wasm-micro-runtime/core/shared/platform/common/math/math.c

/*-
 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
 *
 * Copyright (c) 2004 David Schultz <das@FreeBSD.ORG>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * $FreeBSD$
 */

#include "platform_common.h"

#define __FDLIBM_STDC__

#ifndef FLT_EVAL_METHOD
#define FLT_EVAL_METHOD 0
#endif

typedef uint32_t u_int32_t;
typedef uint64_t u_int64_t;

typedef union u32double_tag {
    int *pint;
    double *pdouble;
} U32DOUBLE;

static inline int *
pdouble2pint(double *pdouble)
{
    U32DOUBLE u;
    u.pdouble = pdouble;
    return u.pint;
}

typedef union
{
    double value;
    struct
    {
        u_int32_t lsw;
        u_int32_t msw;
    } parts;
    struct
    {
        u_int64_t w;
    } xparts;
} ieee_double_shape_type_little;

typedef union
{
    double value;
    struct
    {
        u_int32_t msw;
        u_int32_t lsw;
    } parts;
    struct
    {
        u_int64_t w;
    } xparts;
} ieee_double_shape_type_big;

typedef union {
    double	d;
    struct {
        unsigned int	manl	:32;
        unsigned int	manh	:20;
        unsigned int	exp	:11;
        unsigned int	sign	:1;
    } bits;
} IEEEd2bits_L;

typedef union {
    double	d;
    struct {
        unsigned int	sign	:1;
        unsigned int	exp	:11;
        unsigned int	manh	:20;
        unsigned int	manl	:32;
    } bits;
} IEEEd2bits_B;

typedef union {
    float   f;
    struct {
        unsigned int    man :23;
        unsigned int    exp :8;
        unsigned int    sign    :1;
    } bits;
} IEEEf2bits_L;

typedef union {
    float   f;
    struct {
        unsigned int    sign    :1;
        unsigned int    exp :8;
        unsigned int    man :23;
    } bits;
} IEEEf2bits_B;

static union {
    int a;
    char b;
} __ue = { .a = 1 };

#define is_little_endian() (__ue.b == 1)

#define __HIL(x) *(1+pdouble2pint(&x))
#define __LOL(x) *(pdouble2pint(&x))
#define __HIB(x) *(pdouble2pint(&x))
#define __LOB(x) *(1+pdouble2pint(&x))

/* Get two 32 bit ints from a double.  */

#define EXTRACT_WORDS_L(ix0,ix1,d)                  \
        do {                                        \
            ieee_double_shape_type_little ew_u;     \
            ew_u.value = (d);                       \
            (ix0) = ew_u.parts.msw;                 \
            (ix1) = ew_u.parts.lsw;                 \
        } while (0)

/* Set a double from two 32 bit ints.  */

#define INSERT_WORDS_L(d,ix0,ix1)                   \
        do {                                        \
            ieee_double_shape_type_little iw_u;     \
            iw_u.parts.msw = (ix0);                 \
            iw_u.parts.lsw = (ix1);                 \
            (d) = iw_u.value;                       \
        } while (0)

/* Get two 32 bit ints from a double.  */

#define EXTRACT_WORDS_B(ix0,ix1,d)                  \
        do {                                        \
            ieee_double_shape_type_big ew_u;        \
            ew_u.value = (d);                       \
            (ix0) = ew_u.parts.msw;                 \
            (ix1) = ew_u.parts.lsw;                 \
        } while (0)

/* Set a double from two 32 bit ints.  */

#define INSERT_WORDS_B(d,ix0,ix1)                   \
        do {                                        \
            ieee_double_shape_type_big iw_u;        \
            iw_u.parts.msw = (ix0);                 \
            iw_u.parts.lsw = (ix1);                 \
            (d) = iw_u.value;                       \
        } while (0)

/* Get the more significant 32 bit int from a double.  */
#define GET_HIGH_WORD_L(i,d)                        \
        do {                                        \
            ieee_double_shape_type_little gh_u;     \
            gh_u.value = (d);                       \
            (i) = gh_u.parts.msw;                   \
        } while (0)

/* Get the more significant 32 bit int from a double.  */
#define GET_HIGH_WORD_B(i,d)                        \
        do {                                        \
            ieee_double_shape_type_big gh_u;        \
            gh_u.value = (d);                       \
            (i) = gh_u.parts.msw;                   \
        } while (0)

/* Set the more significant 32 bits of a double from an int.  */
#define SET_HIGH_WORD_L(d,v)                        \
        do {                                        \
            ieee_double_shape_type_little sh_u;     \
            sh_u.value = (d);                       \
            sh_u.parts.msw = (v);                   \
            (d) = sh_u.value;                       \
        } while (0)

