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/*
* SPDX-License-Identifier: BSD-3-Clause
*
* Copyright © 2025 Keith Packard
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
* with the distribution.
*
* 3. Neither the name of the copyright holder nor the names of its
* contributors may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
* INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef _TEST_MATH_H_
#define _TEST_MATH_H_
#ifndef _DEFAULT_SOURCE
#define _DEFAULT_SOURCE
#endif
#include <math.h>
#include <float.h>
#include <complex.h>
#include <inttypes.h>
#include <stdio.h>
#include <string.h>
#include <assert.h>
#if ((__GNUC__ == 4 && __GNUC_MINOR__ >= 2) || __GNUC__ > 4)
#pragma GCC diagnostic ignored "-Wpragmas"
#pragma GCC diagnostic ignored "-Wunknown-warning-option"
#pragma GCC diagnostic ignored "-Woverflow"
#pragma GCC diagnostic ignored "-Wliteral-range"
#pragma GCC diagnostic ignored "-Wdouble-promotion"
#endif
#ifdef __RX__
#define SKIP_DENORM
#endif
#ifdef _RX_PID
#define TEST_CONST
#else
#define TEST_CONST const
#endif
#define count(a) (sizeof(a) / sizeof(a[0]))
#define _MATH_CONCAT(a, b) a##b
#define MATH_CONCAT(a, b) _MATH_CONCAT(a, b)
#define _MATH_STRING(a) #a
#define MATH_STRING(a) _MATH_STRING(a)
#ifdef SKIP_DENORM
#define MY_ABS(x) \
({ \
__typeof(x) __tmp__ = (x); \
__tmp__ < 0 ? -__tmp__ : __tmp__; \
})
#define SKIP_DENORM32(x) (MY_ABS(x) < MIN_BINARY32)
#define SKIP_DENORM64(x) (MY_ABS(x) < MIN_BINARY64)
#define SKIP_DENORM80(x) (MY_ABS(x) < MIN_BINARY80)
#define SKIP_DENORM128(x) (MY_ABS(x) < MIN_BINARY128)
#else
#define SKIP_DENORM32(x) 0
#define SKIP_DENORM64(x) 0
#define SKIP_DENORM80(x) 0
#define SKIP_DENORM128(x) 0
#endif
#define SKIP_CDENORM32(z) (SKIP_DENORM32(creal32(z)) || SKIP_DENORM32(cimag32(z)))
#define SKIP_CDENORM64(z) (SKIP_DENORM64(creal64(z)) || SKIP_DENORM64(cimag64(z)))
#define SKIP_CDENORM80(z) (SKIP_DENORM80(creal80(z)) || SKIP_DENORM80(cimag80(z)))
#define SKIP_CDENORM128(z) (SKIP_DENORM128(creal128(z)) || SKIP_DENORM128(cimag128(z)))
#define MAX_ULP 9999
#define INV_ULP 10000
typedef int32_t ulp_t;
#define PRIdULP PRId32
typedef const struct {
const char *name;
ulp_t b32;
ulp_t b64;
ulp_t b80;
ulp_t b128;
} math_ulps_t;
static TEST_CONST math_ulps_t math_ulps[];
ulp_t max_ulp;
#include "test-ulp.h"
static inline math_ulps_t *
math_find_ulps(void)
{
const char *name = MATH_STRING(TEST_FUNC);
for (size_t i = 0; i < sizeof(math_ulps) / sizeof(math_ulps[0]); i++)
if (strcmp(name, math_ulps[i].name) == 0)
return &math_ulps[i];
assert(0);
return &math_ulps[0];
}
static inline ulp_t
math_find_ulp_binary32(void)
{
math_ulps_t *ulps = math_find_ulps();
return ulps->b32;
}
static inline ulp_t
math_find_ulp_binary64(void)
{
math_ulps_t *ulps = math_find_ulps();
return ulps->b64;
}
static inline ulp_t
math_find_ulp_binary80(void)
{
math_ulps_t *ulps = math_find_ulps();
return ulps->b80;
}
static inline int
math_find_ulp_binary128(void)
{
math_ulps_t *ulps = math_find_ulps();
return ulps->b128;
}
#if __FLT_MANT_DIG__ == 24 && !defined(SKIP_BINARY32)
#define HAS_BINARY32
typedef float binary32;
typedef complex float cbinary32;
#define CMPLX32(a, b) CMPLXF(a, b)
#define creal32(a) crealf(a)
#define cimag32(a) cimagf(a)
#define carg32(a) cargf(a)
#define cabs32(a) cabsf(a)
#define nextafter32(x, y) nextafterf(x, y)
