src/bsp/lk/lib/libm/math_private.h

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

/*
 * from: @(#)fdlibm.h 5.1 93/09/24
 * $FreeBSD$
 */

#ifndef _MATH_PRIVATE_H_
#define _MATH_PRIVATE_H_

#include <sys/types.h>
#include <endian.h>

/*
 * The original fdlibm code used statements like:
 *  n0 = ((*(int*)&one)>>29)^1;     * index of high word *
 *  ix0 = *(n0+(int*)&x);           * high word of x *
 *  ix1 = *((1-n0)+(int*)&x);       * low word of x *
 * to dig two 32 bit words out of the 64 bit IEEE floating point
 * value.  That is non-ANSI, and, moreover, the gcc instruction
 * scheduler gets it wrong.  We instead use the following macros.
 * Unlike the original code, we determine the endianness at compile
 * time, not at run time; I don't see much benefit to selecting
 * endianness at run time.
 */

/*
 * A union which permits us to convert between a double and two 32 bit
 * ints.
 */

#ifdef __arm__
#if defined(__VFP_FP__) || defined(__ARM_EABI__)
#define IEEE_WORD_ORDER BYTE_ORDER
#else
#define IEEE_WORD_ORDER BIG_ENDIAN
#endif
#else /* __arm__ */
#define IEEE_WORD_ORDER BYTE_ORDER
#endif

#if IEEE_WORD_ORDER == BIG_ENDIAN

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

#endif

#if IEEE_WORD_ORDER == LITTLE_ENDIAN

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

#endif

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

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

/* Get a 64-bit int from a double. */
#define EXTRACT_WORD64(ix,d)                    \
do {                                \
  ieee_double_shape_type ew_u;                  \
  ew_u.value = (d);                     \
  (ix) = ew_u.xparts.w;                     \
} while (0)

/* Get the more significant 32 bit int from a double.  */

#define GET_HIGH_WORD(i,d)                  \
do {                                \
  ieee_double_shape_type gh_u;                  \
  gh_u.value = (d);                     \
  (i) = gh_u.parts.msw;                     \
} while (0)

/* Get the less significant 32 bit int from a double.  */

#define GET_LOW_WORD(i,d)                   \
do {                                \
  ieee_double_shape_type gl_u;                  \
  gl_u.value = (d);                     \
  (i) = gl_u.parts.lsw;                     \
} while (0)

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

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

/* Set a double from a 64-bit int. */
#define INSERT_WORD64(d,ix)                 \
do {                                \
  ieee_double_shape_type iw_u;                  \
  iw_u.xparts.w = (ix);                     \
  (d) = iw_u.value;                     \
} while (0)

/* Set the more significant 32 bits of a double from an int.  */

#define SET_HIGH_WORD(d,v)                  \
do {                                \
  ieee_double_shape_type 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(d,v)                   \
do {                                \
  ieee_double_shape_type sl_u;                  \
  sl_u.value = (d);                     \
  sl_u.parts.lsw = (v);                     \
  (d) = sl_u.value;                     \
} 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)

/*
 * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
 * double.
 */

#define EXTRACT_LDBL80_WORDS(ix0,ix1,d)             \
do {                                \
  union IEEEl2bits ew_u;                    \
  ew_u.e = (d);                         \
  (ix0) = ew_u.xbits.expsign;                   \
  (ix1) = ew_u.xbits.man;                   \
} while (0)

/*
 * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
 * long double.
 */

#define EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d)            \
do {                                \
  union IEEEl2bits ew_u;                    \
  ew_u.e = (d);                         \
  (ix0) = ew_u.xbits.expsign;                   \
  (ix1) = ew_u.xbits.manh;                  \
  (ix2) = ew_u.xbits.manl;                  \
} while (0)

/* Get expsign as a 16 bit int from a long double.  */

#define GET_LDBL_EXPSIGN(i,d)                   \
do {                                \
  union IEEEl2bits ge_u;                    \
  ge_u.e = (d);                         \
  (i) = ge_u.xbits.expsign;                 \
} while (0)

