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Unified Diff: fusl/src/math/pow.c

Issue 1714623002: [fusl] clang-format fusl (Closed) Base URL: git@github.com:domokit/mojo.git@master
Patch Set: headers too Created 4 years, 10 months ago
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Index: fusl/src/math/pow.c
diff --git a/fusl/src/math/pow.c b/fusl/src/math/pow.c
index b66f632d8eea9fce118c087677c755f391c6df85..7a9f1a6d91dc00d1cdb957e41e167509b4aebac4 100644
--- a/fusl/src/math/pow.c
+++ b/fusl/src/math/pow.c
@@ -31,14 +31,17 @@
* 9. -1 ** +-INF is 1
* 10. +0 ** (+anything except 0, NAN) is +0
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
- * 12. +0 ** (-anything except 0, NAN) is +INF, raise divbyzero
- * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise divbyzero
+ * 12. +0 ** (-anything except 0, NAN) is +INF, raise
+ * divbyzero
+ * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise
+ * divbyzero
* 14. -0 ** (+odd integer) is -0
* 15. -0 ** (-odd integer) is -INF, raise divbyzero
* 16. +INF ** (+anything except 0,NAN) is +INF
* 17. +INF ** (-anything except 0,NAN) is +0
* 18. -INF ** (+odd integer) is -INF
- * 19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer)
+ * 19. -INF ** (anything) = -0 ** (-anything), (anything except odd
+ * integer)
* 20. (anything) ** 1 is (anything)
* 21. (anything) ** -1 is 1/(anything)
* 22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
@@ -59,270 +62,285 @@
#include "libm.h"
-static const double
-bp[] = {1.0, 1.5,},
-dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
-dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
-two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
-huge = 1.0e300,
-tiny = 1.0e-300,
-/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
-L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
-L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
-L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
-L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
-L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
-L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
-P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
-P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
-P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
-P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
-P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
-lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
-lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
-lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
-ovt = 8.0085662595372944372e-017, /* -(1024-log2(ovfl+.5ulp)) */
-cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
-cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
-cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
-ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
-ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
-ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
+static const double bp[] =
+ {
+ 1.0, 1.5,
+},
+ dp_h[] =
+ {
+ 0.0, 5.84962487220764160156e-01,
+}, /* 0x3FE2B803, 0x40000000 */
+ dp_l[] =
+ {
+ 0.0, 1.35003920212974897128e-08,
+}, /* 0x3E4CFDEB, 0x43CFD006 */
+ two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
+ huge = 1.0e300,
+ tiny = 1.0e-300,
+ /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
