, &expcnt, startp, t - 1, (char) 0, signp);
}
break;
default:
abort ();
}
/* %e/%f/%#g add 0's for precision, others trim 0's */
if (gformat && !pinfo->alt)
{
while (t > startp && *--t == '0');
if (*t != '.')
++t;
}
else
for (; prec--; *t++ = '0');
if (fmtch == 'e' || fmtch == 'E')
{
*t++ = fmtch;
if (expcnt < 0)
{
expcnt = -expcnt;
*t++ = '-';
}
else
*t++ = '+';
p = expbuf;
do
*p++ = '0' + (expcnt % 10);
while ((expcnt /= 10) > 9);
*p++ = '0' + expcnt;
while (p > expbuf)
*t++ = *--p;
}
set_signp:
if (!*signp)
{
if (pinfo->showsign)
*signp = '+';
else if (pinfo->space)
*signp = ' ';
}
return (t - startp);
}