/* Set the more significant 32 bits of a double from an int.  */
#define SET_HIGH_WORD_B(d,v)                        \
        do {                                        \
            ieee_double_shape_type_big sh_u;        \
            sh_u.value = (d);                       \
            sh_u.parts.msw = (v);                   \
            (d) = sh_u.value;                       \
        } while (0)

/* Set the less significant 32 bits of a double from an int.  */
#define SET_LOW_WORD_L(d,v)                         \
        do {                                        \
            ieee_double_shape_type_little sh_u;     \
            sh_u.value = (d);                       \
            sh_u.parts.lsw = (v);                   \
            (d) = sh_u.value;                       \
        } while (0)

/* Set the more significant 32 bits of a double from an int.  */
#define SET_LOW_WORD_B(d,v)                         \
        do {                                        \
            ieee_double_shape_type_big sh_u;        \
            sh_u.value = (d);                       \
            sh_u.parts.lsw = (v);                   \
            (d) = sh_u.value;                       \
        } while (0)

/* Get the less significant 32 bit int from a double.  */
#define GET_LOW_WORD_L(i,d)                         \
        do {                                        \
            ieee_double_shape_type_little gl_u;     \
            gl_u.value = (d);                       \
            (i) = gl_u.parts.lsw;                   \
        } while (0)

/* Get the less significant 32 bit int from a double.  */
#define GET_LOW_WORD_B(i,d)                         \
        do {                                        \
            ieee_double_shape_type_big gl_u;        \
            gl_u.value = (d);                       \
            (i) = gl_u.parts.lsw;                   \
        } while (0)

/*
 * A union which permits us to convert between a float and a 32 bit
 * int.
 */
typedef union
{
    float value;
    /* FIXME: Assumes 32 bit int.  */
    unsigned int 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)

/* Macro wrappers.  */
#define EXTRACT_WORDS(ix0,ix1,d) do {   \
    if (is_little_endian())             \
        EXTRACT_WORDS_L(ix0,ix1,d);     \
    else                                \
        EXTRACT_WORDS_B(ix0,ix1,d);     \
} while (0)

#define INSERT_WORDS(d,ix0,ix1) do {    \
    if (is_little_endian())             \
       INSERT_WORDS_L(d,ix0,ix1);       \
    else                                \
        INSERT_WORDS_B(d,ix0,ix1);      \
} while (0)

#define GET_HIGH_WORD(i,d)              \
    do {                                \
        if (is_little_endian())         \
        GET_HIGH_WORD_L(i,d);           \
        else                            \
        GET_HIGH_WORD_B(i,d);           \
    } while (0)

#define SET_HIGH_WORD(d,v)              \
    do {                                \
        if (is_little_endian())         \
        SET_HIGH_WORD_L(d,v);           \
        else                            \
        SET_HIGH_WORD_B(d,v);           \
    } while (0)

#define GET_LOW_WORD(d,v)               \
    do {                                \
        if (is_little_endian())         \
        GET_LOW_WORD_L(d,v);            \
        else                            \
        GET_LOW_WORD_B(d,v);            \
    } while (0)

#define SET_LOW_WORD(d,v)               \
    do {                                \
        if (is_little_endian())         \
        SET_LOW_WORD_L(d,v);            \
        else                            \
        SET_LOW_WORD_B(d,v);            \
    } while (0)

#define __HI(x) (is_little_endian() ? __HIL(x) : __HIB(x))

#define __LO(x) (is_little_endian() ? __LOL(x) : __LOB(x))

/*
 * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
 */
#if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
#define	STRICT_ASSIGN(type, lval, rval)	((lval) = (rval))
#else
#define	STRICT_ASSIGN(type, lval, rval) do {	\
        volatile type __lval;			\
        \
        if (sizeof(type) >= sizeof(long double))	\
        (lval) = (rval);		\
        else {					\
            __lval = (rval);		\
            (lval) = __lval;		\
        }					\
} while (0)
#endif

#ifdef __FDLIBM_STDC__
static const double huge = 1.0e300;
#else
static double huge = 1.0e300;
#endif

#ifdef __STDC__
static const double
#else
static double
#endif
tiny  = 1.0e-300;

#ifdef __STDC__
static const double
#else
static double
#endif
one=  1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */

#ifdef __STDC__
static const double
#else
static double
#endif
TWO52[2]={
        4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
        -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
};

#ifdef __STDC__
static const double
#else
static double
#endif
atanhi[] = {
  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};

#ifdef __STDC__
static const double
#else
static double
#endif
atanlo[] = {
  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};

#ifdef __STDC__
static const double
#else
static double
#endif
aT[] = {
  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
};

#ifdef __STDC__
static const double
#else
static double
#endif
zero  = 0.0,
pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */

#ifdef __STDC__
static const double
#else
static double
#endif
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
two	=  2.0,
two53	=  9007199254740992.0,	/* 0x43400000, 0x00000000 */
two54   =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
twom54  =  5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/

static double freebsd_sqrt(double x);
static double freebsd_floor(double x);
static double freebsd_ceil(double x);
static double freebsd_fabs(double x);
static double freebsd_rint(double x);
static int freebsd_isnan(double x);
static double freebsd_atan(double x);
static double freebsd_atan2(double y, double x);


static double freebsd_atan(double x)
{
    double w,s1,s2,z;
	int32_t ix,hx,id;

	GET_HIGH_WORD(hx,x);
	ix = hx&0x7fffffff;
	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
	    u_int32_t low;
	    GET_LOW_WORD(low,x);
	    if(ix>0x7ff00000||
		(ix==0x7ff00000&&(low!=0)))
		return x+x;		/* NaN */
	    if(hx>0) return  atanhi[3]+*(volatile double *)&atanlo[3];
	    else     return -atanhi[3]-*(volatile double *)&atanlo[3];
	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
	    if (ix < 0x3e400000) {	/* |x| < 2^-27 */
		if(huge+x>one) return x;	/* raise inexact */
	    }
	    id = -1;
	} else {
	x = freebsd_fabs(x);
	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
		id = 0; x = (2.0*x-one)/(2.0+x);
	    } else {			/* 11/16<=|x|< 19/16 */
		id = 1; x  = (x-one)/(x+one);
	    }
	} else {
	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
		id = 2; x  = (x-1.5)/(one+1.5*x);
	    } else {			/* 2.4375 <= |x| < 2^66 */
		id = 3; x  = -1.0/x;
	    }
	}}
    /* end of argument reduction */
	z = x*x;
	w = z*z;
    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
	if (id<0) return x - x*(s1+s2);
	else {
	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
	    return (hx<0)? -z:z;
	}
}


static double freebsd_atan2(double y, double x)
{
    double z;
	int32_t k,m,hx,hy,ix,iy;
	u_int32_t lx,ly;

	EXTRACT_WORDS(hx,lx,x);
	ix = hx&0x7fffffff;
	EXTRACT_WORDS(hy,ly,y);
	iy = hy&0x7fffffff;
	if(((ix|((lx|-lx)>>31))>0x7ff00000)||
	   ((iy|((ly|-ly)>>31))>0x7ff00000))	/* x or y is NaN */
	   return x+y;
	if(hx==0x3ff00000&&lx==0) return freebsd_atan(y);   /* x=1.0 */
	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */

    /* when y = 0 */
	if((iy|ly)==0) {
	    switch(m) {
		case 0:
		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
	    }
	}
    /* when x = 0 */
	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;

    /* when x is INF */
	if(ix==0x7ff00000) {
	    if(iy==0x7ff00000) {
		switch(m) {
		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
		    case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
		    case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
		}
	    } else {
		switch(m) {
		    case 0: return  zero  ;	/* atan(+...,+INF) */
		    case 1: return -zero  ;	/* atan(-...,+INF) */
		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
		}
	    }
	}
    /* when y is INF */
	if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;

    /* compute y/x */
	k = (iy-ix)>>20;
	if(k > 60) {		 	/* |y/x| >  2**60 */
	    z=pi_o_2+0.5*pi_lo;
	    m&=1;
	}
	else if(hx<0&&k<-60) z=0.0; 	/* 0 > |y|/x > -2**-60 */
	else z=freebsd_atan(fabs(y/x));		/* safe to do y/x */
	switch (m) {
	    case 0: return       z  ;	/* atan(+,+) */
	    case 1: return      -z  ;	/* atan(-,+) */
	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
	    default: /* case 3 */
	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
	}
}

static double freebsd_sqrt(double x)		/* wrapper sqrt */
{
    double z;
    int32_t sign = (int)0x80000000;
    int32_t ix0,s0,q,m,t,i;
    u_int32_t r,t1,s1,ix1,q1;

    EXTRACT_WORDS(ix0,ix1,x);

    /* take care of Inf and NaN */
    if((ix0&0x7ff00000)==0x7ff00000) {
        return x*x+x;		/* sqrt(NaN)=NaN, sqrt(+inf)=+inf
					   sqrt(-inf)=sNaN */
    }
    /* take care of zero */
    if(ix0<=0) {
        if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
        else if(ix0<0)
            return (x-x)/(x-x);		/* sqrt(-ve) = sNaN */
    }
    /* normalize x */
    m = (ix0>>20);
    if(m==0) {				/* subnormal x */
        while(ix0==0) {
            m -= 21;
            ix0 |= (ix1>>11); ix1 <<= 21;
        }
        for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
        m -= i-1;
        ix0 |= (ix1>>(32-i));
        ix1 <<= i;
    }
    m -= 1023;	/* unbias exponent */
    ix0 = (ix0&0x000fffff)|0x00100000;
    if(m&1){	/* odd m, double x to make it even */
        ix0 += ix0 + ((ix1&sign)>>31);
        ix1 += ix1;
    }
    m >>= 1;	/* m = [m/2] */

