micropython/stmhal/mathsincos.c

/*
 * This file is part of the Micro Python project, http://micropython.org/
 *
 * These math functions are taken from newlib 2.1.0, the newlib/libm directory.
 * Appropriate copyright headers are reproduced below.
 *
 * The MIT License (MIT)
 *
 * Copyright (c) 2013, 2014 Damien P. George
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

#include <stdint.h>
#include <math.h>

/* @(#)fdlibm.h 5.1 93/09/24 */
/*
 * ====================================================
 * 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.
 * ====================================================
 */

#define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L)

/* A union which permits us to convert between a float and a 32 bit
   int.  */

typedef union
{
  float value;
  __uint32_t word;
} ieee_float_shape_type;


/* Get a 32 bit int from a float.  */

#define GET_FLOAT_WORD(i,d)					\
do {								\
  ieee_float_shape_type gf_u;					\
  gf_u.value = (d);						\
  (i) = gf_u.word;						\
} while (0)

/* Set a float from a 32 bit int.  */

#define SET_FLOAT_WORD(d,i)					\
do {								\
  ieee_float_shape_type sf_u;					\
  sf_u.word = (i);						\
  (d) = sf_u.value;						\
} while (0)



/* 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.
 * ====================================================
 */

/* 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 */
};

static const float			
zero =  0.0000000000e+00, /* 0x00000000 */
one  =  1.0000000000e+00, /* 0x3f800000 */
two8  =  2.5600000000e+02, /* 0x43800000 */
twon8 =  3.9062500000e-03; /* 0x3b800000 */

int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2) 
{
	__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;
}


/* ef_rem_pio2.c -- float version of e_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.
 * ====================================================
 *
 */

/* __ieee754_rem_pio2f(x,y)
 * 
 * return the remainder of x rem pi/2 in y[0]+y[1] 
 * use __kernel_rem_pio2f()
 */


/*
 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 
 */
static const __int32_t two_over_pi[] = {
0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, 
0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, 
0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, 
0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, 
0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, 
0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, 
0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, 
0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, 
0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, 
0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, 
0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, 
};

/* This array is like the one in e_rem_pio2.c, but the numbers are
   single precision and the last 8 bits are forced to 0.  */
static const __int32_t npio2_hw[] = {
0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
0x4242c700, 0x42490f00
};

/*
 * invpio2:  24 bits of 2/pi
 * pio2_1:   first  17 bit of pi/2
 * pio2_1t:  pi/2 - pio2_1
 * pio2_2:   second 17 bit of pi/2
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 * pio2_3:   third  17 bit of pi/2
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
 */

static const float 
half =  5.0000000000e-01, /* 0x3f000000 */
invpio2 =  6.3661980629e-01, /* 0x3f22f984 */
pio2_1  =  1.5707855225e+00, /* 0x3fc90f80 */
pio2_1t =  1.0804334124e-05, /* 0x37354443 */
pio2_2  =  1.0804273188e-05, /* 0x37354400 */
pio2_2t =  6.0770999344e-11, /* 0x2e85a308 */
pio2_3  =  6.0770943833e-11, /* 0x2e85a300 */
pio2_3t =  6.1232342629e-17; /* 0x248d3132 */

__int32_t __ieee754_rem_pio2f(float x, float *y)
{
	float z,w,t,r,fn;
	float tx[3];
	__int32_t i,j,n,ix,hx;
	int e0,nx;

	GET_FLOAT_WORD(hx,x);
	ix = hx&0x7fffffff;
	if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */
	    {y[0] = x; y[1] = 0; return 0;}
	if(ix<0x4016cbe4) {  /* |x| < 3pi/4, special case with n=+-1 */
	    if(hx>0) { 
		z = x - pio2_1;
		if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
		    y[0] = z - pio2_1t;
		    y[1] = (z-y[0])-pio2_1t;
		} else {		/* near pi/2, use 24+24+24 bit pi */
		    z -= pio2_2;
		    y[0] = z - pio2_2t;
		    y[1] = (z-y[0])-pio2_2t;
		}
		return 1;
	    } else {	/* negative x */
		z = x + pio2_1;
		if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
		    y[0] = z + pio2_1t;
		    y[1] = (z-y[0])+pio2_1t;
		} else {		/* near pi/2, use 24+24+24 bit pi */
		    z += pio2_2;
		    y[0] = z + pio2_2t;
		    y[1] = (z-y[0])+pio2_2t;
		}
		return -1;
	    }
	}
	if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
	    t  = fabsf(x);
	    n  = (__int32_t) (t*invpio2+half);
	    fn = (float)n;
	    r  = t-fn*pio2_1;
	    w  = fn*pio2_1t;	/* 1st round good to 40 bit */
	    if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) {	
		y[0] = r-w;	/* quick check no cancellation */
	    } else {
	        __uint32_t high;
	        j  = ix>>23;
	        y[0] = r-w; 
		GET_FLOAT_WORD(high,y[0]);
	        i = j-((high>>23)&0xff);
	        if(i>8) {  /* 2nd iteration needed, good to 57 */
		    t  = r;
		    w  = fn*pio2_2;	
		    r  = t-w;
		    w  = fn*pio2_2t-((t-r)-w);	
		    y[0] = r-w;
		    GET_FLOAT_WORD(high,y[0]);
		    i = j-((high>>23)&0xff);
		    if(i>25)  {	/* 3rd iteration need, 74 bits acc */
		    	t  = r;	/* will cover all possible cases */
		    	w  = fn*pio2_3;	
		    	r  = t-w;
		    	w  = fn*pio2_3t-((t-r)-w);	
		    	y[0] = r-w;
		    }
		}
	    }
	    y[1] = (r-y[0])-w;
	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
	    else	 return n;
	}
    /* 
     * all other (large) arguments
     */
	if(!FLT_UWORD_IS_FINITE(ix)) {
	    y[0]=y[1]=x-x; return 0;
	}
    /* set z = scalbn(|x|,ilogb(x)-7) */
	e0 	= (int)((ix>>23)-134);	/* e0 = ilogb(z)-7; */
	SET_FLOAT_WORD(z, ix - ((__int32_t)e0<<23));
	for(i=0;i<2;i++) {
		tx[i] = (float)((__int32_t)(z));
		z     = (z-tx[i])*two8;
	}
	tx[2] = z;
	nx = 3;
	while(tx[nx-1]==zero) nx--;	/* skip zero term */
	n  =  __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
	return n;
}


