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glibc  2.9
Functions | Variables
e_lgammaf_r.c File Reference
#include "math.h"
#include "math_private.h"

Go to the source code of this file.

Functions

static float sin_pif (float x)
float __ieee754_lgammaf_r (float x, int *signgamp)

Variables

static float two23 = 8.3886080000e+06
static float half = 5.0000000000e-01
static float one = 1.0000000000e+00
static float pi = 3.1415927410e+00
static float a0 = 7.7215664089e-02
static float a1 = 3.2246702909e-01
static float a2 = 6.7352302372e-02
static float a3 = 2.0580807701e-02
static float a4 = 7.3855509982e-03
static float a5 = 2.8905137442e-03
static float a6 = 1.1927076848e-03
static float a7 = 5.1006977446e-04
static float a8 = 2.2086278477e-04
static float a9 = 1.0801156895e-04
static float a10 = 2.5214456400e-05
static float a11 = 4.4864096708e-05
static float tc = 1.4616321325e+00
static float tf = -1.2148628384e-01
static float tt = 6.6971006518e-09
static float t0 = 4.8383611441e-01
static float t1 = -1.4758771658e-01
static float t2 = 6.4624942839e-02
static float t3 = -3.2788541168e-02
static float t4 = 1.7970675603e-02
static float t5 = -1.0314224288e-02
static float t6 = 6.1005386524e-03
static float t7 = -3.6845202558e-03
static float t8 = 2.2596477065e-03
static float t9 = -1.4034647029e-03
static float t10 = 8.8108185446e-04
static float t11 = -5.3859531181e-04
static float t12 = 3.1563205994e-04
static float t13 = -3.1275415677e-04
static float t14 = 3.3552918467e-04
static float u0 = -7.7215664089e-02
static float u1 = 6.3282704353e-01
static float u2 = 1.4549225569e+00
static float u3 = 9.7771751881e-01
static float u4 = 2.2896373272e-01
static float u5 = 1.3381091878e-02
static float v1 = 2.4559779167e+00
static float v2 = 2.1284897327e+00
static float v3 = 7.6928514242e-01
static float v4 = 1.0422264785e-01
static float v5 = 3.2170924824e-03
static float s0 = -7.7215664089e-02
static float s1 = 2.1498242021e-01
static float s2 = 3.2577878237e-01
static float s3 = 1.4635047317e-01
static float s4 = 2.6642270386e-02
static float s5 = 1.8402845599e-03
static float s6 = 3.1947532989e-05
static float r1 = 1.3920053244e+00
static float r2 = 7.2193557024e-01
static float r3 = 1.7193385959e-01
static float r4 = 1.8645919859e-02
static float r5 = 7.7794247773e-04
static float r6 = 7.3266842264e-06
static float w0 = 4.1893854737e-01
static float w1 = 8.3333335817e-02
static float w2 = -2.7777778450e-03
static float w3 = 7.9365057172e-04
static float w4 = -5.9518753551e-04
static float w5 = 8.3633989561e-04
static float w6 = -1.6309292987e-03
static float zero = 0.0000000000e+00

Function Documentation

float __ieee754_lgammaf_r ( float  x,
int signgamp 
)

Definition at line 154 of file e_lgammaf_r.c.

{
       float t,y,z,nadj,p,p1,p2,p3,q,r,w;
       int i,hx,ix;

       GET_FLOAT_WORD(hx,x);

    /* purge off +-inf, NaN, +-0, and negative arguments */
       *signgamp = 1;
       ix = hx&0x7fffffff;
       if(ix>=0x7f800000) return x*x;
       if(ix==0)
         {
           if (hx < 0)
             *signgamp = -1;
           return one/fabsf(x);
         }
       if(ix<0x1c800000) {  /* |x|<2**-70, return -log(|x|) */
           if(hx<0) {
               *signgamp = -1;
               return -__ieee754_logf(-x);
           } else return -__ieee754_logf(x);
       }
       if(hx<0) {
           if(ix>=0x4b000000)      /* |x|>=2**23, must be -integer */
              return x/zero;
           t = sin_pif(x);
           if(t==zero) return one/fabsf(t); /* -integer */
           nadj = __ieee754_logf(pi/fabsf(t*x));
           if(t<zero) *signgamp = -1;
           x = -x;
       }