+ L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
+ L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
+ L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
+ L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
+ L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
+ L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
+ P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
+ P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
+ P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
+ P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
+ P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
+ lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
+ lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
+ lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
+ ovt = 8.0085662595372944372e-017, /* -(1024-log2(ovfl+.5ulp)) */
+ cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
+ cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
+ cp_l =
+ -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
+ ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
+ ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
+ ivln2_l =
+ 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
-double pow(double x, double y)
-{
- double z,ax,z_h,z_l,p_h,p_l;
- double y1,t1,t2,r,s,t,u,v,w;
- int32_t i,j,k,yisint,n;
- int32_t hx,hy,ix,iy;
- uint32_t lx,ly;
+double pow(double x, double y) {
+ double z, ax, z_h, z_l, p_h, p_l;
+ double y1, t1, t2, r, s, t, u, v, w;
+ int32_t i, j, k, yisint, n;
+ int32_t hx, hy, ix, iy;
+ uint32_t lx, ly;
- EXTRACT_WORDS(hx, lx, x);
- EXTRACT_WORDS(hy, ly, y);
- ix = hx & 0x7fffffff;
- iy = hy & 0x7fffffff;
+ EXTRACT_WORDS(hx, lx, x);
+ EXTRACT_WORDS(hy, ly, y);
+ ix = hx & 0x7fffffff;
+ iy = hy & 0x7fffffff;
- /* x**0 = 1, even if x is NaN */
- if ((iy|ly) == 0)
- return 1.0;
- /* 1**y = 1, even if y is NaN */
- if (hx == 0x3ff00000 && lx == 0)
- return 1.0;
- /* NaN if either arg is NaN */
- if (ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0) ||
- iy > 0x7ff00000 || (iy == 0x7ff00000 && ly != 0))
- return x + y;
+ /* x**0 = 1, even if x is NaN */
+ if ((iy | ly) == 0)
+ return 1.0;
+ /* 1**y = 1, even if y is NaN */
+ if (hx == 0x3ff00000 && lx == 0)
+ return 1.0;
+ /* NaN if either arg is NaN */
+ if (ix > 0x7ff00000 || (ix == 0x7ff00000 && lx != 0) || iy > 0x7ff00000 ||
+ (iy == 0x7ff00000 && ly != 0))
+ return x + y;
- /* determine if y is an odd int when x < 0
- * yisint = 0 ... y is not an integer
- * yisint = 1 ... y is an odd int
- * yisint = 2 ... y is an even int
- */
- yisint = 0;
- if (hx < 0) {
- if (iy >= 0x43400000)
- yisint = 2; /* even integer y */
- else if (iy >= 0x3ff00000) {
- k = (iy>>20) - 0x3ff; /* exponent */
- if (k > 20) {
- j = ly>>(52-k);
- if ((j<<(52-k)) == ly)
- yisint = 2 - (j&1);
- } else if (ly == 0) {
- j = iy>>(20-k);
- if ((j<<(20-k)) == iy)
- yisint = 2 - (j&1);
- }
- }
- }
+ /* determine if y is an odd int when x < 0
+ * yisint = 0 ... y is not an integer
+ * yisint = 1 ... y is an odd int
+ * yisint = 2 ... y is an even int
+ */
+ yisint = 0;
+ if (hx < 0) {
+ if (iy >= 0x43400000)
+ yisint = 2; /* even integer y */
+ else if (iy >= 0x3ff00000) {
+ k = (iy >> 20) - 0x3ff; /* exponent */
+ if (k > 20) {
+ j = ly >> (52 - k);
+ if ((j << (52 - k)) == ly)
+ yisint = 2 - (j & 1);
+ } else if (ly == 0) {
