libm: fix tgamma to actually do return true gamma function

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>

libm/e_lgamma_r.c

@@ -360,31 +360,35 @@ strong_alias(__ieee754_lgamma, gamma)
 #endif
 
 
-/* FIXME! Looks like someone just used __ieee754_gamma_r,
- * believing it's a "true" gamma function, but it was not!
- * Our tgamma is WRONG.
- */
-
 /* double tgamma(double x)
  * Return the Gamma function of x.
  */
 double tgamma(double x)
 {
-	double y;
-	int local_signgam;
+	int sign_of_gamma;
+	int32_t hx;
+	u_int32_t lx;
 
-	y = __ieee754_lgamma_r(x, &local_signgam); // was __ieee754_gamma_r
-	if (local_signgam < 0)
-		y = -y;
-#ifndef _IEEE_LIBM
-	if (_LIB_VERSION == _IEEE_)
-		return y;
-	if (!isfinite(y) && isfinite(x)) {
-		if (floor(x) == x && x <= 0.0)
-			return __kernel_standard(x, x, 41); /* tgamma pole */
-		return __kernel_standard(x, x, 40); /* tgamma overflow */
+	/* We don't have a real gamma implementation now.  We'll use lgamma
+	   and the exp function.  But due to the required boundary
+	   conditions we must check some values separately.  */
+
+	EXTRACT_WORDS(hx, lx, x);
+
+	if (((hx & 0x7fffffff) | lx) == 0) {
+		/* Return value for x == 0 is Inf with divide by zero exception.  */
+		return 1.0 / x;
 	}
-#endif
-	return y;
+	if (hx < 0 && (u_int32_t)hx < 0xfff00000 && rint(x) == x) {
+		/* Return value for integer x < 0 is NaN with invalid exception.  */
+		return (x - x) / (x - x);
+	}
+	if ((u_int32_t)hx == 0xfff00000 && lx == 0) {
+		/* x == -Inf.  According to ISO this is NaN.  */
+		return x - x;
+	}
+
+	x = exp(lgamma_r(x, &sign_of_gamma));
+	return sign_of_gamma >= 0 ? x : -x;
 }
 libm_hidden_def(tgamma)

test/math/Makefile.in

@@ -3,6 +3,7 @@
 
 TESTS := basic-test tst-definitions test-fpucw test-float test-ifloat test-double test-idouble \
     rint signgam ilogb
+# gamma (removed from TESTS, need to add "small errors are ok" machinery there)
 ifeq ($(UCLIBC_HAS_LONG_DOUBLE_MATH),y)
 TESTS += test-ldouble test-ildoubl compile_test c99_test
 else

test/math/c99_test.c

@@ -1,4 +1,3 @@
-//#define _GNU_SOURCE 1
 #include <math.h>
 #include <float.h>
 #include <stdlib.h>

