QOF 0.8.4
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Data Structures | |
struct | _QofNumeric |
Modules | |
Math128 | |
Files | |
file | qofnumeric.h |
An exact-rational-number library for QOF. | |
Typedefs | |
typedef struct _QofNumeric | QofNumeric |
A rational-number type. | |
Standard Arguments to most functions | |
Most of the QofNumeric arithmetic functions take two arguments in addition to their numeric args: 'denom', which is the denominator to use in the output QofNumeric object, and 'how'. which describes how the arithmetic result is to be converted to that denominator. This combination of output denominator and rounding policy allows the results of financial and other rational computations to be properly rounded to the appropriate units. Valid values for denom are: QOF_DENOM_AUTO -- compute denominator exactly integer n -- Force the denominator of the result to be this integer QOF_DENOM_RECIPROCAL -- Use 1/n as the denominator (???huh???) Valid values for 'how' are bitwise combinations of zero or one "rounding instructions" with zero or one "denominator types". Valid rounding instructions are: QOF_HOW_RND_FLOOR QOF_HOW_RND_CEIL QOF_HOW_RND_TRUNC QOF_HOW_RND_PROMOTE QOF_HOW_RND_ROUND_HALF_DOWN QOF_HOW_RND_ROUND_HALF_UP QOF_HOW_RND_ROUND QOF_HOW_RND_NEVER The denominator type specifies how to compute a denominator if QOF_DENOM_AUTO is specified as the 'denom'. Valid denominator types are: QOF_HOW_DENOM_EXACT QOF_HOW_DENOM_REDUCE QOF_HOW_DENOM_LCD QOF_HOW_DENOM_FIXED QOF_HOW_DENOM_SIGFIGS(N) To use traditional rational-number operational semantics (all results are exact and are reduced to relatively-prime fractions) pass the argument QOF_DENOM_AUTO as 'denom' and QOF_HOW_DENOM_REDUCE| QOF_HOW_RND_NEVER as 'how'. To enforce strict financial semantics (such that all operands must have the same denominator as each other and as the result), use QOF_DENOM_AUTO as 'denom' and QOF_HOW_DENOM_FIXED | QOF_HOW_RND_NEVER as 'how'. | |
enum | { QOF_HOW_RND_FLOOR = 0x01, QOF_HOW_RND_CEIL = 0x02, QOF_HOW_RND_TRUNC = 0x03, QOF_HOW_RND_PROMOTE = 0x04, QOF_HOW_RND_ROUND_HALF_DOWN = 0x05, QOF_HOW_RND_ROUND_HALF_UP = 0x06, QOF_HOW_RND_ROUND = 0x07, QOF_HOW_RND_NEVER = 0x08 } |
Rounding/Truncation modes for operations. More... | |
enum | { QOF_HOW_DENOM_EXACT = 0x10, QOF_HOW_DENOM_REDUCE = 0x20, QOF_HOW_DENOM_LCD = 0x30, QOF_HOW_DENOM_FIXED = 0x40, QOF_HOW_DENOM_SIGFIG = 0x50 } |
enum | QofNumericErrorCode { QOF_ERROR_OK = 0, QOF_ERROR_ARG = -1, QOF_ERROR_OVERFLOW = -2, QOF_ERROR_DENOM_DIFF = -3, QOF_ERROR_REMAINDER = -4 } |
#define | QOF_NUMERIC_RND_MASK 0x0000000f |
bitmasks for HOW flags. | |
#define | QOF_NUMERIC_DENOM_MASK 0x000000f0 |
#define | QOF_NUMERIC_SIGFIGS_MASK 0x0000ff00 |
#define | QOF_HOW_DENOM_SIGFIGS(n) ( ((( n ) & 0xff) << 8) | QOF_HOW_DENOM_SIGFIG) |
#define | QOF_HOW_GET_SIGFIGS(a) ( (( a ) & 0xff00 ) >> 8) |
#define | QOF_DENOM_AUTO 0 |
#define | QOF_DENOM_RECIPROCAL(a) (- ( a )) |
Constructors | |
static QofNumeric | qof_numeric_create (gint64 num, gint64 denom) |
static QofNumeric | qof_numeric_zero (void) |
QofNumeric | qof_numeric_from_double (gdouble in, gint64 denom, gint how) |
gboolean | qof_numeric_from_string (const gchar *str, QofNumeric *n) |
QofNumeric | qof_numeric_error (QofNumericErrorCode error_code) |
Value Accessors | |
static gint64 | qof_numeric_num (QofNumeric a) |
static gint64 | qof_numeric_denom (QofNumeric a) |
gdouble | qof_numeric_to_double (QofNumeric in) |
gchar * | qof_numeric_to_string (QofNumeric n) |
gchar * | qof_numeric_dbg_to_string (QofNumeric n) |
Comparisons and Predicates | |
QofNumericErrorCode | qof_numeric_check (QofNumeric a) |
gint | qof_numeric_compare (QofNumeric a, QofNumeric b) |
gboolean | qof_numeric_zero_p (QofNumeric a) |
gboolean | qof_numeric_negative_p (QofNumeric a) |
gboolean | qof_numeric_positive_p (QofNumeric a) |
gboolean | qof_numeric_eq (QofNumeric a, QofNumeric b) |
gboolean | qof_numeric_equal (QofNumeric a, QofNumeric b) |
gint | qof_numeric_same (QofNumeric a, QofNumeric b, gint64 denom, gint how) |
Arithmetic Operations | |
QofNumeric | qof_numeric_add (QofNumeric a, QofNumeric b, gint64 denom, gint how) |
QofNumeric | qof_numeric_sub (QofNumeric a, QofNumeric b, gint64 denom, gint how) |
