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test.c
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test.c
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#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <inttypes.h>
#include <limits.h>
#include <stdarg.h>
#include <stddef.h>
#include <setjmp.h>
#include <cmocka.h>
#include <math.h>
#include "ftfp.h"
#include "test_helper.h"
#include "debug.h"
#include "lut.h"
static void null_test_success(void **state) {
//(void) state;
}
#define CHECK_CONDITION(error_msg, condition, var1, var2) \
if( !(condition) ) { \
char b1[FIX_PRINT_BUFFER_SIZE], b2[FIX_PRINT_BUFFER_SIZE]; \
fix_sprint(b1, var1); fix_sprint(b2, var2); \
fixed difference = fix_sub(var1, var2); \
char b3[FIX_PRINT_BUFFER_SIZE]; fix_sprint(b3, difference); \
fail_msg( error_msg ": \n%s ("FIX_PRINTF_HEX") != %s ("FIX_PRINTF_HEX \
")\n difference %s ("FIX_PRINTF_HEX", "FIX_PRINTF_HEX")", \
b1, var1, b2, var2, b3, difference, ~difference+4); \
}
#define CHECK_EQ(error_msg, var1, var2) \
CHECK_CONDITION(error_msg, fix_eq(var1, var2), var1, var2)
#define CHECK_EQ_NAN(error_msg, var1, var2) \
CHECK_CONDITION(error_msg, fix_eq_nan(var1, var2), var1, var2)
#define CHECK_EQ_VALUE(error_msg, var1, var2, value) \
CHECK_CONDITION(error_msg, fix_eq(var1, var2) == value, var1, var2)
#define CHECK_EQ_NAN_VALUE(error_msg, var1, var2, value) \
CHECK_CONDITION(error_msg, fix_eq_nan(var1, var2) == value, var1, var2)
#define CHECK_VALUE(error_msg, value, expected, fixed1, fixed2) \
CHECK_CONDITION(error_msg, (value) == (expected), fixed1, fixed2)
#define CHECK_DIFFERENCE(error_msg, value, expected, bound) \
CHECK_CONDITION(error_msg, (fix_eq_nan(value, expected) | \
(!( FIX_IS_INF_POS(value) | FIX_IS_INF_NEG(value) | FIX_IS_NAN(value) \
| FIX_IS_INF_POS(expected) | FIX_IS_INF_NEG(expected) | FIX_IS_NAN(expected)) \
& (fix_abs(fix_sub(value, expected)) <= (bound)))), value, expected)
#define CHECK_INT_EQUAL(error_msg, var1, var2) \
if( !(var1 == var2) ) { \
fail_msg( error_msg ": "FIX_PRINTF_DEC" (0x"FIX_PRINTF_HEX") != "FIX_PRINTF_DEC" (0x"FIX_PRINTF_HEX")", (fixed) var1, (fixed) var1, (fixed) var2, (fixed) var2); \
}
#define SQRT_MAX ((fixed) sqrt((double) FIX_INT_MAX))
void p(fixed f) {
char buf[FIX_PRINT_BUFFER_SIZE];
fix_sprint(buf, f);
printf("n: %s ("FIX_PRINTF_HEX")\n", buf, f);
}
void pl(fixed f) {
char buf[FIX_PRINT_BUFFER_SIZE];
fix_sprint(buf, f);
printf("%s ("FIX_PRINTF_HEX")", buf, f);
}
void bounds(fixed f) {
char buf_less[FIX_PRINT_BUFFER_SIZE];
char buf[FIX_PRINT_BUFFER_SIZE];
char buf_more[FIX_PRINT_BUFFER_SIZE];
fixed less = f - 0x4;
fixed more = f + 0x4;
fix_sprint(buf_less, less);
fix_sprint(buf, f);
fix_sprint(buf_more, more);
printf("%s (0x"FIX_PRINTF_HEX") | %s (0x"FIX_PRINTF_HEX") | %s (0x"FIX_PRINTF_HEX")\n", buf_less, less, buf, f, buf_more, more);
}
// Helper macro. Define it to be this for now, for code generation
#define TEST_HELPER(name, code) static void name(void **state) code
//////////////////////////////////////////////////////////////////////////////
#define TEST_ROUND_TO_EVEN(name, value, shift, result) \
TEST_HELPER(round_to_even_##name, { \
int32_t rounded = ROUND_TO_EVEN(value, shift); \
int32_t expected = result; \
CHECK_INT_EQUAL("round_to_even", rounded, expected); \
};)
#define ROUND_TO_EVEN_TESTS \
TEST_ROUND_TO_EVEN(zero , 0x00 , 0x3 , 0x0) \
TEST_ROUND_TO_EVEN(zero_plus , 0x01 , 0x3 , 0x0) \
TEST_ROUND_TO_EVEN(one , 0x02 , 0x3 , 0x0) \
TEST_ROUND_TO_EVEN(one_plus , 0x03 , 0x3 , 0x0) \
TEST_ROUND_TO_EVEN(two , 0x04 , 0x3 , 0x0) /* 0.5 -> 0 */ \
TEST_ROUND_TO_EVEN(two_plus , 0x05 , 0x3 , 0x1) /* 0.55 -> 1 */ \
TEST_ROUND_TO_EVEN(three , 0x06 , 0x3 , 0x1) \
TEST_ROUND_TO_EVEN(three_plus , 0x07 , 0x3 , 0x1) \
TEST_ROUND_TO_EVEN(four , 0x08 , 0x3 , 0x1) /* 1 -> 1 */ \
TEST_ROUND_TO_EVEN(four_plus , 0x09 , 0x3 , 0x1) \
TEST_ROUND_TO_EVEN(five , 0x0a , 0x3 , 0x1) \
TEST_ROUND_TO_EVEN(five_plus , 0x0b , 0x3 , 0x1) \
TEST_ROUND_TO_EVEN(six , 0x0c , 0x3 , 0x2) /* 1.5 -> 2 */ \
TEST_ROUND_TO_EVEN(six_plus , 0x0d , 0x3 , 0x2) \
TEST_ROUND_TO_EVEN(seven , 0x0e , 0x3 , 0x2) \
TEST_ROUND_TO_EVEN(seven_plus , 0x0f , 0x3 , 0x2) \
TEST_ROUND_TO_EVEN(eight , 0x10 , 0x3 , 0x2) \
TEST_ROUND_TO_EVEN(eight_plus , 0x10 , 0x3 , 0x2)
ROUND_TO_EVEN_TESTS
//////////////////////////////////////////////////////////////////////////////
#define TEST_FIXNUM(name, inputint, inputfrac, inf, outputsign, outputint, outputfrac) \
TEST_HELPER(fixnum_##name, { \
fixed g = FIXNUM(inputint, inputfrac); \
fixed expected = (((fixed) (outputint)) << FIX_POINT_BITS) + \
(ROUND_TO_EVEN_64(((fixed) outputfrac), \
(FIX_BITS - FIX_FRAC_BITS)) << FIX_FLAG_BITS); \
if(outputsign == 1) { \
expected = FIX_DATA_BITS((~(fixed) expected) + 0x4); \
} else { \
expected = FIX_DATA_BITS((fixed) expected); \
}\
if(inf == FIX_INF_POS || (outputsign == 0 && outputint >= FIX_INT_MAX)) { \
expected = FIX_INF_POS; \
} \
if(inf == FIX_INF_NEG || (outputsign == 1 && ((outputint > FIX_INT_MAX) || (outputint == FIX_INT_MAX && outputfrac != 0)))) { \
expected = FIX_INF_NEG; \
} \
CHECK_EQ("fixnum", g, expected); \
};)
#define FIXNUM_TESTS \
TEST_FIXNUM(zero , 0 , 0 , 0 , 0 , 0 , 0) \
TEST_FIXNUM(one , 1 , 0 , 0 , 0 , 1 , 0) \
TEST_FIXNUM(one_neg , -1 , 0 , 0 , 1 , 1 , 0) \
TEST_FIXNUM(two , 2 , 0 , 0 , 0 , 2 , 0) \
TEST_FIXNUM(two_neg , -2 , 0 , 0 , 1 , 2 , 0) \
TEST_FIXNUM(many , 1000 , 4 , 0 , 0 , 1000 , 0x6666666666666666) \
TEST_FIXNUM(many_neg , -1000 , 4 , 0 , 1 , 1000 , 0x6666666666666666) \
TEST_FIXNUM(max_int_l1 , FIX_INT_MAX-1 , 0 , 0 , 0 , FIX_INT_MAX-1 , 0 ) \
