CHDK_DE Vorschauversion  Trunk Rev. 5272
 Alle Datenstrukturen Dateien Funktionen Variablen Typdefinitionen Aufzählungen Aufzählungswerte Makrodefinitionen
ef_pow.c-Dateireferenz
#include "fdlibm.h"
#include "stdlib.h"
+ Include-Abhängigkeitsdiagramm für ef_pow.c:

gehe zum Quellcode dieser Datei

Funktionen

float powf (float x, float y)
 

Variablen

static const float bp [] = {1.0, 1.5,}
 
static const float dp_h [] = { 0.0, 5.84960938e-01,}
 
static const float dp_l [] = { 0.0, 1.56322085e-06,}
 
static const float zero = 0.0
 
static const float one = 1.0
 
static const float two = 2.0
 
static const float two24 = 16777216.0
 
static const float huge = 1.0e30
 
static const float tiny = 1.0e-30
 
static const float L1 = 6.0000002384e-01
 
static const float L2 = 4.2857143283e-01
 
static const float L3 = 3.3333334327e-01
 
static const float L4 = 2.7272811532e-01
 
static const float L5 = 2.3066075146e-01
 
static const float L6 = 2.0697501302e-01
 
static const float P1 = 1.6666667163e-01
 
static const float P2 = -2.7777778450e-03
 
static const float P3 = 6.6137559770e-05
 
static const float P4 = -1.6533901999e-06
 
static const float P5 = 4.1381369442e-08
 
static const float lg2 = 6.9314718246e-01
 
static const float lg2_h = 6.93145752e-01
 
static const float lg2_l = 1.42860654e-06
 
static const float ovt = 4.2995665694e-08
 
static const float cp = 9.6179670095e-01
 
static const float cp_h = 9.6179199219e-01
 
static const float cp_l = 4.7017383622e-06
 
static const float ivln2 = 1.4426950216e+00
 
static const float ivln2_h = 1.4426879883e+00
 
static const float ivln2_l = 7.0526075433e-06
 

Dokumentation der Funktionen

float powf ( float  x,
float  y 
)

Definiert in Zeile 52 der Datei ef_pow.c.