/*
 * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
 * mantissa.
 */

#define INSERT_LDBL80_WORDS(d,ix0,ix1)              \
do {                                \
  union IEEEl2bits iw_u;                    \
  iw_u.xbits.expsign = (ix0);                   \
  iw_u.xbits.man = (ix1);                   \
  (d) = iw_u.e;                         \
} while (0)

/*
 * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
 * comprising the mantissa.
 */

#define INSERT_LDBL128_WORDS(d,ix0,ix1,ix2)         \
do {                                \
  union IEEEl2bits iw_u;                    \
  iw_u.xbits.expsign = (ix0);                   \
  iw_u.xbits.manh = (ix1);                  \
  iw_u.xbits.manl = (ix2);                  \
  (d) = iw_u.e;                         \
} while (0)

/* Set expsign of a long double from a 16 bit int.  */

#define SET_LDBL_EXPSIGN(d,v)                   \
do {                                \
  union IEEEl2bits se_u;                    \
  se_u.e = (d);                         \
  se_u.xbits.expsign = (v);                 \
  (d) = se_u.e;                         \
} while (0)

#ifdef __i386__
/* Long double constants are broken on i386. */
#define LD80C(m, ex, v) {                       \
    .xbits.man = __CONCAT(m, ULL),                  \
    .xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0),  \
}
#else
/* The above works on non-i386 too, but we use this to check v. */
#define LD80C(m, ex, v) { .e = (v), }
#endif

#ifdef FLT_EVAL_METHOD
/*
 * 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
#endif /* FLT_EVAL_METHOD */

/* Support switching the mode to FP_PE if necessary. */
#if defined(__i386__) && !defined(NO_FPSETPREC)
#define ENTERI()                \
    long double __retval;           \
    fp_prec_t __oprec;          \
                        \
    if ((__oprec = fpgetprec()) != FP_PE)   \
        fpsetprec(FP_PE)
#define RETURNI(x) do {             \
    __retval = (x);             \
    if (__oprec != FP_PE)           \
        fpsetprec(__oprec);     \
    RETURNF(__retval);          \
} while (0)
#else
#define ENTERI(x)
#define RETURNI(x)  RETURNF(x)
#endif

/* Default return statement if hack*_t() is not used. */
#define      RETURNF(v)      return (v)

/*
 * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
 * a == 0, but is slower.
 */
#define _2sum(a, b) do {    \
    __typeof(a) __s, __w;   \
                \
    __w = (a) + (b);    \
    __s = __w - (a);    \
    (b) = ((a) - (__w - __s)) + ((b) - __s); \
    (a) = __w;      \
} while (0)

/*
 * 2sumF algorithm.
 *
 * "Normalize" the terms in the infinite-precision expression a + b for
 * the sum of 2 floating point values so that b is as small as possible
 * relative to 'a'.  (The resulting 'a' is the value of the expression in
 * the same precision as 'a' and the resulting b is the rounding error.)
 * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
 * exponent overflow or underflow must not occur.  This uses a Theorem of
 * Dekker (1971).  See Knuth (1981) 4.2.2 Theorem C.  The name "TwoSum"
 * is apparently due to Skewchuk (1997).
 *
 * For this to always work, assignment of a + b to 'a' must not retain any
 * extra precision in a + b.  This is required by C standards but broken
 * in many compilers.  The brokenness cannot be worked around using
 * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
 * algorithm would be destroyed by non-null strict assignments.  (The
 * compilers are correct to be broken -- the efficiency of all floating
 * point code calculations would be destroyed similarly if they forced the
 * conversions.)
 *
 * Fortunately, a case that works well can usually be arranged by building
 * any extra precision into the type of 'a' -- 'a' should have type float_t,
 * double_t or long double.  b's type should be no larger than 'a's type.
 * Callers should use these types with scopes as large as possible, to
 * reduce their own extra-precision and efficiciency problems.  In
 * particular, they shouldn't convert back and forth just to call here.
 */
#ifdef DEBUG
#define _2sumF(a, b) do {               \
    __typeof(a) __w;                \
    volatile __typeof(a) __ia, __ib, __r, __vw; \
                            \
    __ia = (a);                 \
    __ib = (b);                 \
    assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib));    \
                            \
    __w = (a) + (b);                \
    (b) = ((a) - __w) + (b);            \
    (a) = __w;                  \
                            \
    /* The next 2 assertions are weak if (a) is already long double. */ \
    assert((long double)__ia + __ib == (long double)(a) + (b)); \
    __vw = __ia + __ib;             \
    __r = __ia - __vw;              \
    __r += __ib;                    \
    assert(__vw == (a) && __r == (b));      \
} while (0)
#else /* !DEBUG */
#define _2sumF(a, b) do {   \
    __typeof(a) __w;    \
                \
    __w = (a) + (b);    \
    (b) = ((a) - __w) + (b); \
    (a) = __w;      \
} while (0)
#endif /* DEBUG */