    /* generate sqrt(x) bit by bit */
    ix0 += ix0 + ((ix1&sign)>>31);
    ix1 += ix1;
    q = q1 = s0 = s1 = 0;	/* [q,q1] = sqrt(x) */
    r = 0x00200000;		/* r = moving bit from right to left */

    while(r!=0) {
        t = s0+r;
        if(t<=ix0) {
            s0   = t+r;
            ix0 -= t;
            q   += r;
        }
        ix0 += ix0 + ((ix1&sign)>>31);
        ix1 += ix1;
        r>>=1;
    }

    r = sign;
    while(r!=0) {
        t1 = s1+r;
        t  = s0;
        if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
            s1  = t1+r;
            if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
            ix0 -= t;
            if (ix1 < t1) ix0 -= 1;
            ix1 -= t1;
            q1  += r;
        }
        ix0 += ix0 + ((ix1&sign)>>31);
        ix1 += ix1;
        r>>=1;
    }

    /* use floating add to find out rounding direction */
    if((ix0|ix1)!=0) {
        z = one-tiny; /* trigger inexact flag */
        if (z>=one) {
            z = one+tiny;
            if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;}
            else if (z>one) {
                if (q1==(u_int32_t)0xfffffffe) q+=1;
                q1+=2;
            } else
                q1 += (q1&1);
        }
    }
    ix0 = (q>>1)+0x3fe00000;
    ix1 =  q1>>1;
    if ((q&1)==1) ix1 |= sign;
    ix0 += (m <<20);

    INSERT_WORDS(z,ix0,ix1);

    return z;
}

static double freebsd_floor(double x)
{
    int32_t i0,i1,j0;
    u_int32_t i,j;

    EXTRACT_WORDS(i0,i1,x);

    j0 = ((i0>>20)&0x7ff)-0x3ff;
    if(j0<20) {
        if(j0<0) { 	/* raise inexact if x != 0 */
            if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
                if(i0>=0) {i0=i1=0;}
                else if(((i0&0x7fffffff)|i1)!=0)
                { i0=0xbff00000;i1=0;}
            }
        } else {
            i = (0x000fffff)>>j0;
            if(((i0&i)|i1)==0) return x; /* x is integral */
            if(huge+x>0.0) {	/* raise inexact flag */
                if(i0<0) i0 += (0x00100000)>>j0;
                i0 &= (~i); i1=0;
            }
        }
    } else if (j0>51) {
        if(j0==0x400) return x+x;	/* inf or NaN */
        else return x;		/* x is integral */
    } else {
        i = ((u_int32_t)(0xffffffff))>>(j0-20);
        if((i1&i)==0) return x;	/* x is integral */
        if(huge+x>0.0) { 		/* raise inexact flag */
            if(i0<0) {
                if(j0==20) i0+=1;
                else {
                    j = i1+(1<<(52-j0));
                    if(j<i1) i0 +=1 ; 	/* got a carry */
                    i1=j;
                }
            }
            i1 &= (~i);
        }
    }

    INSERT_WORDS(x,i0,i1);

    return x;
}

static double freebsd_ceil(double x)
{
    int32_t i0,i1,j0;
    u_int32_t i,j;
    EXTRACT_WORDS(i0,i1,x);
    j0 = ((i0>>20)&0x7ff)-0x3ff;
    if(j0<20) {
        if(j0<0) { 	/* raise inexact if x != 0 */
            if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
                if(i0<0) {i0=0x80000000;i1=0;}
                else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;}
            }
        } else {
            i = (0x000fffff)>>j0;
            if(((i0&i)|i1)==0) return x; /* x is integral */
            if(huge+x>0.0) {	/* raise inexact flag */
                if(i0>0) i0 += (0x00100000)>>j0;
                i0 &= (~i); i1=0;
            }
        }
    } else if (j0>51) {
        if(j0==0x400) return x+x;	/* inf or NaN */
        else return x;		/* x is integral */
    } else {
        i = ((u_int32_t)(0xffffffff))>>(j0-20);
        if((i1&i)==0) return x;	/* x is integral */
        if(huge+x>0.0) { 		/* raise inexact flag */
            if(i0>0) {
                if(j0==20) i0+=1;
                else {
                    j = i1 + (1<<(52-j0));
                    if(j<i1) i0+=1;	/* got a carry */
                    i1 = j;
                }
            }
            i1 &= (~i);
        }
    }
    INSERT_WORDS(x,i0,i1);
    return x;
}