    /* purge off 1 and 2 */
       if (ix==0x3f800000||ix==0x40000000) r = 0;
    /* for x < 2.0 */
       else if(ix<0x40000000) {
           if(ix<=0x3f666666) {    /* lgamma(x) = lgamma(x+1)-log(x) */
              r = -__ieee754_logf(x);
              if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
              else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
              else {y = x; i=2;}
           } else {
              r = zero;
               if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
               else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
              else {y=x-one;i=2;}
           }
           switch(i) {
             case 0:
              z = y*y;
              p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
              p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
              p  = y*p1+p2;
              r  += (p-(float)0.5*y); break;
             case 1:
              z = y*y;
              w = z*y;
              p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));      /* parallel comp */
              p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
              p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
              p  = z*p1-(tt-w*(p2+y*p3));
              r += (tf + p); break;
             case 2:
              p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
              p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
              r += (-(float)0.5*y + p1/p2);
           }
       }
       else if(ix<0x41000000) {                  /* x < 8.0 */
           i = (int)x;
           t = zero;
           y = x-(float)i;
           p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
           q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
           r = half*y+p/q;
           z = one;  /* lgamma(1+s) = log(s) + lgamma(s) */
           switch(i) {
           case 7: z *= (y+(float)6.0);   /* FALLTHRU */
           case 6: z *= (y+(float)5.0);   /* FALLTHRU */
           case 5: z *= (y+(float)4.0);   /* FALLTHRU */
           case 4: z *= (y+(float)3.0);   /* FALLTHRU */
           case 3: z *= (y+(float)2.0);   /* FALLTHRU */
                  r += __ieee754_logf(z); break;
           }
    /* 8.0 <= x < 2**58 */
       } else if (ix < 0x5c800000) {
           t = __ieee754_logf(x);
           z = one/x;
           y = z*z;
           w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
           r = (x-half)*(t-one)+w;
       } else
    /* 2**58 <= x <= inf */
           r =  x*(__ieee754_logf(x)-one);
       if(hx<0) r = nadj - r;
       return r;
}

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static float sin_pif ( float  x) [static]

Definition at line 104 of file e_lgammaf_r.c.

{
       float y,z;
       int n,ix;

       GET_FLOAT_WORD(ix,x);
       ix &= 0x7fffffff;

       if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
       y = -x;              /* x is assume negative */

    /*
     * argument reduction, make sure inexact flag not raised if input
     * is an integer
     */
       z = __floorf(y);
       if(z!=y) {                         /* inexact anyway */
           y  *= (float)0.5;
           y   = (float)2.0*(y - __floorf(y));   /* y = |x| mod 2.0 */
           n   = (int) (y*(float)4.0);
       } else {
            if(ix>=0x4b800000) {
                y = zero; n = 0;                 /* y must be even */
            } else {
                if(ix<0x4b000000) z = y+two23;   /* exact */
              GET_FLOAT_WORD(n,z);
              n &= 1;
                y  = n;
                n<<= 2;
            }
        }
       switch (n) {
           case 0:   y =  __kernel_sinf(pi*y,zero,0); break;
           case 1:
           case 2:   y =  __kernel_cosf(pi*((float)0.5-y),zero); break;
           case 3:
           case 4:   y =  __kernel_sinf(pi*(one-y),zero,0); break;
           case 5:
           case 6:   y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
           default:  y =  __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
           }
       return -y;
}

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Variable Documentation

float a0 = 7.7215664089e-02 [static]

Definition at line 32 of file e_lgammaf_r.c.

float a1 = 3.2246702909e-01 [static]

Definition at line 33 of file e_lgammaf_r.c.

float a10 = 2.5214456400e-05 [static]

Definition at line 42 of file e_lgammaf_r.c.

float a11 = 4.4864096708e-05 [static]

Definition at line 43 of file e_lgammaf_r.c.

float a2 = 6.7352302372e-02 [static]

Definition at line 34 of file e_lgammaf_r.c.

float a3 = 2.0580807701e-02 [static]

Definition at line 35 of file e_lgammaf_r.c.

float a4 = 7.3855509982e-03 [static]

Definition at line 36 of file e_lgammaf_r.c.

float a5 = 2.8905137442e-03 [static]

Definition at line 37 of file e_lgammaf_r.c.

float a6 = 1.1927076848e-03 [static]

Definition at line 38 of file e_lgammaf_r.c.

float a7 = 5.1006977446e-04 [static]

Definition at line 39 of file e_lgammaf_r.c.

float a8 = 2.2086278477e-04 [static]

Definition at line 40 of file e_lgammaf_r.c.

float a9 = 1.0801156895e-04 [static]

Definition at line 41 of file e_lgammaf_r.c.

float half = 5.0000000000e-01 [static]

Definition at line 29 of file e_lgammaf_r.c.

float one = 1.0000000000e+00 [static]

Definition at line 30 of file e_lgammaf_r.c.

float pi = 3.1415927410e+00 [static]

Definition at line 31 of file e_lgammaf_r.c.

float r1 = 1.3920053244e+00 [static]

Definition at line 81 of file e_lgammaf_r.c.

float r2 = 7.2193557024e-01 [static]

Definition at line 82 of file e_lgammaf_r.c.

float r3 = 1.7193385959e-01 [static]

Definition at line 83 of file e_lgammaf_r.c.

float r4 = 1.8645919859e-02 [static]

Definition at line 84 of file e_lgammaf_r.c.

float r5 = 7.7794247773e-04 [static]

Definition at line 85 of file e_lgammaf_r.c.

float r6 = 7.3266842264e-06 [static]