TEST_FIXNUM(max_int , FIX_INT_MAX , 0 , FIX_INF_POS , 0 , 0 , 0 ) \
TEST_FIXNUM(max_int_neg , -FIX_INT_MAX , 0 , 0 , 1 , FIX_INT_MAX , 0 ) \
TEST_FIXNUM(max_int_neg_plus, -FIX_INT_MAX , 5 , FIX_INF_NEG , 1 , 0 , 0 ) \
TEST_FIXNUM(max_int_neg_m1 , -FIX_INT_MAX-1 , 0 , FIX_INF_NEG , 1 , 0 , 0 ) \
TEST_FIXNUM(frac , 0 , 5342 , 0 , 0 , 0 , 0x88c154c985f06f69) \
TEST_FIXNUM(frac_neg , -0 , 5342 , 0 , 1 , 0 , 0x88c154c985f06f69) \
TEST_FIXNUM(regress0 , 0 , 00932 , 0 , 0 , 0 , 0x0262cba732df505d) \
TEST_FIXNUM(regress1 , 100 , 002655 , 0 , 0 , 100 , 0x00adff822bbecaac) \
TEST_FIXNUM(regress12 , 100 , 0026550292968 , 0 , 0 , 100 , 0x00adffffffeae3ae) \
TEST_FIXNUM(regress2 , 1 , 4142150878906 , 0 , 0 , 1 , 0x6a09fffffff8f68f) \
TEST_FIXNUM(regress3 , 1 , 6487121582031 , 0 , 0 , 1 , 0xa611fffffff8f68f) \
TEST_FIXNUM(regress4 , 1 , 99999999999999999999 , 0 , 0 , 2 , 0x0) \
TEST_FIXNUM(regress45 , 0 , 99999999999999999999 , 0 , 0 , 1 , 0x0) \
TEST_FIXNUM(regress5 , -1 , 3862915039 , 0 , 1 , 1 , 0x62e3fffff920c809)
FIXNUM_TESTS
#define TEST_INTCONVERSION(name, inputint, inputfrac, inf, outputsign, outputint) \
TEST_HELPER(fixint_##name, { \
fixed gi64 = fix_convert_from_int64((int64_t) inputint); \
fixed expectedint = (((fixed) (outputint)) << FIX_POINT_BITS); \
if(outputsign == 1) { \
expectedint = FIX_DATA_BITS((~(fixed) expectedint) + 0x4); \
} else { \
expectedint = FIX_DATA_BITS((fixed) expectedint); \
}\
if(inf == FIX_INF_POS || (outputsign == 0 && outputint >= FIX_INT_MAX)) { \
expectedint = FIX_INF_POS; \
} \
if(inf == FIX_INF_NEG || (outputsign == 1 && ((outputint > FIX_INT_MAX) ))) { \
expectedint = FIX_INF_NEG; \
} \
CHECK_EQ("fixint int64", gi64, expectedint); \
};)
#define INTCONVERSION_TESTS \
TEST_INTCONVERSION(zero , 0 , 0 , 0 , 0 , 0 ) \
TEST_INTCONVERSION(one , 1 , 0 , 0 , 0 , 1 ) \
TEST_INTCONVERSION(one_neg , -1 , 0 , 0 , 1 , 1 ) \
TEST_INTCONVERSION(two , 2 , 0 , 0 , 0 , 2 ) \
TEST_INTCONVERSION(two_neg , -2 , 0 , 0 , 1 , 2 ) \
TEST_INTCONVERSION(many , 1000 , 4 , 0 , 0 , 1000 ) \
TEST_INTCONVERSION(many_neg , -1000 , 4 , 0 , 1 , 1000 ) \
TEST_INTCONVERSION(max_int_l1 , FIX_INT_MAX-1 , 0 , 0 , 0 , FIX_INT_MAX-1 ) \
TEST_INTCONVERSION(max_int , FIX_INT_MAX , 0 , FIX_INF_POS , 0 , 0 ) \
TEST_INTCONVERSION(max_int_neg , -FIX_INT_MAX , 0 , 0 , 1 , FIX_INT_MAX ) \
TEST_INTCONVERSION(max_int_neg_m1 , -FIX_INT_MAX-1 , 0 , FIX_INF_NEG , 1 , 0 ) \
TEST_INTCONVERSION(frac , 0 , 5342 , 0 , 0 , 0 ) \
TEST_INTCONVERSION(frac_neg , -0 , 5342 , 0 , 1 , 0 ) \
TEST_INTCONVERSION(regress0 , 0 , 00932 , 0 , 0 , 0 ) \
TEST_INTCONVERSION(regress1 , 100 , 002655 , 0 , 0 , 100 ) \
TEST_INTCONVERSION(regress12 , 100 , 0026550292968 , 0 , 0 , 100 ) \
TEST_INTCONVERSION(regress2 , 1 , 4142150878906 , 0 , 0 , 1 ) \
TEST_INTCONVERSION(regress3 , 1 , 6487121582031 , 0 , 0 , 1 ) \
TEST_INTCONVERSION(regress4 , 2 , 0 , 0 , 0 , 2 ) \
TEST_INTCONVERSION(regress5 , -1 , 3862915039 , 0 , 1 , 1 )
INTCONVERSION_TESTS
//////////////////////////////////////////////////////////////////////////////
/* Doubles only have 53 bits of precision, but we have 64 (minux the flag bits).
* If we end up shifting it left, there will be zero bits on the low end. This
* shouldn't be a test failure, so fix it up. We might also shift some of the
* precision bits off the left of the number.
*
* So, let's compure how many precision bits we should have... Or, more
* usefully, how many 0 bits we have on the lower end of the number. Note that
* we need to check if d is exactly a power of two, and add that in.
*
* */
#define CONVERT_DBL(name, d, bits) \
TEST_HELPER(convert_dbl_##name, { \
fixed expected = bits; \
double locald = (d); \
double log2d = log2(fabs(d)); \
uint32_t ilog2d = (int) ceil(log2d); \
int32_t bottom_zero_bits = ilog2d + 2 - 52 + FIX_FRAC_BITS; \
fixed result; \
if(bottom_zero_bits < 0 ) { \
result = fix_convert_from_double(locald); \
CHECK_EQ_NAN(#name " convert_from_double failed (no mask needed)", result, expected); \
} else { \
\
uint64_t rounding_bit = (1ull) << (bottom_zero_bits + FIX_FLAG_BITS); \
expected = ROUND_TO_EVEN(expected, bottom_zero_bits) << bottom_zero_bits; \
expected |= bits & FIX_FLAGS_MASK; /* ensure we still have flags */\
result = fix_convert_from_double(locald); \
CHECK_CONDITION(#name " convert_from_double failed (mask needed)", \
(!(FIX_IS_INF_POS(bits) | FIX_IS_INF_NEG(bits) | FIX_IS_NAN(bits) ) \
&& (((result - expected) <= rounding_bit) || ((expected - result) <= rounding_bit))) || \
fix_eq_nan(result, expected), result, expected); \
} \
double d2 = fix_convert_to_double(result); \
double limit = (pow(.5, (double)FIX_FRAC_BITS)); \
if( !((fabs(locald - d2) < limit) || \
(isinf(d2) && (isinf(d) || (locald) >= FIX_INT_MAX || locald < -FIX_INT_MAX )) || \
(isnan(d) && isnan(d2))) ) { \
char b1[FIX_PRINT_BUFFER_SIZE]; \
fix_sprint(b1, result); \
fail_msg( #name " convert_to_double failed : %g (%s "FIX_PRINTF_HEX") != %g", d2, b1, result, locald); \
} \
char buf[FIX_PRINT_BUFFER_SIZE]; \
char bitsbuf[FIX_PRINT_BUFFER_SIZE]; \
fix_sprint(buf, result); \
fix_sprint(bitsbuf, bits); \
printf("Test passed: %g == %g == %s == %s\n", locald, d2, buf, bitsbuf); \
};)
#define CONVERT_DBL_TESTS \
CONVERT_DBL(zero , 0 , FIX_ZERO) \
CONVERT_DBL(one , 1 , FIXNUM(1 , 0)) \
CONVERT_DBL(one_neg , -1 , FIXNUM(-1 , 0)) \
CONVERT_DBL(two , 2 , FIXNUM(2 , 0)) \
CONVERT_DBL(two_neg , -2 , FIXNUM(-2 , 0)) \
CONVERT_DBL(many , 1000.4 , FIXNUM(1000 , 4)) \
CONVERT_DBL(many_neg , -1000.4 , FIXNUM(-1000, 4)) \
CONVERT_DBL(frac , 0.5342 , FIXNUM(0 , 5342)) \