static double freebsd_rint(double x)
{
    int32_t i0,j0,sx;
    u_int32_t i,i1;
    double w,t;
    EXTRACT_WORDS(i0,i1,x);
    sx = (i0>>31)&1;
    j0 = ((i0>>20)&0x7ff)-0x3ff;
    if(j0<20) {
        if(j0<0) {
            if(((i0&0x7fffffff)|i1)==0) return x;
            i1 |= (i0&0x0fffff);
            i0 &= 0xfffe0000;
            i0 |= ((i1|-i1)>>12)&0x80000;
            SET_HIGH_WORD(x,i0);
            STRICT_ASSIGN(double,w,TWO52[sx]+x);
            t =  w-TWO52[sx];
            GET_HIGH_WORD(i0,t);
            SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31));
            return t;
        } else {
            i = (0x000fffff)>>j0;
            if(((i0&i)|i1)==0) return x; /* x is integral */
            i>>=1;
            if(((i0&i)|i1)!=0) {
                /*
                 * Some bit is set after the 0.5 bit.  To avoid the
                 * possibility of errors from double rounding in
                 * w = TWO52[sx]+x, adjust the 0.25 bit to a lower
                 * guard bit.  We do this for all j0<=51.  The
                 * adjustment is trickiest for j0==18 and j0==19
                 * since then it spans the word boundary.
                 */
                if(j0==19) i1 = 0x40000000; else
                    if(j0==18) i1 = 0x80000000; else
                        i0 = (i0&(~i))|((0x20000)>>j0);
            }
        }
    } else if (j0>51) {
        if(j0==0x400) return x+x;	/* inf or NaN */
        else return x;		/* x is integral */
    } else {
        i = ((u_int32_t)(0xffffffff))>>(j0-20);
        if((i1&i)==0) return x;	/* x is integral */
        i>>=1;
        if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20));
    }
    INSERT_WORDS(x,i0,i1);
    STRICT_ASSIGN(double,w,TWO52[sx]+x);
    return w-TWO52[sx];
}

static int freebsd_isnan(double d)
{
    if (is_little_endian()) {
        IEEEd2bits_L u;
        u.d = d;
        return (u.bits.exp == 2047 && (u.bits.manl != 0 || u.bits.manh != 0));
    }
    else {
        IEEEd2bits_B u;
        u.d = d;
        return (u.bits.exp == 2047 && (u.bits.manl != 0 || u.bits.manh != 0));
    }
}

static double freebsd_fabs(double x)
{
    u_int32_t high;
    GET_HIGH_WORD(high,x);
    SET_HIGH_WORD(x,high&0x7fffffff);
    return x;
}

static const float huge_f = 1.0e30F;

static const float
TWO23[2]={
    8.3886080000e+06, /* 0x4b000000 */
    -8.3886080000e+06, /* 0xcb000000 */
};

static float
freebsd_truncf(float x)
{
    int32_t i0,j0;
    u_int32_t i;
    GET_FLOAT_WORD(i0,x);
    j0 = ((i0>>23)&0xff)-0x7f;
    if(j0<23) {
        if(j0<0) {  /* raise inexact if x != 0 */
            if(huge_f+x>0.0F)     /* |x|<1, so return 0*sign(x) */
                i0 &= 0x80000000;
        } else {
            i = (0x007fffff)>>j0;
            if((i0&i)==0) return x; /* x is integral */
            if(huge_f+x>0.0F)     /* raise inexact flag */
                i0 &= (~i);
        }
    } else {
        if(j0==0x80) return x+x;    /* inf or NaN */
        else return x;      /* x is integral */
    }
    SET_FLOAT_WORD(x,i0);
    return x;
}

static float
freebsd_rintf(float x)
{
    int32_t i0,j0,sx;
    float w,t;
    GET_FLOAT_WORD(i0,x);
    sx = (i0>>31)&1;
    j0 = ((i0>>23)&0xff)-0x7f;
    if(j0<23) {
        if(j0<0) {
            if((i0&0x7fffffff)==0) return x;
            STRICT_ASSIGN(float,w,TWO23[sx]+x);
            t =  w-TWO23[sx];
            GET_FLOAT_WORD(i0,t);
            SET_FLOAT_WORD(t,(i0&0x7fffffff)|(sx<<31));
            return t;
        }
        STRICT_ASSIGN(float,w,TWO23[sx]+x);
        return w-TWO23[sx];
    }
    if(j0==0x80) return x+x;    /* inf or NaN */
    else return x;          /* x is integral */
}

static float
freebsd_ceilf(float x)
{
    int32_t i0,j0;
    u_int32_t i;