+ j = iy >> (20 - k);
+ if ((j << (20 - k)) == iy)
+ yisint = 2 - (j & 1);
+ }
+ }
+ }
- /* special value of y */
- if (ly == 0) {
- if (iy == 0x7ff00000) { /* y is +-inf */
- if (((ix-0x3ff00000)|lx) == 0) /* (-1)**+-inf is 1 */
- return 1.0;
- else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
- return hy >= 0 ? y : 0.0;
- else /* (|x|<1)**+-inf = 0,inf */
- return hy >= 0 ? 0.0 : -y;
- }
- if (iy == 0x3ff00000) { /* y is +-1 */
- if (hy >= 0)
- return x;
- y = 1/x;
-#if FLT_EVAL_METHOD!=0
- {
- union {double f; uint64_t i;} u = {y};
- uint64_t i = u.i & -1ULL/2;
- if (i>>52 == 0 && (i&(i-1)))
- FORCE_EVAL((float)y);
- }
+ /* special value of y */
+ if (ly == 0) {
+ if (iy == 0x7ff00000) { /* y is +-inf */
+ if (((ix - 0x3ff00000) | lx) == 0) /* (-1)**+-inf is 1 */
+ return 1.0;
+ else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
+ return hy >= 0 ? y : 0.0;
+ else /* (|x|<1)**+-inf = 0,inf */
+ return hy >= 0 ? 0.0 : -y;
+ }
+ if (iy == 0x3ff00000) { /* y is +-1 */
+ if (hy >= 0)
+ return x;
+ y = 1 / x;
+#if FLT_EVAL_METHOD != 0
+ {
+ union {
+ double f;
+ uint64_t i;
+ } u = {y};
+ uint64_t i = u.i & -1ULL / 2;
+ if (i >> 52 == 0 && (i & (i - 1)))
+ FORCE_EVAL((float)y);
+ }
#endif
- return y;
- }
- if (hy == 0x40000000) /* y is 2 */
- return x*x;
- if (hy == 0x3fe00000) { /* y is 0.5 */
- if (hx >= 0) /* x >= +0 */
- return sqrt(x);
- }
- }
+ return y;
+ }
+ if (hy == 0x40000000) /* y is 2 */
+ return x * x;
+ if (hy == 0x3fe00000) { /* y is 0.5 */
+ if (hx >= 0) /* x >= +0 */
+ return sqrt(x);
+ }
+ }
- ax = fabs(x);
- /* special value of x */
- if (lx == 0) {
- if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) { /* x is +-0,+-inf,+-1 */
- z = ax;
- if (hy < 0) /* z = (1/|x|) */
- z = 1.0/z;
- if (hx < 0) {
- if (((ix-0x3ff00000)|yisint) == 0) {
- z = (z-z)/(z-z); /* (-1)**non-int is NaN */
- } else if (yisint == 1)
- z = -z; /* (x<0)**odd = -(|x|**odd) */
- }
- return z;
- }
- }
+ ax = fabs(x);
+ /* special value of x */
+ if (lx == 0) {
+ if (ix == 0x7ff00000 || ix == 0 ||
+ ix == 0x3ff00000) { /* x is +-0,+-inf,+-1 */
+ z = ax;
+ if (hy < 0) /* z = (1/|x|) */
+ z = 1.0 / z;
+ if (hx < 0) {
+ if (((ix - 0x3ff00000) | yisint) == 0) {
+ z = (z - z) / (z - z); /* (-1)**non-int is NaN */
+ } else if (yisint == 1)
+ z = -z; /* (x<0)**odd = -(|x|**odd) */
+ }
+ return z;
+ }
+ }
- s = 1.0; /* sign of result */
- if (hx < 0) {
- if (yisint == 0) /* (x<0)**(non-int) is NaN */
- return (x-x)/(x-x);
- if (yisint == 1) /* (x<0)**(odd int) */
- s = -1.0;
- }
+ s = 1.0; /* sign of result */
+ if (hx < 0) {
+ if (yisint == 0) /* (x<0)**(non-int) is NaN */
+ return (x - x) / (x - x);
+ if (yisint == 1) /* (x<0)**(odd int) */
+ s = -1.0;
+ }
- /* |y| is huge */
- if (iy > 0x41e00000) { /* if |y| > 2**31 */
- if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
- if (ix <= 0x3fefffff)
- return hy < 0 ? huge*huge : tiny*tiny;
- if (ix >= 0x3ff00000)
- return hy > 0 ? huge*huge : tiny*tiny;
- }
- /* over/underflow if x is not close to one */
- if (ix < 0x3fefffff)
- return hy < 0 ? s*huge*huge : s*tiny*tiny;
- if (ix > 0x3ff00000)
- return hy > 0 ? s*huge*huge : s*tiny*tiny;
- /* now |1-x| is tiny <= 2**-20, suffice to compute
- log(x) by x-x^2/2+x^3/3-x^4/4 */
- t = ax - 1.0; /* t has 20 trailing zeros */
- w = (t*t)*(0.5 - t*(0.3333333333333333333333-t*0.25));
