| Index: fusl/src/math/powf.c
|
| diff --git a/fusl/src/math/powf.c b/fusl/src/math/powf.c
|
| index 427c8965b9e8e78bca69660427a4e313087c3e0a..ee4bd98855291ab79e4cc9dec1604d35eee4816c 100644
|
| --- a/fusl/src/math/powf.c
|
| +++ b/fusl/src/math/powf.c
|
| @@ -15,245 +15,257 @@
|
|
|
| #include "libm.h"
|
|
|
| -static const float
|
| -bp[] = {1.0, 1.5,},
|
| -dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
|
| -dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
|
| -two24 = 16777216.0, /* 0x4b800000 */
|
| -huge = 1.0e30,
|
| -tiny = 1.0e-30,
|
| -/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
| -L1 = 6.0000002384e-01, /* 0x3f19999a */
|
| -L2 = 4.2857143283e-01, /* 0x3edb6db7 */
|
| -L3 = 3.3333334327e-01, /* 0x3eaaaaab */
|
| -L4 = 2.7272811532e-01, /* 0x3e8ba305 */
|
| -L5 = 2.3066075146e-01, /* 0x3e6c3255 */
|
| -L6 = 2.0697501302e-01, /* 0x3e53f142 */
|
| -P1 = 1.6666667163e-01, /* 0x3e2aaaab */
|
| -P2 = -2.7777778450e-03, /* 0xbb360b61 */
|
| -P3 = 6.6137559770e-05, /* 0x388ab355 */
|
| -P4 = -1.6533901999e-06, /* 0xb5ddea0e */
|
| -P5 = 4.1381369442e-08, /* 0x3331bb4c */
|
| -lg2 = 6.9314718246e-01, /* 0x3f317218 */
|
| -lg2_h = 6.93145752e-01, /* 0x3f317200 */
|
| -lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
|
| -ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
|
| -cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
|
| -cp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */
|
| -cp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */
|
| -ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
|
| -ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
|
| -ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
|
| +static const float bp[] =
|
| + {
|
| + 1.0, 1.5,
|
| +},
|
| + dp_h[] =
|
| + {
|
| + 0.0, 5.84960938e-01,
|
| +}, /* 0x3f15c000 */
|
| + dp_l[] =
|
| + {
|
| + 0.0, 1.56322085e-06,
|
| +}, /* 0x35d1cfdc */
|
| + two24 = 16777216.0, /* 0x4b800000 */
|
| + huge = 1.0e30,
|
| + tiny = 1.0e-30,
|
| + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
| + L1 = 6.0000002384e-01, /* 0x3f19999a */
|
| + L2 = 4.2857143283e-01, /* 0x3edb6db7 */
|
| + L3 = 3.3333334327e-01, /* 0x3eaaaaab */
|
| + L4 = 2.7272811532e-01, /* 0x3e8ba305 */
|
| + L5 = 2.3066075146e-01, /* 0x3e6c3255 */
|
| + L6 = 2.0697501302e-01, /* 0x3e53f142 */
|
| + P1 = 1.6666667163e-01, /* 0x3e2aaaab */
|
| + P2 = -2.7777778450e-03, /* 0xbb360b61 */
|
| + P3 = 6.6137559770e-05, /* 0x388ab355 */
|
| + P4 = -1.6533901999e-06, /* 0xb5ddea0e */
|
| + P5 = 4.1381369442e-08, /* 0x3331bb4c */
|
| + lg2 = 6.9314718246e-01, /* 0x3f317218 */
|
| + lg2_h = 6.93145752e-01, /* 0x3f317200 */
|
| + lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
|
| + ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
|
| + cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
|
| + cp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */
|
| + cp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */
|
| + ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
|
| + ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
|
| + ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
|
|
|
| -float powf(float x, float y)
|
| -{
|
| - float z,ax,z_h,z_l,p_h,p_l;
|
| - float y1,t1,t2,r,s,sn,t,u,v,w;
|
| - int32_t i,j,k,yisint,n;
|
| - int32_t hx,hy,ix,iy,is;
|
| +float powf(float x, float y) {
|
| + float z, ax, z_h, z_l, p_h, p_l;
|
| + float y1, t1, t2, r, s, sn, t, u, v, w;
|
| + int32_t i, j, k, yisint, n;
|
| + int32_t hx, hy, ix, iy, is;
|
|
|
| - GET_FLOAT_WORD(hx, x);
|
| - GET_FLOAT_WORD(hy, y);
|
| - ix = hx & 0x7fffffff;
|
| - iy = hy & 0x7fffffff;
|
| + GET_FLOAT_WORD(hx, x);
|
| + GET_FLOAT_WORD(hy, y);
|
| + ix = hx & 0x7fffffff;
|
| + iy = hy & 0x7fffffff;
|
|
|
| - /* x**0 = 1, even if x is NaN */
|
| - if (iy == 0)
|
| - return 1.0f;
|
| - /* 1**y = 1, even if y is NaN */
|
| - if (hx == 0x3f800000)
|
| - return 1.0f;
|
| - /* NaN if either arg is NaN */
|
| - if (ix > 0x7f800000 || iy > 0x7f800000)
|
| - return x + y;
|
| + /* x**0 = 1, even if x is NaN */
|
| + if (iy == 0)
|
| + return 1.0f;
|
| + /* 1**y = 1, even if y is NaN */
|
| + if (hx == 0x3f800000)
|
| + return 1.0f;
|
| + /* NaN if either arg is NaN */
|
| + if (ix > 0x7f800000 || iy > 0x7f800000)
|
| + 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 >= 0x4b800000)
|
| - yisint = 2; /* even integer y */
|
| - else if (iy >= 0x3f800000) {
|
| - k = (iy>>23) - 0x7f; /* exponent */
|
| - j = iy>>(23-k);
|
| - if ((j<<(23-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 >= 0x4b800000)
|
| + yisint = 2; /* even integer y */
|
| + else if (iy >= 0x3f800000) {
|
| + k = (iy >> 23) - 0x7f; /* exponent */
|
| + j = iy >> (23 - k);
|
| + if ((j << (23 - k)) == iy)
|
| + yisint = 2 - (j & 1);
|
| + }
|
| + }
|
|
|
| - /* special value of y */
|
| - if (iy == 0x7f800000) { /* y is +-inf */
|
| - if (ix == 0x3f800000) /* (-1)**+-inf is 1 */
|
| - return 1.0f;
|
| - else if (ix > 0x3f800000) /* (|x|>1)**+-inf = inf,0 */
|
| - return hy >= 0 ? y : 0.0f;
|
| - else /* (|x|<1)**+-inf = 0,inf */
|
| - return hy >= 0 ? 0.0f: -y;
|
| - }
|
| - if (iy == 0x3f800000) /* y is +-1 */
|
| - return hy >= 0 ? x : 1.0f/x;
|
| - if (hy == 0x40000000) /* y is 2 */
|
| - return x*x;
|
| - if (hy == 0x3f000000) { /* y is 0.5 */
|
| - if (hx >= 0) /* x >= +0 */
|
| - return sqrtf(x);
|
| - }
|
| + /* special value of y */
|
| + if (iy == 0x7f800000) { /* y is +-inf */
|
| + if (ix == 0x3f800000) /* (-1)**+-inf is 1 */
|
| + return 1.0f;
|
| + else if (ix > 0x3f800000) /* (|x|>1)**+-inf = inf,0 */
|
| + return hy >= 0 ? y : 0.0f;
|
| + else /* (|x|<1)**+-inf = 0,inf */
|
| + return hy >= 0 ? 0.0f : -y;
|
| + }
|
| + if (iy == 0x3f800000) /* y is +-1 */
|
| + return hy >= 0 ? x : 1.0f / x;
|
| + if (hy == 0x40000000) /* y is 2 */
|
| + return x * x;
|
| + if (hy == 0x3f000000) { /* y is 0.5 */
|
| + if (hx >= 0) /* x >= +0 */
|
