The old tgamma=exp(lgamma) implementation had high rounding error on
large outputs, exceeding the 16ulp specification for approx. x>8
(hence the test failure in strict conformance mode).
Replace this with an implementation based on glibc's
http://sources.debian.net/src/glibc/2.19-17/sysdeps/ieee754/flt-32/e_gammaf_r.c/
Signed-off-by: Rebecca Palmer <rebecca_pal...@zoho.com>
diff --git a/backend/src/libocl/tmpl/ocl_math.tmpl.cl
b/backend/src/libocl/tmpl/ocl_math.tmpl.cl
index da5b9a9..49edd95 100644
--- a/backend/src/libocl/tmpl/ocl_math.tmpl.cl
+++ b/backend/src/libocl/tmpl/ocl_math.tmpl.cl
@@ -1744,12 +1744,6 @@ OVERLOADABLE float __gen_ocl_internal_exp(float x) {
}
}
-INLINE_OVERLOADABLE float tgamma(float x) {
- float y;
- int s;
- y=lgamma_r(x,&s);
- return __gen_ocl_internal_exp(y)*s;
-}
/* erf,erfc from glibc s_erff.c -- float version of s_erf.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, i...@cygnus.com.
@@ -3165,6 +3159,95 @@ float __gen_ocl_internal_pown(float x, int y) {
return sn*z;
}
+OVERLOADABLE float tgamma (float x)
+{
+ /* based on glibc __ieee754_gammaf_r by Ulrich Drepper <drep...@cygnus.com>
*/
+
+ unsigned int hx;
+ GEN_OCL_GET_FLOAT_WORD(hx,x);
+ if (hx == 0xff800000)
+ {
+ /* x == -Inf. According to ISO this is NaN. */
+ return NAN;
+ }
+ if ((hx & 0x7f800000) == 0x7f800000)
+ {
+ /* Positive infinity (return positive infinity) or NaN (return
+ NaN). */
+ return x;
+ }
+ if (x < 0.0f && __gen_ocl_internal_floor (x) == x)
+ {
+ /* integer x < 0 */
+ return NAN;
+ }
+
+ if (x >= 36.0f)
+ {
+ /* Overflow. */
+ return INFINITY;
+ }
+ else if (x <= 0.0f && x >= -FLT_EPSILON / 4.0f)
+ {
+ return 1.0f / x;
+ }
+ else
+ {
+ float sinpix = __gen_ocl_internal_sinpi(x);
+ if (x <= -42.0f)
+ /* Underflow. */
+ {return 0.0f * sinpix /*for sign*/;}
+ int exp2_adj = 0;
+ float x_abs = __gen_ocl_fabs(x);
+ float gam0;
+
+ if (x_abs < 4.0f) {
+ /* gamma = exp(lgamma) is only accurate for small lgamma */
+ float prod,x_adj;
+ if (x_abs < 0.5f) {
+ prod = 1.0f / x_abs;
+ x_adj = x_abs + 1.0f;
+ } else if (x_abs <= 1.5f) {
+ prod = 1.0f;
+ x_adj = x_abs;
+ } else if (x_abs < 2.5f) {
+ x_adj = x_abs - 1.0f;
+ prod = x_adj;
+ } else {
+ x_adj = x_abs - 2.0f;
+ prod = x_adj * (x_abs - 1.0f);
+ }
+ gam0 = __gen_ocl_internal_exp (lgamma (x_adj)) * prod;
+ }
+ else {
+ /* Compute gamma (X) using Stirling's approximation,
+ starting by computing pow (X, X) with a power of 2
+ factored out to avoid intermediate overflow. */
+ float x_int = __gen_ocl_internal_round (x_abs);
+ float x_frac = x_abs - x_int;
+ int x_log2;
+ float x_mant = frexp (x_abs, &x_log2);
+ if (x_mant < M_SQRT1_2_F)
+ {
+ x_log2--;
+ x_mant *= 2.0f;
+ }
+ exp2_adj = x_log2 * (int) x_int;
+ float ret = (__gen_ocl_internal_pow(x_mant, x_abs)
+ * exp2 (x_log2 * x_frac)
+ * __gen_ocl_internal_exp (-x_abs)
+ * sqrt (2.0f * M_PI_F / x_abs) );
+
+ float x2 = x_abs * x_abs;
+ float bsum = (0x3.403404p-12f / x2 -0xb.60b61p-12f) / x2 +
0x1.555556p-4f;
+ gam0 = ret + ret * __gen_ocl_internal_expm1 (bsum / x_abs);
+ }
+ if (x > 0.0f) {return __gen_ocl_internal_ldexp (gam0, exp2_adj);}
+ float gam1 = M_PI_F / (-x * sinpix * gam0);
+ return __gen_ocl_internal_ldexp (gam1, -exp2_adj);
+ }
+}
+
OVERLOADABLE float hypot(float x, float y) {
if (__ocl_math_fastpath_flag)
return __gen_ocl_internal_fastpath_hypot(x, y);
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