/*
 * Set x += c, where x is represented in extra precision as a + b.
 * x must be sufficiently normalized and sufficiently larger than c,
 * and the result is then sufficiently normalized.
 *
 * The details of ordering are that |a| must be >= |c| (so that (a, c)
 * can be normalized without extra work to swap 'a' with c).  The details of
 * the normalization are that b must be small relative to the normalized 'a'.
 * Normalization of (a, c) makes the normalized c tiny relative to the
 * normalized a, so b remains small relative to 'a' in the result.  However,
 * b need not ever be tiny relative to 'a'.  For example, b might be about
 * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
 * That is usually enough, and adding c (which by normalization is about
 * 2**53 times smaller than a) cannot change b significantly.  However,
 * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
 * significantly relative to b.  The caller must ensure that significant
 * cancellation doesn't occur, either by having c of the same sign as 'a',
 * or by having |c| a few percent smaller than |a|.  Pre-normalization of
 * (a, b) may help.
 *
 * This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
 * exercise 19).  We gain considerable efficiency by requiring the terms to
 * be sufficiently normalized and sufficiently increasing.
 */
#define _3sumF(a, b, c) do {    \
    __typeof(a) __tmp;  \
                \
    __tmp = (c);        \
    _2sumF(__tmp, (a)); \
    (b) += (a);     \
    (a) = __tmp;        \
} while (0)

/*
 * Common routine to process the arguments to nan(), nanf(), and nanl().
 */
void _scan_nan(uint32_t *__words, int __num_words, const char *__s);

#ifdef _COMPLEX_H

/*
 * C99 specifies that complex numbers have the same representation as
 * an array of two elements, where the first element is the real part
 * and the second element is the imaginary part.
 */
typedef union {
    float complex f;
    float a[2];
} float_complex;
typedef union {
    double complex f;
    double a[2];
} double_complex;
typedef union {
    long double complex f;
    long double a[2];
} long_double_complex;
#define REALPART(z) ((z).a[0])
#define IMAGPART(z) ((z).a[1])

/*
 * Inline functions that can be used to construct complex values.
 *
 * The C99 standard intends x+I*y to be used for this, but x+I*y is
 * currently unusable in general since gcc introduces many overflow,
 * underflow, sign and efficiency bugs by rewriting I*y as
 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
 * to -0.0+I*0.0.
 */
static __inline float complex
cpackf(float x, float y)
{
    float_complex z;

    REALPART(z) = x;
    IMAGPART(z) = y;
    return (z.f);
}

static __inline double complex
cpack(double x, double y)
{
    double_complex z;

    REALPART(z) = x;
    IMAGPART(z) = y;
    return (z.f);
}

static __inline long double complex
cpackl(long double x, long double y)
{
    long_double_complex z;

    REALPART(z) = x;
    IMAGPART(z) = y;
    return (z.f);
}
#endif /* _COMPLEX_H */

#ifdef __GNUCLIKE_ASM

/* Asm versions of some functions. */

#ifdef __amd64__
static __inline int
irint(double x)
{
    int n;

    asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x));
    return (n);
}
#define HAVE_EFFICIENT_IRINT
#endif

#ifdef __i386__
static __inline int
irint(double x)
{
    int n;

    asm("fistl %0" : "=m" (n) : "t" (x));
    return (n);
}
#define HAVE_EFFICIENT_IRINT
#endif

#if defined(__amd64__) || defined(__i386__)
static __inline int
irintl(long double x)
{
    int n;

    asm("fistl %0" : "=m" (n) : "t" (x));
    return (n);
}
#define HAVE_EFFICIENT_IRINTL
#endif

