mirror of
https://github.com/jart/cosmopolitan.git
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retab: manually, fix damage
Some places were written assuming ts=2, others assuming ts=8. I did my best to restore everything.
This commit is contained in:
Jōshin
parent
f224719b1d
commit
a228426480
2 changed files with 385 additions and 385 deletions
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@ -292,229 +292,229 @@ static long double powil(long double, int);
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long double powl(long double x, long double y)
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long double powl(long double x, long double y)
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{
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{
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/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
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/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
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int i, nflg, iyflg, yoddint;
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int i, nflg, iyflg, yoddint;
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long e;
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long e;
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volatile long double z=0;
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volatile long double z=0;
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long double w=0, W=0, Wa=0, Wb=0, ya=0, yb=0, u=0;
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long double w=0, W=0, Wa=0, Wb=0, ya=0, yb=0, u=0;
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/* make sure no invalid exception is raised by nan comparision */
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/* make sure no invalid exception is raised by nan comparision */
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if (isnan(x)) {
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if (isnan(x)) {
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if (!isnan(y) && y == 0.0)
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if (!isnan(y) && y == 0.0)
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return 1.0;
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return 1.0;
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return x;
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return x;
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}
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}
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if (isnan(y)) {
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if (isnan(y)) {
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if (x == 1.0)
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if (x == 1.0)
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return 1.0;
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return 1.0;
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return y;
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return y;
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}
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}
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if (x == 1.0)
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if (x == 1.0)
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return 1.0; /* 1**y = 1, even if y is nan */
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return 1.0; /* 1**y = 1, even if y is nan */
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if (x == -1.0 && !isfinite(y))
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if (x == -1.0 && !isfinite(y))
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return 1.0; /* -1**inf = 1 */
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return 1.0; /* -1**inf = 1 */
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if (y == 0.0)
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if (y == 0.0)
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return 1.0; /* x**0 = 1, even if x is nan */
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return 1.0; /* x**0 = 1, even if x is nan */
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if (y == 1.0)
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if (y == 1.0)
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return x;
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return x;
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if (y >= LDBL_MAX) {
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if (y >= LDBL_MAX) {
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if (x > 1.0 || x < -1.0)
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if (x > 1.0 || x < -1.0)
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return INFINITY;
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return INFINITY;
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if (x != 0.0)
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if (x != 0.0)
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return 0.0;
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return 0.0;
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}
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}
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if (y <= -LDBL_MAX) {
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if (y <= -LDBL_MAX) {
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if (x > 1.0 || x < -1.0)
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if (x > 1.0 || x < -1.0)
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return 0.0;
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return 0.0;
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if (x != 0.0 || y == -INFINITY)
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if (x != 0.0 || y == -INFINITY)
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return INFINITY;
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return INFINITY;
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}
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}
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if (x >= LDBL_MAX) {
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if (x >= LDBL_MAX) {
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if (y > 0.0)
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if (y > 0.0)
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return INFINITY;
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return INFINITY;
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return 0.0;
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return 0.0;
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}
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}
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w = floorl(y);
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w = floorl(y);
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/* Set iyflg to 1 if y is an integer. */
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/* Set iyflg to 1 if y is an integer. */
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iyflg = 0;
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iyflg = 0;
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if (w == y)
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if (w == y)
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iyflg = 1;
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iyflg = 1;
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/* Test for odd integer y. */
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/* Test for odd integer y. */
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yoddint = 0;
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yoddint = 0;
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if (iyflg) {
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if (iyflg) {
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ya = fabsl(y);
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ya = fabsl(y);
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ya = floorl(0.5 * ya);
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ya = floorl(0.5 * ya);
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yb = 0.5 * fabsl(w);
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yb = 0.5 * fabsl(w);
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if( ya != yb )
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if( ya != yb )
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yoddint = 1;
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yoddint = 1;
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}
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}
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if (x <= -LDBL_MAX) {
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if (x <= -LDBL_MAX) {
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if (y > 0.0) {
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if (y > 0.0) {
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if (yoddint)
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if (yoddint)
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return -INFINITY;
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return -INFINITY;
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return INFINITY;
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return INFINITY;
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}
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}
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if (y < 0.0) {
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if (y < 0.0) {
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if (yoddint)
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if (yoddint)
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return -0.0;
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return -0.0;
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return 0.0;
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return 0.0;
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}
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}
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}
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}
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nflg = 0; /* (x<0)**(odd int) */
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nflg = 0; /* (x<0)**(odd int) */
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if (x <= 0.0) {
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if (x <= 0.0) {
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if (x == 0.0) {
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if (x == 0.0) {
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if (y < 0.0) {
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if (y < 0.0) {
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if (signbit(x) && yoddint)
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if (signbit(x) && yoddint)
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/* (-0.0)**(-odd int) = -inf, divbyzero */
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/* (-0.0)**(-odd int) = -inf, divbyzero */
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return -1.0/0.0;
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return -1.0/0.0;
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/* (+-0.0)**(negative) = inf, divbyzero */