53 {
54  float z,ax,z_h,z_l,p_h,p_l;
55  float y1,t1,t2,r,s,t,u,v,w;
56  int i,j,k,yisint,n;
57  int hx,hy,ix,iy,is;
58 
59  GET_FLOAT_WORD(hx,x);
60  GET_FLOAT_WORD(hy,y);
61  ix = hx&0x7fffffff; iy = hy&0x7fffffff;
62 
63  /* y==zero: x**0 = 1 */
64  if(FLT_UWORD_IS_ZERO(iy)) return one;
65 
66  /* +-NaN return x+y */
67  if(FLT_UWORD_IS_NAN(ix) ||
68  FLT_UWORD_IS_NAN(iy))
69  return x+y;
70 
71  /* determine if y is an odd int when x < 0
72  * yisint = 0 ... y is not an integer
73  * yisint = 1 ... y is an odd int
74  * yisint = 2 ... y is an even int
75  */
76  yisint = 0;
77  if(hx<0) {
78  if(iy>=0x4b800000) yisint = 2; /* even integer y */
79  else if(iy>=0x3f800000) {
80  k = (iy>>23)-0x7f; /* exponent */
81  j = iy>>(23-k);
82  if((j<<(23-k))==iy) yisint = 2-(j&1);
83  }
84  }
85 
86  /* special value of y */
87  if (FLT_UWORD_IS_INFINITE(iy)) { /* y is +-inf */
88  if (ix==0x3f800000)
89  return y - y; /* inf**+-1 is NaN */
90  else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
91  return (hy>=0)? y: zero;
92  else /* (|x|<1)**-,+inf = inf,0 */
93  return (hy<0)?-y: zero;
94  }
95  if(iy==0x3f800000) { /* y is +-1 */
96  if(hy<0) return one/x; else return x;
97  }
98  if(hy==0x40000000) return x*x; /* y is 2 */
99  if(hy==0x3f000000) { /* y is 0.5 */
100  if(hx>=0) /* x >= +0 */
101  return sqrtf(x);
102  }
103 
104  ax = fabsf(x);
105  /* special value of x */
106  if(FLT_UWORD_IS_INFINITE(ix)||FLT_UWORD_IS_ZERO(ix)||ix==0x3f800000){
107  z = ax; /*x is +-0,+-inf,+-1*/
108  if(hy<0) z = one/z; /* z = (1/|x|) */
109  if(hx<0) {
110  if(((ix-0x3f800000)|yisint)==0) {
111  z = (z-z)/(z-z); /* (-1)**non-int is NaN */
112  } else if(yisint==1)
113  z = -z; /* (x<0)**odd = -(|x|**odd) */
114  }
115  return z;
116  }
117 
118  /* (x<0)**(non-int) is NaN */
119  if(((((unsigned int)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
120 
121  /* |y| is huge */
122  if(iy>0x4d000000) { /* if |y| > 2**27 */
123  /* over/underflow if x is not close to one */
124  if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
125  if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
126  /* now |1-x| is tiny <= 2**-20, suffice to compute
127  log(x) by x-x^2/2+x^3/3-x^4/4 */
128  t = x-1; /* t has 20 trailing zeros */
129  w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
130  u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
131  v = t*ivln2_l-w*ivln2;
132  t1 = u+v;
133  GET_FLOAT_WORD(is,t1);
134  SET_FLOAT_WORD(t1,is&0xfffff000);
135  t2 = v-(t1-u);
136  } else {
137  float s2,s_h,s_l,t_h,t_l;
138  n = 0;
139  /* take care subnormal number */
140  if(FLT_UWORD_IS_SUBNORMAL(ix))
141  {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
142  n += ((ix)>>23)-0x7f;
143  j = ix&0x007fffff;
144  /* determine interval */
145  ix = j|0x3f800000; /* normalize ix */
146  if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
147  else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
148  else {k=0;n+=1;ix -= 0x00800000;}
149  SET_FLOAT_WORD(ax,ix);
150 
151  /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
152  u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
153  v = one/(ax+bp[k]);
154  s = u*v;
155  s_h = s;
156  GET_FLOAT_WORD(is,s_h);
157  SET_FLOAT_WORD(s_h,is&0xfffff000);
158  /* t_h=ax+bp[k] High */
159  SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
160  t_l = ax - (t_h-bp[k]);
161  s_l = v*((u-s_h*t_h)-s_h*t_l);
162  /* compute log(ax) */
163  s2 = s*s;
164  r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
165  r += s_l*(s_h+s);
166  s2 = s_h*s_h;
167  t_h = (float)3.0+s2+r;
168  GET_FLOAT_WORD(is,t_h);
169  SET_FLOAT_WORD(t_h,is&0xfffff000);
170  t_l = r-((t_h-(float)3.0)-s2);
171  /* u+v = s*(1+...) */
172  u = s_h*t_h;
173  v = s_l*t_h+t_l*s;
174  /* 2/(3log2)*(s+...) */
175  p_h = u+v;
176  GET_FLOAT_WORD(is,p_h);
177  SET_FLOAT_WORD(p_h,is&0xfffff000);
178  p_l = v-(p_h-u);
179  z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
180  z_l = cp_l*p_h+p_l*cp+dp_l[k];
181  /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
182  t = (float)n;
183  t1 = (((z_h+z_l)+dp_h[k])+t);
184  GET_FLOAT_WORD(is,t1);
185  SET_FLOAT_WORD(t1,is&0xfffff000);
186  t2 = z_l-(((t1-t)-dp_h[k])-z_h);
187  }
188 
189  s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
190  if(((((unsigned int)hx>>31)-1)|(yisint-1))==0)
191  s = -one; /* (-ve)**(odd int) */
192 
193  /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
194  GET_FLOAT_WORD(is,y);
195  SET_FLOAT_WORD(y1,is&0xfffff000);
196  p_l = (y-y1)*t1+y*t2;
197  p_h = y1*t1;
198  z = p_l+p_h;
199  GET_FLOAT_WORD(j,z);
200  i = j&0x7fffffff;
201  if (j>0) {
202  if (i>FLT_UWORD_EXP_MAX)
203  return s*huge*huge; /* overflow */
204  else if (i==FLT_UWORD_EXP_MAX)
205  if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
206  } else {
207  if (i>FLT_UWORD_EXP_MIN)
208  return s*tiny*tiny; /* underflow */
209  else if (i==FLT_UWORD_EXP_MIN)
210  if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
211  }
212  /*
213  * compute 2**(p_h+p_l)
214  */
215  k = (i>>23)-0x7f;
216  n = 0;
217  if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
218  n = j+(0x00800000>>(k+1));
219  k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
220  SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
221  n = ((n&0x007fffff)|0x00800000)>>(23-k);
222  if(j<0) n = -n;
223  p_h -= t;
224  }
225  t = p_l+p_h;
226  GET_FLOAT_WORD(is,t);
227  SET_FLOAT_WORD(t,is&0xfffff000);
228  u = t*lg2_h;
229  v = (p_l-(t-p_h))*lg2+t*lg2_l;
230  z = u+v;
231  w = v-(z-u);
232  t = z*z;
233  t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
234  r = (z*t1)/(t1-two)-(w+z*w);
235  z = one-(r-z);
236  GET_FLOAT_WORD(j,z);
237  j += (n<<23);
238  if((j>>23)<=0) z = scalbnf(z,(int)n); /* subnormal output */
239  else SET_FLOAT_WORD(z,j);
240  return s*z;
241 }