CONVERT_DBL(frac_neg , -0.5342 , FIXNUM(-0 , 5342)) \
CONVERT_DBL(underflow, 1e-60 , FIX_ZERO) \
CONVERT_DBL(max , (double) FIX_INT_MAX , FIX_INF_POS) \
CONVERT_DBL(max_neg , -((double) FIX_INT_MAX) , FIXNUM(-FIX_INT_MAX,0)) \
CONVERT_DBL(inf_pos , INFINITY , FIX_INF_POS) \
CONVERT_DBL(inf_neg , -INFINITY , FIX_INF_NEG) \
CONVERT_DBL(nan , nan("0") , FIX_NAN)
CONVERT_DBL_TESTS
//////////////////////////////////////////////////////////////////////////////
#define TEST_EQ(name, op1, op2, value, valuenan) \
TEST_HELPER(equal_##name, { \
fixed o1 = op1; \
fixed o2 = op2; \
CHECK_EQ_VALUE("values not right", o1, o2, value ); \
CHECK_EQ_NAN_VALUE("NaN values not right", o1, o2, valuenan ); \
CHECK_EQ_VALUE("values not right", o2, o1, value ); \
CHECK_EQ_NAN_VALUE("NaN values not right", o2, o1, valuenan ); \
};)
#define EQ_TESTS \
TEST_EQ(zero , 0 , 0 , 1 , 1) \
TEST_EQ(one , FIXNUM(1,0) , FIXNUM(1,0) , 1 , 1) \
TEST_EQ(one_neg , FIXNUM(1,0) , FIXNUM(-1,0) , 0 , 0) \
TEST_EQ(frac , FIXNUM(0,314159) , FIXNUM(0,314159) , 1 , 1) \
TEST_EQ(frac_ne , FIXNUM(0,314159) , FIXNUM(3,314159) , 0 , 0) \
TEST_EQ(nan , FIX_NAN , FIX_NAN , 0 , 1) \
TEST_EQ(nan_inf , FIX_NAN , FIX_INF_POS , 0 , 0) \
TEST_EQ(nan_inf_neg , FIX_NAN , FIX_INF_NEG , 0 , 0) \
TEST_EQ(nan_num , FIX_NAN , FIXNUM(0,0) , 0 , 0) \
TEST_EQ(inf , FIX_INF_POS , FIX_INF_POS , 1 , 1) \
TEST_EQ(inf_inf_neg , FIX_INF_POS , FIX_INF_NEG , 0 , 0) \
TEST_EQ(inf_num , FIX_INF_POS , FIXNUM(0,0) , 0 , 0) \
TEST_EQ(inf_neg , FIX_INF_NEG , FIX_INF_NEG , 1 , 1) \
TEST_EQ(inf_neg_num , FIX_INF_NEG , FIXNUM(0,0) , 0 , 0)
EQ_TESTS
//////////////////////////////////////////////////////////////////////////////
#define TEST_ROUNDING(name, value, res_even, res_up, res_ceil, res_floor) \
TEST_HELPER(rounding_##name, { \
fixed input = value; \
/* Trust that FIXNUM is doing its job correctly. Therefore, if input is \
* infinity, we can fix up the expected values below... */ \
int64_t round_even = fix_convert_to_int64(input); \
int64_t exp_even = FIX_IS_INF_POS(input) ? INT64_MAX : FIX_IS_INF_NEG(input) ? INT64_MIN : (res_even); \
CHECK_INT_EQUAL("round to even" , round_even , exp_even); \
int64_t round_up = fix_round_up_int64(input); \
int64_t exp_up = FIX_IS_INF_POS(input) ? INT64_MAX : FIX_IS_INF_NEG(input) ? INT64_MIN : (res_up); \
CHECK_INT_EQUAL("round up" , round_up , exp_up); \
int64_t round_ceil = fix_ceil64(input); \
int64_t exp_ceil = FIX_IS_INF_POS(input) ? INT64_MAX : FIX_IS_INF_NEG(input) ? INT64_MIN : (res_ceil); \
CHECK_INT_EQUAL("ceiling" , round_ceil , exp_ceil); \
int64_t round_floor = fix_floor64(input); \
int64_t exp_floor = FIX_IS_INF_POS(input) ? INT64_MAX : FIX_IS_INF_NEG(input) ? INT64_MIN : (res_floor); \
CHECK_INT_EQUAL("floor" , round_floor , exp_floor); \
};)
/* Sometimes, if there's only one fractional bit, the numbers get a little
* mangled. For example, 1.3 becomes 1.5, which rounds up to 2. Use the
* "Single Fraction Adjustment" for some tests. */
#if FIX_FRAC_BITS == 1
#define SFA +1
#else
#define SFA 0
#endif
/* Modding by FIX_INT_MAX allows us to correct for situations where FIX_INT_MAX
* is 1 -- that is, when there is one integer bit. In these situations,
* the fixnum being tested is always +/- 0.5, and rounds to zero. */
/* Name Value Even Up Ceil Floor */
#define ROUNDING_TESTS \
\
TEST_ROUNDING(zero , FIXNUM(0 , 0) , (0)+0 , (0)+0 , (0 )+0 , (0)+0) \
TEST_ROUNDING(zero3 , FIXNUM(0 , 3) , (0)+0 , (0)+0 +SFA , (0 )+1 , (0)+0) \
TEST_ROUNDING(zero5 , FIXNUM(0 , 5) , (0)+0 , (0)+1 , (0 )+1 , (0)+0) \
TEST_ROUNDING(zero7 , FIXNUM(0 , 7) , (0)+1 -SFA , (0)+1 , (0 )+1 , (0)+0) \
\
TEST_ROUNDING(one , FIXNUM(1 , 0) , (1)+0 , (1)+0 , (1 )+0 , (1)+0) \
TEST_ROUNDING(one3 , FIXNUM(1 , 3) , (1)+0 +SFA , (1)+0 +SFA , (1 )+1 , (1)+0) \
TEST_ROUNDING(one5 , FIXNUM(1 , 5) , (1)+1 , (1)+1 , (1 )+1 , (1)+0) \
TEST_ROUNDING(one7 , FIXNUM(1 , 7) , (1)+1 , (1)+1 , (1 )+1 , (1)+0) \
\
TEST_ROUNDING(two , FIXNUM(2 , 0) , (2)+0 , (2)+0 , (2 )+0 , (2)+0) \
TEST_ROUNDING(two3 , FIXNUM(2 , 3) , (2)+0 , (2)+0 +SFA , (2 )+1 , (2)+0) \
TEST_ROUNDING(two5 , FIXNUM(2 , 5) , (2)+0 , (2)+1 , (2 )+1 , (2)+0) \
TEST_ROUNDING(two7 , FIXNUM(2 , 7) , (2)+1 -SFA , (2)+1 , (2 )+1 , (2)+0) \
\
TEST_ROUNDING(zero_neg , FIXNUM(-0 , 0) , (0)-0 , (0)-0 , (0 )-0 , (0)-0) \
TEST_ROUNDING(zero3_neg , FIXNUM(-0 , 3) , (0)-0 , (0)-0 , (0 )-0 , (0)-1) \
TEST_ROUNDING(zero5_neg , FIXNUM(-0 , 5) , (0)-0 , (0)-0 , (0 )-0 , (0)-1) \
TEST_ROUNDING(zero7_neg , FIXNUM(-0 , 7) , (0)-1 +SFA , (0)-1+SFA , (0 )-0 , (0)-1) \
\
TEST_ROUNDING(one_neg , FIXNUM(-1 , 0) , -(1)-0 , -(1)-0 , -(1 )-0 , -(1)-0) \
TEST_ROUNDING(one3_neg , FIXNUM(-1 , 3) , -(1)-0-SFA , -(1)-0 , -(1 )-0 , -(1)-1) \
TEST_ROUNDING(one5_neg , FIXNUM(-1 , 5) , -(1)-1 , -(1)-0 , -(1 )-0 , -(1)-1) \
TEST_ROUNDING(one7_neg , FIXNUM(-1 , 7) , -(1)-1 , -(1)-1+SFA , -(1 )-0 , -(1)-1) \
\
TEST_ROUNDING(two_neg , FIXNUM(-2 , 0) , -(2)-0 , -(2)-0 , -(2 )-0 , -(2)-0) \
TEST_ROUNDING(two3_neg , FIXNUM(-2 , 3) , -(2)-0 , -(2)-0 , -(2 )-0 , -(2)-1) \
TEST_ROUNDING(two5_neg , FIXNUM(-2 , 5) , -(2)-0 , -(2)-0 , -(2 )-0 , -(2)-1) \
TEST_ROUNDING(two7_neg , FIXNUM(-2 , 7) , -(2)-1+SFA , -(2)-1+SFA , -(2 )-0 , -(2)-1) \
\
TEST_ROUNDING(max , FIX_MAX , FIX_INT_MAX , FIX_INT_MAX , FIX_INT_MAX , FIX_INT_MAX-1) \
TEST_ROUNDING(min , FIX_MIN , -FIX_INT_MAX , -FIX_INT_MAX , -FIX_INT_MAX , -FIX_INT_MAX) \
TEST_ROUNDING(nan , FIX_NAN , 0 , 0 , 0 , 0) \
TEST_ROUNDING(inf , FIX_INF_POS , INT_MAX , INT_MAX , INT_MAX , INT_MAX) \
TEST_ROUNDING(inf_neg , FIX_INF_NEG , INT_MIN , INT_MIN , INT_MIN , INT_MIN)