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/* (+-0.0)**(negative) = inf, divbyzero */
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return 1.0/0.0;
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return 1.0/0.0;
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}
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}
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if (signbit(x) && yoddint)
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if (signbit(x) && yoddint)
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return -0.0;
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return -0.0;
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return 0.0;
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return 0.0;
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}
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}
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if (iyflg == 0)
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if (iyflg == 0)
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return (x - x) / (x - x); /* (x<0)**(non-int) is NaN */
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return (x - x) / (x - x); /* (x<0)**(non-int) is NaN */
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/* (x<0)**(integer) */
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/* (x<0)**(integer) */
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if (yoddint)
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if (yoddint)
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nflg = 1; /* negate result */
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nflg = 1; /* negate result */
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x = -x;
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x = -x;
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}
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}
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/* (+integer)**(integer) */
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/* (+integer)**(integer) */
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if (iyflg && floorl(x) == x && fabsl(y) < 32768.0) {
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if (iyflg && floorl(x) == x && fabsl(y) < 32768.0) {
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w = powil(x, (int)y);
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w = powil(x, (int)y);
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return nflg ? -w : w;
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return nflg ? -w : w;
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}
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}
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/* separate significand from exponent */
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/* separate significand from exponent */
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x = frexpl(x, &i);
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x = frexpl(x, &i);
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e = i;
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e = i;
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/* find significand in antilog table A[] */
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/* find significand in antilog table A[] */
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i = 1;
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i = 1;
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if (x <= A[17])
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if (x <= A[17])
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i = 17;
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i = 17;
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if (x <= A[i+8])
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if (x <= A[i+8])
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i += 8;
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i += 8;
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if (x <= A[i+4])
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if (x <= A[i+4])
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i += 4;
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i += 4;
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if (x <= A[i+2])
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if (x <= A[i+2])
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i += 2;
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i += 2;
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if (x >= A[1])
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if (x >= A[1])
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i = -1;
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i = -1;
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i += 1;
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i += 1;
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/* Find (x - A[i])/A[i]
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/* Find (x - A[i])/A[i]
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* in order to compute log(x/A[i]):
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* in order to compute log(x/A[i]):
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*
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*
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* log(x) = log( a x/a ) = log(a) + log(x/a)
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* log(x) = log( a x/a ) = log(a) + log(x/a)
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*
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*
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* log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
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* log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
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*/
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*/
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x -= A[i];
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x -= A[i];
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x -= B[i/2];
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x -= B[i/2];
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x /= A[i];
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x /= A[i];
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/* rational approximation for log(1+v):
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/* rational approximation for log(1+v):
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*
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*
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* log(1+v) = v - v**2/2 + v**3 P(v) / Q(v)
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* log(1+v) = v - v**2/2 + v**3 P(v) / Q(v)
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*/
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*/
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z = x*x;
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z = x*x;
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w = x * (z * __polevll(x, P, 3) / __p1evll(x, Q, 3));
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w = x * (z * __polevll(x, P, 3) / __p1evll(x, Q, 3));
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w = w - 0.5*z;
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w = w - 0.5*z;
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/* Convert to base 2 logarithm:
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/* Convert to base 2 logarithm:
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* multiply by log2(e) = 1 + LOG2EA
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* multiply by log2(e) = 1 + LOG2EA
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*/
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*/
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z = LOG2EA * w;
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z = LOG2EA * w;
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z += w;
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z += w;
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z += LOG2EA * x;
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z += LOG2EA * x;
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z += x;
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z += x;
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/* Compute exponent term of the base 2 logarithm. */
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/* Compute exponent term of the base 2 logarithm. */
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w = -i;
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w = -i;
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w /= NXT;
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w /= NXT;
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w += e;
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w += e;
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/* Now base 2 log of x is w + z. */
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/* Now base 2 log of x is w + z. */
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/* Multiply base 2 log by y, in extended precision. */
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/* Multiply base 2 log by y, in extended precision. */
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/* separate y into large part ya
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/* separate y into large part ya
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* and small part yb less than 1/NXT
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* and small part yb less than 1/NXT
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*/
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*/
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ya = reducl(y);
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ya = reducl(y);
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yb = y - ya;
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yb = y - ya;
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/* (w+z)(ya+yb)
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/* (w+z)(ya+yb)
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* = w*ya + w*yb + z*y
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* = w*ya + w*yb + z*y
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*/
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*/
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F = z * y + w * yb;
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F = z * y + w * yb;
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Fa = reducl(F);
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Fa = reducl(F);
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Fb = F - Fa;
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Fb = F - Fa;
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G = Fa + w * ya;
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G = Fa + w * ya;
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Ga = reducl(G);
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Ga = reducl(G);
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Gb = G - Ga;
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Gb = G - Ga;
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H = Fb + Gb;
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H = Fb + Gb;
