The return value from \fIproc\fR is only used during read and
write tracing.
During unset traces, the return value is ignored and all relevant
trace procedures will always be invoked.
.SH "RESTRICTIONS"
.PP
A trace procedure can be called at any time, even when there
are partially formed results stored in the interpreter.  If
the trace procedure does anything that could damage this result (such
as calling \fBTcl_Eval\fR) then it must use the \fBTcl_SaveInterpState\fR
and related routines to save and restore the original state of
the interpreter before it returns.
.SH "UNDEFINED VARIABLES"
.PP
It is legal to set a trace on an undefined variable.
The variable will still appear to be undefined until the
first time its value is set.
If an undefined variable is traced and then unset, the unset will fail
with an error

	     * long range get auto-narrowed to tclIntType, while all the
	     * values in the unsigned long range will fit in a long.
	     */

	    mp_int big;

	    UNPACK_BIGNUM(objPtr, big);
	    if ((size_t) big.used <= (CHAR_BIT * sizeof(long) + MP_DIGIT_BIT - 1)
		    / MP_DIGIT_BIT) {
		unsigned long value = 0, numBytes = sizeof(long);
		long scratch;
		unsigned char *bytes = (unsigned char *) &scratch;

		if (mp_to_unsigned_bin_n(&big, bytes, &numBytes) == MP_OKAY) {
		    while (numBytes-- > 0) {
			value = (value << CHAR_BIT) | *bytes++;

	     * Tcl_WideInt, even when auto-narrowing is enabled.
	     */

	    mp_int big;

	    UNPACK_BIGNUM(objPtr, big);
	    if ((size_t) big.used <= (CHAR_BIT * sizeof(Tcl_WideInt)
		     + MP_DIGIT_BIT - 1) / MP_DIGIT_BIT) {
		Tcl_WideUInt value = 0;
		unsigned long numBytes = sizeof(Tcl_WideInt);
		Tcl_WideInt scratch;
		unsigned char *bytes = (unsigned char *) &scratch;

		if (mp_to_unsigned_bin_n(&big, bytes, &numBytes) == MP_OKAY) {
		    while (numBytes-- > 0) {

    Tcl_Obj *objPtr,		/* Object to set */
    mp_int *bignumValue)	/* Value to store */
{
    if (Tcl_IsShared(objPtr)) {
	Tcl_Panic("%s called with shared object", "Tcl_SetBignumObj");
    }
    if ((size_t) bignumValue->used
	    <= (CHAR_BIT * sizeof(long) + MP_DIGIT_BIT - 1) / MP_DIGIT_BIT) {
	unsigned long value = 0, numBytes = sizeof(long);
	long scratch;
	unsigned char *bytes = (unsigned char *) &scratch;

	if (mp_to_unsigned_bin_n(bignumValue, bytes, &numBytes) != MP_OKAY) {
	    goto tooLargeForLong;
	}

	}
	mp_clear(bignumValue);
	return;
    }
  tooLargeForLong:
#ifndef TCL_WIDE_INT_IS_LONG
    if ((size_t) bignumValue->used
	    <= (CHAR_BIT * sizeof(Tcl_WideInt) + MP_DIGIT_BIT - 1) / MP_DIGIT_BIT) {
	Tcl_WideUInt value = 0;
	unsigned long numBytes = sizeof(Tcl_WideInt);
	Tcl_WideInt scratch;
	unsigned char *bytes = (unsigned char *)&scratch;

	if (mp_to_unsigned_bin_n(bignumValue, bytes, &numBytes) != MP_OKAY) {
	    goto tooLargeForWide;

     * significand (the most significant) corresponds to the
     * 2**(binExponent+M2 + 1) bit of 2*M2*v. Allocate enough digits to hold
     * that quantity, then convert the significand to a large integer, scaled
     * appropriately. Then multiply by the appropriate power of 5.
     */

    msb = binExponent + M2;	/* 1008 */
    nDigits = msb / MP_DIGIT_BIT + 1;
    mp_init_size(&twoMv, nDigits);
    i = (msb % MP_DIGIT_BIT + 1);
    twoMv.used = nDigits;
    significand *= SafeLdExp(1.0, i);
    while (--nDigits >= 0) {
	twoMv.dp[nDigits] = (mp_digit) significand;
	significand -= (mp_digit) significand;
	significand = SafeLdExp(significand, MP_DIGIT_BIT);
    }
    for (i = 0; i <= 8; ++i) {
	if (M5 & (1 << i)) {
	    mp_mul(&twoMv, pow5+i, &twoMv);
	}
    }

static inline int
ShouldBankerRoundUpPowD(
    mp_int *b,			/* Numerator of the fraction. */
    int sd,			/* Denominator is 2**(sd*DIGIT_BIT). */
    int isodd)			/* 1 if the digit is odd, 0 if even. */
{
    int i;
    static const mp_digit topbit = ((mp_digit)1) << (MP_DIGIT_BIT - 1);

    if (b->used < sd || (b->dp[sd-1] & topbit) == 0) {
	return 0;
    }
    if (b->dp[sd-1] != topbit) {
	return 1;
    }

