void test(double d1, double d2, float f1, float f2,
long double ld1, long double ld2)
{
+ /* Test logN(1) -> 0. */
#define LOG_1(LOG) \
extern void link_failure_##LOG##_1(void); \
if (LOG(1.0) != 0.0 || LOG##f(1.0F) != 0.0F || LOG##l(1.0L) != 0.0L) \
LOG_1(log2);
LOG_1(log10);
+ /* Test logN(N) -> 1. */
#define LOG_N(LOG, BASE) \
extern void link_failure_##LOG##_N(void); \
if (LOG(BASE) != 1.0 || LOG##f(BASE##F) != 1.0F || LOG##l(BASE##L) != 1.0L) \
LOG_N(log2, 2.0);
LOG_N(log10, 10.0);
+ /* Test logN(expN(x)) -> x. */
#define LOGEXP_SAME(LOG, EXP) \
extern void link_failure_##LOG##_##EXP##_same(void); \
if (LOG(EXP(d1)) != d1 || LOG##f(EXP##f(f1)) != f1 \
LOGEXP_SAME(log10,exp10);
LOGEXP_SAME(log10,pow10);
+ /* Test logN(expM(x)) -> x*logN(M). */
#define LOGEXP(LOG, EXP, BASE) \
extern void link_failure_##LOG##_##EXP(void); \
if (LOG(EXP(d1)) != d1*LOG(BASE) || LOG##f(EXP##f(f1)) != f1*LOG##f(BASE##F) \
LOGEXP(log10,exp10,10.0);
LOGEXP(log10,pow10,10.0);
+ /* Test logN(sqrt(x)) -> 0.5*logN(x). */
#define LOG_SQRT(LOG) \
extern void link_failure_##LOG##_sqrt(void); \
if (LOG(sqrt(d1)) != 0.5*LOG(d1) || LOG##f(sqrtf(f1)) != 0.5F*LOG##f(f1) \
LOG_SQRT(log2);
LOG_SQRT(log10);
+ /* Test sqrt(expN(x)) -> expN(x*0.5). */
+#define SQRT_EXP(EXP) \
+ extern void link_failure_sqrt_##EXP(void); \
+ if (sqrt(EXP(d1)) != EXP(d1*0.5) || sqrtf(EXP##f(f1)) != EXP##f(f1*0.5F) \
+ || sqrtl(EXP##l(ld1)) != EXP##l(ld1*0.5L)) link_failure_sqrt_##EXP()
+
+ SQRT_EXP(exp);
+ SQRT_EXP(exp2);
+ SQRT_EXP(exp10);
+ SQRT_EXP(pow10);
+
+ /* Test logN(cbrt(x)) -> (1/3)*logN(x). */
#define LOG_CBRT(LOG) \
extern void link_failure_##LOG##_cbrt(void); \
if (LOG(cbrt(d1)) != (1.0/3)*LOG(d1) \
LOG_CBRT(log2);
LOG_CBRT(log10);
-#define LOGPOW(LOG, POW) \
+ /* Test logN(pow(x,y)) -> y*logN(x). */
+#define LOG_POW(LOG, POW) \
extern void link_failure_##LOG##_##POW(void); \
if (LOG(POW(d1,d2)) != d2*LOG(d1) || LOG##f(POW##f(f1,f2)) != f2*LOG##f(f1) \
|| LOG##l(POW##l(ld1,ld2)) != ld2*LOG##l(ld1)) link_failure_##LOG##_##POW()
- LOGPOW(log,pow);
- LOGPOW(log2,pow);
- LOGPOW(log10,pow);
+ LOG_POW(log,pow);
+ LOG_POW(log2,pow);
+ LOG_POW(log10,pow);
+
+ /* Test pow(expN(x),y)) -> expN(x*y). */
+#define POW_EXP(POW, EXP) \
+ extern void link_failure_##POW##_##EXP(void); \
+ if (POW(EXP(d1),d2) != EXP(d1*d2) || POW##f(EXP##f(f1),f2) != EXP##f(f1*f2) \
+ || POW##l(EXP##l(ld1),ld2) != EXP##l(ld1*ld2)) link_failure_##POW##_##EXP()
+
+ POW_EXP(pow, exp);
+ POW_EXP(pow, exp2);
+ POW_EXP(pow, exp10);
+ POW_EXP(pow, pow10);
+ /* Test expN(0) -> 1. */
#define EXP_0(EXP) \
extern void link_failure_##EXP##_0(void); \
if (EXP(0.0) != 1.0 || EXP##f(0.0F) != 1.0F || EXP##l(0.0L) != 1.0L) \
EXP_0(exp10);
EXP_0(pow10);
+ /* Test expN(1) -> N. */
#define EXP_N(EXP, BASE) \
extern void link_failure_##EXP##_N(void); \
if (EXP(1.0) != BASE || EXP##f(1.0F) != BASE##F || EXP##l(1.0L) != BASE##L) \
EXP_N(exp10, 10.0);
EXP_N(pow10, 10.0);
+ /* Test expN(integer) -> N*N*N*... */
#define EXP_INT(EXP, BASE) \
extern void link_failure_##EXP##_INT(void); \
if (EXP(5.0) < (BASE)*(BASE)*(BASE)*(BASE)*(BASE) - PREC \
EXP_INT(exp10, 10.0);
EXP_INT(pow10, 10.0);
+ /* Test expN(logN(x)) -> x. */
#define EXPLOG_SAME(EXP, LOG) \
extern void link_failure_##EXP##_##LOG##_same(void); \
if (EXP(LOG(d1)) != d1 || EXP##f(LOG##f(f1)) != f1 \
EXPLOG_SAME(exp10, log10);
EXPLOG_SAME(pow10, log10);
+ /* Test expN(x)*expN(y)) -> expN(x+y). */
#define EXPXEXP(EXP) \
extern void link_failure_##EXP##X##EXP(void); \
if (EXP(d1)*EXP(d2) != EXP(d1+d2) || EXP##f(f1)*EXP##f(f2) != EXP##f(f1+f2) \
EXPXEXP(exp10);
EXPXEXP(pow10);
+ /* Test x/expN(y) -> x*expN(-y). */
+ /* Test expN(x)/expN(y) -> expN(x-y). */
#define DIVEXP(EXP) \
extern void link_failure_div1_##EXP(void); \
if (d1/EXP(d2) != d1*EXP(-d2) || f1/EXP##f(f2) != f1*EXP##f(-f2) \