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Ha = reducl(H);
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Ha = reducl(H);
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w = (Ga + Ha) * NXT;
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w = (Ga + Ha) * NXT;
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/* Test the power of 2 for overflow */
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/* Test the power of 2 for overflow */
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if (w > MEXP)
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if (w > MEXP)
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return huge * huge; /* overflow */
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return huge * huge; /* overflow */
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if (w < MNEXP)
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if (w < MNEXP)
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return twom10000 * twom10000; /* underflow */
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return twom10000 * twom10000; /* underflow */
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e = w;
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e = w;
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Hb = H - Ha;
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Hb = H - Ha;
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if (Hb > 0.0) {
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if (Hb > 0.0) {
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e += 1;
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e += 1;
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Hb -= 1.0/NXT; /*0.0625L;*/
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Hb -= 1.0/NXT; /*0.0625L;*/
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}
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}
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/* Now the product y * log2(x) = Hb + e/NXT.
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/* Now the product y * log2(x) = Hb + e/NXT.
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*
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*
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* Compute base 2 exponential of Hb,
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* Compute base 2 exponential of Hb,
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* where -0.0625 <= Hb <= 0.
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* where -0.0625 <= Hb <= 0.
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*/
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*/
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z = Hb * __polevll(Hb, R, 6); /* z = 2**Hb - 1 */
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z = Hb * __polevll(Hb, R, 6); /* z = 2**Hb - 1 */
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/* Express e/NXT as an integer plus a negative number of (1/NXT)ths.
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/* Express e/NXT as an integer plus a negative number of (1/NXT)ths.
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* Find lookup table entry for the fractional power of 2.
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* Find lookup table entry for the fractional power of 2.
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*/
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*/
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if (e < 0)
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if (e < 0)
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i = 0;
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i = 0;
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else
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else
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i = 1;
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i = 1;
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i = e/NXT + i;
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i = e/NXT + i;
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e = NXT*i - e;
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e = NXT*i - e;
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w = A[e];
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w = A[e];
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z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
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z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
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z = z + w;
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z = z + w;
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z = scalbnl(z, i); /* multiply by integer power of 2 */
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z = scalbnl(z, i); /* multiply by integer power of 2 */
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if (nflg)
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if (nflg)
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z = -z;
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z = -z;
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return z;
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return z;
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}
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}
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/* Find a multiple of 1/NXT that is within 1/NXT of x. */
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/* Find a multiple of 1/NXT that is within 1/NXT of x. */
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static long double reducl(long double x)
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static long double reducl(long double x)
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{
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{
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long double t;
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long double t;
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t = x * NXT;
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t = x * NXT;
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t = floorl(t);
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t = floorl(t);
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t = t / NXT;
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t = t / NXT;
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return t;
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return t;
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}
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}
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/*
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/*
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@ -551,66 +551,66 @@ static long double reducl(long double x)
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static long double powil(long double x, int nn)
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static long double powil(long double x, int nn)
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{
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{
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long double ww, y;
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long double ww, y;
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long double s;
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long double s;
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int n, e, sign, lx;
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int n, e, sign, lx;
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if (nn == 0)
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if (nn == 0)
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return 1.0;
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return 1.0;
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if (nn < 0) {
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if (nn < 0) {
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sign = -1;
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sign = -1;
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n = -nn;
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n = -nn;
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} else {
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} else {
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sign = 1;
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sign = 1;
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n = nn;
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n = nn;
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}
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}
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/* Overflow detection */
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/* Overflow detection */
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/* Calculate approximate logarithm of answer */
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/* Calculate approximate logarithm of answer */
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s = x;
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s = x;
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s = frexpl( s, &lx);
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s = frexpl( s, &lx);
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e = (lx - 1)*n;
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e = (lx - 1)*n;
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if ((e == 0) || (e > 64) || (e < -64)) {
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if ((e == 0) || (e > 64) || (e < -64)) {
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s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L);
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s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L);
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s = (2.9142135623730950L * s - 0.5 + lx) * nn * LOGE2L;
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s = (2.9142135623730950L * s - 0.5 + lx) * nn * LOGE2L;
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} else {
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} else {
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s = LOGE2L * e;
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s = LOGE2L * e;
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}
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}
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if (s > MAXLOGL)
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if (s > MAXLOGL)
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return huge * huge; /* overflow */
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return huge * huge; /* overflow */
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if (s < MINLOGL)
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if (s < MINLOGL)
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return twom10000 * twom10000; /* underflow */
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return twom10000 * twom10000; /* underflow */
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/* Handle tiny denormal answer, but with less accuracy
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/* Handle tiny denormal answer, but with less accuracy
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* since roundoff error in 1.0/x will be amplified.