test/math/gamma.c

@@ -0,0 +1,73 @@
+#include <math.h>
+#include <float.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <stdio.h>
+
+#define check_d1(func, param, expected) \
+do { \
+	int err; hex_union ur; hex_union up; \
+	double result = func(param); up.f = param; ur.f = result; \
+	errors += (err = (result != (expected))); \
+	err \
+	? printf("FAIL: %s(%g/"HEXFMT")=%g/"HEXFMT" (expected %g)\n", \
+		#func, (double)(param), (long long)up.hex, result, (long long)ur.hex, (double)(expected)) \
+	: printf("PASS: %s(%g)=%g\n", #func, (double)(param), result); \
+} while (0)
+
+#define HEXFMT "%08llx"
+typedef union {
+	double f;
+	uint64_t hex;
+} hex_union;
+double result;
+
+#define M_2_SQRT_PIl   3.5449077018110320545963349666822903L   /* 2 sqrt (M_PIl)  */
+#define M_SQRT_PIl     1.7724538509055160272981674833411451L   /* sqrt (M_PIl)  */
+
+double zero = 0.0;
+double minus_zero = 0.0;
+double nan_value = 0.0;
+int errors = 0;
+
+int main(void)
+{
+        nan_value /= nan_value;
+        minus_zero = copysign(zero, -1.0);
+
+	//check_d1(tgamma, HUGE_VAL, NAN);
+	//check_d1(tgamma, negative_integer, NAN);
+	check_d1(tgamma, 0.0, HUGE_VAL); /* pole */
+	check_d1(tgamma, minus_zero, -HUGE_VAL); /* pole */
+	check_d1(tgamma, DBL_MAX/2, HUGE_VAL); /* overflow to inf */
+	check_d1(tgamma, DBL_MAX, HUGE_VAL); /* overflow to inf */
+	check_d1(tgamma, HUGE_VAL, HUGE_VAL); /* overflow to inf */
+	check_d1(tgamma, 7, 2*3*4*5*6); /* normal value */
+	check_d1(tgamma, -0.5, -M_2_SQRT_PIl); /* normal value (testing negative points) */
+
+	check_d1(lgamma, -HUGE_VAL, HUGE_VAL);
+	//check_d1(lgamma, HUGE_VAL, NAN);
+	check_d1(lgamma, 0.0, HUGE_VAL); /* pole */
+	check_d1(lgamma, minus_zero, HUGE_VAL); /* pole */
+	check_d1(lgamma, 1.0, 0.0);
+	check_d1(lgamma, 2.0, 0.0);
+	check_d1(lgamma, DBL_MAX/2, HUGE_VAL); /* overflow to inf */
+	check_d1(lgamma, DBL_MAX, HUGE_VAL); /* overflow to inf */
+	check_d1(lgamma, HUGE_VAL, HUGE_VAL); /* overflow to inf */
+	check_d1(lgamma, 7, log(2*3*4*5*6)); /* normal value */
+
+	/* In glibc, gamma == lgamma. (In BSD, it's == tgamma */
+	check_d1(gamma, -HUGE_VAL, HUGE_VAL);
+	//check_d1(gamma, HUGE_VAL, NAN);
+	check_d1(gamma, 0.0, HUGE_VAL); /* pole */
+	check_d1(gamma, minus_zero, HUGE_VAL); /* pole */
+	check_d1(gamma, 1.0, 0.0);
+	check_d1(gamma, 2.0, 0.0);
+	check_d1(gamma, DBL_MAX/2, HUGE_VAL); /* overflow to inf */
+	check_d1(gamma, DBL_MAX, HUGE_VAL); /* overflow to inf */
+	check_d1(gamma, HUGE_VAL, HUGE_VAL); /* overflow to inf */
+	check_d1(gamma, 7, log(2*3*4*5*6)); /* normal value */
+
+	printf("Errors: %d\n", errors);
+	return errors;
+}

test/math/ilogb.c

@@ -1,4 +1,5 @@
 #include <math.h>
+#include <float.h>
 #include <stdlib.h>
 #include <stdint.h>
 #include <limits.h>

test/math/rint.c

@@ -1,4 +1,5 @@
 #include <math.h>
+#include <float.h>
 #include <stdlib.h>
 #include <stdint.h>
 #include <stdio.h>
@@ -6,12 +7,12 @@
 #define check_d1(func, param, expected) \
 do { \
 	int err; hex_union ur; hex_union up; \
-	up.f = param; ur.f = result = func(param); \
-	errors += (err = (result != expected)); \
+	double result = func(param); up.f = param; ur.f = result; \
+	errors += (err = (result != (expected))); \
 	err \
 	? printf("FAIL: %s(%g/"HEXFMT")=%g/"HEXFMT" (expected %g)\n", \
-		#func, (param), (long long)up.hex, result, (long long)ur.hex, expected) \
-	: printf("PASS: %s(%g)=%g\n", #func, (param), result); \
+		#func, (double)(param), (long long)up.hex, result, (long long)ur.hex, (double)(expected)) \
+	: printf("PASS: %s(%g)=%g\n", #func, (double)(param), result); \
 } while (0)
 
 #define HEXFMT "%08llx"
@@ -27,6 +28,6 @@ int main(void)
 {
 	check_d1(rint, 0.6, 1.0);
 
-        printf("Errors: %d\n", errors);
-        return errors;
+	printf("Errors: %d\n", errors);
+	return errors;
 }

test/math/signgam.c

@@ -1,5 +1,6 @@
 #define _XOPEN_SOURCE 600
 #include <math.h>
+#include <float.h>
 #include <stdio.h>
 
 double zero = 0.0;