ROUNDING_TESTS
//////////////////////////////////////////////////////////////////////////////
#define FLOOR_CEIL(name, value, floor_result, ceil_result) \
TEST_HELPER(floor_ceil_##name, { \
fixed input = value; \
fixed floor = fix_floor(input); \
fixed floor_expected = FIX_IS_INF_POS(input) ? FIX_INF_POS : \
FIX_IS_INF_NEG(input) ? FIX_INF_NEG : \
(floor_result); \
CHECK_EQ_NAN("floor "#name, floor, floor_expected); \
fixed ceil = fix_ceil(input); \
fixed ceil_expected = FIX_IS_INF_POS(input) ? FIX_INF_POS : \
FIX_IS_INF_NEG(input) ? FIX_INF_NEG : \
(ceil_result); \
CHECK_EQ_NAN("ceil "#name, ceil, ceil_expected); \
};)
#define FIX_SMALLEST_INT (1ull << 63)
#define FLOOR_CEIL_TESTS \
FLOOR_CEIL(zero , FIXNUM(0 , 0) , FIXNUM(0 , 0) , FIXNUM(0 , 0)) \
FLOOR_CEIL(half , FIXNUM(0 , 5) , FIXNUM(0 , 0) , FIXNUM(1 , 0)) \
FLOOR_CEIL(half_neg , FIXNUM(-0 , 5) , FIXNUM(-1 , 0) , FIXNUM(0 , 0)) \
FLOOR_CEIL(one , FIXNUM(1 , 0) , FIXNUM(1 , 0) , FIXNUM(1 , 0)) \
FLOOR_CEIL(one_neg , FIXNUM(-1 , 0) , FIXNUM(-1 , 0) , FIXNUM(-1 , 0)) \
FLOOR_CEIL(pi , FIX_PI , FIXNUM(3 , 0) , \
FIX_INT_BITS > 3 ? FIXNUM(4 -SFA , 0) : FIX_INF_POS) \
FLOOR_CEIL(pi_neg , fix_neg(FIX_PI) , FIXNUM(-4 +SFA , 0) , FIXNUM(-3 , 0)) \
FLOOR_CEIL(max , FIX_MAX , FIXNUM(FIX_INT_MAX-1, 0), FIX_INF_POS) \
FLOOR_CEIL(max_almost,fix_sub(FIX_MAX, FIXNUM(1,0)), FIXNUM(FIX_INT_MAX-2, 0), FIXNUM(FIX_INT_MAX-1,0)) \
FLOOR_CEIL(min , FIX_MIN , FIX_SMALLEST_INT, FIX_SMALLEST_INT) \
FLOOR_CEIL(min_almost,fix_add(fix_neg(FIX_MAX), FIXNUM(1,0)), \
FIXNUM(-FIX_INT_MAX+1,0), \
FIXNUM(-FIX_INT_MAX+2,0)) \
FLOOR_CEIL(inf_pos , FIX_INF_POS , FIX_INF_POS , FIX_INF_POS) \
FLOOR_CEIL(inf_neg , FIX_INF_NEG , FIX_INF_NEG , FIX_INF_NEG) \
FLOOR_CEIL(nan , FIX_NAN , FIX_NAN , FIX_NAN)
FLOOR_CEIL_TESTS
//////////////////////////////////////////////////////////////////////////////
static void constants(void **state) {
fixed lpi = FIXNUM(3,1415926535897932385);
fixed ltau = FIXNUM(6,2831853071795864769);
fixed le = FIXNUM(2,7182818284590452354);
CHECK_EQ("pi", FIX_PI, lpi);
CHECK_EQ("tau", FIX_TAU, ltau);
CHECK_EQ("e", FIX_E, le);
if(FIX_INT_MAX > 7) {
// Do some basic functional tests
fixed temp = fix_abs(fix_sub(fix_sub(FIX_TAU, FIX_PI), FIX_PI));
fixed limit = FIX_ZERO;
for(int i = 0; i < 10; i++ ) {
limit = fix_add(limit, FIX_EPSILON);
}
char b1[FIX_PRINT_BUFFER_SIZE], b2[FIX_PRINT_BUFFER_SIZE];
fix_sprint(b1, temp);
fix_sprint(b2, FIX_PI);
if(fix_cmp(temp, limit) >= 0) {
fail_msg( "Tau - Pi - Pi is %s ("FIX_PRINTF_HEX
"), not near zero. Pi is %s ("FIX_PRINTF_HEX")",
b1, temp, b2, FIX_PI);
}
printf( "Tau - Pi - Pi is %s ("FIX_PRINTF_HEX")\n", b1, temp);
}
}
#define CONSTANT_TESTS cmocka_unit_test(constants),
//////////////////////////////////////////////////////////////////////////////
#define TEST_CMP(name, op1, op2, result) \
TEST_HELPER(cmp_##name, { \
fixed o1 = op1; \
fixed o2 = op2; \
int8_t cmp = fix_cmp(o1, o2); \
int8_t expected = result; \
CHECK_VALUE("cmp failed", cmp, expected, o1, o2); \
CHECK_VALUE("ne failed", fix_ne(o1, o2), ( (FIX_IS_NAN(o1) | FIX_IS_NAN(o2))) | (expected != 0), o1, o2); \
CHECK_VALUE("lt failed", fix_lt(o1, o2), (!(FIX_IS_NAN(o1) | FIX_IS_NAN(o2))) & (expected < 0), o1, o2); \
CHECK_VALUE("gt failed", fix_gt(o1, o2), (!(FIX_IS_NAN(o1) | FIX_IS_NAN(o2))) & (expected > 0), o1, o2); \
CHECK_VALUE("le failed", fix_le(o1, o2), (!(FIX_IS_NAN(o1) | FIX_IS_NAN(o2))) & (expected <= 0), o1, o2); \
CHECK_VALUE("ge failed", fix_ge(o1, o2), (!(FIX_IS_NAN(o1) | FIX_IS_NAN(o2))) & (expected >= 0), o1, o2); \
};)
#define CMP_TESTS \
TEST_CMP(zero_zero_eq , FIXNUM(0 , 0) , FIXNUM(0 , 0) , 0) \
TEST_CMP(pos_zero_gt , FIXNUM(1 , 0) , FIXNUM(0 , 0) , 1) \
TEST_CMP(neg_zero_lt , FIXNUM(-1 , 0) , FIXNUM(0 , 0) , -1) \
TEST_CMP(pos_pos_gt , FIXNUM(1 , 4) , FIXNUM(0 , 5) , 1) \
TEST_CMP(pos_pos_lt , FIXNUM(0 , 2) , FIXNUM(0 , 5) , -1) \
TEST_CMP(pos_pos_eq , FIXNUM(0 , 5) , FIXNUM(0 , 5) , 0) \
TEST_CMP(neg_neg_gt , FIXNUM(-0 , 4) , FIXNUM(-1 , 5) , 1) \
TEST_CMP(neg_neg_lt , FIXNUM(-0 , 9) , FIXNUM(-0 , 5) , -1) \
TEST_CMP(neg_neg_eq , FIXNUM(-0 , 5) , FIXNUM(-0 , 5) , 0) \
TEST_CMP(nan_nan , FIX_NAN , FIX_NAN , 1) \
TEST_CMP(nan_inf_pos , FIX_NAN , FIX_INF_POS , 1) \
TEST_CMP(nan_inf_neg , FIX_NAN , FIX_INF_NEG , 1) \
TEST_CMP(nan_pos , FIX_NAN , FIXNUM(0 , 5) , 1) \
TEST_CMP(nan_neg , FIX_NAN , FIXNUM(-0 , 5) , 1) \
TEST_CMP(pos_nan , FIXNUM(0 , 5) , FIX_NAN , 1) \
TEST_CMP(neg_nan , FIXNUM(-0 , 5) , FIX_NAN , 1) \
TEST_CMP(inf_inf , FIX_INF_POS , FIX_INF_POS , 0) \
TEST_CMP(inf_pos , FIX_INF_POS , FIXNUM(0 , 5) , 1) \
TEST_CMP(inf_neg , FIX_INF_POS , FIXNUM(-0 , 5) , 1) \
TEST_CMP(inf_inf_neg , FIX_INF_POS , FIX_INF_NEG , 1) \
TEST_CMP(pos_inf , FIXNUM(0 , 5) , FIX_INF_POS , -1) \
TEST_CMP(neg_inf , FIXNUM(-0 , 5) , FIX_INF_POS , -1) \
TEST_CMP(pos_inf_neg , FIXNUM(0 , 5) , FIX_INF_NEG , 1) \
TEST_CMP(neg_inf_neg , FIXNUM(-0 , 5) , FIX_INF_NEG , 1) \
TEST_CMP(inf_neg_inf_pos , FIX_INF_NEG , FIX_INF_POS , -1) \
TEST_CMP(inf_neg_pos , FIX_INF_NEG , FIXNUM(0 , 5) , -1) \
TEST_CMP(inf_neg_neg , FIX_INF_NEG , FIXNUM(-0 , 5) , -1) \
TEST_CMP(pos_neg , FIXNUM(17 , 3) , FIXNUM(-24 , 5) , 1) \
TEST_CMP(neg_pos , FIXNUM(-16 , 3) , FIXNUM(24 , 5) , -1)
CMP_TESTS
//////////////////////////////////////////////////////////////////////////////
#define ADD(name, op1, op2, result) \
TEST_HELPER(add_##name, { \
fixed o1 = op1; \
fixed o2 = op2; \
fixed added = fix_add(o1,o2); \
fixed expected = result; \
CHECK_EQ_NAN("add", added, expected); \
added = fix_add(o2,o1); \