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* since roundoff error in 1.0/x will be amplified.
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* The precise demarcation should be the gradual underflow threshold.
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* The precise demarcation should be the gradual underflow threshold.
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*/
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*/
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if (s < -MAXLOGL+2.0) {
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if (s < -MAXLOGL+2.0) {
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x = 1.0/x;
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x = 1.0/x;
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sign = -sign;
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sign = -sign;
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}
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}
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/* First bit of the power */
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/* First bit of the power */
|
||||||
if (n & 1)
|
if (n & 1)
|
||||||
y = x;
|
y = x;
|
||||||
else
|
else
|
||||||
y = 1.0;
|
y = 1.0;
|
||||||
|
|
||||||
ww = x;
|
ww = x;
|
||||||
n >>= 1;
|
n >>= 1;
|
||||||
while (n) {
|
while (n) {
|
||||||
ww = ww * ww; /* arg to the 2-to-the-kth power */
|
ww = ww * ww; /* arg to the 2-to-the-kth power */
|
||||||
if (n & 1) /* if that bit is set, then include in product */
|
if (n & 1) /* if that bit is set, then include in product */
|
||||||
y *= ww;
|
y *= ww;
|
||||||
n >>= 1;
|
n >>= 1;
|
||||||
}
|
}
|
||||||
|
|
||||||
if (sign < 0)
|
if (sign < 0)
|
||||||
y = 1.0/y;
|
y = 1.0/y;
|
||||||
return y;
|
return y;
|
||||||
}
|
}
|
||||||
|
|
||||||
#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
|
#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
|
||||||
|
|
@ -649,35 +649,35 @@ Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>\"");
|
||||||
|
|
||||||
/* powl(x,y) return x**y
|
/* powl(x,y) return x**y
|
||||||
*
|
*
|
||||||
* n
|
* n
|
||||||
* Method: Let x = 2 * (1+f)
|
* Method: Let x = 2 * (1+f)
|
||||||
* 1. Compute and return log2(x) in two pieces:
|
* 1. Compute and return log2(x) in two pieces:
|
||||||
* log2(x) = w1 + w2,
|
* log2(x) = w1 + w2,
|
||||||
* where w1 has 113-53 = 60 bit trailing zeros.
|
* where w1 has 113-53 = 60 bit trailing zeros.
|
||||||
* 2. Perform y*log2(x) = n+y' by simulating multi-precision
|
* 2. Perform y*log2(x) = n+y' by simulating multi-precision
|
||||||
* arithmetic, where |y'|<=0.5.
|
* arithmetic, where |y'|<=0.5.
