106 lines
2.9 KiB
C
106 lines
2.9 KiB
C
/*
|
|
* This file is part of the MicroPython 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_tan.c -- float version of k_tan.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 "libm.h"
|
|
#ifdef __STDC__
|
|
static const float
|
|
#else
|
|
static float
|
|
#endif
|
|
one = 1.0000000000e+00f, /* 0x3f800000 */
|
|
pio4 = 7.8539812565e-01f, /* 0x3f490fda */
|
|
pio4lo= 3.7748947079e-08f, /* 0x33222168 */
|
|
T[] = {
|
|
3.3333334327e-01f, /* 0x3eaaaaab */
|
|
1.3333334029e-01f, /* 0x3e088889 */
|
|
5.3968254477e-02f, /* 0x3d5d0dd1 */
|
|
2.1869488060e-02f, /* 0x3cb327a4 */
|
|
8.8632395491e-03f, /* 0x3c11371f */
|
|
3.5920790397e-03f, /* 0x3b6b6916 */
|
|
1.4562094584e-03f, /* 0x3abede48 */
|
|
5.8804126456e-04f, /* 0x3a1a26c8 */
|
|
2.4646313977e-04f, /* 0x398137b9 */
|
|
7.8179444245e-05f, /* 0x38a3f445 */
|
|
7.1407252108e-05f, /* 0x3895c07a */
|
|
-1.8558637748e-05f, /* 0xb79bae5f */
|
|
2.5907305826e-05f, /* 0x37d95384 */
|
|
};
|
|
|
|
#ifdef __STDC__
|
|
float __kernel_tanf(float x, float y, int iy)
|
|
#else
|
|
float __kernel_tanf(x, y, iy)
|
|
float x,y; int iy;
|
|
#endif
|
|
{
|
|
float z,r,v,w,s;
|
|
__int32_t ix,hx;
|
|
GET_FLOAT_WORD(hx,x);
|
|
ix = hx&0x7fffffff; /* high word of |x| */
|
|
if(ix<0x31800000) /* x < 2**-28 */
|
|
{if((int)x==0) { /* generate inexact */
|
|
if((ix|(iy+1))==0) return one/fabsf(x);
|
|
else return (iy==1)? x: -one/x;
|
|
}
|
|
}
|
|
if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
|
|
if(hx<0) {x = -x; y = -y;}
|
|
z = pio4-x;
|
|
w = pio4lo-y;
|
|
x = z+w; y = 0.0;
|
|
}
|
|
z = x*x;
|
|
w = z*z;
|
|
/* Break x^5*(T[1]+x^2*T[2]+...) into
|
|
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
|
|
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
|
|
*/
|
|
r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
|
|
v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
|
|
s = z*x;
|
|
r = y + z*(s*(r+v)+y);
|
|
r += T[0]*s;
|
|
w = x+r;
|
|
if(ix>=0x3f2ca140) {
|
|
v = (float)iy;
|
|
return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
|
|
}
|
|
if(iy==1) return w;
|
|
else { /* if allow error up to 2 ulp,
|
|
simply return -1.0/(x+r) here */
|
|
/* compute -1.0/(x+r) accurately */
|
|
float a,t;
|
|
__int32_t i;
|
|
z = w;
|
|
GET_FLOAT_WORD(i,z);
|
|
SET_FLOAT_WORD(z,i&0xfffff000);
|
|
v = r-(z - x); /* z+v = r+x */
|
|
t = a = -(float)1.0/w; /* a = -1.0/w */
|
|
GET_FLOAT_WORD(i,t);
|
|
SET_FLOAT_WORD(t,i&0xfffff000);
|
|
s = (float)1.0+t*z;
|
|
return t+a*(s+t*v);
|
|
}
|
|
}
|