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kf_rem_pio2.c
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/*
* This file is part of the Micro Python project, http://micropython.org/
*
* These math functions are taken from newlib-nano-2, the newlib/libm/math
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
*
* Appropriate copyright headers are reproduced below.
*/
/* kf_rem_pio2.c -- float version of k_rem_pio2.c
* Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
*/
/*
* ====================================================
* 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;
}