math: fix underflow in exp*.c and long double handling in exp2l

* don't care about inexact flag
* use double_t and float_t (faster, smaller, more precise on x86)
* exp: underflow when result is zero or subnormal and not -inf
* exp2: underflow when result is zero or subnormal and not exact
* expm1: underflow when result is zero or subnormal
* expl: don't underflow on -inf
* exp2: fix incorrect comment
* expm1: simplify special case handling and overflow properly
* expm1: cleanup final scaling and fix negative left shift ub (twopk)

1 files changed, 26 insertions, 39 deletions

diff --git a/src/math/expm1f.c b/src/math/expm1f.c
index d9568466..698ab45f 100644
--- a/src/math/expm1f.c
+++ b/src/math/expm1f.c
@@ -16,8 +16,6 @@
 #include "libm.h"
 
 static const float
-huge        = 1.0e+30,
-tiny        = 1.0e-30,
 o_threshold = 8.8721679688e+01, /* 0x42b17180 */
 ln2_hi      = 6.9313812256e-01, /* 0x3f317180 */
 ln2_lo      = 9.0580006145e-06, /* 0x3717f7d1 */
@@ -32,35 +30,27 @@ Q2 =  1.5807170421e-3; /*  0xcf3010.0p-33 */
 
 float expm1f(float x)
 {
-	float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
-	int32_t k,xsb;
-	uint32_t hx;
-
-	GET_FLOAT_WORD(hx, x);
-	xsb = hx&0x80000000;  /* sign bit of x */
-	hx &= 0x7fffffff;     /* high word of |x| */
+	float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
+	union {float f; uint32_t i;} u = {x};
+	uint32_t hx = u.i & 0x7fffffff;
+	int k, sign = u.i >> 31;
 
 	/* filter out huge and non-finite argument */
 	if (hx >= 0x4195b844) {  /* if |x|>=27*ln2 */
-		if (hx >= 0x42b17218) {  /* if |x|>=88.721... */
-			if (hx > 0x7f800000)  /* NaN */
-				return x+x;
-			if (hx == 0x7f800000) /* exp(+-inf)={inf,-1} */
-				return xsb==0 ? x : -1.0;
-			if (x > o_threshold)
-				return huge*huge; /* overflow */
-		}
-		if (xsb != 0) {  /* x < -27*ln2 */
-			/* raise inexact */
-			if (x+tiny < 0.0f)
-				return tiny-1.0f;  /* return -1 */
+		if (hx > 0x7f800000)  /* NaN */
+			return x;
+		if (sign)
+			return -1;
+		if (x > o_threshold) {
+			x *= 0x1p127f;
+			return x;
 		}
 	}
 
 	/* argument reduction */
 	if (hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
 		if (hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
-			if (xsb == 0) {
+			if (!sign) {
 				hi = x - ln2_hi;
 				lo = ln2_lo;
 				k =  1;
@@ -70,7 +60,7 @@ float expm1f(float x)
 				k = -1;
 			}
 		} else {
-			k  = invln2*x + (xsb==0 ? 0.5f : -0.5f);
+			k  = invln2*x + (sign ? -0.5f : 0.5f);
 			t  = k;
 			hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
 			lo = t*ln2_lo;
@@ -78,8 +68,9 @@ float expm1f(float x)
 		STRICT_ASSIGN(float, x, hi - lo);
 		c = (hi-x)-lo;
 	} else if (hx < 0x33000000) {  /* when |x|<2**-25, return x */
-		t = huge+x; /* return x with inexact flags when x!=0 */
-		return x - (t-(huge+x));
+		if (hx < 0x00800000)
+			FORCE_EVAL(x*x);
+		return x;
 	} else
 		k = 0;
 
@@ -91,9 +82,9 @@ float expm1f(float x)
 	e  = hxs*((r1-t)/(6.0f - x*t));
 	if (k == 0)  /* c is 0 */
 		return x - (x*e-hxs);
-	SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));   /* 2^k */
 	e  = x*(e-c) - c;
 	e -= hxs;
+	/* exp(x) ~ 2^k (x_reduced - e + 1) */
 	if (k == -1)
 		return 0.5f*(x-e) - 0.5f;
 	if (k == 1) {
@@ -101,24 +92,20 @@ float expm1f(float x)
 			return -2.0f*(e-(x+0.5f));
 		return 1.0f + 2.0f*(x-e);
 	}
-	if (k <= -2 || k > 56) {   /* suffice to return exp(x)-1 */
-		y = 1.0f - (e - x);
+	u.i = (0x7f+k)<<23;  /* 2^k */
+	twopk = u.f;
+	if (k < 0 || k > 56) {   /* suffice to return exp(x)-1 */
+		y = x - e + 1.0f;
 		if (k == 128)
 			y = y*2.0f*0x1p127f;
 		else
 			y = y*twopk;
 		return y - 1.0f;
 	}
-	t = 1.0f;
-	if (k < 23) {
-		SET_FLOAT_WORD(t, 0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
-		y = t - (e - x);
-		y = y*twopk;
-	} else {
-		SET_FLOAT_WORD(t, (0x7f-k)<<23);  /* 2^-k */
-		y = x - (e + t);
-		y += 1.0f;
-		y = y*twopk;
-	}
+	u.i = (0x7f-k)<<23;  /* 2^-k */
+	if (k < 23)
+		y = (x-e+(1-u.f))*twopk;
+	else
+		y = (x-(e+u.f)+1)*twopk;
 	return y;
 }