	     * The denominator is a power of 2, so we can replace division by
	     * digit shifts. First we round up s2 to a multiple of DIGIT_BIT,
	     * and adjust m2 and b2 accordingly. Then we launch into a version
	     * of the comparison that's specialized for the 'power of mp_digit
	     * in the denominator' case.
	     */

	    if (s2 % MP_DIGIT_BIT != 0) {
		int delta = MP_DIGIT_BIT - (s2 % MP_DIGIT_BIT);

		b2 += delta;
		m2plus += delta;
		m2minus += delta;
		s2 += delta;
	    }
	    return ShorteningBignumConversionPowD(&d, convType, bw, b2, b5,
		    m2plus, m2minus, m5, s2/MP_DIGIT_BIT, k, len, ilim, ilim1,
		    decpt, endPtr);
	} else {
	    /*
	     * Alas, there's no helpful special case; use full-up bignum
	     * arithmetic for the conversion.
	     */

	     * The denominator is a power of 2, so we can replace division by
	     * digit shifts. First we round up s2 to a multiple of DIGIT_BIT,
	     * and adjust m2 and b2 accordingly. Then we launch into a version
	     * of the comparison that's specialized for the 'power of mp_digit
	     * in the denominator' case.
	     */

	    if (s2 % MP_DIGIT_BIT != 0) {
		int delta = MP_DIGIT_BIT - (s2 % MP_DIGIT_BIT);

		b2 += delta;
		s2 += delta;
	    }
	    return StrictBignumConversionPowD(&d, convType, bw, b2, b5,
		    s2/MP_DIGIT_BIT, k, len, ilim, ilim1, decpt, endPtr);
	} else {
	    /*
	     * There are no helpful special cases, but at least we know in
	     * advance how many digits we will convert. We can run the
	     * conversion in steps of DIGIT_GROUP digits, so as to have many
	     * fewer mp_int divisions.
	     */

     * the significand of a double.
     */

    maxDigits = (int) ((DBL_MAX_EXP * log((double) FLT_RADIX)
	    + 0.5 * log(10.)) / log(10.));
    minDigits = (int) floor((DBL_MIN_EXP - DBL_MANT_DIG)
	    * log((double) FLT_RADIX) / log(10.));
    log10_DIGIT_MAX = (int) floor(MP_DIGIT_BIT * log(2.) / log(10.));

    /*
     * Nokia 770's software-emulated floating point is "middle endian": the
     * bytes within a 32-bit word are little-endian (like the native
     * integers), but the two words of a 'double' are presented most
     * significant word first.
     */

    /*
     * Accumulate the result, one mp_digit at a time.
     */

    r = 0.0;
    for (i=b.used-1 ; i>=0 ; --i) {
	r = ldexp(r, MP_DIGIT_BIT) + b.dp[i];
    }
    mp_clear(&b);

    /*
     * Scale the result to the correct number of bits.
     */

	    } else {
		mp_copy(a, &b);
	    }
	    if (!exact) {
		mp_add_d(&b, 1, &b);
	    }
	    for (i=b.used-1 ; i>=0 ; --i) {
		r = ldexp(r, MP_DIGIT_BIT) + b.dp[i];
	    }
	    r = ldexp(r, bits - mantBits);
	}
    }
    mp_clear(&b);
    return r;
}

		mp_mul_2d(a, shift, &b);
	    } else if (shift < 0) {
		mp_div_2d(a, -shift, &b, NULL);
	    } else {
		mp_copy(a, &b);
	    }
	    for (i=b.used-1 ; i>=0 ; --i) {
		r = ldexp(r, MP_DIGIT_BIT) + b.dp[i];
	    }
	    r = ldexp(r, bits - mantBits);
	}
    }
    mp_clear(&b);
    return r;
}

    /*
     * Accumulate the result, one mp_digit at a time.
     */

    r = 0.0;
    for (i=b.used-1; i>=0; --i) {
	r = ldexp(r, MP_DIGIT_BIT) + b.dp[i];
    }
    mp_clear(&b);