- u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
- v = t*ivln2_l - w*ivln2;
- t1 = u + v;
- SET_LOW_WORD(t1, 0);
- t2 = v - (t1-u);
- } else {
- double ss,s2,s_h,s_l,t_h,t_l;
- n = 0;
- /* take care subnormal number */
- if (ix < 0x00100000) {
- ax *= two53;
- n -= 53;
- GET_HIGH_WORD(ix,ax);
- }
- n += ((ix)>>20) - 0x3ff;
- j = ix & 0x000fffff;
- /* determine interval */
- ix = j | 0x3ff00000; /* normalize ix */
- if (j <= 0x3988E) /* |x|<sqrt(3/2) */
- k = 0;
- else if (j < 0xBB67A) /* |x|<sqrt(3) */
- k = 1;
- else {
- k = 0;
- n += 1;
- ix -= 0x00100000;
- }
- SET_HIGH_WORD(ax, ix);
+ /* |y| is huge */
+ if (iy > 0x41e00000) { /* if |y| > 2**31 */
+ if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
+ if (ix <= 0x3fefffff)
+ return hy < 0 ? huge * huge : tiny * tiny;
+ if (ix >= 0x3ff00000)
+ return hy > 0 ? huge * huge : tiny * tiny;
+ }
+ /* over/underflow if x is not close to one */
+ if (ix < 0x3fefffff)
+ return hy < 0 ? s * huge * huge : s * tiny * tiny;
+ if (ix > 0x3ff00000)
+ return hy > 0 ? s * huge * huge : s * tiny * tiny;
+ /* now |1-x| is tiny <= 2**-20, suffice to compute
+ log(x) by x-x^2/2+x^3/3-x^4/4 */
+ t = ax - 1.0; /* t has 20 trailing zeros */
+ w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
+ u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
+ v = t * ivln2_l - w * ivln2;
+ t1 = u + v;
+ SET_LOW_WORD(t1, 0);
+ t2 = v - (t1 - u);
+ } else {
+ double ss, s2, s_h, s_l, t_h, t_l;
+ n = 0;
+ /* take care subnormal number */
+ if (ix < 0x00100000) {
+ ax *= two53;
+ n -= 53;
+ GET_HIGH_WORD(ix, ax);
+ }
+ n += ((ix) >> 20) - 0x3ff;
+ j = ix & 0x000fffff;
+ /* determine interval */
+ ix = j | 0x3ff00000; /* normalize ix */
+ if (j <= 0x3988E) /* |x|<sqrt(3/2) */
+ k = 0;
+ else if (j < 0xBB67A) /* |x|<sqrt(3) */
+ k = 1;
+ else {
+ k = 0;
+ n += 1;
+ ix -= 0x00100000;
+ }
+ SET_HIGH_WORD(ax, ix);
- /* compute ss = 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 */
- v = 1.0/(ax+bp[k]);
- ss = u*v;
- s_h = ss;
- SET_LOW_WORD(s_h, 0);
- /* t_h=ax+bp[k] High */
- t_h = 0.0;
- SET_HIGH_WORD(t_h, ((ix>>1)|0x20000000) + 0x00080000 + (k<<18));
- t_l = ax - (t_h-bp[k]);
- s_l = v*((u-s_h*t_h)-s_h*t_l);
- /* compute log(ax) */
- s2 = ss*ss;
- r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
- r += s_l*(s_h+ss);
- s2 = s_h*s_h;
- t_h = 3.0 + s2 + r;
- SET_LOW_WORD(t_h, 0);
- t_l = r - ((t_h-3.0)-s2);
- /* u+v = ss*(1+...) */
- u = s_h*t_h;
- v = s_l*t_h + t_l*ss;
- /* 2/(3log2)*(ss+...) */
- p_h = u + v;
- SET_LOW_WORD(p_h, 0);
- p_l = v - (p_h-u);
- 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];
- /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
- t = (double)n;
- t1 = ((z_h + z_l) + dp_h[k]) + t;
- SET_LOW_WORD(t1, 0);
- t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
- }
+ /* compute ss = 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 */
+ v = 1.0 / (ax + bp[k]);
+ ss = u * v;
+ s_h = ss;
+ SET_LOW_WORD(s_h, 0);
+ /* t_h=ax+bp[k] High */
+ t_h = 0.0;
+ SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
+ t_l = ax - (t_h - bp[k]);
+ s_l = v * ((u - s_h * t_h) - s_h * t_l);
+ /* compute log(ax) */
+ s2 = ss * ss;
+ r = s2 * s2 *
+ (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
+ r += s_l * (s_h + ss);
+ s2 = s_h * s_h;
+ t_h = 3.0 + s2 + r;
+ SET_LOW_WORD(t_h, 0);
+ t_l = r - ((t_h - 3.0) - s2);