|
||||||
* 3. Return x**y = 2**n*exp(y'*log2)
|
* 3. Return x**y = 2**n*exp(y'*log2)
|
||||||
*
|
*
|
||||||
* Special cases:
|
* Special cases:
|
||||||
* 1. (anything) ** 0 is 1
|
* 1. (anything) ** 0 is 1
|
||||||
* 2. (anything) ** 1 is itself
|
* 2. (anything) ** 1 is itself
|
||||||
* 3. (anything) ** NAN is NAN
|
* 3. (anything) ** NAN is NAN
|
||||||
* 4. NAN ** (anything except 0) is NAN
|
* 4. NAN ** (anything except 0) is NAN
|
||||||
* 5. +-(|x| > 1) ** +INF is +INF
|
* 5. +-(|x| > 1) ** +INF is +INF
|
||||||
* 6. +-(|x| > 1) ** -INF is +0
|
* 6. +-(|x| > 1) ** -INF is +0
|
||||||
* 7. +-(|x| < 1) ** +INF is +0
|
* 7. +-(|x| < 1) ** +INF is +0
|
||||||
* 8. +-(|x| < 1) ** -INF is +INF
|
* 8. +-(|x| < 1) ** -INF is +INF
|
||||||
* 9. +-1 ** +-INF is NAN
|
* 9. +-1 ** +-INF is NAN
|
||||||
* 10. +0 ** (+anything except 0, NAN) is +0
|
* 10. +0 ** (+anything except 0, NAN) is +0
|
||||||
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
|
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
|
||||||
* 12. +0 ** (-anything except 0, NAN) is +INF
|
* 12. +0 ** (-anything except 0, NAN) is +INF
|
||||||
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
|
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
|
||||||
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
|
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
|
||||||
* 15. +INF ** (+anything except 0,NAN) is +INF
|
* 15. +INF ** (+anything except 0,NAN) is +INF
|
||||||
* 16. +INF ** (-anything except 0,NAN) is +0
|
* 16. +INF ** (-anything except 0,NAN) is +0
|
||||||
* 17. -INF ** (anything) = -0 ** (-anything)
|
* 17. -INF ** (anything) = -0 ** (-anything)
|
||||||
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
|
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
|
||||||
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
|
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
|
||||||
*
|
*
|
||||||
*/
|
*/
|
||||||
|
|
||||||
|
|
@ -792,10 +792,10 @@ powl(long double x, long double y)
|
||||||
/* +-NaN return x+y */
|
/* +-NaN return x+y */
|
||||||
if ((ix > 0x7fff0000)
|
if ((ix > 0x7fff0000)
|
||||||
|| ((ix == 0x7fff0000)
|
|| ((ix == 0x7fff0000)
|
||||||
&& ((p.parts32.mswlo | p.parts32.lswhi | p.parts32.lswlo) != 0))
|
&& ((p.parts32.mswlo | p.parts32.lswhi | p.parts32.lswlo) != 0))
|
||||||
|| (iy > 0x7fff0000)
|
|| (iy > 0x7fff0000)
|
||||||
|| ((iy == 0x7fff0000)
|
|| ((iy == 0x7fff0000)
|
||||||
&& ((q.parts32.mswlo | q.parts32.lswhi | q.parts32.lswlo) != 0)))
|
&& ((q.parts32.mswlo | q.parts32.lswhi | q.parts32.lswlo) != 0)))
|
||||||
return nan_mix(x, y);
|
return nan_mix(x, y);
|
||||||
|
|
||||||
/* determine if y is an odd int when x < 0
|
/* determine if y is an odd int when x < 0
|
||||||
|
|
@ -806,48 +806,48 @@ powl(long double x, long double y)
|
||||||
yisint = 0;
|
yisint = 0;
|
||||||
if (hx < 0)
|
if (hx < 0)
|
||||||
{
|
{
|
||||||
if (iy >= 0x40700000) /* 2^113 */
|
if (iy >= 0x40700000) /* 2^113 */
|
||||||
yisint = 2; /* even integer y */
|
yisint = 2; /* even integer y */
|
||||||
else if (iy >= 0x3fff0000) /* 1.0 */
|
else if (iy >= 0x3fff0000) /* 1.0 */
|
||||||
{
|
{
|
||||||
if (floorl (y) == y)
|
if (floorl (y) == y)
|
||||||
{
|
{
|
||||||
z = 0.5 * y;
|
z = 0.5 * y;
|
||||||
if (floorl (z) == z)
|
if (floorl (z) == z)
|
||||||
yisint = 2;
|
yisint = 2;
|
||||||
else
|
else
|
||||||
yisint = 1;