    GET_FLOAT_WORD(i0,x);
    j0 = ((i0>>23)&0xff)-0x7f;
    if(j0<23) {
        if(j0<0) {  /* raise inexact if x != 0 */
            if(huge_f+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
                if(i0<0) {i0=0x80000000;}
                else if(i0!=0) { i0=0x3f800000;}
            }
        } else {
            i = (0x007fffff)>>j0;
            if((i0&i)==0) return x; /* x is integral */
            if(huge_f+x>(float)0.0) { /* raise inexact flag */
                if(i0>0) i0 += (0x00800000)>>j0;
                i0 &= (~i);
            }
        }
    } else {
        if(j0==0x80) return x+x;    /* inf or NaN */
        else return x;      /* x is integral */
    }
    SET_FLOAT_WORD(x,i0);
    return x;
}

static float
freebsd_floorf(float x)
{
    int32_t i0,j0;
    u_int32_t i;
    GET_FLOAT_WORD(i0,x);
    j0 = ((i0>>23)&0xff)-0x7f;
    if(j0<23) {
        if(j0<0) {  /* raise inexact if x != 0 */
            if(huge_f+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
                if(i0>=0) {i0=0;}
                else if((i0&0x7fffffff)!=0)
                { i0=0xbf800000;}
            }
        } else {
            i = (0x007fffff)>>j0;
            if((i0&i)==0) return x; /* x is integral */
            if(huge_f+x>(float)0.0) { /* raise inexact flag */
                if(i0<0) i0 += (0x00800000)>>j0;
                i0 &= (~i);
            }
        }
    } else {
        if(j0==0x80) return x+x;    /* inf or NaN */
        else return x;      /* x is integral */
    }
    SET_FLOAT_WORD(x,i0);
    return x;
}

static float
freebsd_fminf(float x, float y)
{
    if (is_little_endian()) {
        IEEEf2bits_L u[2];

        u[0].f = x;
        u[1].f = y;

        /* Check for NaNs to avoid raising spurious exceptions. */
        if (u[0].bits.exp == 255 && u[0].bits.man != 0)
            return (y);
        if (u[1].bits.exp == 255 && u[1].bits.man != 0)
            return (x);

        /* Handle comparisons of signed zeroes. */
        if (u[0].bits.sign != u[1].bits.sign)
            return (u[u[1].bits.sign].f);
    }
    else {
        IEEEf2bits_B u[2];

        u[0].f = x;
        u[1].f = y;

        /* Check for NaNs to avoid raising spurious exceptions. */
        if (u[0].bits.exp == 255 && u[0].bits.man != 0)
            return (y);
        if (u[1].bits.exp == 255 && u[1].bits.man != 0)
            return (x);

        /* Handle comparisons of signed zeroes. */
        if (u[0].bits.sign != u[1].bits.sign)
            return (u[u[1].bits.sign].f);
    }

    return (x < y ? x : y);
}

static float
freebsd_fmaxf(float x, float y)
{
    if (is_little_endian()) {
        IEEEf2bits_L u[2];

        u[0].f = x;
        u[1].f = y;

        /* Check for NaNs to avoid raising spurious exceptions. */
        if (u[0].bits.exp == 255 && u[0].bits.man != 0)
            return (y);
        if (u[1].bits.exp == 255 && u[1].bits.man != 0)
            return (x);

        /* Handle comparisons of signed zeroes. */
        if (u[0].bits.sign != u[1].bits.sign)
            return (u[u[0].bits.sign].f);
    }
    else {
        IEEEf2bits_B u[2];

        u[0].f = x;
        u[1].f = y;

        /* Check for NaNs to avoid raising spurious exceptions. */
        if (u[0].bits.exp == 255 && u[0].bits.man != 0)
            return (y);
        if (u[1].bits.exp == 255 && u[1].bits.man != 0)
            return (x);

        /* Handle comparisons of signed zeroes. */
        if (u[0].bits.sign != u[1].bits.sign)
            return (u[u[0].bits.sign].f);
    }

    return (x > y ? x : y);
}

static double
freebsd_copysign(double x, double y)
{
    u_int32_t hx,hy;
    GET_HIGH_WORD(hx,x);
    GET_HIGH_WORD(hy,y);
    SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000));
        return x;
}

static double
freebsd_scalbn(double x, int n)
{
    int32_t k,hx,lx;
    EXTRACT_WORDS(hx,lx,x);
    k = (hx&0x7ff00000)>>20;        /* extract exponent */
    if (k==0) {             /* 0 or subnormal x */
        if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
        x *= two54;
        GET_HIGH_WORD(hx,x);
        k = ((hx&0x7ff00000)>>20) - 54;
        if (n< -50000) return tiny*x;   /*underflow*/
    }
    if (k==0x7ff) return x+x;       /* NaN or Inf */
    k = k+n;
    if (k >  0x7fe) return huge*freebsd_copysign(huge,x); /* overflow  */
    if (k > 0)              /* normal result */
    {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;}
    if (k <= -54) {
        if (n > 50000)  /* in case integer overflow in n+k */
            return huge*freebsd_copysign(huge,x);   /*overflow*/
        else return tiny*freebsd_copysign(tiny,x);  /*underflow*/
    }
    k += 54;                /* subnormal result */
    SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20));
    return x*twom54;
}

static double
freebsd_pow(double x, double y)
{
	double z,ax,z_h,z_l,p_h,p_l;
	double y1,t1,t2,r,s,t,u,v,w;
	int32_t i,j,k,yisint,n;
	int32_t hx,hy,ix,iy;
	u_int32_t lx,ly;