| + return sqrtf(x);
|
| + }
|
|
|
| - ax = fabsf(x);
|
| - /* special value of x */
|
| - if (ix == 0x7f800000 || ix == 0 || ix == 0x3f800000) { /* x is +-0,+-inf,+-1 */
|
| - z = ax;
|
| - if (hy < 0) /* z = (1/|x|) */
|
| - z = 1.0f/z;
|
| - if (hx < 0) {
|
| - if (((ix-0x3f800000)|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 = fabsf(x);
|
| + /* special value of x */
|
| + if (ix == 0x7f800000 || ix == 0 ||
|
| + ix == 0x3f800000) { /* x is +-0,+-inf,+-1 */
|
| + z = ax;
|
| + if (hy < 0) /* z = (1/|x|) */
|
| + z = 1.0f / z;
|
| + if (hx < 0) {
|
| + if (((ix - 0x3f800000) | 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;
|
| + }
|
|
|
| - sn = 1.0f; /* 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) */
|
| - sn = -1.0f;
|
| - }
|
| + sn = 1.0f; /* 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) */
|
| + sn = -1.0f;
|
| + }
|
|
|
| - /* |y| is huge */
|
| - if (iy > 0x4d000000) { /* if |y| > 2**27 */
|
| - /* over/underflow if x is not close to one */
|
| - if (ix < 0x3f7ffff8)
|
| - return hy < 0 ? sn*huge*huge : sn*tiny*tiny;
|
| - if (ix > 0x3f800007)
|
| - return hy > 0 ? sn*huge*huge : sn*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; /* t has 20 trailing zeros */
|
| - w = (t*t)*(0.5f - t*(0.333333333333f - t*0.25f));
|
| - u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
|
| - v = t*ivln2_l - w*ivln2;
|
| - t1 = u + v;
|
| - GET_FLOAT_WORD(is, t1);
|
| - SET_FLOAT_WORD(t1, is & 0xfffff000);
|
| - t2 = v - (t1-u);
|
| - } else {
|
| - float s2,s_h,s_l,t_h,t_l;
|
| - n = 0;
|
| - /* take care subnormal number */
|
| - if (ix < 0x00800000) {
|
| - ax *= two24;
|
| - n -= 24;
|
| - GET_FLOAT_WORD(ix, ax);
|
| - }
|
| - n += ((ix)>>23) - 0x7f;
|
| - j = ix & 0x007fffff;
|
| - /* determine interval */
|
| - ix = j | 0x3f800000; /* normalize ix */
|
| - if (j <= 0x1cc471) /* |x|<sqrt(3/2) */
|
| - k = 0;
|
| - else if (j < 0x5db3d7) /* |x|<sqrt(3) */
|
| - k = 1;
|
| - else {
|
| - k = 0;
|
| - n += 1;
|
| - ix -= 0x00800000;
|
| - }
|
| - SET_FLOAT_WORD(ax, ix);
|
| + /* |y| is huge */
|
| + if (iy > 0x4d000000) { /* if |y| > 2**27 */
|
| + /* over/underflow if x is not close to one */
|
| + if (ix < 0x3f7ffff8)
|
| + return hy < 0 ? sn * huge * huge : sn * tiny * tiny;
|
| + if (ix > 0x3f800007)
|
| + return hy > 0 ? sn * huge * huge : sn * 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; /* t has 20 trailing zeros */
|
| + w = (t * t) * (0.5f - t * (0.333333333333f - t * 0.25f));
|
| + u = ivln2_h * t; /* ivln2_h has 16 sig. bits */
|
| + v = t * ivln2_l - w * ivln2;
|
| + t1 = u + v;
|
| + GET_FLOAT_WORD(is, t1);
|
| + SET_FLOAT_WORD(t1, is & 0xfffff000);
|
| + t2 = v - (t1 - u);
|
| + } else {
|
| + float s2, s_h, s_l, t_h, t_l;
|
| + n = 0;
|
| + /* take care subnormal number */
|
| + if (ix < 0x00800000) {
|
| + ax *= two24;
|
| + n -= 24;
|
| + GET_FLOAT_WORD(ix, ax);
|
| + }
|
| + n += ((ix) >> 23) - 0x7f;
|
| + j = ix & 0x007fffff;