CHECK_EQ_NAN("add (reversed)", added, expected); \
};)
#define ADD_TESTS \
ADD(zero_zero , FIXNUM(0 ,0) , FIXNUM(0,0 ) , FIXNUM(0,0)) \
ADD(frac_zero , FIXNUM(0 ,5) , FIXNUM(0,0 ) , FIXNUM(0,5)) \
ADD(frac_frac , FIXNUM(0 ,5) , FIXNUM(0,6 ) , FIXNUM(1,1)) \
ADD(one_zero , FIXNUM(1 ,0) , FIXNUM(0,0 ) , FIXNUM(1,0)) \
ADD(one_one , FIXNUM(1 ,0) , FIXNUM(1,0 ) , FIXNUM(2,0)) \
ADD(fifteen_one , FIXNUM(15,0) , FIXNUM(1,0 ) , FIXNUM(16,0)) \
ADD(pos_neg , FIXNUM(15,0) , FIXNUM(-1,5 ) , FIXNUM(13,5)) \
ADD(pos_neg_cross_zero, FIXNUM(0,5) , FIXNUM(-18,0) , FIXNUM(-17,5)) \
ADD(overflow , FIXNUM(FIX_INT_MAX-1,5), FIXNUM(FIX_INT_MAX-1,5) , FIX_INF_POS) \
ADD(overflow_neg , FIXNUM(-FIX_INT_MAX,0) , FIXNUM(-FIX_INT_MAX+1,5), FIX_INF_NEG) \
ADD(inf_number , FIX_INF_POS , FIXNUM(0 ,5) , FIX_INF_POS) \
ADD(inf_number_neg , FIX_INF_POS , FIXNUM(-1,0) , FIX_INF_POS) \
ADD(inf_neg_number , FIX_INF_NEG , FIXNUM(0 ,5) , FIX_INF_NEG) \
ADD(inf_neg_numberlneg, FIX_INF_NEG , FIXNUM(-1,0) , FIX_INF_NEG) \
ADD(nan , FIX_NAN , FIX_ZERO , FIX_NAN) \
ADD(nan_inf , FIX_NAN , FIX_INF_POS , FIX_NAN) \
ADD(nan_frac , FIX_NAN , FIXNUM(0,5) , FIX_NAN) \
ADD(inf_nan , FIX_INF_POS , FIX_NAN , FIX_NAN) \
ADD(nan_inf_neg , FIX_NAN , FIX_INF_NEG , FIX_NAN) \
ADD(inf_inf_neg , FIX_INF_POS , FIX_INF_NEG , FIX_INF_POS)
ADD_TESTS
//////////////////////////////////////////////////////////////////////////////
#define MUL(name, op1, op2, result) \
TEST_HELPER(mul_##name, { \
fixed o1 = op1; \
fixed o2 = op2; \
fixed muld = fix_mul(o1,o2); \
fixed expected = result; \
CHECK_EQ_NAN("multiply", muld, expected); \
};)
#define MUL_TESTS \
MUL(half_zero , FIXNUM(0,5) , FIXNUM(0,0) , FIXNUM(0,0)) \
MUL(one_one , FIXNUM(1,0) , FIXNUM(1,0) , FIXNUM(1,0)) \
MUL(fifteen_one , FIXNUM(15,0) , FIXNUM(1,0) , FIXNUM(15,0)) \
MUL(fifteen_two , FIXNUM(15,0) , FIXNUM(2,0) , FIXNUM(30,0)) \
MUL(nthree_15 , FIXNUM(-3,0) , FIXNUM(15,0) , FIXNUM(-45,0)) \
MUL(nthree_n15 , FIXNUM(-3,0) , FIXNUM(-15,0) , FIXNUM(45,0)) \
MUL(three_n15 , FIXNUM(3,0) , FIXNUM(-15,0) , FIXNUM(-45,0)) \
MUL(nfrac5_15 , FIXNUM(-0,5) , FIXNUM(-16,0) , FIXNUM(8,0)) \
MUL(inf_ten , FIX_INF_POS , FIXNUM(10,0) , FIX_INF_POS) \
MUL(inf_neg , FIX_INF_POS , FIXNUM(-10,0) , FIX_INF_NEG) \
MUL(ninf_neg , FIX_INF_NEG , FIXNUM(-10,0) , FIX_INF_POS) \
MUL(neg_inf , FIXNUM(-10,0) , FIX_INF_POS , FIX_INF_NEG) \
MUL(neg_ninf , FIXNUM(-10,0) , FIX_INF_NEG , FIX_INF_POS) \
MUL(pos_nan , FIXNUM(10,0) , FIX_NAN , FIX_NAN) \
MUL(neg_nan , FIXNUM(-10,0) , FIX_NAN , FIX_NAN) \
MUL(inf_nan , FIX_INF_POS , FIX_NAN , FIX_NAN) \
MUL(ninf_nan , FIX_INF_NEG , FIX_NAN , FIX_NAN) \
MUL(nan_pos , FIX_NAN , FIXNUM(10,0) , FIX_NAN) \
MUL(nan_neg , FIX_NAN , FIXNUM(-10,0) , FIX_NAN) \
MUL(nan_inf , FIX_NAN , FIX_INF_POS , FIX_NAN) \
MUL(nan_ninf , FIX_NAN , FIX_INF_NEG , FIX_NAN) \
MUL(overflow , FIXNUM(FIX_INT_MAX-1,5) , FIXNUM(2,0) , FIX_INF_POS) \
MUL(tinyoverflow , FIXNUM((SQRT_MAX+10),5) , FIXNUM((SQRT_MAX+10),5) , FIX_INF_POS) \
MUL(tinyoverflow_neg , FIXNUM((SQRT_MAX+10),5) , FIXNUM(-(SQRT_MAX+10),5) , FIX_INF_NEG) \
MUL(tinyoverflow_neg_neg , FIXNUM(-(SQRT_MAX+10),5), FIXNUM(-(SQRT_MAX+10),5) , FIX_INF_POS) \
MUL(underflow , FIX_EPSILON , FIX_EPSILON , FIX_ZERO) \
MUL(underflow_neg , fix_neg(FIX_EPSILON) , FIXNUM(0,0555) , FIX_ZERO) \
MUL(underflow_neg_rte , fix_neg(FIX_EPSILON) , FIXNUM(0,4555) , FIX_ZERO) \
MUL(zero_inf , FIXNUM(0,0) , FIX_INF_POS , FIXNUM(0,0)) \
MUL(zero_ninf , FIXNUM(0,0) , FIX_INF_NEG , FIXNUM(0,0)) \
MUL(zero_nan , FIXNUM(0,0) , FIX_NAN , FIX_NAN)
MUL_TESTS
//////////////////////////////////////////////////////////////////////////////
#define DIV(name, op1, op2, result) \
TEST_HELPER(div_##name, { \
fixed o1 = op1; \
fixed o2 = op2; \
fixed divd = fix_div(o1,o2); \
fixed expected = result; \
CHECK_EQ_NAN("divide", divd, expected); \
};)
#define DIV_TESTS \
DIV(one_one , FIXNUM(1,0) , FIXNUM(1,0) ,FIXNUM(1,0)) \
DIV(fifteen_one , FIXNUM(15,0) , FIXNUM(1,0) ,FIXNUM(15,0)) \
DIV(sixteen_two , FIXNUM(16,0) , FIXNUM(2,0) ,(FIX_INT_BITS > 5) ? FIXNUM(8,0) : FIX_INF_POS) \
DIV(fifteen_nthree , FIXNUM(15,0) , FIXNUM(-3,0) ,(FIX_INT_BITS > 4) ? FIXNUM(-5,0) : FIX_INF_NEG) \
DIV(nfifteen_nthree , FIXNUM(-15,0) , FIXNUM(-3,0) ,(FIX_INT_BITS > 4) ? FIXNUM(5,0) : FIX_INF_POS) \
DIV(nfifteen_three , FIXNUM(-15,0) , FIXNUM(3,0) ,(FIX_INT_BITS > 4) ? FIXNUM(-5,0) : FIX_INF_NEG) \
DIV(fifteen_frac5 , FIXNUM(15,0) , FIXNUM(0,5) ,FIXNUM(30,0)) \
DIV(overflow , FIXNUM(FIX_INT_MAX-1,5), FIXNUM(0,5) ,FIX_INF_POS) \
DIV(overflow2 , FIXNUM(FIX_INT_MAX-1,5), FIX_EPSILON ,FIX_INF_POS) \
DIV(underflow , FIX_EPSILON , FIXNUM(10,0) ,FIXNUM(0,0)) \
\
DIV(max_neg_ovf , FIXNUM(-FIX_INT_MAX,0) , FIXNUM(0,5) ,FIX_INF_NEG) \
DIV(max_neg_ovf_neg , FIXNUM(-FIX_INT_MAX,0) , FIXNUM(-0,5) ,FIX_INF_POS) \
DIV(max_neg_one , FIXNUM(-FIX_INT_MAX,0) , FIXNUM(1,0) ,(FIX_INT_BITS == 1) ? FIXNUM(0,0) : FIXNUM(-FIX_INT_MAX,0)) \
DIV(max_neg5_one , FIXNUM(-FIX_INT_MAX+1,5) , FIXNUM(1,0) ,(FIX_INT_BITS == 1) ? FIXNUM(0,0) : FIXNUM(-FIX_INT_MAX+1,5)) \
DIV(max_neg_two , FIXNUM(-FIX_INT_MAX,0) , FIXNUM(2,0) ,(FIX_INT_BITS <= 2) ? FIXNUM(0,0) : FIXNUM(-(FIX_INT_MAX/2),0)) \
DIV(max_neg5_two , FIXNUM(-FIX_INT_MAX+1,5) , FIXNUM(2,0) ,(FIX_INT_BITS <= 2) ? FIXNUM(0,0) : FIXNUM(-(FIX_INT_MAX/2)+1,75)) \
\
DIV(zero_zero , FIXNUM(0,0) , FIXNUM(0,0) ,FIX_NAN) \
DIV(one_zero , FIXNUM(1,0) , FIXNUM(0,0) ,FIX_INF_POS) \
DIV(none_zero , FIXNUM(-1,0) , FIXNUM(0,0) ,FIX_INF_NEG) \
DIV(inf_zero , FIX_INF_POS , FIXNUM(0,0) ,FIX_INF_POS) \
DIV(ninf_zero , FIX_INF_NEG , FIXNUM(0,0) ,FIX_INF_NEG) \
