micropython/lib/libm/kf_rem_pio2.c
Damien George 873853f1a8 lib/libm: Format code to pass gcc v6.1.1 warning.
gcc 6.1.1 warns when indentation is misleading, and in this case the
formatting of the code really is misleading.  So adjust the formatting
to be clear of the meaning of the code.
2016-06-25 22:28:43 +01:00

219 lines
5.4 KiB
C

/*
* 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, 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;
}