|
yisint = 1;
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
/* special value of y */
|
/* special value of y */
|
||||||
if ((q.parts32.mswlo | q.parts32.lswhi | q.parts32.lswlo) == 0)
|
if ((q.parts32.mswlo | q.parts32.lswhi | q.parts32.lswlo) == 0)
|
||||||
{
|
{
|
||||||
if (iy == 0x7fff0000) /* y is +-inf */
|
if (iy == 0x7fff0000) /* y is +-inf */
|
||||||
{
|
{
|
||||||
if (((ix - 0x3fff0000) | p.parts32.mswlo | p.parts32.lswhi |
|
if (((ix - 0x3fff0000) | p.parts32.mswlo | p.parts32.lswhi |
|
||||||
p.parts32.lswlo) == 0)
|
p.parts32.lswlo) == 0)
|
||||||
return y - y; /* +-1**inf is NaN */
|
return y - y; /* +-1**inf is NaN */
|
||||||
else if (ix >= 0x3fff0000) /* (|x|>1)**+-inf = inf,0 */
|
else if (ix >= 0x3fff0000) /* (|x|>1)**+-inf = inf,0 */
|
||||||
return (hy >= 0) ? y : zero;
|
return (hy >= 0) ? y : zero;
|
||||||
else /* (|x|<1)**-,+inf = inf,0 */
|
else /* (|x|<1)**-,+inf = inf,0 */
|
||||||
return (hy < 0) ? -y : zero;
|
return (hy < 0) ? -y : zero;
|
||||||
}
|
}
|
||||||
if (iy == 0x3fff0000)
|
if (iy == 0x3fff0000)
|
||||||
{ /* y is +-1 */
|
{ /* y is +-1 */
|
||||||
if (hy < 0)
|
if (hy < 0)
|
||||||
return one / x;
|
return one / x;
|
||||||
else
|
else
|
||||||
return x;
|
return x;
|
||||||
}
|
}
|
||||||
if (hy == 0x40000000)
|
if (hy == 0x40000000)
|
||||||
return x * x; /* y is 2 */
|
return x * x; /* y is 2 */
|
||||||
if (hy == 0x3ffe0000)
|
if (hy == 0x3ffe0000)
|
||||||
{ /* y is 0.5 */
|
{ /* y is 0.5 */
|
||||||
if (hx >= 0) /* x >= +0 */
|
if (hx >= 0) /* x >= +0 */
|
||||||
return sqrtl (x);
|
return sqrtl (x);
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
ax = fabsl (x);
|
ax = fabsl (x);
|
||||||
|
|
@ -855,21 +855,21 @@ powl(long double x, long double y)
|
||||||
if ((p.parts32.mswlo | p.parts32.lswhi | p.parts32.lswlo) == 0)
|
if ((p.parts32.mswlo | p.parts32.lswhi | p.parts32.lswlo) == 0)
|
||||||
{
|
{
|
||||||
if (ix == 0x7fff0000 || ix == 0 || ix == 0x3fff0000)
|
if (ix == 0x7fff0000 || ix == 0 || ix == 0x3fff0000)
|
||||||
{
|
{
|
||||||
z = ax; /*x is +-0,+-inf,+-1 */
|
z = ax; /*x is +-0,+-inf,+-1 */
|
||||||
if (hy < 0)
|
if (hy < 0)
|
||||||
z = one / z; /* z = (1/|x|) */
|
z = one / z; /* z = (1/|x|) */
|
||||||
if (hx < 0)
|
if (hx < 0)
|
||||||
{
|
{
|
||||||
if (((ix - 0x3fff0000) | yisint) == 0)
|
if (((ix - 0x3fff0000) | yisint) == 0)
|
||||||
{
|
{
|
||||||
z = (z - z) / (z - z); /* (-1)**non-int is NaN */
|
z = (z - z) / (z - z); /* (-1)**non-int is NaN */
|
||||||
}
|
}
|
||||||
else if (yisint == 1)
|
else if (yisint == 1)
|
||||||
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
||||||
}
|
}
|
||||||
return z;
|
return z;
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
/* (x<0)**(non-int) is NaN */
|
/* (x<0)**(non-int) is NaN */
|
||||||
|
|
@ -883,17 +883,17 @@ powl(long double x, long double y)
|
||||||
{
|
{
|
||||||
/* if (1 - 2^-113)^y underflows, y > 1.1873e38 */
|
/* if (1 - 2^-113)^y underflows, y > 1.1873e38 */
|
||||||
if (iy > 0x407d654b)
|
if (iy > 0x407d654b)
|
||||||
{
|
{
|
||||||
if (ix <= 0x3ffeffff)
|
if (ix <= 0x3ffeffff)
|
||||||
return (hy < 0) ? huge * huge : tiny * tiny;
|
return (hy < 0) ? huge * huge : tiny * tiny;
|
||||||
if (ix >= 0x3fff0000)
|
if (ix >= 0x3fff0000)
|
||||||
return (hy > 0) ? huge * huge : tiny * tiny;
|
return (hy > 0) ? huge * huge : tiny * tiny;
|
||||||
}
|
}
|
||||||