DIV(nan_zero , FIX_NAN , FIXNUM(0,0) ,FIX_NAN) \
\
DIV(zero_inf , FIXNUM(0,0) , FIX_INF_POS ,FIXNUM(0,0)) \
DIV(inf_neg , FIX_INF_POS , FIXNUM(-1,0) ,FIX_INF_NEG) \
DIV(ninf_neg , FIX_INF_NEG , FIXNUM(-1,0) ,FIX_INF_POS) \
DIV(neg_inf , FIXNUM(-1,0) , FIX_INF_POS ,FIXNUM(0,0)) \
DIV(neg_ninf , FIXNUM(-1,0) , FIX_INF_NEG ,FIXNUM(0,0)) \
DIV(pos_nan , FIXNUM(0,5) , FIX_NAN ,FIX_NAN) \
DIV(neg_nan , FIXNUM(-0,5) , FIX_NAN ,FIX_NAN) \
DIV(inf_inf , FIX_INF_POS , FIX_INF_POS ,FIX_INF_POS) \
DIV(ninf_inf , FIX_INF_NEG , FIX_INF_POS ,FIX_INF_NEG) \
DIV(inf_ninf , FIX_INF_POS , FIX_INF_NEG ,FIX_INF_NEG) \
DIV(inf_nan , FIX_INF_POS , FIX_NAN ,FIX_NAN) \
DIV(ninf_nan , FIX_INF_NEG , FIX_NAN ,FIX_NAN) \
DIV(nan_pos , FIX_NAN , FIXNUM(10,0) ,FIX_NAN) \
DIV(nan_neg , FIX_NAN , FIXNUM(-10,0) ,FIX_NAN) \
DIV(nan_inf , FIX_NAN , FIX_INF_POS ,FIX_NAN) \
DIV(nan_ninf , FIX_NAN , FIX_INF_NEG ,FIX_NAN)
DIV_TESTS
//////////////////////////////////////////////////////////////////////////////
#define NEG(name, op1, result) \
TEST_HELPER(neg_##name, { \
fixed o1 = op1; \
fixed negd = fix_neg(o1); \
fixed expected = result; \
CHECK_EQ_NAN(#name, negd, expected); \
};)
#define NEG_TESTS \
NEG(zero, FIXNUM(0,0) , FIXNUM(0,0)) \
NEG(half, FIXNUM(0,5) , FIXNUM(-0,5)) \
NEG(half_neg,FIXNUM(-0,5) , FIXNUM(0,5)) \
NEG(min, FIXNUM(-FIX_INT_MAX,0), FIX_INF_POS) \
NEG(inf, FIX_INF_POS , FIX_INF_NEG) \
NEG(inf_neg, FIX_INF_NEG , FIX_INF_POS) \
NEG(nan, FIX_NAN , FIX_NAN)
NEG_TESTS
//////////////////////////////////////////////////////////////////////////////
#define ABS(name, op1, result) \
TEST_HELPER(abs_##name, { \
fixed o1 = op1; \
fixed absd = fix_abs(o1); \
fixed expected = result; \
CHECK_EQ_NAN(#name, absd, expected); \
};)
#define ABS_TESTS \
ABS(zero , FIXNUM(0,0) , FIXNUM(0,0)) \
ABS(half , FIXNUM(0,5) , FIXNUM(0,5)) \
ABS(half_neg , FIXNUM(-0,5) , FIXNUM(0,5)) \
ABS(one , FIXNUM(1,0) , FIXNUM(1,0)) \
ABS(one_neg , FIXNUM(-1,0) , FIXNUM(1,0)) \
ABS(two , FIXNUM(2,0) , FIXNUM(2,0)) \
ABS(max_neg , FIXNUM(-FIX_INT_MAX,0), FIX_INF_POS) \
ABS(inf , FIX_INF_POS , FIX_INF_POS) \
ABS(inf_neg , FIX_INF_NEG , FIX_INF_POS) \
ABS(nan , FIX_NAN , FIX_NAN)
ABS_TESTS
//////////////////////////////////////////////////////////////////////////////
#define LN(name, op1, result) \
TEST_HELPER(ln_##name, { \
fixed o1 = op1; \
fixed ln = fix_ln(o1); \
fixed expected = result; \
if(FIX_IS_INF_POS(op1)) { \
expected = FIX_INF_POS; \
} \
CHECK_DIFFERENCE(#name, ln, expected, FIXNUM(0,000000000000004) | FIX_EPSILON); \
};)
#define LN_TESTS \
LN(zero , FIX_ZERO , FIX_INF_NEG) \
LN(half , FIXNUM(0,5) , FIXNUM(-0,6931471805599453094172321215)) \
LN(one , FIXNUM(1,0) , FIXNUM(0 , 0)) \
LN(two , FIXNUM(2,0) , FIXNUM(0,6931471805599453094172321215)) \
LN(four , FIXNUM(4,0) , FIXNUM(1,386294361119890618834464243)) \
LN(e , FIX_E , FIXNUM(1,0) ) \
LN(two75 , FIXNUM(2,75) , FIXNUM(1,011600911678479925227479335)) \
LN(ten , FIXNUM(10,0) , FIXNUM(2,302585092994045684017991455) ) \
LN(63 , FIXNUM(63,0) , FIXNUM(4,143134726391532687895843217)) \
LN(64 , FIXNUM(64,0) , FIXNUM(4,158883083359671856503392729)) \
LN(64_5 , FIXNUM(64,5) , FIXNUM(4,166665223801726805450855629)) \
LN(epsilon, FIX_EPSILON , FIX_TEST_LN_epsilon) \
LN(big , FIXNUM(536870911,0), FIXNUM(20,10126823437576882213405101290619719824480))\
LN(max , FIX_MAX , FIX_TEST_LN_max) \
LN(inf , FIX_INF_POS , FIX_INF_POS) \
LN(neg , FIXNUM(-1,0) , FIX_NAN) \
LN(nan , FIX_NAN , FIX_NAN)
LN_TESTS
//////////////////////////////////////////////////////////////////////////////
#define LOG2(name, op1, result) \
TEST_HELPER(log2_##name, { \
fixed o1 = op1; \
fixed log2 = fix_log2(o1); \
fixed expected = result; \
if(FIX_IS_INF_POS(op1)) { \
expected = FIX_INF_POS; \
} \
CHECK_DIFFERENCE(#name, log2, expected, FIXNUM(0,000000000000004) | FIX_EPSILON); \
};)
#define LOG2_TESTS \
LOG2(zero , FIX_ZERO , FIX_INF_NEG) \
LOG2(one , FIXNUM(1,0) , FIXNUM(0 , 0)) \
LOG2(two , FIXNUM(2,0) , FIXNUM(1 , 0)) \
LOG2(two75 , FIXNUM(2,75) , FIXNUM(1,4594316186372973)) \
LOG2(ten , FIXNUM(10,0) , FIXNUM(3,3219280948873626) ) \
LOG2(63 , FIXNUM(63,0) , FIXNUM(5,977279923499917)) \
LOG2(64 , FIXNUM(64,0) , FIXNUM(6, 0) ) \
LOG2(64_5 , FIXNUM(64,5) , FIXNUM(6,011227255423254)) \
LOG2(epsilon, FIX_EPSILON , FIX_TEST_LOG2_epsilon) \
LOG2(max , FIX_MAX , FIX_TEST_LOG2_max ) \
LOG2(min , FIX_MIN , FIX_NAN ) \
LOG2(inf , FIX_INF_POS , FIX_INF_POS) \
LOG2(neg , FIXNUM(-1,0) , FIX_NAN) \
LOG2(nan , FIX_NAN , FIX_NAN)
LOG2_TESTS
//////////////////////////////////////////////////////////////////////////////
#define LOG10(name, op1, result) \
TEST_HELPER(log10_##name, { \
fixed o1 = op1; \
fixed log10 = fix_log10(o1); \
fixed expected = result; \
if(FIX_IS_INF_POS(op1)) { \
expected = FIX_INF_POS; \
} \
CHECK_DIFFERENCE(#name, log10, expected, FIXNUM(0,000000000000004) | FIX_EPSILON); \
};)
#define LOG10_TESTS \
LOG10(zero , FIX_ZERO , FIX_INF_NEG) \
LOG10(half , FIXNUM(0,5) , FIXNUM(-0,3010299956639811952137388947)) \
LOG10(one , FIXNUM(1,0) , FIXNUM(0,0)) \
LOG10(two , FIXNUM(2,0) , FIXNUM(0,3010299956639811952137388947)) \
LOG10(two75 , FIXNUM(2,75) , FIXNUM(0,4393326938302626503227221818) ) \
LOG10(ten , FIXNUM(10,0) , FIXNUM(1,0) ) \
LOG10(fifteen, FIXNUM(15,0) , FIXNUM(1,176091259055681242081289009)) \
LOG10(63 , FIXNUM(63,0) , FIXNUM(1,799340549453581705302272065)) \
LOG10(64 , FIXNUM(64,0) , FIXNUM(1,806179973983887171282433368) ) \
LOG10(64_5 , FIXNUM(64,5) , FIXNUM(1,809559714635267768486377162)) \
LOG10(epsilon, FIX_EPSILON , FIX_TEST_LOG10_epsilon) \
