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[/] [openrisc/] [trunk/] [gnu-stable/] [newlib-1.18.0/] [newlib/] [libm/] [math/] [kf_rem_pio2.c] - Rev 859
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/* kf_rem_pio2.c -- float version of k_rem_pio2.c * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include "fdlibm.h" /* In the float version, the input parameter x contains 8 bit integers, not 24 bit integers. 113 bit precision is not supported. */ #ifdef __STDC__ static const int init_jk[] = {4,7,9}; /* initial value for jk */ #else static int init_jk[] = {4,7,9}; #endif #ifdef __STDC__ static const float PIo2[] = { #else static float PIo2[] = { #endif 1.5703125000e+00, /* 0x3fc90000 */ 4.5776367188e-04, /* 0x39f00000 */ 2.5987625122e-05, /* 0x37da0000 */ 7.5437128544e-08, /* 0x33a20000 */ 6.0026650317e-11, /* 0x2e840000 */ 7.3896444519e-13, /* 0x2b500000 */ 5.3845816694e-15, /* 0x27c20000 */ 5.6378512969e-18, /* 0x22d00000 */ 8.3009228831e-20, /* 0x1fc40000 */ 3.2756352257e-22, /* 0x1bc60000 */ 6.3331015649e-25, /* 0x17440000 */ }; #ifdef __STDC__ static const float #else static float #endif zero = 0.0, one = 1.0, two8 = 2.5600000000e+02, /* 0x43800000 */ twon8 = 3.9062500000e-03; /* 0x3b800000 */ #ifdef __STDC__ int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2) #else int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2) float x[], y[]; int e0,nx,prec; __int32_t ipio2[]; #endif { __int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; float z,fw,f[20],fq[20],q[20]; /* initialize jk*/ jk = init_jk[prec]; jp = jk; /* determine jx,jv,q0, note that 3>q0 */ jx = nx-1; jv = (e0-3)/8; if(jv<0) jv=0; q0 = e0-8*(jv+1); /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ j = jv-jx; m = jx+jk; for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; /* compute q[0],q[1],...q[jk] */ for (i=0;i<=jk;i++) { for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; } jz = jk; recompute: /* distill q[] into iq[] reversingly */ for(i=0,j=jz,z=q[jz];j>0;i++,j--) { fw = (float)((__int32_t)(twon8* z)); iq[i] = (__int32_t)(z-two8*fw); z = q[j-1]+fw; } /* compute n */ z = scalbnf(z,(int)q0); /* actual value of z */ z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ n = (__int32_t) z; z -= (float)n; ih = 0; if(q0>0) { /* need iq[jz-1] to determine n */ i = (iq[jz-1]>>(8-q0)); n += i; iq[jz-1] -= i<<(8-q0); ih = iq[jz-1]>>(7-q0); } else if(q0==0) ih = iq[jz-1]>>8; else if(z>=(float)0.5) ih=2; if(ih>0) { /* q > 0.5 */ n += 1; carry = 0; for(i=0;i<jz ;i++) { /* compute 1-q */ j = iq[i]; if(carry==0) { if(j!=0) { carry = 1; iq[i] = 0x100- j; } } else iq[i] = 0xff - j; } if(q0>0) { /* rare case: chance is 1 in 12 */ switch(q0) { case 1: iq[jz-1] &= 0x7f; break; case 2: iq[jz-1] &= 0x3f; break; } } if(ih==2) { z = one - z; if(carry!=0) z -= scalbnf(one,(int)q0); } } /* check if recomputation is needed */ if(z==zero) { j = 0; for (i=jz-1;i>=jk;i--) j |= iq[i]; if(j==0) { /* need recomputation */ for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ f[jx+i] = (float) ipio2[jv+i]; for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; } jz += k; goto recompute; } } /* chop off zero terms */ if(z==(float)0.0) { jz -= 1; q0 -= 8; while(iq[jz]==0) { jz--; q0-=8;} } else { /* break z into 8-bit if necessary */ z = scalbnf(z,-(int)q0); if(z>=two8) { fw = (float)((__int32_t)(twon8*z)); iq[jz] = (__int32_t)(z-two8*fw); jz += 1; q0 += 8; iq[jz] = (__int32_t) fw; } else iq[jz] = (__int32_t) z ; } /* convert integer "bit" chunk to floating-point value */ fw = scalbnf(one,(int)q0); for(i=jz;i>=0;i--) { q[i] = fw*(float)iq[i]; fw*=twon8; } /* compute PIo2[0,...,jp]*q[jz,...,0] */ for(i=jz;i>=0;i--) { for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; fq[jz-i] = fw; } /* compress fq[] into y[] */ switch(prec) { case 0: fw = 0.0; for (i=jz;i>=0;i--) fw += fq[i]; y[0] = (ih==0)? fw: -fw; break; case 1: case 2: fw = 0.0; for (i=jz;i>=0;i--) fw += fq[i]; y[0] = (ih==0)? fw: -fw; fw = fq[0]-fw; for (i=1;i<=jz;i++) fw += fq[i]; y[1] = (ih==0)? fw: -fw; break; case 3: /* painful */ for (i=jz;i>0;i--) { fw = fq[i-1]+fq[i]; fq[i] += fq[i-1]-fw; fq[i-1] = fw; } for (i=jz;i>1;i--) { fw = fq[i-1]+fq[i]; fq[i] += fq[i-1]-fw; fq[i-1] = fw; } for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; if(ih==0) { y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; } else { y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; } } return n&7; }
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