#define MIN_BINARY32 FLT_MIN
#define FN32(a) a##f
#define TEST_FUNC_32 MATH_CONCAT(TEST_FUNC, f)
// #define FMT32 "% -14.8e"
#define FMT32 "% -15.6a"
#define P32(a) ((double)(a))
#endif
#ifdef HAS_BINARY32
typedef struct {
binary32 x, y;
} unary32;
typedef struct {
cbinary32 x, y;
} cunary32;
static inline ulp_t
ulp32(binary32 a, binary32 b)
{
if (a == b)
return 0;
if (isnan(a) && isnan(b))
return 0;
if (isnan(a) || isnan(b)) {
#ifdef __RX__
printf("RX fails to generate NaN, ignoring\n");
return 0;
#endif
return INV_ULP;
}
ulp_t ulp = 0;
while (a != b) {
a = nextafter32(a, b);
ulp++;
if (ulp == MAX_ULP)
break;
}
return ulp;
}
static inline ulp_t
culp32(cbinary32 a, cbinary32 b)
{
if (a == b)
return 0;
binary32 a_r = cabs32(a);
binary32 d_r = cabs32(a - b);
return ulp32(a_r + d_r, a_r);
}
#endif
#if __DBL_MANT_DIG__ == 53 && !defined(SKIP_BINARY64)
#define HAS_BINARY64
typedef double binary64;
typedef complex double cbinary64;
#define CMPLX64(a, b) CMPLX(a, b)
#define creal64(a) creal(a)
#define cimag64(a) cimag(a)
#define carg64(a) carg(a)
#define cabs64(a) cabs(a)
#define clog64(a) clog(a)
#define nextafter64(x, y) nextafter(x, y)
#define TEST_FUNC_64 TEST_FUNC
#define MIN_BINARY64 DBL_MIN
#define FN64(a) a
#define FMT64 "% -23.13a"
#define P64(a) (a)
#elif __LDBL_MANT_DIG__ == 53 && defined(_TEST_LONG_DOUBLE) && !defined(SKIP_BINARY64)
#define HAS_BINARY64
typedef long double binary64;
typedef complex long double cbinary64;
#define CMPLX64(a, b) CMPLXL(a, b)
#define creal64(a) creall(a)
#define cimag64(a) cimagl(a)
#define carg64(a) cargl(a)
#define cabs64(a) cabsl(a)
#define clog64(a) clogl(a)
#define nextafter64(x, y) nextafterl(x, y)
#define TEST_FUNC_64 MATH_CONCAT(TEST_FUNC, l)
#define MIN_BINARY64 LDBL_MIN
#define FN64(a) a##l
#define FMT64 "%La"
#define P64(a) (a)
#endif
#ifdef HAS_BINARY64
typedef struct {
binary64 x, y;
} unary64;
typedef struct {
cbinary64 x, y;
} cunary64;
static inline ulp_t
ulp64(binary64 a, binary64 b)
{
if (a == b)
return 0;
if (isnan(a) && isnan(b))
return 0;
/* sometimes inf != inf on m68k? */
if (isinf(a) && isinf(b) && (a > 0) == (b > 0))
return 0;
if (isnan(a) || isnan(b)) {
#ifdef __RX__
printf("RX fails to generate NaN, ignoring\n");
return 0;
#endif
return INV_ULP;
}
ulp_t ulp = 0;
while (a != b) {
a = nextafter64(a, b);
ulp++;
if (ulp == MAX_ULP)
break;
}
return ulp;
}
static inline ulp_t
culp64(cbinary64 a, cbinary64 b)
{
if (a == b)
return 0;
binary64 a_r = cabs64(a);
binary64 d_r = cabs64(a - b);
return ulp64(a_r + d_r, a_r);
}
#endif
#if __LDBL_MANT_DIG__ == 64 && defined(_TEST_LONG_DOUBLE) && !defined(SKIP_BINARY80)
#define HAS_BINARY80
typedef long double binary80;
typedef complex long double cbinary80;
#define CMPLX80(a, b) CMPLXL(a, b)
#define creal80(a) creall(a)
#define cimag80(a) cimagl(a)
#define carg80(a) cargl(a)
#define cabs80(a) cabsl(a)
#define clog80(a) clogl(a)
#define frexp80(a, e) frexpl(a, e);
#define nextafter80(x, y) nextafterl(x, y)
#define TEST_FUNC_80 MATH_CONCAT(TEST_FUNC, l)
#define MIN_BINARY80 LDBL_MIN
#define FN80(a) a##l
#define FMT80 "%La"
#define P80(a) (a)
#endif
#ifdef HAS_BINARY80
static inline int
skip_binary80(void)
{
#ifdef __m68k__
volatile long double zero = 0.0L;
volatile long double one = 1.0L;
volatile long double check = nextafterl(zero, one);
if (check + check == zero) {