|
| + /* determine interval */
|
| + ix = j | 0x3f800000; /* normalize ix */
|
| + if (j <= 0x1cc471) /* |x|<sqrt(3/2) */
|
| + k = 0;
|
| + else if (j < 0x5db3d7) /* |x|<sqrt(3) */
|
| + k = 1;
|
| + else {
|
| + k = 0;
|
| + n += 1;
|
| + ix -= 0x00800000;
|
| + }
|
| + SET_FLOAT_WORD(ax, ix);
|
|
|
| - /* 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 */
|
| - v = 1.0f/(ax+bp[k]);
|
| - s = u*v;
|
| - s_h = s;
|
| - GET_FLOAT_WORD(is, s_h);
|
| - SET_FLOAT_WORD(s_h, is & 0xfffff000);
|
| - /* t_h=ax+bp[k] High */
|
| - is = ((ix>>1) & 0xfffff000) | 0x20000000;
|
| - SET_FLOAT_WORD(t_h, is + 0x00400000 + (k<<21));
|
| - t_l = ax - (t_h - bp[k]);
|
| - s_l = v*((u - s_h*t_h) - s_h*t_l);
|
| - /* compute log(ax) */
|
| - s2 = s*s;
|
| - r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
|
| - r += s_l*(s_h+s);
|
| - s2 = s_h*s_h;
|
| - t_h = 3.0f + s2 + r;
|
| - GET_FLOAT_WORD(is, t_h);
|
| - SET_FLOAT_WORD(t_h, is & 0xfffff000);
|
| - t_l = r - ((t_h - 3.0f) - s2);
|
| - /* u+v = s*(1+...) */
|
| - u = s_h*t_h;
|
| - v = s_l*t_h + t_l*s;
|
| - /* 2/(3log2)*(s+...) */
|
| - p_h = u + v;
|
| - GET_FLOAT_WORD(is, p_h);
|
| - SET_FLOAT_WORD(p_h, is & 0xfffff000);
|
| - 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) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
| - t = (float)n;
|
| - t1 = (((z_h + z_l) + dp_h[k]) + t);
|
| - GET_FLOAT_WORD(is, t1);
|
| - SET_FLOAT_WORD(t1, is & 0xfffff000);
|
| - t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
|
| - }
|
| + /* 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 */
|
| + v = 1.0f / (ax + bp[k]);
|
| + s = u * v;
|
| + s_h = s;
|
| + GET_FLOAT_WORD(is, s_h);
|
| + SET_FLOAT_WORD(s_h, is & 0xfffff000);
|
| + /* t_h=ax+bp[k] High */
|
| + is = ((ix >> 1) & 0xfffff000) | 0x20000000;
|
| + SET_FLOAT_WORD(t_h, is + 0x00400000 + (k << 21));
|
| + t_l = ax - (t_h - bp[k]);
|
| + s_l = v * ((u - s_h * t_h) - s_h * t_l);
|
| + /* compute log(ax) */
|
| + s2 = s * s;
|
| + r = s2 * s2 *
|
| + (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
|
| + r += s_l * (s_h + s);
|
| + s2 = s_h * s_h;
|
| + t_h = 3.0f + s2 + r;
|
| + GET_FLOAT_WORD(is, t_h);
|
| + SET_FLOAT_WORD(t_h, is & 0xfffff000);
|
| + t_l = r - ((t_h - 3.0f) - s2);
|
| + /* u+v = s*(1+...) */
|
| + u = s_h * t_h;
|
| + v = s_l * t_h + t_l * s;
|
| + /* 2/(3log2)*(s+...) */
|
| + p_h = u + v;
|
| + GET_FLOAT_WORD(is, p_h);
|
| + SET_FLOAT_WORD(p_h, is & 0xfffff000);
|
| + 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) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
| + t = (float)n;
|
| + t1 = (((z_h + z_l) + dp_h[k]) + t);
|
| + GET_FLOAT_WORD(is, t1);
|
| + SET_FLOAT_WORD(t1, is & 0xfffff000);
|
| + t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
|
| + }
|
|
|
| - /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
| - GET_FLOAT_WORD(is, y);
|
| - SET_FLOAT_WORD(y1, is & 0xfffff000);
|
| - p_l = (y-y1)*t1 + y*t2;
|
| - p_h = y1*t1;