LOG10(max , FIX_MAX , FIX_TEST_LOG10_max ) \
LOG10(inf , FIX_INF_POS , FIX_INF_POS) \
LOG10(neg , FIXNUM(-1,0) , FIX_NAN) \
LOG10(nan , FIX_NAN , FIX_NAN)
LOG10_TESTS
//////////////////////////////////////////////////////////////////////////////
#define EXP(name, op1, result) \
TEST_HELPER(exp_##name, { \
fixed o1 = op1; \
fixed exp = fix_exp(o1); \
fixed expected = result; \
if(FIX_IS_INF_POS(op1)) { \
expected = FIX_INF_POS; \
} else if (FIX_IS_INF_NEG(op1)) { \
expected = FIX_ZERO; \
}\
CHECK_DIFFERENCE(#name, exp, expected, ((expected >> 54) | FIX_EPSILON)); \
};)
/* Make sure we get the top 54 bits of expected right */
#define EXP_TESTS \
EXP(zero , FIX_ZERO , FIXNUM(1,0)) \
EXP(half , FIXNUM(0,5) , FIXNUM(1,648721270700128146848650787814163571653776100710148011575079)) \
EXP(half_neg , FIXNUM(-0,5) , FIXNUM(0,606530659712633423603799534991180453441918135487186955682892)) \
EXP(one , FIXNUM(1,0) , FIXNUM(2,718281828459045235360287471352662497757247093699959574966967)) \
EXP(one_neg , FIXNUM(-1,0) , FIXNUM(0,367879441171442321595523770161460867445811131031767834507836)) \
EXP(one_5 , FIXNUM( 1,5) , FIXNUM(4,481689070338064822602055460119275819005749868369667056772650)) \
EXP(one_5_neg, FIXNUM(-1,5) , FIXNUM(0,223130160148429828933280470764012521342171629361079328743835)) \
EXP(two , FIXNUM(2,0) , FIXNUM(7,389056098930650227230427460575007813180315570551847324087127)) \
EXP(two_neg , FIXNUM(-2,0) , FIXNUM(0,135335283236612691893999494972484403407631545909575881468158)) \
EXP(three5 , FIXNUM(3,5) , FIXNUM(33,11545195869231375065324935038861629247172822647794098886094)) \
EXP(three5_neg, FIXNUM(-3,5) , FIXNUM(0,030197383422318500739786292363619845071660532247657006671340)) \
EXP(four , FIXNUM(4,0) , FIXNUM(54,59815003314423907811026120286087840279073703861406872582659)) \
EXP(four_neg , FIXNUM(-4,0) , FIXNUM(0,018315638888734180293718021273241242211912067553475594769599)) \
EXP(ten , FIXNUM(10,0) , FIXNUM(22026,46579480671651695790064528424436635351261855678107423542)) \
EXP(ten_neg , FIXNUM(-10,0) , FIXNUM(0,000045399929762484851535591515560550610237918088866564969259)) \
EXP(neg_many , FIXNUM(-128,0) , FIXNUM(0,000000000000000000000000000000000000000000000000000000000000)) \
EXP(forty , FIXNUM(40,0) , FIXNUM(235385266837019985,40789991074903480450887161725455546)) \
EXP(max , FIX_MAX , FIX_INF_POS) \
EXP(nan , FIX_NAN , FIX_NAN) \
EXP(inf , FIX_INF_POS , FIX_INF_POS) \
EXP(inf_neg , FIX_INF_NEG , FIX_ZERO)
EXP_TESTS
//////////////////////////////////////////////////////////////////////////////
// Sometimes we compute results with doubles, and those results can be wrong due
// to double's 53-bit precision. Set a pretty high difference when comparing the
// sqrt results, but re-check by computing the square of the sqrt.
#define SQRT(name, op1, result) \
TEST_HELPER(sqrt_##name, { \
fixed o1 = op1; \
fixed fsqrt = fix_sqrt(o1); \
fixed expected = result; \
fixed square = fix_mul(fsqrt, fsqrt); \
if(!FIX_EQ_NAN(fsqrt, expected)) { \
/* compute the square error bars using doubles. If the square root is within
* an Epsilon of the the real square root, the squared square root will be
* how far from the original number?
*
* Because doubles are dumb, check that there's enough bits...
* */ \
double dsqrt = fix_convert_to_double(expected); \
double eps = fix_convert_to_double(FIX_EPSILON); \
if(fixed_log2(expected) > 53) { \
/* adding epsilon to expected as a double won't do anything; make epsilon
* larger */ \
eps = fix_convert_to_double(FIX_DATA_BITS(expected >> 52)); \
} \
double squarederror = ((dsqrt+eps)*(dsqrt+eps)) - (dsqrt * dsqrt); \
fixed errorbar = fix_convert_from_double(squarederror); \
CHECK_DIFFERENCE(#name " sqrt", fsqrt, expected, 0x80); \
CHECK_DIFFERENCE(#name " square", square, op1, errorbar); \
} else { \
CHECK_EQ_NAN(#name, fsqrt, expected); \
} \
};)
#define SQRT_TESTS \
SQRT(zero , FIX_ZERO , FIXNUM(0,0)) \
SQRT(half , FIXNUM(0,5) , FIXNUM(0,7071067811865475244008443621)) \
SQRT(one , FIXNUM(1,0) , FIXNUM(1,0)) \
SQRT(two , FIXNUM(2,0) , FIX_INT_BITS >= 3 ? FIXNUM(1,4142135623730951) : FIX_INF_POS) \
SQRT(e , FIX_E , FIX_INT_BITS >= 3 ? FIXNUM(1,6487212707001282) : FIX_INF_POS) \
SQRT(ten , FIXNUM(10,0) , FIX_INT_BITS >= 5 ? FIXNUM(3,1622776601683795) : FIX_INF_POS) \
SQRT(big , FIXNUM(10000,5345), FIX_INT_BITS > 14 ? FIXNUM(100,00267246428967) : FIX_INF_POS) \
SQRT(max , FIX_MAX , SQRT_MAX_FIXED) \
SQRT(inf , FIX_INF_POS , FIX_INF_POS) \
SQRT(neg , FIXNUM(-1,0) , FIX_NAN) \
SQRT(nan , FIX_NAN , FIX_NAN)
SQRT_TESTS
//////////////////////////////////////////////////////////////////////////////
#define POW(name, op1, op2, result, bitaccuracy) \
TEST_HELPER(pow_##name, { \
fixed o1 = op1; \
fixed o2 = op2; \
fixed powresult = fix_pow(o1, o2); \
fixed expected = result; \
if(FIX_IS_INF_POS(o1) && !FIX_IS_NAN(o2)) { \
expected = FIX_INF_POS; \
} \
if(FIX_IS_INF_NEG(o1) && !FIX_IS_NAN(o2) && (FIX_IS_INF_POS(o2))) { \
expected = FIX_INF_NEG; \
} \
fixed bound = ((FIX_EPSILON) + FIX_DATA_BITS( (((bitaccuracy) >= 0) ? ((expected) >> (bitaccuracy)) : ((expected) << (-(bitaccuracy))) )) ); \
CHECK_DIFFERENCE(#name, powresult, expected, bound); \
};)
/* We add FIX_EPSILON to the shifted result above in order to ignore rounding
* issues when shifting expected, and to always allow a FIX_EPSILON upper bound on error. */
#define POW_TESTS \
POW(zero_zero , FIX_ZERO , FIX_ZERO , FIXNUM(1,0) , 63) \
POW(zero_one , FIX_ZERO , FIXNUM(1,0) , FIX_ZERO , 63) \
POW(half_zero , FIXNUM(0,5) , FIX_ZERO , FIXNUM(1,0) , 63 ) \