#endif /* __GNUCLIKE_ASM */

#ifdef DEBUG
#if defined(__amd64__) || defined(__i386__)
#define breakpoint()    asm("int $3")
#else
#include <signal.h>

#define breakpoint()    raise(SIGTRAP)
#endif
#endif

/* Write a pari script to test things externally. */
#ifdef DOPRINT
#include <stdio.h>

#ifndef DOPRINT_SWIZZLE
#define DOPRINT_SWIZZLE     0
#endif

#ifdef DOPRINT_LD80

#define DOPRINT_START(xp) do {                      \
    uint64_t __lx;                          \
    uint16_t __hx;                          \
                                    \
    /* Hack to give more-problematic args. */           \
    EXTRACT_LDBL80_WORDS(__hx, __lx, *xp);              \
    __lx ^= DOPRINT_SWIZZLE;                    \
    INSERT_LDBL80_WORDS(*xp, __hx, __lx);               \
    printf("x = %.21Lg; ", (long double)*xp);           \
} while (0)
#define DOPRINT_END1(v)                         \
    printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define DOPRINT_END2(hi, lo)                        \
    printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",      \
        (long double)(hi), (long double)(lo))

#elif defined(DOPRINT_D64)

#define DOPRINT_START(xp) do {                      \
    uint32_t __hx, __lx;                        \
                                    \
    EXTRACT_WORDS(__hx, __lx, *xp);                 \
    __lx ^= DOPRINT_SWIZZLE;                    \
    INSERT_WORDS(*xp, __hx, __lx);                  \
    printf("x = %.21Lg; ", (long double)*xp);           \
} while (0)
#define DOPRINT_END1(v)                         \
    printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define DOPRINT_END2(hi, lo)                        \
    printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",      \
        (long double)(hi), (long double)(lo))

#elif defined(DOPRINT_F32)

#define DOPRINT_START(xp) do {                      \
    uint32_t __hx;                          \
                                    \
    GET_FLOAT_WORD(__hx, *xp);                  \
    __hx ^= DOPRINT_SWIZZLE;                    \
    SET_FLOAT_WORD(*xp, __hx);                  \
    printf("x = %.21Lg; ", (long double)*xp);           \
} while (0)
#define DOPRINT_END1(v)                         \
    printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define DOPRINT_END2(hi, lo)                        \
    printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",      \
        (long double)(hi), (long double)(lo))

#else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */

#ifndef DOPRINT_SWIZZLE_HIGH
#define DOPRINT_SWIZZLE_HIGH    0
#endif

#define DOPRINT_START(xp) do {                      \
    uint64_t __lx, __llx;                       \
    uint16_t __hx;                          \
                                    \
    EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp);          \
    __llx ^= DOPRINT_SWIZZLE;                   \
    __lx ^= DOPRINT_SWIZZLE_HIGH;                   \
    INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx);           \
    printf("x = %.36Lg; ", (long double)*xp);                   \
} while (0)
#define DOPRINT_END1(v)                         \
    printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define DOPRINT_END2(hi, lo)                        \
    printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n",      \
        (long double)(hi), (long double)(lo))

#endif /* DOPRINT_LD80 */

#else /* !DOPRINT */
#define DOPRINT_START(xp)
#define DOPRINT_END1(v)
#define DOPRINT_END2(hi, lo)
#endif /* DOPRINT */

#define RETURNP(x) do {         \
    DOPRINT_END1(x);        \
    RETURNF(x);         \
} while (0)
#define RETURNPI(x) do {        \
    DOPRINT_END1(x);        \
    RETURNI(x);         \
} while (0)
#define RETURN2P(x, y) do {     \
    DOPRINT_END2((x), (y));     \
    RETURNF((x) + (y));     \
} while (0)
#define RETURN2PI(x, y) do {        \
    DOPRINT_END2((x), (y));     \
    RETURNI((x) + (y));     \
} while (0)
#ifdef STRUCT_RETURN
#define RETURNSP(rp) do {       \
    if (!(rp)->lo_set)      \
        RETURNP((rp)->hi);  \
    RETURN2P((rp)->hi, (rp)->lo);   \
} while (0)
#define RETURNSPI(rp) do {      \
    if (!(rp)->lo_set)      \
        RETURNPI((rp)->hi); \
    RETURN2PI((rp)->hi, (rp)->lo);  \
} while (0)
#endif
#define SUM2P(x, y) ({          \
    const __typeof (x) __x = (x);   \
    const __typeof (y) __y = (y);   \
                    \
    DOPRINT_END2(__x, __y);     \
    __x + __y;          \
})

