0,0 → 1,214 |
/* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */ |
/* k_rem_pio2f.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. |
* ==================================================== |
*/ |
|
#if defined(LIBM_SCCS) && !defined(lint) |
static char rcsid[] = "$Id: k_rem_pio2f.c,v 1.2 1994/08/18 23:06:12 jtc Exp $"; |
#endif |
|
#include "math.h" |
#include "math_private.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,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,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,-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,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; |
} |
Property changes: |
Added: svn:executable |
+* |
\ No newline at end of property |