|
| - z = p_l + p_h;
|
| - GET_FLOAT_WORD(j, z);
|
| - if (j > 0x43000000) /* if z > 128 */
|
| - return sn*huge*huge; /* overflow */
|
| - else if (j == 0x43000000) { /* if z == 128 */
|
| - if (p_l + ovt > z - p_h)
|
| - return sn*huge*huge; /* overflow */
|
| - } else if ((j&0x7fffffff) > 0x43160000) /* z < -150 */ // FIXME: check should be (uint32_t)j > 0xc3160000
|
| - return sn*tiny*tiny; /* underflow */
|
| - else if (j == 0xc3160000) { /* z == -150 */
|
| - if (p_l <= z-p_h)
|
| - return sn*tiny*tiny; /* underflow */
|
| - }
|
| - /*
|
| - * compute 2**(p_h+p_l)
|
| - */
|
| - i = j & 0x7fffffff;
|
| - k = (i>>23) - 0x7f;
|
| - n = 0;
|
| - if (i > 0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
|
| - n = j + (0x00800000>>(k+1));
|
| - k = ((n&0x7fffffff)>>23) - 0x7f; /* new k for n */
|
| - SET_FLOAT_WORD(t, n & ~(0x007fffff>>k));
|
| - n = ((n&0x007fffff)|0x00800000)>>(23-k);
|
| - if (j < 0)
|
| - n = -n;
|
| - p_h -= t;
|
| - }
|
| - t = p_l + p_h;
|
| - GET_FLOAT_WORD(is, t);
|
| - SET_FLOAT_WORD(t, is & 0xffff8000);
|
| - 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)/(t1-2.0f) - (w+z*w);
|
| - z = 1.0f - (r - z);
|
| - GET_FLOAT_WORD(j, z);
|
| - j += n<<23;
|
| - if ((j>>23) <= 0) /* subnormal output */
|
| - z = scalbnf(z, n);
|
| - else
|
| - SET_FLOAT_WORD(z, j);
|
| - return sn*z;
|
| + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
| + GET_FLOAT_WORD(is, y);
|
| + SET_FLOAT_WORD(y1, is & 0xfffff000);
|
| + p_l = (y - y1) * t1 + y * t2;
|
| + p_h = y1 * t1;
|
| + z = p_l + p_h;
|
| + GET_FLOAT_WORD(j, z);
|
| + if (j > 0x43000000) /* if z > 128 */
|
| + return sn * huge * huge; /* overflow */
|
| + else if (j == 0x43000000) { /* if z == 128 */
|
| + if (p_l + ovt > z - p_h)
|
| + return sn * huge * huge; /* overflow */
|
| + } else if ((j & 0x7fffffff) > 0x43160000) /* z < -150 */ // FIXME: check
|
| + // should be
|
| + // (uint32_t)j >
|
| + // 0xc3160000
|
| + return sn * tiny * tiny; /* underflow */
|
| + else if (j == 0xc3160000) { /* z == -150 */
|
| + if (p_l <= z - p_h)
|
| + return sn * tiny * tiny; /* underflow */
|
| + }
|
| + /*
|
| + * compute 2**(p_h+p_l)
|
| + */
|
| + i = j & 0x7fffffff;
|
| + k = (i >> 23) - 0x7f;
|
| + n = 0;
|
| + if (i > 0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
|
| + n = j + (0x00800000 >> (k + 1));
|
| + k = ((n & 0x7fffffff) >> 23) - 0x7f; /* new k for n */
|
| + SET_FLOAT_WORD(t, n & ~(0x007fffff >> k));
|
| + n = ((n & 0x007fffff) | 0x00800000) >> (23 - k);
|
| + if (j < 0)
|
| + n = -n;
|
| + p_h -= t;
|
| + }
|
| + t = p_l + p_h;
|
| + GET_FLOAT_WORD(is, t);
|
| + SET_FLOAT_WORD(t, is & 0xffff8000);
|
| + 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 - 2.0f) - (w + z * w);
|
| + z = 1.0f - (r - z);
|
| + GET_FLOAT_WORD(j, z);
|
| + j += n << 23;
|
| + if ((j >> 23) <= 0) /* subnormal output */
|
| + z = scalbnf(z, n);
|
| + else
|
| + SET_FLOAT_WORD(z, j);
|
| + return sn * z;
|
| }
|
|
|