/* over/underflow if x is not close to one */
|
/* over/underflow if x is not close to one */
|
||||||
if (ix < 0x3ffeffff)
|
if (ix < 0x3ffeffff)
|
||||||
return (hy < 0) ? huge * huge : tiny * tiny;
|
return (hy < 0) ? huge * huge : tiny * tiny;
|
||||||
if (ix > 0x3fff0000)
|
if (ix > 0x3fff0000)
|
||||||
return (hy > 0) ? huge * huge : tiny * tiny;
|
return (hy > 0) ? huge * huge : tiny * tiny;
|
||||||
}
|
}
|
||||||
|
|
||||||
n = 0;
|
n = 0;
|
||||||
|
|
@ -908,11 +908,11 @@ powl(long double x, long double y)
|
||||||
n += ((ix) >> 16) - 0x3fff;
|
n += ((ix) >> 16) - 0x3fff;
|
||||||
j = ix & 0x0000ffff;
|
j = ix & 0x0000ffff;
|
||||||
/* determine interval */
|
/* determine interval */
|
||||||
ix = j | 0x3fff0000; /* normalize ix */
|
ix = j | 0x3fff0000; /* normalize ix */
|
||||||
if (j <= 0x3988)
|
if (j <= 0x3988)
|
||||||
k = 0; /* |x|<sqrt(3/2) */
|
k = 0; /* |x|<sqrt(3/2) */
|
||||||
else if (j < 0xbb67)
|
else if (j < 0xbb67)
|
||||||
k = 1; /* |x|<sqrt(3) */
|
k = 1; /* |x|<sqrt(3) */
|
||||||
else
|
else
|
||||||
{
|
{
|
||||||
k = 0;
|
k = 0;
|
||||||
|
|
@ -925,7 +925,7 @@ powl(long double x, long double y)
|
||||||
ax = o.value;
|
ax = o.value;
|
||||||
|
|
||||||
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
||||||
u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
||||||
v = one / (ax + bp[k]);
|
v = one / (ax + bp[k]);
|
||||||
s = u * v;
|
s = u * v;
|
||||||
s_h = s;
|
s_h = s;
|
||||||
|
|
@ -965,7 +965,7 @@ powl(long double x, long double y)
|
||||||
o.parts32.lswhi &= 0xf8000000;
|
o.parts32.lswhi &= 0xf8000000;
|
||||||
p_h = o.value;
|
p_h = o.value;
|
||||||
p_l = v - (p_h - u);
|
p_l = v - (p_h - u);
|
||||||
z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
|
z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
|
||||||
z_l = cp_l * p_h + p_l * cp + dp_l[k];
|
z_l = cp_l * p_h + p_l * cp + dp_l[k];
|
||||||
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
||||||
t = (long double) n;
|
t = (long double) n;
|
||||||
|
|
@ -979,7 +979,7 @@ powl(long double x, long double y)
|
||||||
/* s (sign of result -ve**odd) = -1 else = 1 */
|
/* s (sign of result -ve**odd) = -1 else = 1 */
|
||||||
s = one;
|
s = one;
|
||||||
if (((((uint32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
|
if (((((uint32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
|
||||||
s = -one; /* (-ve)**(odd int) */
|
s = -one; /* (-ve)**(odd int) */
|
||||||
|
|
||||||
/* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */
|
/* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */
|
||||||
yy1 = y;
|
yy1 = y;
|
||||||
|
|
@ -996,33 +996,33 @@ powl(long double x, long double y)
|
||||||
{
|
{
|
||||||
/* if z > 16384 */
|
/* if z > 16384 */
|
||||||
if (((j - 0x400d0000) | o.parts32.mswlo | o.parts32.lswhi |
|
if (((j - 0x400d0000) | o.parts32.mswlo | o.parts32.lswhi |
|
||||||
o.parts32.lswlo) != 0)
|
o.parts32.lswlo) != 0)
|
||||||
return s * huge * huge; /* overflow */
|
return s * huge * huge; /* overflow */
|
||||||
else
|
else
|
||||||
{
|
{
|
||||||
if (p_l + ovt > z - p_h)
|
if (p_l + ovt > z - p_h)
|
||||||
return s * huge * huge; /* overflow */
|
return s * huge * huge; /* overflow */
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
else if ((j & 0x7fffffff) >= 0x400d01b9) /* z <= -16495 */
|
else if ((j & 0x7fffffff) >= 0x400d01b9) /* z <= -16495 */
|
||||||
{
|
{
|
||||||
/* z < -16495 */
|