QofNumeric | qof_numeric_mul (QofNumeric a, QofNumeric b, gint64 denom, gint how) |
QofNumeric | qof_numeric_div (QofNumeric x, QofNumeric y, gint64 denom, gint how) |
QofNumeric | qof_numeric_neg (QofNumeric a) |
QofNumeric | qof_numeric_abs (QofNumeric a) |
static QofNumeric | qof_numeric_add_fixed (QofNumeric a, QofNumeric b) |
static QofNumeric | qof_numeric_sub_fixed (QofNumeric a, QofNumeric b) |
Arithmetic Functions with Exact Error Returns | |
QofNumeric | qof_numeric_add_with_error (QofNumeric a, QofNumeric b, gint64 denom, gint how, QofNumeric *error) |
QofNumeric | qof_numeric_sub_with_error (QofNumeric a, QofNumeric b, gint64 denom, gint how, QofNumeric *error) |
QofNumeric | qof_numeric_mul_with_error (QofNumeric a, QofNumeric b, gint64 denom, gint how, QofNumeric *error) |
QofNumeric | qof_numeric_div_with_error (QofNumeric a, QofNumeric b, gint64 denom, gint how, QofNumeric *error) |
Change Denominator | |
QofNumeric | qof_numeric_convert (QofNumeric in, gint64 denom, gint how) |
QofNumeric | qof_numeric_convert_with_error (QofNumeric in, gint64 denom, gint how, QofNumeric *error) |
QofNumeric | qof_numeric_reduce (QofNumeric in) |
Deprecated, backwards-compatible definitions | |
#define | QOF_RND_FLOOR QOF_HOW_RND_FLOOR |
#define | QOF_RND_CEIL QOF_HOW_RND_CEIL |
#define | QOF_RND_TRUNC QOF_HOW_RND_TRUNC |
#define | QOF_RND_PROMOTE QOF_HOW_RND_PROMOTE |
#define | QOF_RND_ROUND_HALF_DOWN QOF_HOW_RND_ROUND_HALF_DOWN |
#define | QOF_RND_ROUND_HALF_UP QOF_HOW_RND_ROUND_HALF_UP |
#define | QOF_RND_ROUND QOF_HOW_RND_ROUND |
#define | QOF_RND_NEVER QOF_HOW_RND_NEVER |
#define | QOF_DENOM_EXACT QOF_HOW_DENOM_EXACT |
#define | QOF_DENOM_REDUCE QOF_HOW_DENOM_REDUCE |
#define | QOF_DENOM_LCD QOF_HOW_DENOM_LCD |
#define | QOF_DENOM_FIXED QOF_HOW_DENOM_FIXED |
#define | QOF_DENOM_SIGFIG QOF_HOW_DENOM_SIGFIG |
#define | QOF_DENOM_SIGFIGS(X) QOF_HOW_DENOM_SIGFIGS(X) |
#define | QOF_NUMERIC_GET_SIGFIGS(X) QOF_HOW_GET_SIGFIGS(X) |
The 'Numeric' functions provide a way of working with rational numbers while maintaining strict control over rounding errors when adding rationals with different denominators. The Numeric class is primarily used for working with monetary amounts, where the denominator typically represents the smallest fraction of the currency (e.g. pennies, centimes). The numeric class can handle any fraction (e.g. twelfth's) and is not limited to fractions that are powers of ten.
A 'Numeric' value represents a number in rational form, with a 64-bit integer as numerator and denominator. Rationals are ideal for many uses, such as performing exact, roundoff-error-free addition and multiplication, but 64-bit rationals do not have the dynamic range of floating point numbers.
#define QOF_DENOM_AUTO 0 |
Values that can be passed as the 'denom' argument. The include a positive number n to be used as the denominator of the output value. Other possibilities include the list below: Compute an appropriate denominator automatically. Flags in the 'how' argument will specify how to compute the denominator.
Definition at line 231 of file qofnumeric.h.
#define QOF_DENOM_RECIPROCAL | ( | a | ) | (- ( a )) |
Use the value 1/n as the denominator of the output value.
Definition at line 234 of file qofnumeric.h.
#define QOF_HOW_DENOM_SIGFIGS | ( | n | ) | ( ((( n ) & 0xff) << 8) | QOF_HOW_DENOM_SIGFIG) |
Build a 'how' value that will generate a denominator that will keep at least n significant figures in the result.
Definition at line 203 of file qofnumeric.h.
#define QOF_NUMERIC_RND_MASK 0x0000000f |
bitmasks for HOW flags.
bits 8-15 of 'how' are reserved for the number of significant digits to use in the output with QOF_HOW_DENOM_SIGFIG
Definition at line 116 of file qofnumeric.h.
typedef struct _QofNumeric QofNumeric |
A rational-number type.
This is a rational number, defined by numerator and denominator.
Definition at line 61 of file qofnumeric.h.
anonymous enum |
Rounding/Truncation modes for operations.
Rounding instructions control how fractional parts in the specified denominator affect the result. For example, if a computed result is "3/4" but the specified denominator for the return value is 2, should the return value be "1/2" or "2/2"?
Possible rounding instructions are:
Definition at line 129 of file qofnumeric.h.
{ QOF_HOW_RND_FLOOR = 0x01, QOF_HOW_RND_CEIL = 0x02, QOF_HOW_RND_TRUNC = 0x03, QOF_HOW_RND_PROMOTE = 0x04, QOF_HOW_RND_ROUND_HALF_DOWN = 0x05, QOF_HOW_RND_ROUND_HALF_UP = 0x06, QOF_HOW_RND_ROUND = 0x07, QOF_HOW_RND_NEVER = 0x08 };
anonymous enum |
How to compute a denominator, or'ed into the "how" field.
Definition at line 167 of file qofnumeric.h.
{ QOF_HOW_DENOM_EXACT = 0x10, QOF_HOW_DENOM_REDUCE = 0x20, QOF_HOW_DENOM_LCD = 0x30, QOF_HOW_DENOM_FIXED = 0x40, QOF_HOW_DENOM_SIGFIG = 0x50 };
enum QofNumericErrorCode |
Error codes
Definition at line 207 of file qofnumeric.h.
{ QOF_ERROR_OK = 0, QOF_ERROR_ARG = -1, QOF_ERROR_OVERFLOW = -2, QOF_ERROR_DENOM_DIFF = -3, QOF_ERROR_REMAINDER = -4 } QofNumericErrorCode;
QofNumeric qof_numeric_abs | ( | QofNumeric | a | ) |
Return the absolute value of the argument
Definition at line 645 of file qofnumeric.c.
{ if (qof_numeric_check (a)) return qof_numeric_error (QOF_ERROR_ARG); return qof_numeric_create (ABS (a.num), a.denom); }
QofNumeric qof_numeric_add | ( | QofNumeric | a, |
QofNumeric | b, | ||
gint64 | denom, | ||
gint | how | ||
) |
Return a+b.
Definition at line 295 of file qofnumeric.c.
{ QofNumeric sum; if (qof_numeric_check (a) || qof_numeric_check (b)) return qof_numeric_error (QOF_ERROR_ARG); if ((denom == QOF_DENOM_AUTO) && (how & QOF_NUMERIC_DENOM_MASK) == QOF_HOW_DENOM_FIXED) { if (a.denom == b.denom) denom = a.denom; else if (b.num == 0) { denom = a.denom; b.denom = a.denom; } else if (a.num == 0) { denom = b.denom; a.denom = b.denom; } else return qof_numeric_error (QOF_ERROR_DENOM_DIFF); } if (a.denom < 0) { a.num *= -a.denom; /* BUG: overflow not handled. */ a.denom = 1; } if (b.denom < 0) { b.num *= -b.denom; /* BUG: overflow not handled. */ b.denom = 1; } /* Get an exact answer.. same denominator is the common case. */ if (a.denom == b.denom) { sum.num = a.num + b.num; /* BUG: overflow not handled. */ sum.denom = a.denom; } else { /* We want to do this: * sum.num = a.num*b.denom + b.num*a.denom; * sum.denom = a.denom*b.denom; * but the multiply could overflow. * Computing the LCD minimizes likelihood of overflow */ gint64 lcd; QofInt128 ca, cb, cab; lcd = qof_numeric_lcd (a, b); if (QOF_ERROR_ARG == lcd) return qof_numeric_error (QOF_ERROR_OVERFLOW); ca = mult128 (a.num, lcd / a.denom); if (ca.isbig) return qof_numeric_error (QOF_ERROR_OVERFLOW); cb = mult128 (b.num, lcd / b.denom); if (cb.isbig) return qof_numeric_error (QOF_ERROR_OVERFLOW); cab = add128 (ca, cb); if (cab.isbig) return qof_numeric_error (QOF_ERROR_OVERFLOW); sum.num = cab.lo; if (cab.isneg) sum.num = -sum.num; sum.denom = lcd; } if ((denom == QOF_DENOM_AUTO) && ((how & QOF_NUMERIC_DENOM_MASK) == QOF_HOW_DENOM_LCD)) { denom = qof_numeric_lcd (a, b); how = how & QOF_NUMERIC_RND_MASK; } return qof_numeric_convert (sum, denom, how); }
static QofNumeric qof_numeric_add_fixed | ( | QofNumeric | a, |
QofNumeric | b | ||
) | [inline, static] |
Shortcut for common case: QofNumeric_add(a, b, QOF_DENOM_AUTO, QOF_HOW_DENOM_FIXED | QOF_HOW_RND_NEVER);
Definition at line 411 of file qofnumeric.h.
{ return qof_numeric_add (a, b, QOF_DENOM_AUTO, QOF_HOW_DENOM_FIXED | QOF_HOW_RND_NEVER); }
QofNumeric qof_numeric_add_with_error | ( | QofNumeric | a, |
QofNumeric | b, | ||
gint64 | denom, | ||
gint | how, | ||
QofNumeric * | error | ||
) |
The same as QofNumeric_add, but uses 'error' for accumulating conversion roundoff error.
Definition at line 1009 of file qofnumeric.c.
{ QofNumeric sum = qof_numeric_add (a, b, denom, how); QofNumeric exact = qof_numeric_add (a, b, QOF_DENOM_AUTO, QOF_HOW_DENOM_REDUCE); QofNumeric err = qof_numeric_sub (sum, exact, QOF_DENOM_AUTO, QOF_HOW_DENOM_REDUCE); if (error) *error = err; return sum; }
QofNumericErrorCode qof_numeric_check | ( | QofNumeric | a | ) |
Check for error signal in value. Returns QOF_ERROR_OK (==0) if the number appears to be valid, otherwise it returns the type of error. Error values always have a denominator of zero.
Definition at line 39 of file qofnumeric.c.
{ if (in.denom != 0) return QOF_ERROR_OK; else if (in.num) { if ((0 < in.num) || (-4 > in.num)) in.num = (gint64) QOF_ERROR_OVERFLOW; return (QofNumericErrorCode) in.num; } else return QOF_ERROR_ARG; }
gint qof_numeric_compare | ( | QofNumeric | a, |
QofNumeric | b | ||
) |
Returns 1 if a>b, -1 if b>a, 0 if a == b
Definition at line 169 of file qofnumeric.c.
{ gint64 aa, bb; QofInt128 l, r; if (qof_numeric_check (a) || qof_numeric_check (b)) return 0; if (a.denom == b.denom) { if (a.num == b.num) return 0; if (a.num > b.num) return 1; return -1; } if ((a.denom > 0) && (b.denom > 0)) { /* Avoid overflows using 128-bit intermediate math */ l = mult128 (a.num, b.denom); r = mult128 (b.num, a.denom); return cmp128 (l, r); } if (a.denom < 0) a.denom *= -1; if (b.denom < 0) b.denom *= -1; /* BUG: Possible overflow here.. Also, doesn't properly deal with * reciprocal denominators. */ aa = a.num * a.denom; bb = b.num * b.denom; if (aa == bb) return 0; if (aa > bb) return 1; return -1; }
QofNumeric qof_numeric_convert | ( | QofNumeric | in, |
gint64 | denom, | ||
gint | how | ||
) |
Change the denominator of a QofNumeric value to the specified denominator under standard arguments 'denom' and 'how'.
Definition at line 657 of file qofnumeric.c.
{ QofNumeric out; QofNumeric temp; gint64 temp_bc; gint64 temp_a; gint64 remainder; gint64 sign; gint denom_neg = 0; gdouble ratio, logratio; gdouble sigfigs; QofInt128 nume, newm; temp.num = 0; temp.denom = 0; if (qof_numeric_check (in)) return qof_numeric_error (QOF_ERROR_ARG); if (denom == QOF_DENOM_AUTO) { switch (how & QOF_NUMERIC_DENOM_MASK) { default: case QOF_HOW_DENOM_LCD: /* LCD is meaningless with AUTO in here */ case QOF_HOW_DENOM_EXACT: return in; break; case QOF_HOW_DENOM_REDUCE: /* reduce the input to a relatively-prime fraction */ return qof_numeric_reduce (in); break; case QOF_HOW_DENOM_FIXED: if (in.denom != denom) return qof_numeric_error (QOF_ERROR_DENOM_DIFF); else return in; break; case QOF_HOW_DENOM_SIGFIG: ratio = fabs (qof_numeric_to_double (in)); if (ratio < 10e-20) logratio = 0; else { logratio = log10 (ratio); logratio = ((logratio > 0.0) ? (floor (logratio) + 1.0) : (ceil (logratio))); } sigfigs = QOF_HOW_GET_SIGFIGS (how); if (sigfigs - logratio >= 0) denom = (gint64) (pow (10, sigfigs - logratio)); else denom = -((gint64) (pow (10, logratio - sigfigs))); how = how & ~QOF_HOW_DENOM_SIGFIG & ~QOF_NUMERIC_SIGFIGS_MASK; break; } } /* Make sure we need to do the work */ if (in.denom == denom) return in; if (in.num == 0) { out.num = 0; out.denom = denom; return out; } /* If the denominator of the input value is negative, get rid of that. */ if (in.denom < 0) { in.num = in.num * (-in.denom); /* BUG: overflow not handled. */ in.denom = 1; } sign = (in.num < 0) ? -1 : 1; /* If the denominator is less than zero, we are to interpret it as * the reciprocal of its magnitude. */ if (denom < 0) { /* XXX FIXME: use 128-bit math here ... */ denom = -denom; denom_neg = 1; temp_a = (in.num < 0) ? -in.num : in.num; temp_bc = in.denom * denom; /* BUG: overflow not handled. */ remainder = temp_a % temp_bc; out.num = temp_a / temp_bc; out.denom = -denom; } else { /* Do all the modulo and int division on positive values to make * things a little clearer. Reduce the fraction denom/in.denom to * help with range errors */ temp.num = denom; temp.denom = in.denom; temp = qof_numeric_reduce (temp); /* Symbolically, do the following: * out.num = in.num * temp.num; * remainder = out.num % temp.denom; * out.num = out.num / temp.denom; * out.denom = denom; */ nume = mult128 (in.num, temp.num); newm = div128 (nume, temp.denom); remainder = rem128 (nume, temp.denom); if (newm.isbig) return qof_numeric_error (QOF_ERROR_OVERFLOW); out.num = newm.lo; out.denom = denom; } if (remainder) { switch (how & QOF_NUMERIC_RND_MASK) { case QOF_HOW_RND_FLOOR: if (sign < 0) out.num = out.num + 1; break; case QOF_HOW_RND_CEIL: if (sign > 0) out.num = out.num + 1; break; case QOF_HOW_RND_TRUNC: break; case QOF_HOW_RND_PROMOTE: out.num = out.num + 1; break; case QOF_HOW_RND_ROUND_HALF_DOWN: if (denom_neg) { if ((2 * remainder) > in.denom * denom) out.num = out.num + 1; } else if ((2 * remainder) > temp.denom) out.num = out.num + 1; /* check that 2*remainder didn't over-flow */ else if (((2 * remainder) < remainder) && (remainder > (temp.denom / 2))) out.num = out.num + 1; break; case QOF_HOW_RND_ROUND_HALF_UP: if (denom_neg) { if ((2 * remainder) >= in.denom * denom) out.num = out.num + 1; } else if ((2 * remainder) >= temp.denom) out.num = out.num + 1; /* check that 2*remainder didn't over-flow */ else if (((2 * remainder) < remainder) && (remainder >= (temp.denom / 2))) out.num = out.num + 1; break; case QOF_HOW_RND_ROUND: if (denom_neg) { if ((2 * remainder) > in.denom * denom) out.num = out.num + 1; else if ((2 * remainder) == in.denom * denom) { if (out.num % 2) out.num = out.num + 1; } } else { if ((2 * remainder) > temp.denom) out.num = out.num + 1; /* check that 2*remainder didn't over-flow */ else if (((2 * remainder) < remainder) && (remainder > (temp.denom / 2))) { out.num = out.num + 1; } else if ((2 * remainder) == temp.denom) { if (out.num % 2) out.num = out.num + 1; } /* check that 2*remainder didn't over-flow */ else if (((2 * remainder) < remainder) && (remainder == (temp.denom / 2))) { if (out.num % 2) out.num = out.num + 1; } } break; case QOF_HOW_RND_NEVER: return qof_numeric_error (QOF_ERROR_REMAINDER); break; } } out.num = (sign > 0) ? out.num : (-out.num); return out; }
QofNumeric qof_numeric_convert_with_error | ( | QofNumeric | in, |
gint64 | denom, | ||
gint | how, | ||
QofNumeric * | error | ||
) |
Same as QofNumeric_convert, but return a remainder value for accumulating conversion error.
static QofNumeric qof_numeric_create | ( | gint64 | num, |
gint64 | denom | ||
) | [inline, static] |
Make a QofNumeric from numerator and denominator
Definition at line 243 of file qofnumeric.h.
{ QofNumeric out; out.num = num; out.denom = denom; return out; }
gchar* qof_numeric_dbg_to_string | ( | QofNumeric | n | ) |
Convert to string. Uses a static, non-thread-safe buffer. For internal use only.
Definition at line 1098 of file qofnumeric.c.
{ static gchar buff[1000]; static gchar *p = buff; gint64 tmpnum = n.num; gint64 tmpdenom = n.denom; p += 100; if (p - buff >= 1000) p = buff; sprintf (p, "%" G_GINT64_FORMAT "/%" G_GINT64_FORMAT, tmpnum, tmpdenom); return p; }
static gint64 qof_numeric_denom | ( | QofNumeric | a | ) | [inline, static] |
QofNumeric qof_numeric_div | ( | QofNumeric | x, |
QofNumeric | y, | ||
gint64 | denom, | ||
gint | how | ||
) |
Division. Note that division can overflow, in the following sense: if we write x=a/b and y=c/d then x/y = (a*d)/(b*c) If, after eliminating all common factors between the numerator (a*d) and the denominator (b*c), then if either the numerator and/or the denominator are *still* greater than 2^63, then the division has overflowed.
Definition at line 511 of file qofnumeric.c.
{ QofNumeric quotient; QofInt128 nume, deno; if (qof_numeric_check (a) || qof_numeric_check (b)) return qof_numeric_error (QOF_ERROR_ARG); if ((denom == QOF_DENOM_AUTO) && (how & QOF_NUMERIC_DENOM_MASK) == QOF_HOW_DENOM_FIXED) { if (a.denom == b.denom) denom = a.denom; else if (a.denom == 0) denom = b.denom; else return qof_numeric_error (QOF_ERROR_DENOM_DIFF); } if (a.denom < 0) { a.num *= -a.denom; /* BUG: overflow not handled. */ a.denom = 1; } if (b.denom < 0) { b.num *= -b.denom; /* BUG: overflow not handled. */ b.denom = 1; } if (a.denom == b.denom) { quotient.num = a.num; quotient.denom = b.num; } else { gint64 sgn = 1; if (0 > a.num) { sgn = -sgn; a.num = -a.num; } if (0 > b.num) { sgn = -sgn; b.num = -b.num; } nume = mult128 (a.num, b.denom); deno = mult128 (b.num, a.denom); /* Try to avoid overflow by removing common factors */ if (nume.isbig && deno.isbig) { QofNumeric ra = qof_numeric_reduce (a); QofNumeric rb = qof_numeric_reduce (b); gint64 gcf_nume = gcf64 (ra.num, rb.num); gint64 gcf_deno = gcf64 (rb.denom, ra.denom); nume = mult128 (ra.num / gcf_nume, rb.denom / gcf_deno); deno = mult128 (rb.num / gcf_nume, ra.denom / gcf_deno); } if ((0 == nume.isbig) && (0 == deno.isbig)) { quotient.num = sgn * nume.lo; quotient.denom = deno.lo; goto dive_done; } else if (0 == deno.isbig) { quotient = reduce128 (nume, deno.lo); if (0 == qof_numeric_check (quotient)) { quotient.num *= sgn; goto dive_done; } } /* If rounding allowed, then shift until there's no * more overflow. The conversion at the end will fix * things up for the final value. */ if ((how & QOF_NUMERIC_RND_MASK) == QOF_HOW_RND_NEVER) return qof_numeric_error (QOF_ERROR_OVERFLOW); while (nume.isbig || deno.isbig) { nume = shift128 (nume); deno = shift128 (deno); } quotient.num = sgn * nume.lo; quotient.denom = deno.lo; if (0 == quotient.denom) { return qof_numeric_error (QOF_ERROR_OVERFLOW); } } if (quotient.denom < 0) { quotient.num = -quotient.num; quotient.denom = -quotient.denom; } dive_done: if ((denom == QOF_DENOM_AUTO) && ((how & QOF_NUMERIC_DENOM_MASK) == QOF_HOW_DENOM_LCD)) { denom = qof_numeric_lcd (a, b); how = how & QOF_NUMERIC_RND_MASK; } return qof_numeric_convert (quotient, denom, how); }
QofNumeric qof_numeric_div_with_error | ( | QofNumeric | a, |
QofNumeric | b, | ||
gint64 | denom, | ||
gint | how, | ||
QofNumeric * | error | ||
) |
The same as QofNumeric_div, but uses error for accumulating conversion roundoff error.
Definition at line 1066 of file qofnumeric.c.
{ QofNumeric quot = qof_numeric_div (a, b, denom, how); QofNumeric exact = qof_numeric_div (a, b, QOF_DENOM_AUTO, QOF_HOW_DENOM_REDUCE); QofNumeric err = qof_numeric_sub (quot, exact, QOF_DENOM_AUTO, QOF_HOW_DENOM_REDUCE); if (error) *error = err; return quot; }
gboolean qof_numeric_eq | ( | QofNumeric | a, |
QofNumeric | b | ||
) |
Equivalence predicate: Returns TRUE (1) if a and b are exactly the same (have the same numerator and denominator)
Definition at line 218 of file qofnumeric.c.
{
return ((a.num == b.num) && (a.denom == b.denom));
}
gboolean qof_numeric_equal | ( | QofNumeric | a, |
QofNumeric | b | ||
) |
Equivalence predicate: Returns TRUE (1) if a and b represent the same number. That is, return TRUE if the ratios, when reduced by eliminating common factors, are identical.
Definition at line 228 of file qofnumeric.c.
{ QofInt128 l, r; if ((a.denom == b.denom) && (a.denom > 0)) return (a.num == b.num); if ((a.denom > 0) && (b.denom > 0)) { // return (a.num*b.denom == b.num*a.denom); l = mult128 (a.num, b.denom); r = mult128 (b.num, a.denom); return equal128 (l, r); #if ALT_WAY_OF_CHECKING_EQUALITY QofNumeric ra = QofNumeric_reduce (a); QofNumeric rb = QofNumeric_reduce (b); if (ra.denom != rb.denom) return 0; if (ra.num != rb.num) return 0; return 1; #endif } if ((a.denom < 0) && (b.denom < 0)) { l = mult128 (a.num, -a.denom); r = mult128 (b.num, -b.denom); return equal128 (l, r); } else { /* BUG: One of the numbers has a reciprocal denom, and the other does not. I just don't know to handle this case in any reasonably overflow-proof yet simple way. So, this funtion will simply get it wrong whenever the three multiplies overflow 64-bits. -CAS */ if (a.denom < 0) return ((a.num * -a.denom * b.denom) == b.num); else return (a.num == (b.num * a.denom * -b.denom)); } return ((a.num * b.denom) == (a.denom * b.num)); }
QofNumeric qof_numeric_error | ( | QofNumericErrorCode | error_code | ) |
Create a QofNumeric object that signals the error condition noted by error_code, rather than a number.
Definition at line 999 of file qofnumeric.c.
{ return qof_numeric_create (error_code, 0LL); }
QofNumeric qof_numeric_from_double | ( | gdouble | in, |
gint64 | denom, | ||
gint | how | ||
) |
Convert a floating-point number to a QofNumeric. Both 'denom' and 'how' are used as in arithmetic, but QOF_DENOM_AUTO is not recognized; a denominator must be specified either explicitctly or through sigfigs.
Definition at line 914 of file qofnumeric.c.
{ QofNumeric out; gint64 int_part = 0; gdouble frac_part; gint64 frac_int = 0; gdouble logval; gdouble sigfigs; if ((denom == QOF_DENOM_AUTO) && (how & QOF_HOW_DENOM_SIGFIG)) { if (fabs (in) < 10e-20) logval = 0; else { logval = log10 (fabs (in)); logval = ((logval > 0.0) ? (floor (logval) + 1.0) : (ceil (logval))); } sigfigs = QOF_HOW_GET_SIGFIGS (how); if (sigfigs - logval >= 0) denom = (gint64) (pow (10, sigfigs - logval)); else denom = -((gint64) (pow (10, logval - sigfigs))); how = how & ~QOF_HOW_DENOM_SIGFIG & ~QOF_NUMERIC_SIGFIGS_MASK; } int_part = (gint64) (floor (fabs (in))); frac_part = in - (double) int_part; int_part = int_part * denom; frac_part = frac_part * (double) denom; switch (how & QOF_NUMERIC_RND_MASK) { case QOF_HOW_RND_FLOOR: frac_int = (gint64) floor (frac_part); break; case QOF_HOW_RND_CEIL: frac_int = (gint64) ceil (frac_part); break; case QOF_HOW_RND_TRUNC: frac_int = (gint64) frac_part; break; case QOF_HOW_RND_ROUND: case QOF_HOW_RND_ROUND_HALF_UP: frac_int = (gint64) rint (frac_part); break; case QOF_HOW_RND_NEVER: frac_int = (gint64) floor (frac_part); if (frac_part != (double) frac_int) { /* signal an error */ } break; } out.num = int_part + frac_int; out.denom = denom; return out; }
gboolean qof_numeric_from_string | ( | const gchar * | str, |
QofNumeric * | n | ||
) |
Read a QofNumeric from str, skipping any leading whitespace. Return TRUE on success and store the resulting value in "n". Return NULL on error.
Definition at line 1116 of file qofnumeric.c.
{ size_t G_GNUC_UNUSED num_read; gint64 tmpnum; gint64 tmpdenom; if (!str) return FALSE; tmpnum = strtoll (str, NULL, 0); str = strchr (str, '/'); if (!str) return FALSE; str++; tmpdenom = strtoll (str, NULL, 0); num_read = strspn (str, "0123456789"); n->num = tmpnum; n->denom = tmpdenom; return TRUE; }
QofNumeric qof_numeric_mul | ( | QofNumeric | a, |
QofNumeric | b, | ||
gint64 | denom, | ||
gint | how | ||
) |
Multiply a times b, returning the product. An overflow may occur if the result of the multiplication can't be represented as a ratio of 64-bit int's after removing common factors.
Definition at line 400 of file qofnumeric.c.
{ QofNumeric product, result; QofInt128 bignume, bigdeno; if (qof_numeric_check (a) || qof_numeric_check (b)) return qof_numeric_error (QOF_ERROR_ARG); if ((denom == QOF_DENOM_AUTO) && (how & QOF_NUMERIC_DENOM_MASK) == QOF_HOW_DENOM_FIXED) { if (a.denom == b.denom) denom = a.denom; else if (b.num == 0) denom = a.denom; else if (a.num == 0) denom = b.denom; else return qof_numeric_error (QOF_ERROR_DENOM_DIFF); } if ((denom == QOF_DENOM_AUTO) && ((how & QOF_NUMERIC_DENOM_MASK) == QOF_HOW_DENOM_LCD)) { denom = qof_numeric_lcd (a, b); how = how & QOF_NUMERIC_RND_MASK; } if (a.denom < 0) { a.num *= -a.denom; /* BUG: overflow not handled. */ a.denom = 1; } if (b.denom < 0) { b.num *= -b.denom; /* BUG: overflow not handled. */ b.denom = 1; } bignume = mult128 (a.num, b.num); bigdeno = mult128 (a.denom, b.denom); product.num = a.num * b.num; product.denom = a.denom * b.denom; /* If it looks to be overflowing, try to reduce the fraction ... */ if (bignume.isbig || bigdeno.isbig) { gint64 tmp; a = qof_numeric_reduce (a); b = qof_numeric_reduce (b); tmp = a.num; a.num = b.num; b.num = tmp; a = qof_numeric_reduce (a); b = qof_numeric_reduce (b); bignume = mult128 (a.num, b.num); bigdeno = mult128 (a.denom, b.denom); product.num = a.num * b.num; product.denom = a.denom * b.denom; } /* If it its still overflowing, and rounding is allowed then round */ if (bignume.isbig || bigdeno.isbig) { /* If rounding allowed, then shift until there's no * more overflow. The conversion at the end will fix * things up for the final value. Else overflow. */ if ((how & QOF_NUMERIC_RND_MASK) == QOF_HOW_RND_NEVER) { if (bigdeno.isbig) return qof_numeric_error (QOF_ERROR_OVERFLOW); product = reduce128 (bignume, product.denom); if (qof_numeric_check (product)) return qof_numeric_error (QOF_ERROR_OVERFLOW); } else { while (bignume.isbig || bigdeno.isbig) { bignume = shift128 (bignume); bigdeno = shift128 (bigdeno); } product.num = bignume.lo; if (bignume.isneg) product.num = -product.num; product.denom = bigdeno.lo; if (0 == product.denom) return qof_numeric_error (QOF_ERROR_OVERFLOW); } } #if 0 /* currently, product denom won't ever be zero */ if (product.denom < 0) { product.num = -product.num; product.denom = -product.denom; } #endif result = qof_numeric_convert (product, denom, how); return result; }
QofNumeric qof_numeric_mul_with_error | ( | QofNumeric | a, |
QofNumeric | b, | ||
gint64 | denom, | ||
gint | how, | ||
QofNumeric * | error | ||
) |
The same as QofNumeric_mul, but uses error for accumulating conversion roundoff error.
Definition at line 1047 of file qofnumeric.c.
{ QofNumeric prod = qof_numeric_mul (a, b, denom, how); QofNumeric exact = qof_numeric_mul (a, b, QOF_DENOM_AUTO, QOF_HOW_DENOM_REDUCE); QofNumeric err = qof_numeric_sub (prod, exact, QOF_DENOM_AUTO, QOF_HOW_DENOM_REDUCE); if (error) *error = err; return prod; }
QofNumeric qof_numeric_neg | ( | QofNumeric | a | ) |
Negate the argument
Definition at line 632 of file qofnumeric.c.
{ if (qof_numeric_check (a)) return qof_numeric_error (QOF_ERROR_ARG); return qof_numeric_create (-a.num, a.denom); }
gboolean qof_numeric_negative_p | ( | QofNumeric | a | ) |
Returns 1 if a < 0, otherwise returns 0.
Definition at line 132 of file qofnumeric.c.
{ if (qof_numeric_check (a)) return 0; else { if ((a.num < 0) && (a.denom != 0)) return 1; else return 0; } }
static gint64 qof_numeric_num | ( | QofNumeric | a | ) | [inline, static] |
gboolean qof_numeric_positive_p | ( | QofNumeric | a | ) |
Returns 1 if a > 0, otherwise returns 0.
Definition at line 150 of file qofnumeric.c.
{ if (qof_numeric_check (a)) return 0; else { if ((a.num > 0) && (a.denom != 0)) return 1; else return 0; } }
QofNumeric qof_numeric_reduce | ( | QofNumeric | in | ) |
Return input after reducing it by Greated Common Factor (GCF) elimination
Definition at line 883 of file qofnumeric.c.
{ gint64 t; gint64 num = (in.num < 0) ? (-in.num) : in.num; gint64 denom = in.denom; QofNumeric out; if (qof_numeric_check (in)) return qof_numeric_error (QOF_ERROR_ARG); /* The strategy is to use Euclid's algorithm */ while (denom > 0) { t = num % denom; num = denom; denom = t; } /* num now holds the GCD (Greatest Common Divisor) */ /* All calculations are done on positive num, since it's not * well defined what % does for negative values */ out.num = in.num / num; out.denom = in.denom / num; return out; }
gint qof_numeric_same | ( | QofNumeric | a, |
QofNumeric | b, | ||
gint64 | denom, | ||
gint | how | ||
) |
Equivalence predicate: Convert both a and b to denom using the specified DENOM and method HOW, and compare numerators the results using QofNumeric_equal.
For example, if a == 7/16 and b == 3/4, QofNumeric_same(a, b, 2, QOF_HOW_RND_TRUNC) == 1 because both 7/16 and 3/4 round to 1/2 under truncation. However, QofNumeric_same(a, b, 2, QOF_HOW_RND_ROUND) == 0 because 7/16 rounds to 1/2 under unbiased rounding but 3/4 rounds to 2/2.
Definition at line 280 of file qofnumeric.c.
{ QofNumeric aconv, bconv; aconv = qof_numeric_convert (a, denom, how); bconv = qof_numeric_convert (b, denom, how); return (qof_numeric_equal (aconv, bconv)); }
QofNumeric qof_numeric_sub | ( | QofNumeric | a, |
QofNumeric | b, | ||
gint64 | denom, | ||
gint | how | ||
) |
Return a-b.
Definition at line 383 of file qofnumeric.c.
{ QofNumeric nb; if (qof_numeric_check (a) || qof_numeric_check (b)) return qof_numeric_error (QOF_ERROR_ARG); nb = b; nb.num = -nb.num; return qof_numeric_add (a, nb, denom, how); }
static QofNumeric qof_numeric_sub_fixed | ( | QofNumeric | a, |
QofNumeric | b | ||
) | [inline, static] |
Shortcut for most common case: QofNumeric_sub(a, b, QOF_DENOM_AUTO, QOF_HOW_DENOM_FIXED | QOF_HOW_RND_NEVER);
Definition at line 422 of file qofnumeric.h.
{ return qof_numeric_sub (a, b, QOF_DENOM_AUTO, QOF_HOW_DENOM_FIXED | QOF_HOW_RND_NEVER); }
QofNumeric qof_numeric_sub_with_error | ( | QofNumeric | a, |
QofNumeric | b, | ||
gint64 | denom, | ||
gint | how, | ||
QofNumeric * | error | ||
) |
The same as QofNumeric_sub, but uses error for accumulating conversion roundoff error.
Definition at line 1029 of file qofnumeric.c.
{ QofNumeric diff = qof_numeric_sub (a, b, denom, how); QofNumeric exact = qof_numeric_sub (a, b, QOF_DENOM_AUTO, QOF_HOW_DENOM_REDUCE); QofNumeric err = qof_numeric_sub (diff, exact, QOF_DENOM_AUTO, QOF_HOW_DENOM_REDUCE); if (error) *error = err; return diff; }
gdouble qof_numeric_to_double | ( | QofNumeric | in | ) |
Convert numeric to floating-point value.
Definition at line 986 of file qofnumeric.c.
{ if (in.denom > 0) return (gdouble) in.num / (gdouble) in.denom; else return (gdouble) (in.num * -in.denom); }
gchar* qof_numeric_to_string | ( | QofNumeric | n | ) |
Convert to string. The returned buffer is to be g_free'd by the caller (it was allocated through g_strdup)
Definition at line 1084 of file qofnumeric.c.
{ gchar *result; gint64 tmpnum = n.num; gint64 tmpdenom = n.denom; result = g_strdup_printf ("%" G_GINT64_FORMAT "/%" G_GINT64_FORMAT, tmpnum, tmpdenom); return result; }
static QofNumeric qof_numeric_zero | ( | void | ) | [inline, static] |
create a zero-value QofNumeric
Definition at line 253 of file qofnumeric.h.
{ return qof_numeric_create (0, 1); }
gboolean qof_numeric_zero_p | ( | QofNumeric | a | ) |
Returns 1 if the given QofNumeric is 0 (zero), else returns 0.
Definition at line 114 of file qofnumeric.c.
{ if (qof_numeric_check (a)) return 0; else { if ((a.num == 0) && (a.denom != 0)) return 1; else return 0; } }