	EXTRACT_WORDS(hx,lx,x);
	EXTRACT_WORDS(hy,ly,y);
	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;

    /* y==zero: x**0 = 1 */
	if((iy|ly)==0) return one;

    /* x==1: 1**y = 1, even if y is NaN */
	if (hx==0x3ff00000 && lx == 0) return one;

    /* y!=zero: result is NaN if either arg is NaN */
	if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
	   iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
		return (x+0.0)+(y+0.0);

    /* determine if y is an odd int when x < 0
     * yisint = 0	... y is not an integer
     * yisint = 1	... y is an odd int
     * yisint = 2	... y is an even int
     */
	yisint  = 0;
	if(hx<0) {
	    if(iy>=0x43400000) yisint = 2; /* even integer y */
	    else if(iy>=0x3ff00000) {
		k = (iy>>20)-0x3ff;	   /* exponent */
		if(k>20) {
		    j = ly>>(52-k);
		    if((j<<(52-k))==ly) yisint = 2-(j&1);
		} else if(ly==0) {
		    j = iy>>(20-k);
		    if((j<<(20-k))==iy) yisint = 2-(j&1);
		}
	    }
	}

    /* special value of y */
	if(ly==0) {
	    if (iy==0x7ff00000) {	/* y is +-inf */
	        if(((ix-0x3ff00000)|lx)==0)
		    return  one;	/* (-1)**+-inf is NaN */
	        else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
		    return (hy>=0)? y: zero;
	        else			/* (|x|<1)**-,+inf = inf,0 */
		    return (hy<0)?-y: zero;
	    }
	    if(iy==0x3ff00000) {	/* y is  +-1 */
		if(hy<0) return one/x; else return x;
	    }
            if(hy==0x40000000) return x*x;   /* y is  2 */
            if(hy==0x40080000) return x*x*x; /* y is  3 */
            if(hy==0x40100000) {             /* y is  4 */
                u = x*x;
                return u*u;
            }
	    if(hy==0x3fe00000) {             /* y is  0.5 */
		if(hx>=0)	/* x >= +0 */
                    return sqrt(x);
	    }
	}

	ax   = fabs(x);
    /* special value of x */
	if(lx==0) {
	    if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
		z = ax;			/*x is +-0,+-inf,+-1*/
		if(hy<0) z = one/z;	/* z = (1/|x|) */
		if(hx<0) {
		    if(((ix-0x3ff00000)|yisint)==0) {
			z = (z-z)/(z-z); /* (-1)**non-int is NaN */
		    } else if(yisint==1)
			z = -z;		/* (x<0)**odd = -(|x|**odd) */
		}
		return z;
	    }
	}

    /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be
	n = (hx>>31)+1;
       but ANSI C says a right shift of a signed negative quantity is
       implementation defined.  */
	n = ((u_int32_t)hx>>31)-1;

    /* (x<0)**(non-int) is NaN */
	if((n|yisint)==0) return (x-x)/(x-x);

	s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
	if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */

    /* |y| is huge */
	if(iy>0x41e00000) { /* if |y| > 2**31 */
	    if(iy>0x43f00000){	/* if |y| > 2**64, must o/uflow */
		if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
		if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
	    }
	/* over/underflow if x is not close to one */
	    if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
	    if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
	/* now |1-x| is tiny <= 2**-20, suffice to compute
	   log(x) by x-x^2/2+x^3/3-x^4/4 */
	    t = ax-one;		/* t has 20 trailing zeros */
	    w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
	    u = ivln2_h*t;	/* ivln2_h has 21 sig. bits */
	    v = t*ivln2_l-w*ivln2;
	    t1 = u+v;
	    SET_LOW_WORD(t1,0);
	    t2 = v-(t1-u);
	} else {
	    double ss,s2,s_h,s_l,t_h,t_l;
	    n = 0;
	/* take care subnormal number */
	    if(ix<0x00100000)
		{ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
	    n  += ((ix)>>20)-0x3ff;
	    j  = ix&0x000fffff;
	/* determine interval */
	    ix = j|0x3ff00000;		/* normalize ix */
	    if(j<=0x3988E) k=0;		/* |x|<sqrt(3/2) */
	    else if(j<0xBB67A) k=1;	/* |x|<sqrt(3)   */
	    else {k=0;n+=1;ix -= 0x00100000;}
	    SET_HIGH_WORD(ax,ix);