/* kf_sin.c -- float version of k_sin.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.
 * ====================================================
 */


static const float 
S1  = -1.6666667163e-01, /* 0xbe2aaaab */
S2  =  8.3333337680e-03, /* 0x3c088889 */
S3  = -1.9841270114e-04, /* 0xb9500d01 */
S4  =  2.7557314297e-06, /* 0x3638ef1b */
S5  = -2.5050759689e-08, /* 0xb2d72f34 */
S6  =  1.5896910177e-10; /* 0x2f2ec9d3 */

float __kernel_sinf(float x, float y, int iy) /* iy=0 if y is zero */
{
	float z,r,v;
	__int32_t ix;
	GET_FLOAT_WORD(ix,x);
	ix &= 0x7fffffff;			/* high word of x */
	if(ix<0x32000000)			/* |x| < 2**-27 */
	   {if((int)x==0) return x;}		/* generate inexact */
	z	=  x*x;
	v	=  z*x;
	r	=  S2+z*(S3+z*(S4+z*(S5+z*S6)));
	if(iy==0) return x+v*(S1+z*r);
	else      return x-((z*(half*y-v*r)-y)-v*S1);
}



/* kf_cos.c -- float version of k_cos.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.
 * ====================================================
 */


static const float 
C1  =  4.1666667908e-02, /* 0x3d2aaaab */
C2  = -1.3888889225e-03, /* 0xbab60b61 */
C3  =  2.4801587642e-05, /* 0x37d00d01 */
C4  = -2.7557314297e-07, /* 0xb493f27c */
C5  =  2.0875723372e-09, /* 0x310f74f6 */
C6  = -1.1359647598e-11; /* 0xad47d74e */

float __kernel_cosf(float x, float y)
{
	float a,hz,z,r,qx;
	__int32_t ix;
	GET_FLOAT_WORD(ix,x);
	ix &= 0x7fffffff;			/* ix = |x|'s high word*/
	if(ix<0x32000000) {			/* if x < 2**27 */
	    if(((int)x)==0) return one;		/* generate inexact */
	}
	z  = x*x;
	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
	if(ix < 0x3e99999a) 			/* if |x| < 0.3 */ 
	    return one - ((float)0.5*z - (z*r - x*y));
	else {
	    if(ix > 0x3f480000) {		/* x > 0.78125 */
		qx = (float)0.28125;
	    } else {
	        SET_FLOAT_WORD(qx,ix-0x01000000);	/* x/4 */
	    }
	    hz = (float)0.5*z-qx;
	    a  = one-qx;
	    return a - (hz - (z*r-x*y));
	}
}


/* sf_sin.c -- float version of s_sin.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.
 * ====================================================
 */


float sinf(float x)
{
	float y[2],z=0.0;
	__int32_t n,ix;

	GET_FLOAT_WORD(ix,x);

    /* |x| ~< pi/4 */
	ix &= 0x7fffffff;
	if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0);

    /* sin(Inf or NaN) is NaN */
	else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;

    /* argument reduction needed */
	else {
	    n = __ieee754_rem_pio2f(x,y);
	    switch(n&3) {
		case 0: return  __kernel_sinf(y[0],y[1],1);
		case 1: return  __kernel_cosf(y[0],y[1]);
		case 2: return -__kernel_sinf(y[0],y[1],1);
		default:
			return -__kernel_cosf(y[0],y[1]);
	    }
	}
}


/* sf_cos.c -- float version of s_cos.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.
 * ====================================================
 */


float cosf(float x)
{
	float y[2],z=0.0;
	__int32_t n,ix;

	GET_FLOAT_WORD(ix,x);

    /* |x| ~< pi/4 */
	ix &= 0x7fffffff;
	if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);

    /* cos(Inf or NaN) is NaN */
	else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;

    /* argument reduction needed */
	else {
	    n = __ieee754_rem_pio2f(x,y);
	    switch(n&3) {
		case 0: return  __kernel_cosf(y[0],y[1]);
		case 1: return -__kernel_sinf(y[0],y[1],1);
		case 2: return -__kernel_cosf(y[0],y[1]);
		default:
		        return  __kernel_sinf(y[0],y[1],1);
	    }
	}
}