POW(half_square , FIXNUM(0,5) , FIXNUM(2,0) , FIX_INT_BITS < 3 ? FIX_ZERO : FIXNUM(0,25) , FIX_FRAC_BITS < 47 ? FIX_FRAC_BITS-1 : 46) \
POW(half_nsquare , FIXNUM(0,5) , FIXNUM(-2,0) , FIX_INT_BITS < 4 ? FIX_INF_POS : FIXNUM(4,0), FIX_FRAC_BITS < 47 ? FIX_FRAC_BITS-1 : 46) \
POW(half_neight , FIXNUM(0,5) , FIXNUM(-8,0) , FIX_INT_BITS < 4 ? FIX_INF_POS : \
FIX_INT_BITS < 9 ? FIX_INF_POS : FIXNUM(256 ,0), FIX_FRAC_BITS <= 1 ? FIX_FRAC_BITS - 6 : \
FIX_FRAC_BITS < 48 ? FIX_FRAC_BITS-4 : 44) \
POW(sqrt , FIXNUM(536870911,0), FIXNUM(0,5) , \
FIX_INT_BITS <= 29 ? FIX_INF_POS : \
FIXNUM(23170,4749843416028319405320375889409653360224397842555396195) \
, FIX_FRAC_BITS >= 48 ? 48 : FIX_FRAC_BITS) \
/* (1 + 2^-13) */ \
POW(epsilon , FIXNUM(1,0001220703125), FIXNUM(70911,0), \
FIX_INT_BITS <= 17 ? FIX_INF_POS : \
FIXNUM(5742,211216908114514755729967881141948869288460297210364158767605983527118659), \
FIX_FRAC_BITS < 13 ? 0 : \
FIX_FRAC_BITS <= 15 ? FIX_FRAC_BITS - 20 : \
FIX_FRAC_BITS <= 47 ? FIX_FRAC_BITS - 16 : \
31 \
) \
\
POW(one2 , FIXNUM( 1,0) , FIXNUM( 2,0) , FIXNUM(1 ,0) , FIX_FRAC_BITS < 47 ? FIX_FRAC_BITS-2 : 46) \
POW(one4 , FIXNUM( 1,0) , FIXNUM( 4,0) , FIXNUM(1 ,0) , FIX_FRAC_BITS < 48 ? FIX_FRAC_BITS-3 : 45) \
POW(two_sqrt , FIXNUM( 2,0) , FIXNUM( 0,5) , FIXNUM(1 ,41421356237309504880168872421) , FIX_FRAC_BITS < 48 ? FIX_FRAC_BITS-1 : 48) \
POW(ten_sqrt , FIXNUM(10,0) , FIXNUM( 0,5) , FIXNUM(3 ,16227766016837933199889354443) , FIX_FRAC_BITS < 36 ? FIX_FRAC_BITS : 35) \
POW(ten_square , FIXNUM(10,0) , FIXNUM( 2,0) , FIXNUM(100 ,0) , FIX_FRAC_BITS < 47 ? FIX_FRAC_BITS-2 : 46) \
POW(ten_odd , FIXNUM(10,0) , FIXNUM( 1,5) , FIXNUM(31 ,6227766016837933199889354443) , FIX_FRAC_BITS < 48 ? FIX_FRAC_BITS-1 : 47) \
POW(ten_cubed , FIXNUM(10,0) , FIXNUM( 3,0) , FIXNUM(1000,0) , FIX_FRAC_BITS < 47 ? FIX_FRAC_BITS-2 : 46) \
POW(neg_one2 , FIXNUM(-1,0) , FIXNUM( 2,0) , FIX_INT_BITS <= 2 ? FIXNUM(-1, 0) : FIXNUM(1,0), FIX_FRAC_BITS < 47 ? FIX_FRAC_BITS-2 : 46) \
POW(neg_one3 , FIXNUM(-1,0) , FIXNUM( 3,0) , FIXNUM(-1 ,0) , FIX_FRAC_BITS < 47 ? FIX_FRAC_BITS-2 : 46) \
POW(neg_two2 , FIXNUM(-1,5) , FIXNUM( 2,0) , FIX_INT_BITS <= 2 ? FIX_INF_NEG : FIXNUM(2,25), FIX_FRAC_BITS < 47 ? FIX_FRAC_BITS-2 : 46) \
POW(neg_two3 , FIXNUM(-2,0) , FIXNUM( 3,0) , FIX_INT_BITS <= 3 ? FIX_INF_NEG : FIXNUM(-8,0), FIX_FRAC_BITS < 47 ? FIX_FRAC_BITS-2 : 46) \
POW(neg_two_neg2 , FIXNUM(-2,0) , FIXNUM(-2,0) , FIX_INT_BITS <= 1 ? FIX_INF_NEG : \
FIX_INT_BITS <= 2 ? FIX_INF_POS : FIXNUM(0,25), FIX_FRAC_BITS < 47 ? FIX_FRAC_BITS-2 : 46) \
POW(neg_nan , FIXNUM(-0,5) , FIXNUM( 0,5) , FIX_NAN, 63) \
POW(neg_pos_oflw , FIXNUM(-2,0) , FIXNUM(536870910,0), FIX_INT_BITS <= 29 ? FIX_INF_NEG : FIX_INF_POS, 63) \
\
POW(nan_not , FIX_NAN , FIXNUM(1,0) , FIX_NAN, 63) \
POW(not_nan , FIXNUM(0,5) , FIX_NAN , FIX_NAN, 63) \
\
POW(oflw_inf_gt , FIXNUM( 1,5) , FIX_INF_POS , FIX_INF_POS , 63) \
POW(oflw_inf_one , FIXNUM( 1,0) , FIX_INF_POS , FIXNUM(1,0) , 63) \
POW(oflw_inf_hlf , FIXNUM( 0,5) , FIX_INF_POS , FIX_ZERO , 63) \
POW(oflw_inf_zero , FIXNUM( 0,0) , FIX_INF_POS , FIX_ZERO , 63) \
POW(oflw_inf_nhlf , FIXNUM(-0,5) , FIX_INF_POS , FIX_ZERO , 63) \
POW(oflw_inf_none , FIXNUM(-1,0) , FIX_INF_POS , FIXNUM(-1,0), 63) \
POW(oflw_inf_ngt , FIXNUM(-1,5) , FIX_INF_POS , FIX_INF_NEG , 63) \
\
POW(oflw_ninf_gt , FIXNUM( 1,5) , FIX_INF_NEG , FIX_ZERO , 63) \
POW(oflw_ninf_one , FIXNUM( 1,0) , FIX_INF_NEG , FIXNUM(1,0) , 63) \
POW(oflw_ninf_hlf , FIXNUM( 0,5) , FIX_INF_NEG , FIX_INF_POS , 63) \
POW(oflw_ninf_zero , FIXNUM( 0,0) , FIX_INF_NEG , FIX_ZERO , 63) \
POW(oflw_ninf_nhlf , FIXNUM(-0,5) , FIX_INF_NEG , FIX_INF_NEG , 63) \
POW(oflw_ninf_none , FIXNUM(-1,0) , FIX_INF_NEG , FIXNUM(-1,0), 63) \
POW(oflw_ninf_ngt , FIXNUM(-1,5) , FIX_INF_NEG , FIX_INT_BITS < 2 ? FIX_INF_NEG : FIX_ZERO, 63) \
\
POW(neg_overflow , FIXNUM(-2,0) , FIXNUM(127,0), FIX_INF_NEG, 63) \
POW(pos_overflow , FIXNUM( 2,0) , FIXNUM(100,0), FIX_INF_POS, 63) \
POW(inf_not , FIX_INF_POS , FIXNUM(1,0) , FIX_INF_POS, 63)
POW_TESTS
//////////////////////////////////////////////////////////////////////////////
// To print out all sins:
//int roots_of_unity = 16;
//fixed x = fix_neg(FIX_TAU);
//fixed step = fix_div(FIX_TAU, FIXINT(roots_of_unity));
//for(int i = 0; i <= roots_of_unity * 4; i++) {
// printf("\nsin of:");
// pl(x);
// printf(": ");
// pl(fix_sin(x));
// x = fix_add(x, step);
//}
//printf("\n");
//p(fix_sin(FIX_PI));
/**#define SIN(name, op1, result) \
*TEST_HELPER(sin_##name, { \
* fixed o1 = op1; \
* fixed sin = fix_sin_fast(o1); \
* fixed expected = result; \
* CHECK_EQ_NAN(#name, sin, expected); \
*};)
*#define SIN_TESTS \
*SIN(zero , FIX_ZERO , 0) \
*SIN(pi_2 , fix_div(FIX_PI , FIXNUM(2 , 0)) , 0x1fffc) \
*SIN(pi , FIX_PI , 0xfffffffc) \
*SIN(pi3_2 , fix_div(fix_mul(FIX_PI, FIXNUM(3,0)), FIXNUM(2,0)) , 0xfffe0000) \
*SIN(pi2 , fix_mul(FIX_PI, FIXNUM(2,0)) , 0) \
*SIN(pi5_2 , fix_div(fix_mul(FIX_PI, FIXNUM(5,0)), FIXNUM(2,0)) , 0x1fffc) \
*SIN(pi3 , fix_mul(FIX_PI, FIXNUM(3,0)) , 0xfffffffc) \
*SIN(pi7_2 , fix_div(fix_mul(FIX_PI, FIXNUM(7,0)), FIXNUM(2,0)) , 0xfffe0000) \
*SIN(pi4 , fix_mul(FIX_PI, FIXNUM(4,0)) , 0x4) \
* \
*SIN(neg_pi_2 , fix_neg(fix_div(FIX_PI , FIXNUM(2 , 0))) , 0xfffe0000) \
*SIN(neg_pi , fix_neg(FIX_PI) , 0x0) \
*SIN(neg_pi3_2 , fix_neg(fix_div(fix_mul(FIX_PI, FIXNUM(3,0)), FIXNUM(2,0))) , 0x1fffc) \
*SIN(neg_pi2 , fix_neg(fix_mul(FIX_PI, FIXNUM(2,0))) , 0xfffffffc) \
* \
*SIN(inf_pos , FIX_INF_POS , FIX_INF_POS) \
*SIN(inf_neg , FIX_INF_NEG , FIX_INF_NEG) \
*SIN(nan , FIX_NAN , FIX_NAN)
*SIN_TESTS