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glibc  2.9
Functions | Variables
e_rem_pio2f.c File Reference
#include "math.h"
#include "math_private.h"

Go to the source code of this file.

Functions

int32_t __ieee754_rem_pio2f (float x, y)

Variables

static int32_t two_over_pi []
static int32_t npio2_hw []
static float zero = 0.0000000000e+00
static float half = 5.0000000000e-01
static float two8 = 2.5600000000e+02
static float invpio2 = 6.3661980629e-01
static float pio2_1 = 1.5707855225e+00
static float pio2_1t = 1.0804334124e-05
static float pio2_2 = 1.0804273188e-05
static float pio2_2t = 6.0770999344e-11
static float pio2_3 = 6.0770943833e-11
static float pio2_3t = 6.1232342629e-17

Function Documentation

int32_t __ieee754_rem_pio2f ( float  x,
y   
)

Definition at line 105 of file e_rem_pio2f.c.

{
       float z,w,t,r,fn;
       float tx[3];
       int32_t e0,i,j,nx,n,ix,hx;

       GET_FLOAT_WORD(hx,x);
       ix = hx&0x7fffffff;
       if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */
           {y[0] = x; y[1] = 0; return 0;}
       if(ix<0x4016cbe4) {  /* |x| < 3pi/4, special case with n=+-1 */
           if(hx>0) {
              z = x - pio2_1;
              if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
                  y[0] = z - pio2_1t;
                  y[1] = (z-y[0])-pio2_1t;
              } else {             /* near pi/2, use 24+24+24 bit pi */
                  z -= pio2_2;
                  y[0] = z - pio2_2t;
                  y[1] = (z-y[0])-pio2_2t;
              }
              return 1;
           } else {  /* negative x */
              z = x + pio2_1;
              if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
                  y[0] = z + pio2_1t;
                  y[1] = (z-y[0])+pio2_1t;
              } else {             /* near pi/2, use 24+24+24 bit pi */
                  z += pio2_2;
                  y[0] = z + pio2_2t;
                  y[1] = (z-y[0])+pio2_2t;
              }
              return -1;
           }
       }
       if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
           t  = fabsf(x);
           n  = (int32_t) (t*invpio2+half);
           fn = (float)n;
           r  = t-fn*pio2_1;
           w  = fn*pio2_1t; /* 1st round good to 40 bit */
           if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) {
              y[0] = r-w;   /* quick check no cancellation */
           } else {
               u_int32_t high;
               j  = ix>>23;
               y[0] = r-w;
              GET_FLOAT_WORD(high,y[0]);
               i = j-((high>>23)&0xff);
               if(i>8) {  /* 2nd iteration needed, good to 57 */
                  t  = r;
                  w  = fn*pio2_2;
                  r  = t-w;
                  w  = fn*pio2_2t-((t-r)-w);
                  y[0] = r-w;
                  GET_FLOAT_WORD(high,y[0]);
                  i = j-((high>>23)&0xff);
                  if(i>25)  {      /* 3rd iteration need, 74 bits acc */
                     t  = r;       /* will cover all possible cases */
                     w  = fn*pio2_3;
                     r  = t-w;
                     w  = fn*pio2_3t-((t-r)-w);
                     y[0] = r-w;
                  }
              }
           }
           y[1] = (r-y[0])-w;
           if(hx<0)  {y[0] = -y[0]; y[1] = -y[1]; return -n;}
           else       return n;
       }
    /*
     * all other (large) arguments
     */
       if(ix>=0x7f800000) {        /* x is inf or NaN */
           y[0]=y[1]=x-x; return 0;
       }
    /* set z = scalbn(|x|,ilogb(x)-7) */
       e0     = (ix>>23)-134;             /* e0 = ilogb(z)-7; */
       SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
       for(i=0;i<2;i++) {
              tx[i] = (float)((int32_t)(z));
              z     = (z-tx[i])*two8;
       }
       tx[2] = z;
       nx = 3;
       while(tx[nx-1]==zero) nx--; /* skip zero term */
       n  =  __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
       if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
       return n;
}

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Variable Documentation

float half = 5.0000000000e-01 [static]

Definition at line 92 of file e_rem_pio2f.c.

float invpio2 = 6.3661980629e-01 [static]

Definition at line 94 of file e_rem_pio2f.c.

int32_t npio2_hw[] [static]
Initial value:
 {

0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
0x4242c700, 0x42490f00
}

Definition at line 66 of file e_rem_pio2f.c.

float pio2_1 = 1.5707855225e+00 [static]

Definition at line 95 of file e_rem_pio2f.c.

float pio2_1t = 1.0804334124e-05 [static]

Definition at line 96 of file e_rem_pio2f.c.

float pio2_2 = 1.0804273188e-05 [static]

Definition at line 97 of file e_rem_pio2f.c.

float pio2_2t = 6.0770999344e-11 [static]

Definition at line 98 of file e_rem_pio2f.c.

float pio2_3 = 6.0770943833e-11 [static]

Definition at line 99 of file e_rem_pio2f.c.

float pio2_3t = 6.1232342629e-17 [static]

Definition at line 100 of file e_rem_pio2f.c.

float two8 = 2.5600000000e+02 [static]

Definition at line 93 of file e_rem_pio2f.c.

int32_t two_over_pi[] [static]
Initial value:
 {

0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
}

Definition at line 35 of file e_rem_pio2f.c.

float zero = 0.0000000000e+00 [static]

Definition at line 91 of file e_rem_pio2f.c.