Definition at line 86 of file e_lgammaf_r.c.

float s0 = -7.7215664089e-02 [static]

Definition at line 74 of file e_lgammaf_r.c.

float s1 = 2.1498242021e-01 [static]

Definition at line 75 of file e_lgammaf_r.c.

float s2 = 3.2577878237e-01 [static]

Definition at line 76 of file e_lgammaf_r.c.

float s3 = 1.4635047317e-01 [static]

Definition at line 77 of file e_lgammaf_r.c.

float s4 = 2.6642270386e-02 [static]

Definition at line 78 of file e_lgammaf_r.c.

float s5 = 1.8402845599e-03 [static]

Definition at line 79 of file e_lgammaf_r.c.

float s6 = 3.1947532989e-05 [static]

Definition at line 80 of file e_lgammaf_r.c.

float t0 = 4.8383611441e-01 [static]

Definition at line 48 of file e_lgammaf_r.c.

float t1 = -1.4758771658e-01 [static]

Definition at line 49 of file e_lgammaf_r.c.

float t10 = 8.8108185446e-04 [static]

Definition at line 58 of file e_lgammaf_r.c.

float t11 = -5.3859531181e-04 [static]

Definition at line 59 of file e_lgammaf_r.c.

float t12 = 3.1563205994e-04 [static]

Definition at line 60 of file e_lgammaf_r.c.

float t13 = -3.1275415677e-04 [static]

Definition at line 61 of file e_lgammaf_r.c.

float t14 = 3.3552918467e-04 [static]

Definition at line 62 of file e_lgammaf_r.c.

float t2 = 6.4624942839e-02 [static]

Definition at line 50 of file e_lgammaf_r.c.

float t3 = -3.2788541168e-02 [static]

Definition at line 51 of file e_lgammaf_r.c.

float t4 = 1.7970675603e-02 [static]

Definition at line 52 of file e_lgammaf_r.c.

float t5 = -1.0314224288e-02 [static]

Definition at line 53 of file e_lgammaf_r.c.

float t6 = 6.1005386524e-03 [static]

Definition at line 54 of file e_lgammaf_r.c.

float t7 = -3.6845202558e-03 [static]

Definition at line 55 of file e_lgammaf_r.c.

float t8 = 2.2596477065e-03 [static]

Definition at line 56 of file e_lgammaf_r.c.

float t9 = -1.4034647029e-03 [static]

Definition at line 57 of file e_lgammaf_r.c.

float tc = 1.4616321325e+00 [static]

Definition at line 44 of file e_lgammaf_r.c.

float tf = -1.2148628384e-01 [static]

Definition at line 45 of file e_lgammaf_r.c.

float tt = 6.6971006518e-09 [static]

Definition at line 47 of file e_lgammaf_r.c.

float two23 = 8.3886080000e+06 [static]

Definition at line 28 of file e_lgammaf_r.c.

float u0 = -7.7215664089e-02 [static]

Definition at line 63 of file e_lgammaf_r.c.

float u1 = 6.3282704353e-01 [static]

Definition at line 64 of file e_lgammaf_r.c.

float u2 = 1.4549225569e+00 [static]

Definition at line 65 of file e_lgammaf_r.c.

float u3 = 9.7771751881e-01 [static]

Definition at line 66 of file e_lgammaf_r.c.

float u4 = 2.2896373272e-01 [static]

Definition at line 67 of file e_lgammaf_r.c.

float u5 = 1.3381091878e-02 [static]

Definition at line 68 of file e_lgammaf_r.c.

float v1 = 2.4559779167e+00 [static]

Definition at line 69 of file e_lgammaf_r.c.

float v2 = 2.1284897327e+00 [static]

Definition at line 70 of file e_lgammaf_r.c.

float v3 = 7.6928514242e-01 [static]

Definition at line 71 of file e_lgammaf_r.c.

float v4 = 1.0422264785e-01 [static]

Definition at line 72 of file e_lgammaf_r.c.

float v5 = 3.2170924824e-03 [static]

Definition at line 73 of file e_lgammaf_r.c.

float w0 = 4.1893854737e-01 [static]

Definition at line 87 of file e_lgammaf_r.c.

float w1 = 8.3333335817e-02 [static]

Definition at line 88 of file e_lgammaf_r.c.

float w2 = -2.7777778450e-03 [static]

Definition at line 89 of file e_lgammaf_r.c.

float w3 = 7.9365057172e-04 [static]

Definition at line 90 of file e_lgammaf_r.c.

float w4 = -5.9518753551e-04 [static]

Definition at line 91 of file e_lgammaf_r.c.

float w5 = 8.3633989561e-04 [static]

Definition at line 92 of file e_lgammaf_r.c.

float w6 = -1.6309292987e-03 [static]

Definition at line 93 of file e_lgammaf_r.c.

float zero = 0.0000000000e+00 [static]

Definition at line 98 of file e_lgammaf_r.c.