float.h

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/*-------------------------------------------------------------------------
 *
 * float.h
 *    Definitions for the built-in floating-point types
 *
 * Portions Copyright (c) 1996-2026, 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
 
extern PGDLLIMPORT int extra_float_digits;
 
/*
 * Utility functions in float.c
 */
pg_noreturn extern void float_overflow_error(void);
pg_noreturn extern void float_underflow_error(void);
pg_noreturn extern void float_zero_divide_error(void);
extern float8 float_overflow_error_ext(struct Node *escontext);
extern float8 float_underflow_error_ext(struct Node *escontext);
extern float8 float_zero_divide_error_ext(struct Node *escontext);
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);
 
/*
 * Postgres requires IEEE-standard float arithmetic, including infinities
 * and NaNs.  We used to support pre-C99 compilers on which <math.h> might
 * not supply the standard macros INFINITY and NAN.  We no longer do so,
 * but these wrapper functions are still preferred over using those macros
 * directly.
 *
 * If you change these functions, see copies in interfaces/ecpg/ecpglib/data.c.
 */
 
static inline float4
get_float4_infinity(void)
{
    /* C99 standard way */
    return (float4) INFINITY;
}
 
static inline float8
get_float8_infinity(void)
{
    /* C99 standard way */
    return (float8) INFINITY;
}
 
/* The C standard allows implementations to omit NAN, but we don't */
#ifndef NAN
#error "Postgres requires support for IEEE quiet NaNs"
#endif
 
static inline float4
get_float4_nan(void)
{
    /* C99 standard way */
    return (float4) NAN;
}
 
static inline float8
get_float8_nan(void)
{
    /* C99 standard way */
    return (float8) NAN;
}
 
/*
 * 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_safe(const float8 val1, const float8 val2, struct Node *escontext)
{
    float8      result;
 
    result = val1 + val2;
    if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
        return float_overflow_error_ext(escontext);
 
    return result;
}
 
static inline float8
float8_pl(const float8 val1, const float8 val2)
{
    return float8_pl_safe(val1, val2, NULL);
}
 
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_safe(const float8 val1, const float8 val2, struct Node *escontext)
{
    float8      result;
 
    result = val1 - val2;
    if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
        return float_overflow_error_ext(escontext);
 
    return result;
}
 
static inline float8
float8_mi(const float8 val1, const float8 val2)
{
    return float8_mi_safe(val1, val2, NULL);
}
 
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_safe(const float8 val1, const float8 val2, struct Node *escontext)
{
    float8      result;
 
    result = val1 * val2;
    if (unlikely(isinf(result)) && !isinf(val1) && !isinf(val2))
        return float_overflow_error_ext(escontext);
    if (unlikely(result == 0.0) && val1 != 0.0 && val2 != 0.0)
        return float_underflow_error_ext(escontext);
 
    return result;
}
 
static inline float8
float8_mul(const float8 val1, const float8 val2)
{
    return float8_mul_safe(val1, val2, NULL);
}
 
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_safe(const float8 val1, const float8 val2, struct Node *escontext)
{
    float8      result;
 
    if (unlikely(val2 == 0.0) && !isnan(val1))
        return float_zero_divide_error_ext(escontext);
    result = val1 / val2;
    if (unlikely(isinf(result)) && !isinf(val1))
        return float_overflow_error_ext(escontext);
    if (unlikely(result == 0.0) && val1 != 0.0 && !isinf(val2))
        return float_underflow_error_ext(escontext);
 
    return result;
}
 
static inline float8
float8_div(const float8 val1, const float8 val2)
{
    return float8_div_safe(val1, val2, NULL);
}
 
/*
 * 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 */