    /*
     * Return the result with the appropriate sign.
     */

		    bits = uw;
		    while (uw) {
			numDigits++;
			uw /= base;
		    }
#endif
		} else if (useBig && big.used) {
		    int leftover = (big.used * MP_DIGIT_BIT) % numBits;
		    mp_digit mask = (~(mp_digit)0) << (MP_DIGIT_BIT-leftover);

		    numDigits = 1 +
			    (((Tcl_WideInt) big.used * MP_DIGIT_BIT) / numBits);
		    while ((mask & big.dp[big.used-1]) == 0) {
			numDigits--;
			mask >>= numBits;
		    }
		    if (numDigits > INT_MAX) {
			msg = overflow;
			errCode = "OVERFLOW";

		bytes = TclGetString(pure);
		toAppend = length = (int) numDigits;
		while (numDigits--) {
		    int digitOffset;

		    if (useBig && big.used) {
			if (index < big.used && (size_t) shift <
				CHAR_BIT*sizeof(Tcl_WideUInt) - MP_DIGIT_BIT) {
			    bits |= ((Tcl_WideUInt) big.dp[index++]) << shift;
			    shift += MP_DIGIT_BIT;
			}
			shift -= numBits;
		    }
		    digitOffset = (int) (bits % base);
		    if (digitOffset > 9) {
			if (ch == 'X') {
			    bytes[numDigits] = 'A' + digitOffset - 10;

/* LibTomMath, multiple-precision integer library -- Tom St Denis */








/* SPDX-License-Identifier: Unlicense */

#ifndef BN_H_
#define BN_H_

#include "tclTomMathDecls.h"
#ifndef MODULE_SCOPE
#define MODULE_SCOPE extern
#endif

#   define DIGIT_BIT (((CHAR_BIT * MP_SIZEOF_MP_DIGIT) - 1))  /* bits per digit */
#endif

#define MP_DIGIT_BIT     DIGIT_BIT
#define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
#define MP_DIGIT_MAX     MP_MASK

typedef int mp_sign;
#define MP_ZPOS       0   /* positive integer */
#define MP_NEG        1   /* negative */
typedef int mp_ord;
#define MP_LT        -1   /* less than */
#define MP_EQ         0   /* equal to */
#define MP_GT         1   /* greater than */
typedef int mp_bool;
#define MP_YES        1   /* yes response */
#define MP_NO         0   /* no response */
typedef int mp_err;
#define MP_OKAY       0   /* ok result */
#define MP_ERR        -1  /* unknown error */
#define MP_MEM        -2  /* out of mem */
#define MP_VAL        -3  /* invalid input */
#define MP_RANGE      MP_VAL
#define MP_ITER       -4  /* Max. iterations reached */




/* Primality generation flags */
#define LTM_PRIME_BBS      0x0001 /* BBS style prime */
#define LTM_PRIME_SAFE     0x0002 /* Safe prime (p-1)/2 == prime */
#define LTM_PRIME_2MSB_ON  0x0008 /* force 2nd MSB to 1 */

/* tunable cutoffs */

/* define this to use lower memory usage routines (exptmods mostly) */
/* #define MP_LOW_MEM */

/* default precision */
#ifndef MP_PREC
#   ifndef MP_LOW_MEM
#      define MP_PREC 32        /* default digits of precision */
#   elif defined(MP_8BIT)
#      define MP_PREC 16        /* default digits of precision */
#   else
#      define MP_PREC 8         /* default digits of precision */
#   endif
#endif

/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
#define MP_WARRAY               (1u << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) + 1))

/*
 * MP_WUR - warn unused result
 * ---------------------------
 *
 * The result of functions annotated with MP_WUR must be
 * checked and cannot be ignored.
 *
 * Most functions in libtommath return an error code.
 * This error code must be checked in order to prevent crashes or invalid
 * results.
 *
 * If you still want to avoid the error checks for quick and dirty programs
 * without robustness guarantees, you can `#define MP_WUR` before including
 * tommath.h, disabling the warnings.
 */
#ifndef MP_WUR
#  if defined(__GNUC__) && __GNUC__ >= 4
#     define MP_WUR __attribute__((warn_unused_result))
#  else
#     define MP_WUR
#  endif
#endif

#if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 301)
#  define MP_DEPRECATED(x) __attribute__((deprecated("replaced by " #x)))
#  define PRIVATE_MP_DEPRECATED_PRAGMA(s) _Pragma(#s)
#  define MP_DEPRECATED_PRAGMA(s) PRIVATE_MP_DEPRECATED_PRAGMA(GCC warning s)
#elif defined(_MSC_VER) && _MSC_VER >= 1500
#  define MP_DEPRECATED(x) __declspec(deprecated("replaced by " #x))
#  define MP_DEPRECATED_PRAGMA(s) __pragma(message(s))
#else
#  define MP_DEPRECATED
#  define MP_DEPRECATED_PRAGMA(s)
#endif