printf("m68k emulating long double with double, skipping\n");
return 1;
}
#endif
return 0;
}
typedef struct {
binary80 x, y;
} unary80;
typedef struct {
cbinary80 x, y;
} cunary80;
static inline ulp_t
ulp80(binary80 a, binary80 b)
{
if (a == b)
return 0;
if (isnan(a) && isnan(b))
return 0;
if (isnan(a) || isnan(b))
return INV_ULP;
ulp_t ulp = 0;
while (a != b) {
a = nextafterl(a, b);
ulp++;
if (ulp == MAX_ULP)
break;
}
return ulp;
}
static inline ulp_t
culp80(cbinary80 a, cbinary80 b)
{
if (a == b)
return 0;
binary80 a_r = cabs80(a);
binary80 d_r = cabs80(a - b);
return ulp80(a_r + d_r, a_r);
}
#endif
#if __LDBL_MANT_DIG__ == 113 && defined(_TEST_LONG_DOUBLE) && !defined(SKIP_BINARY128)
#define HAS_BINARY128
typedef long double binary128;
typedef complex long double cbinary128;
#define CMPLX128(a, b) CMPLXL(a, b)
#define creal128(a) creall(a)
#define cimag128(a) cimagl(a)
#define carg128(a) cargl(a)
#define cabs128(a) cabsl(a)
#define nextafter128(x, y) nextafterl(x, y)
#define TEST_FUNC_128 MATH_CONCAT(TEST_FUNC, l)
#define MIN_BINARY128 LDBL_MIN
#define FN128(a) a##l
#define FMT128 "%La"
#define P128(a) (a)
#endif
#ifdef HAS_BINARY128
typedef struct {
binary128 x, y;
} unary128;
typedef struct {
cbinary128 x, y;
} cunary128;
static inline ulp_t
ulp128(binary128 a, binary128 b)
{
if (a == b)
return 0;
if (isnan(a) && isnan(b))
return 0;
if (isnan(a) || isnan(b))
return INV_ULP;
ulp_t ulp = 0;
while (a != b) {
a = nextafter128(a, b);
ulp++;
if (ulp == MAX_ULP)
break;
}
return ulp;
}
static inline ulp_t
culp128(cbinary128 a, cbinary128 b)
{
if (a == b)
return 0;
binary128 a_r = cabs128(a);
binary128 d_r = cabs128(a - b);
return ulp128(a_r + d_r, a_r);
}
#endif
#define sincos_sin 1
#define sincos_cos 2
#if TEST_FUNC == sincos_sin
#define TEST_FUNC_SINCOS_SIN
#elif TEST_FUNC == sincos_cos
#define TEST_FUNC_SINCOS_COS
#endif
#undef sincos_sin
#undef sincos_cos
#ifdef TEST_FUNC_SINCOS_SIN
#ifdef TEST_FUNC_32
binary32 TEST_FUNC_32(binary32 x);
binary32
TEST_FUNC_32(binary32 x)
{
binary32 s, c;
FN32(sincos)(x, &s, &c);
return s;
}
#endif
#ifdef HAS_BINARY64
binary64 TEST_FUNC_64(binary64 x);
binary64
TEST_FUNC_64(binary64 x)
{
binary64 s, c;
FN64(sincos)(x, &s, &c);
return s;
}
#endif
#ifdef HAS_BINARY80
binary80 TEST_FUNC_80(binary80 x);
binary80
TEST_FUNC_80(binary80 x)
{
binary80 s, c;
FN80(sincos)(x, &s, &c);
return s;
}
#endif
#ifdef HAS_BINARY128
binary128 TEST_FUNC_128(binary128 x);
binary128
TEST_FUNC_128(binary128 x)
{
binary128 s, c;
FN128(sincos)(x, &s, &c);
return s;
}
#endif
#endif /* TEST_FUNC_SINCOS_SIN */
#ifdef TEST_FUNC_SINCOS_COS
#ifdef TEST_FUNC_32
binary32 TEST_FUNC_32(binary32 x);
binary32
TEST_FUNC_32(binary32 x)
{
binary32 s, c;
FN32(sincos)(x, &s, &c);
return c;
}
#endif
#ifdef HAS_BINARY64
binary64 TEST_FUNC_64(binary64 x);
binary64
TEST_FUNC_64(binary64 x)
{
binary64 s, c;
FN64(sincos)(x, &s, &c);
return c;
}
#endif
#ifdef HAS_BINARY80
binary80 TEST_FUNC_80(binary80 x);
binary80
TEST_FUNC_80(binary80 x)
{
binary80 s, c;
FN80(sincos)(x, &s, &c);
return c;
}
#endif
#ifdef HAS_BINARY128
binary128 TEST_FUNC_128(binary128 x);
binary128
TEST_FUNC_128(binary128 x)
{
binary128 s, c;
FN128(sincos)(x, &s, &c);
return c;
}
#endif
#endif /* TEST_FUNC_SINCOS_COS */
#endif /* _TEST_MATH_H_ */
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