+ /* u+v = ss*(1+...) */
+ u = s_h * t_h;
+ v = s_l * t_h + t_l * ss;
+ /* 2/(3log2)*(ss+...) */
+ p_h = u + v;
+ SET_LOW_WORD(p_h, 0);
+ p_l = v - (p_h - u);
+ 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];
+ /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+ t = (double)n;
+ t1 = ((z_h + z_l) + dp_h[k]) + t;
+ SET_LOW_WORD(t1, 0);
+ t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
+ }
- /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
- y1 = y;
- SET_LOW_WORD(y1, 0);
- p_l = (y-y1)*t1 + y*t2;
- p_h = y1*t1;
- z = p_l + p_h;
- EXTRACT_WORDS(j, i, z);
- if (j >= 0x40900000) { /* z >= 1024 */
- if (((j-0x40900000)|i) != 0) /* if z > 1024 */
- return s*huge*huge; /* overflow */
- if (p_l + ovt > z - p_h)
- return s*huge*huge; /* overflow */
- } else if ((j&0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */ // FIXME: instead of abs(j) use unsigned j
- if (((j-0xc090cc00)|i) != 0) /* z < -1075 */
- return s*tiny*tiny; /* underflow */
- if (p_l <= z - p_h)
- return s*tiny*tiny; /* underflow */
- }
- /*
- * compute 2**(p_h+p_l)
- */
- i = j & 0x7fffffff;
- k = (i>>20) - 0x3ff;
- n = 0;
- if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
- n = j + (0x00100000>>(k+1));
- k = ((n&0x7fffffff)>>20) - 0x3ff; /* new k for n */
- t = 0.0;
- SET_HIGH_WORD(t, n & ~(0x000fffff>>k));
- n = ((n&0x000fffff)|0x00100000)>>(20-k);
- if (j < 0)
- n = -n;
- p_h -= t;
- }
- t = p_l + p_h;
- SET_LOW_WORD(t, 0);
- u = t*lg2_h;
- v = (p_l-(t-p_h))*lg2 + t*lg2_l;
- z = u + v;
- w = v - (z-u);
- t = z*z;
- t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
- r = (z*t1)/(t1-2.0) - (w + z*w);
- z = 1.0 - (r-z);
- GET_HIGH_WORD(j, z);
- j += n<<20;
- if ((j>>20) <= 0) /* subnormal output */
- z = scalbn(z,n);
- else
- SET_HIGH_WORD(z, j);
- return s*z;
+ /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+ y1 = y;
+ SET_LOW_WORD(y1, 0);
+ p_l = (y - y1) * t1 + y * t2;
+ p_h = y1 * t1;
+ z = p_l + p_h;
+ EXTRACT_WORDS(j, i, z);
+ if (j >= 0x40900000) { /* z >= 1024 */
+ if (((j - 0x40900000) | i) != 0) /* if z > 1024 */
+ return s * huge * huge; /* overflow */
+ if (p_l + ovt > z - p_h)
+ return s * huge * huge; /* overflow */
+ } else if ((j & 0x7fffffff) >= 0x4090cc00) {
+ /* z <= -1075 */ // FIXME: instead of abs(j) use unsigned j
+ if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */
+ return s * tiny * tiny; /* underflow */
+ if (p_l <= z - p_h)
+ return s * tiny * tiny; /* underflow */
+ }
+ /*
+ * compute 2**(p_h+p_l)
+ */
+ i = j & 0x7fffffff;
+ k = (i >> 20) - 0x3ff;
+ n = 0;
+ if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
+ n = j + (0x00100000 >> (k + 1));
+ k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
+ t = 0.0;
+ SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
+ n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
+ if (j < 0)
+ n = -n;
+ p_h -= t;
+ }
+ t = p_l + p_h;
+ SET_LOW_WORD(t, 0);
+ u = t * lg2_h;
+ v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
+ z = u + v;
+ w = v - (z - u);
+ t = z * z;
+ t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
+ r = (z * t1) / (t1 - 2.0) - (w + z * w);
+ z = 1.0 - (r - z);
+ GET_HIGH_WORD(j, z);
+ j += n << 20;
+ if ((j >> 20) <= 0) /* subnormal output */
+ z = scalbn(z, n);
+ else
+ SET_HIGH_WORD(z, j);
+ return s * z;
}
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