/*
 * ieee style elementary functions
 *
 * We rename functions here to improve other sources' diffability
 * against fdlibm.
 */
#define __ieee754_sqrt  sqrt
#define __ieee754_acos  acos
#define __ieee754_acosh acosh
#define __ieee754_log   log
#define __ieee754_log2  log2
#define __ieee754_atanh atanh
#define __ieee754_asin  asin
#define __ieee754_atan2 atan2
#define __ieee754_exp   exp
#define __ieee754_cosh  cosh
#define __ieee754_fmod  fmod
#define __ieee754_pow   pow
#define __ieee754_lgamma lgamma
#define __ieee754_gamma gamma
#define __ieee754_lgamma_r lgamma_r
#define __ieee754_gamma_r gamma_r
#define __ieee754_log10 log10
#define __ieee754_sinh  sinh
#define __ieee754_hypot hypot
#define __ieee754_j0    j0
#define __ieee754_j1    j1
#define __ieee754_y0    y0
#define __ieee754_y1    y1
#define __ieee754_jn    jn
#define __ieee754_yn    yn
#define __ieee754_remainder remainder
#define __ieee754_scalb scalb
#define __ieee754_sqrtf sqrtf
#define __ieee754_acosf acosf
#define __ieee754_acoshf acoshf
#define __ieee754_logf  logf
#define __ieee754_atanhf atanhf
#define __ieee754_asinf asinf
#define __ieee754_atan2f atan2f
#define __ieee754_expf  expf
#define __ieee754_coshf coshf
#define __ieee754_fmodf fmodf
#define __ieee754_powf  powf
#define __ieee754_lgammaf lgammaf
#define __ieee754_gammaf gammaf
#define __ieee754_lgammaf_r lgammaf_r
#define __ieee754_gammaf_r gammaf_r
#define __ieee754_log10f log10f
#define __ieee754_log2f log2f
#define __ieee754_sinhf sinhf
#define __ieee754_hypotf hypotf
#define __ieee754_j0f   j0f
#define __ieee754_j1f   j1f
#define __ieee754_y0f   y0f
#define __ieee754_y1f   y1f
#define __ieee754_jnf   jnf
#define __ieee754_ynf   ynf
#define __ieee754_remainderf remainderf
#define __ieee754_scalbf scalbf

/* fdlibm kernel function */
int __kernel_rem_pio2(double*,double*,int,int,int);

/* double precision kernel functions */
#ifndef INLINE_REM_PIO2
int __ieee754_rem_pio2(double,double*);
#endif
double  __kernel_sin(double,double,int);
double  __kernel_cos(double,double);
double  __kernel_tan(double,double,int);
double  __ldexp_exp(double,int);
#ifdef _COMPLEX_H
double complex __ldexp_cexp(double complex,int);
#endif

/* float precision kernel functions */
#ifndef INLINE_REM_PIO2F
int __ieee754_rem_pio2f(float,double*);
#endif
#ifndef INLINE_KERNEL_SINDF
float   __kernel_sindf(double);
#endif
#ifndef INLINE_KERNEL_COSDF
float   __kernel_cosdf(double);
#endif
#ifndef INLINE_KERNEL_TANDF
float   __kernel_tandf(double,int);
#endif
float   __ldexp_expf(float,int);
#ifdef _COMPLEX_H
float complex __ldexp_cexpf(float complex,int);
#endif

/* long double precision kernel functions */
long double __kernel_sinl(long double, long double, int);
long double __kernel_cosl(long double, long double);
long double __kernel_tanl(long double, long double, int);

#endif /* !_MATH_PRIVATE_H_ */