	/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
	    u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
	    v = one/(ax+bp[k]);
	    ss = u*v;
	    s_h = ss;
	    SET_LOW_WORD(s_h,0);
	/* t_h=ax+bp[k] High */
	    t_h = zero;
	    SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
	    t_l = ax - (t_h-bp[k]);
	    s_l = v*((u-s_h*t_h)-s_h*t_l);
	/* compute log(ax) */
	    s2 = ss*ss;
	    r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
	    r += s_l*(s_h+ss);
	    s2  = s_h*s_h;
	    t_h = 3.0+s2+r;
	    SET_LOW_WORD(t_h,0);
	    t_l = r-((t_h-3.0)-s2);
	/* u+v = ss*(1+...) */
	    u = s_h*t_h;
	    v = s_l*t_h+t_l*ss;
	/* 2/(3log2)*(ss+...) */
	    p_h = u+v;
	    SET_LOW_WORD(p_h,0);
	    p_l = v-(p_h-u);
	    z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
	    z_l = cp_l*p_h+p_l*cp+dp_l[k];
	/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
	    t = (double)n;
	    t1 = (((z_h+z_l)+dp_h[k])+t);
	    SET_LOW_WORD(t1,0);
	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
	}

    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
	y1  = y;
	SET_LOW_WORD(y1,0);
	p_l = (y-y1)*t1+y*t2;
	p_h = y1*t1;
	z = p_l+p_h;
	EXTRACT_WORDS(j,i,z);
	if (j>=0x40900000) {				/* z >= 1024 */
	    if(((j-0x40900000)|i)!=0)			/* if z > 1024 */
		return s*huge*huge;			/* overflow */
	    else {
		if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
	    }
	} else if((j&0x7fffffff)>=0x4090cc00 ) {	/* z <= -1075 */
	    if(((j-0xc090cc00)|i)!=0) 		/* z < -1075 */
		return s*tiny*tiny;		/* underflow */
	    else {
		if(p_l<=z-p_h) return s*tiny*tiny;	/* underflow */
	    }
	}
    /*
     * compute 2**(p_h+p_l)
     */
	i = j&0x7fffffff;
	k = (i>>20)-0x3ff;
	n = 0;
	if(i>0x3fe00000) {		/* if |z| > 0.5, set n = [z+0.5] */
	    n = j+(0x00100000>>(k+1));
	    k = ((n&0x7fffffff)>>20)-0x3ff;	/* new k for n */
	    t = zero;
	    SET_HIGH_WORD(t,n&~(0x000fffff>>k));
	    n = ((n&0x000fffff)|0x00100000)>>(20-k);
	    if(j<0) n = -n;
	    p_h -= t;
	}
	t = p_l+p_h;
	SET_LOW_WORD(t,0);
	u = t*lg2_h;
	v = (p_l-(t-p_h))*lg2+t*lg2_l;
	z = u+v;
	w = v-(z-u);
	t  = z*z;
	t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
	r  = (z*t1)/(t1-two)-(w+z*w);
	z  = one-(r-z);
	GET_HIGH_WORD(j,z);
	j += (n<<20);
	if((j>>20)<=0) z = freebsd_scalbn(z,n);	/* subnormal output */
	else SET_HIGH_WORD(z,j);
	return s*z;
}

double atan(double x)
{
    return freebsd_atan(x);
}

double atan2(double y, double x)
{
    return freebsd_atan2(y, x);
}

double sqrt(double x)
{
    return freebsd_sqrt(x);
}

double floor(double x)
{
    return freebsd_floor(x);
}

double ceil(double x)
{
    return freebsd_ceil(x);
}

double fmin(double x, double y)
{
    return x < y ? x : y;
}

double fmax(double x, double y)
{
    return x > y ? x : y;
}

double rint(double x)
{
    return freebsd_rint(x);
}

double fabs(double x)
{
    return freebsd_fabs(x);
}

int isnan(double x)
{
    return freebsd_isnan(x);
}

double trunc(double x)
{
    return (x > 0) ? freebsd_floor(x) : freebsd_ceil(x);
}

int signbit(double x)
{
    return ((__HI(x) & 0x80000000) >> 31);
}

float
truncf(float x)
{
    return freebsd_truncf(x);
}

float
rintf(float x)
{
    return freebsd_rintf(x);
}

float
ceilf(float x)
{
    return freebsd_ceilf(x);
}

float
floorf(float x)
{
    return freebsd_floorf(x);
}

float
fminf(float x, float y)
{
    return freebsd_fminf(x, y);
}

float
fmaxf(float x, float y)
{
    return freebsd_fmaxf(x, y);
}

double
pow(double x, double y)
{
    return freebsd_pow(x, y);
}

double
scalbn(double x, int n)
{
    return freebsd_scalbn(x, n);
}