/* z < -16495 */
|
||||||
if (((j - 0xc00d01bc) | o.parts32.mswlo | o.parts32.lswhi |
|
if (((j - 0xc00d01bc) | o.parts32.mswlo | o.parts32.lswhi |
|
||||||
o.parts32.lswlo)
|
o.parts32.lswlo)
|
||||||
!= 0)
|
!= 0)
|
||||||
return s * tiny * tiny; /* underflow */
|
return s * tiny * tiny; /* underflow */
|
||||||
else
|
else
|
||||||
{
|
{
|
||||||
if (p_l <= z - p_h)
|
if (p_l <= z - p_h)
|
||||||
return s * tiny * tiny; /* underflow */
|
return s * tiny * tiny; /* underflow */
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
/* compute 2**(p_h+p_l) */
|
/* compute 2**(p_h+p_l) */
|
||||||
i = j & 0x7fffffff;
|
i = j & 0x7fffffff;
|
||||||
k = (i >> 16) - 0x3fff;
|
k = (i >> 16) - 0x3fff;
|
||||||
n = 0;
|
n = 0;
|
||||||
if (i > 0x3ffe0000)
|
if (i > 0x3ffe0000)
|
||||||
{ /* if |z| > 0.5, set n = [z+0.5] */
|
{ /* if |z| > 0.5, set n = [z+0.5] */
|
||||||
n = floorl (z + 0.5L);
|
n = floorl (z + 0.5L);
|
||||||
t = n;
|
t = n;
|
||||||
p_h -= t;
|
p_h -= t;
|
||||||
|
|
@ -1047,7 +1047,7 @@ powl(long double x, long double y)
|
||||||
j = o.parts32.mswhi;
|
j = o.parts32.mswhi;
|
||||||
j += (n << 16);
|
j += (n << 16);
|
||||||
if ((j >> 16) <= 0)
|
if ((j >> 16) <= 0)
|
||||||
z = scalbnl (z, n); /* subnormal output */
|
z = scalbnl (z, n); /* subnormal output */
|
||||||
else
|
else
|
||||||
{
|
{
|
||||||
o.parts32.mswhi = j;
|
o.parts32.mswhi = j;
|
||||||
|
|
|
||||||
|
|
@ -34,41 +34,41 @@ static const float zero = 0.0;
|
||||||
float
|
float
|
||||||
remainderf2(float x, float p)
|
remainderf2(float x, float p)
|
||||||
{
|
{
|
||||||
int32_t hx,hp;
|
int32_t hx,hp;
|
||||||
uint32_t sx;
|
uint32_t sx;
|
||||||
float p_half;
|
float p_half;
|
||||||
|
|
||||||
GET_FLOAT_WORD(hx,x);
|
GET_FLOAT_WORD(hx,x);
|
||||||
GET_FLOAT_WORD(hp,p);
|
GET_FLOAT_WORD(hp,p);
|
||||||
sx = hx&0x80000000;
|
sx = hx&0x80000000;
|
||||||
hp &= 0x7fffffff;
|
hp &= 0x7fffffff;
|
||||||
hx &= 0x7fffffff;
|
hx &= 0x7fffffff;
|
||||||
|
|
||||||
/* purge off exception values */
|
/* purge off exception values */
|
||||||
if((hp==0)|| /* p = 0 */
|
if((hp==0)|| /* p = 0 */
|
||||||
(hx>=0x7f800000)|| /* x not finite */
|
(hx>=0x7f800000)|| /* x not finite */
|
||||||
((hp>0x7f800000))) /* p is NaN */
|
((hp>0x7f800000))) /* p is NaN */
|
||||||
return nan_mix_op(x, p, *)/nan_mix_op(x, p, *);
|
return nan_mix_op(x, p, *)/nan_mix_op(x, p, *);
|
||||||
|
|
||||||
|
|
||||||
if (hp<=0x7effffff) x = fmodf(x,p+p); /* now x < 2p */
|
if (hp<=0x7effffff) x = fmodf(x,p+p); /* now x < 2p */
|
||||||
if ((hx-hp)==0) return zero*x;
|
if ((hx-hp)==0) return zero*x;
|
||||||
x = fabsf(x);
|
x = fabsf(x);
|
||||||
p = fabsf(p);
|
p = fabsf(p);
|
||||||
if (hp<0x01000000) {
|
if (hp<0x01000000) {
|
||||||
if(x+x>p) {
|
if(x+x>p) {
|
||||||
x-=p;
|
x-=p;
|
||||||
if(x+x>=p) x -= p;
|
if(x+x>=p) x -= p;
|
||||||
}
|
}
|
||||||
} else {
|
} else {
|
||||||
p_half = (float)0.5*p;
|
p_half = (float)0.5*p;
|
||||||
if(x>p_half) {
|
if(x>p_half) {
|
||||||
x-=p;
|
x-=p;
|
||||||
if(x>=p_half) x -= p;
|
if(x>=p_half) x -= p;
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
GET_FLOAT_WORD(hx,x);
|
GET_FLOAT_WORD(hx,x);
|
||||||
if ((hx&0x7fffffff)==0) hx = 0;
|
if ((hx&0x7fffffff)==0) hx = 0;
|
||||||
SET_FLOAT_WORD(x,hx^sx);
|
SET_FLOAT_WORD(x,hx^sx);
|
||||||
return x;
|
return x;
|
||||||
}
|
}
|
||||||
|
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue