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/*-------------------------------------------------------------------------
*
* float.h
* Definitions for the built-in floating-point types
*
* Portions Copyright (c) 1996-2023, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California
*
*
* IDENTIFICATION
* src/include/utils/float.h
*
*-------------------------------------------------------------------------
*/
#ifndef FLOAT_H
#define FLOAT_H
#include <math.h>
/* X/Open (XSI) requires <math.h> to provide M_PI, but core POSIX does not */
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
/* Radians per degree, a.k.a. PI / 180 */
#define RADIANS_PER_DEGREE 0.0174532925199432957692
/* Visual C++ etc lacks NAN, and won't accept 0.0/0.0. */
#if defined(WIN32) && !defined(NAN)
static const uint32 nan[2] = {0xffffffff, 0x7fffffff};
#define NAN (*(const float8 *) nan)
#endif
extern PGDLLIMPORT int extra_float_digits;
/*
* Utility functions in float.c
*/
extern void float_overflow_error(void) pg_attribute_noreturn();
extern void float_underflow_error(void) pg_attribute_noreturn();
extern void float_zero_divide_error(void) pg_attribute_noreturn();
extern int is_infinite(float8 val);
extern float8 float8in_internal(char *num, char **endptr_p,
const char *type_name, const char *orig_string,
struct Node *escontext);
extern float4 float4in_internal(char *num, char **endptr_p,
const char *type_name, const char *orig_string,
struct Node *escontext);
extern char *float8out_internal(float8 num);
extern int float4_cmp_internal(float4 a, float4 b);
extern int float8_cmp_internal(float8 a, float8 b);
/*
* Routines to provide reasonably platform-independent handling of
* infinity and NaN
*
* We assume that isinf() and isnan() are available and work per spec.
* (On some platforms, we have to supply our own; see src/port.) However,
* generating an Infinity or NaN in the first place is less well standardized;
* pre-C99 systems tend not to have C99's INFINITY and NaN macros. We
* centralize our workarounds for this here.
*/
/*
* The funny placements of the two #pragmas is necessary because of a
* long lived bug in the Microsoft compilers.
* See http://support.microsoft.com/kb/120968/en-us for details
*/
#ifdef _MSC_VER
#pragma warning(disable:4756)
#endif
static inline float4
get_float4_infinity(void)
{
#ifdef INFINITY
/* C99 standard way */
return (float4) INFINITY;
#else
#ifdef _MSC_VER
#pragma warning(default:4756)
#endif
/*
* On some platforms, HUGE_VAL is an infinity, elsewhere it's just the
* largest normal float8. We assume forcing an overflow will get us a
* true infinity.
*/
return (float4) (HUGE_VAL * HUGE_VAL);
#endif
}
static inline float8
get_float8_infinity(void)
{
#ifdef INFINITY
/* C99 standard way */
return (float8) INFINITY;
#else
/*
* On some platforms, HUGE_VAL is an infinity, elsewhere it's just the
* largest normal float8. We assume forcing an overflow will get us a
* true infinity.
*/
return (float8) (HUGE_VAL * HUGE_VAL);
#endif
}
static inline float4
get_float4_nan(void)
{
#ifdef NAN
/* C99 standard way */
return (float4) NAN;
#else
/* Assume we can get a NAN via zero divide */
return (float4) (0.0 / 0.0);
#endif
}
static inline float8
get_float8_nan(void)
{
/* (float8) NAN doesn't work on some NetBSD/MIPS releases */
#if defined(NAN) && !(defined(__NetBSD__) && defined(__mips__))
/* C99 standard way */
return (float8) NAN;
#else
/* Assume we can get a NaN via zero divide */
return (float8) (0.0 / 0.0);
#endif
}
/*
* Floating-point arithmetic with overflow/underflow reported as errors
*
* There isn't any way to check for underflow of addition/subtraction
* because numbers near the underflow value have already been rounded to
* the point where we can't detect that the two values were originally
* different, e.g. on x86, '1e-45'::float4 == '2e-45'::float4 ==
* 1.4013e-45.
*/
static inline float4
float4_pl(const float4 val1, const float4 val2)
{
float4 result;
result = val1 + val2;
if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
float_overflow_error();
return result;
}
static inline float8
float8_pl(const float8 val1, const float8 val2)
{
float8 result;
result = val1 + val2;
if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
float_overflow_error();
return result;
}
static inline float4
float4_mi(const float4 val1, const float4 val2)
{
float4 result;
result = val1 - val2;
if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
float_overflow_error();
return result;
}
static inline float8
float8_mi(const float8 val1, const float8 val2)
{
float8 result;
result = val1 - val2;
if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
float_overflow_error();
return result;
}
static inline float4
float4_mul(const float4 val1, const float4 val2)
{
float4 result;
result = val1 * val2;
if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
float_overflow_error();
if (unlikely(result == 0.0f) && val1 != 0.0f && val2 != 0.0f)
float_underflow_error();
return result;
}
static inline float8
float8_mul(const float8 val1, const float8 val2)
{
float8 result;
result = val1 * val2;
if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
float_overflow_error();
if (unlikely(result == 0.0) && val1 != 0.0 && val2 != 0.0)
float_underflow_error();
return result;
}
static inline float4
float4_div(const float4 val1, const float4 val2)
{
float4 result;
if (unlikely(val2 == 0.0f) && !isnan(val1))
float_zero_divide_error();
result = val1 / val2;
if (unlikely(isinf(result)) && !isinf(val1))
float_overflow_error();
if (unlikely(result == 0.0f) && val1 != 0.0f && !isinf(val2))
float_underflow_error();
return result;
}
static inline float8
float8_div(const float8 val1, const float8 val2)
{
float8 result;
if (unlikely(val2 == 0.0) && !isnan(val1))
float_zero_divide_error();
result = val1 / val2;
if (unlikely(isinf(result)) && !isinf(val1))
float_overflow_error();
if (unlikely(result == 0.0) && val1 != 0.0 && !isinf(val2))
float_underflow_error();
return result;
}
/*
* Routines for NaN-aware comparisons
*
* We consider all NaNs to be equal and larger than any non-NaN. This is
* somewhat arbitrary; the important thing is to have a consistent sort
* order.
*/
static inline bool
float4_eq(const float4 val1, const float4 val2)
{
return isnan(val1) ? isnan(val2) : !isnan(val2) && val1 == val2;
}
static inline bool
float8_eq(const float8 val1, const float8 val2)
{
return isnan(val1) ? isnan(val2) : !isnan(val2) && val1 == val2;
}
static inline bool
float4_ne(const float4 val1, const float4 val2)
{
return isnan(val1) ? !isnan(val2) : isnan(val2) || val1 != val2;
}
static inline bool
float8_ne(const float8 val1, const float8 val2)
{
return isnan(val1) ? !isnan(val2) : isnan(val2) || val1 != val2;
}
static inline bool
float4_lt(const float4 val1, const float4 val2)
{
return !isnan(val1) && (isnan(val2) || val1 < val2);
}
static inline bool
float8_lt(const float8 val1, const float8 val2)
{
return !isnan(val1) && (isnan(val2) || val1 < val2);
}
static inline bool
float4_le(const float4 val1, const float4 val2)
{
return isnan(val2) || (!isnan(val1) && val1 <= val2);
}
static inline bool
float8_le(const float8 val1, const float8 val2)
{
return isnan(val2) || (!isnan(val1) && val1 <= val2);
}
static inline bool
float4_gt(const float4 val1, const float4 val2)
{
return !isnan(val2) && (isnan(val1) || val1 > val2);
}
static inline bool
float8_gt(const float8 val1, const float8 val2)
{
return !isnan(val2) && (isnan(val1) || val1 > val2);
}
static inline bool
float4_ge(const float4 val1, const float4 val2)
{
return isnan(val1) || (!isnan(val2) && val1 >= val2);
}
static inline bool
float8_ge(const float8 val1, const float8 val2)
{
return isnan(val1) || (!isnan(val2) && val1 >= val2);
}
static inline float4
float4_min(const float4 val1, const float4 val2)
{
return float4_lt(val1, val2) ? val1 : val2;
}
static inline float8
float8_min(const float8 val1, const float8 val2)
{
return float8_lt(val1, val2) ? val1 : val2;
}
static inline float4
float4_max(const float4 val1, const float4 val2)
{
return float4_gt(val1, val2) ? val1 : val2;
}
static inline float8
float8_max(const float8 val1, const float8 val2)
{
return float8_gt(val1, val2) ? val1 : val2;
}
#endif /* FLOAT_H */