#define USED(m)    ((m)->used)
#define DIGIT(m,k) ((m)->dp[(k)])
#define SIGN(m)    ((m)->sign)

/* the infamous mp_int structure */
#ifndef MP_INT_DECLARED
#define MP_INT_DECLARED
typedef struct mp_int mp_int;
#endif
struct mp_int {
   int used, alloc, sign;
   mp_digit *dp;
};

/* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);






/* error code to char* string */
const char *mp_error_to_string(int code);

/* ---> init and deinit bignum functions <--- */
/* init a bignum */
/*
int mp_init(mp_int *a);

#define XFREE(mem, size)                TclBNFree(mem)
#define XREALLOC(mem, oldsize, newsize) TclBNRealloc(mem, newsize)


/* Rename the global symbols in libtommath to avoid linkage conflicts */

#define bn_reverse TclBN_reverse
#define s_mp_reverse TclBN_reverse
#define fast_s_mp_mul_digs TclBN_fast_s_mp_mul_digs
#define s_mp_mul_digs_fast TclBN_fast_s_mp_mul_digs
#define fast_s_mp_sqr TclBN_fast_s_mp_sqr
#define s_mp_sqr_fast TclBN_fast_s_mp_sqr
#define mp_add TclBN_mp_add
#define mp_add_d TclBN_mp_add_d
#define mp_and TclBN_mp_and
#define mp_clamp TclBN_mp_clamp
#define mp_clear TclBN_mp_clear
#define mp_clear_multi TclBN_mp_clear_multi
#define mp_cmp TclBN_mp_cmp

#define mp_init TclBN_mp_init
#define mp_init_copy TclBN_mp_init_copy
#define mp_init_multi TclBN_mp_init_multi
#define mp_init_set TclBN_mp_init_set
#define mp_init_set_int TclBN_mp_init_set_int
#define mp_init_size TclBN_mp_init_size
#define mp_karatsuba_mul TclBN_mp_karatsuba_mul
#define s_mp_karatsuba_mul TclBN_mp_karatsuba_mul
#define mp_karatsuba_sqr TclBN_mp_karatsuba_sqr
#define s_mp_karatsuba_sqr TclBN_mp_karatsuba_sqr
#define mp_lshd TclBN_mp_lshd
#define mp_mod TclBN_mp_mod
#define mp_mod_2d TclBN_mp_mod_2d
#define mp_mul TclBN_mp_mul
#define mp_mul_2 TclBN_mp_mul_2
#define mp_mul_2d TclBN_mp_mul_2d
#define mp_mul_d TclBN_mp_mul_d

#define mp_tc_and TclBN_mp_tc_and
#define mp_tc_div_2d TclBN_mp_tc_div_2d
#define mp_tc_or TclBN_mp_tc_or
#define mp_tc_xor TclBN_mp_tc_xor
#define mp_to_unsigned_bin TclBN_mp_to_unsigned_bin
#define mp_to_unsigned_bin_n TclBN_mp_to_unsigned_bin_n
#define mp_toom_mul TclBN_mp_toom_mul
#define s_mp_toom_mul TclBN_mp_toom_mul
#define mp_toom_sqr TclBN_mp_toom_sqr
#define s_mp_toom_sqr TclBN_mp_toom_sqr
#define mp_toradix_n TclBN_mp_toradix_n
#define mp_unsigned_bin_size TclBN_mp_unsigned_bin_size
#define mp_xor TclBN_mp_xor
#define mp_zero TclBN_mp_zero
#define s_mp_add TclBN_s_mp_add
#define s_mp_mul_digs TclBN_s_mp_mul_digs
#define s_mp_sqr TclBN_s_mp_sqr

    /*
     * Store the magnitude in the bignum.
     */

    p = a->dp;
    while (v) {
	*p++ = (mp_digit) (v & MP_MASK);
	v >>= MP_DIGIT_BIT;
    }
    a->used = p - a->dp;
}

/*
 *----------------------------------------------------------------------
 *

    /*
     * Store the magnitude in the bignum.
     */

    p = a->dp;
    while (v) {
	*p++ = (mp_digit) (v & MP_MASK);
	v >>= MP_DIGIT_BIT;
    }
    a->used = p - a->dp;
}

/*
 * Local Variables:
 * mode: c
 * c-basic-offset: 4
 * fill-column: 78
 * End:
 */