Variablen-Dokumentation

const float bp[] = {1.0, 1.5,}
static

Definiert in Zeile 20 der Datei ef_pow.c.

const float cp = 9.6179670095e-01
static

Definiert in Zeile 45 der Datei ef_pow.c.

const float cp_h = 9.6179199219e-01
static

Definiert in Zeile 46 der Datei ef_pow.c.

const float cp_l = 4.7017383622e-06
static

Definiert in Zeile 47 der Datei ef_pow.c.

const float dp_h[] = { 0.0, 5.84960938e-01,}
static

Definiert in Zeile 21 der Datei ef_pow.c.

const float dp_l[] = { 0.0, 1.56322085e-06,}
static

Definiert in Zeile 22 der Datei ef_pow.c.

const float huge = 1.0e30
static

Definiert in Zeile 27 der Datei ef_pow.c.

const float ivln2 = 1.4426950216e+00
static

Definiert in Zeile 48 der Datei ef_pow.c.

const float ivln2_h = 1.4426879883e+00
static

Definiert in Zeile 49 der Datei ef_pow.c.

const float ivln2_l = 7.0526075433e-06
static

Definiert in Zeile 50 der Datei ef_pow.c.

const float L1 = 6.0000002384e-01
static

Definiert in Zeile 30 der Datei ef_pow.c.

const float L2 = 4.2857143283e-01
static

Definiert in Zeile 31 der Datei ef_pow.c.

const float L3 = 3.3333334327e-01
static

Definiert in Zeile 32 der Datei ef_pow.c.

const float L4 = 2.7272811532e-01
static

Definiert in Zeile 33 der Datei ef_pow.c.

const float L5 = 2.3066075146e-01
static

Definiert in Zeile 34 der Datei ef_pow.c.

const float L6 = 2.0697501302e-01
static

Definiert in Zeile 35 der Datei ef_pow.c.

const float lg2 = 6.9314718246e-01
static

Definiert in Zeile 41 der Datei ef_pow.c.

const float lg2_h = 6.93145752e-01
static

Definiert in Zeile 42 der Datei ef_pow.c.

const float lg2_l = 1.42860654e-06
static

Definiert in Zeile 43 der Datei ef_pow.c.

const float one = 1.0
static

Definiert in Zeile 24 der Datei ef_pow.c.

const float ovt = 4.2995665694e-08
static

Definiert in Zeile 44 der Datei ef_pow.c.

const float P1 = 1.6666667163e-01
static

Definiert in Zeile 36 der Datei ef_pow.c.

const float P2 = -2.7777778450e-03
static

Definiert in Zeile 37 der Datei ef_pow.c.

const float P3 = 6.6137559770e-05
static

Definiert in Zeile 38 der Datei ef_pow.c.

const float P4 = -1.6533901999e-06
static

Definiert in Zeile 39 der Datei ef_pow.c.

const float P5 = 4.1381369442e-08
static

Definiert in Zeile 40 der Datei ef_pow.c.

const float tiny = 1.0e-30
static

Definiert in Zeile 28 der Datei ef_pow.c.

const float two = 2.0
static

Definiert in Zeile 25 der Datei ef_pow.c.

const float two24 = 16777216.0
static

Definiert in Zeile 26 der Datei ef_pow.c.

const float zero = 0.0
static

Definiert in Zeile 23 der Datei ef_pow.c.