math: expf.c cleanup

similar to exp.c cleanup: use scalbnf, don't return excess precision,
drop some optimizatoins.
exp.c was changed to be more consistent with expf.c code.

src/math/exp.c

@@ -80,7 +80,7 @@ P5   =  4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
 
 double exp(double x)
 {
-	double hi, lo, c, z;
+	double hi, lo, c, xx;
 	int k, sign;
 	uint32_t hx;
 
@@ -92,24 +92,26 @@ double exp(double x)
 	if (hx >= 0x40862e42) {  /* if |x| >= 709.78... */
 		if (isnan(x))
 			return x;
+		if (hx == 0x7ff00000 && sign) /* -inf */
+			return 0;
 		if (x > 709.782712893383973096) {
 			/* overflow if x!=inf */
 			STRICT_ASSIGN(double, x, 0x1p1023 * x);
 			return x;
 		}
 		if (x < -745.13321910194110842) {
-			/* underflow if x!=-inf */
+			/* underflow */
-			STRICT_ASSIGN(double, x, 0x1p-1000 / -x * 0x1p-1000);
+			STRICT_ASSIGN(double, x, 0x1p-1000 * 0x1p-1000);
 			return x;
 		}
 	}
 
 	/* argument reduction */
 	if (hx > 0x3fd62e42) {  /* if |x| > 0.5 ln2 */
-		if (hx < 0x3ff0a2b2)  /* if |x| < 1.5 ln2 */
+		if (hx >= 0x3ff0a2b2)  /* if |x| >= 1.5 ln2 */
-			k = 1 - sign - sign; /* optimization */
-		else
 			k = (int)(invln2*x + half[sign]);
+		else
+			k = 1 - sign - sign;
 		hi = x - k*ln2hi;  /* k*ln2hi is exact here */
 		lo = k*ln2lo;
 		STRICT_ASSIGN(double, x, hi - lo);
@@ -124,9 +126,9 @@ double exp(double x)
 	}
 
 	/* x is now in primary range */
-	z = x*x;
+	xx = x*x;
-	c = x - z*(P1+z*(P2+z*(P3+z*(P4+z*P5))));
+	c = x - xx*(P1+xx*(P2+xx*(P3+xx*(P4+xx*P5))));
-	x = 1 + ((x*c/(2-c) - lo) + hi);
+	x = 1 + (x*c/(2-c) - lo + hi);
 	if (k == 0)
 		return x;
 	return scalbn(x, k);

src/math/expf.c

@@ -16,79 +16,69 @@
 #include "libm.h"
 
 static const float
-halF[2] = {0.5,-0.5,},
+half[2] = {0.5,-0.5},
-huge    = 1.0e+30,
+ln2hi   = 6.9314575195e-1f,  /* 0x3f317200 */
-o_threshold =  8.8721679688e+01,  /* 0x42b17180 */
+ln2lo   = 1.4286067653e-6f,  /* 0x35bfbe8e */
-u_threshold = -1.0397208405e+02,  /* 0xc2cff1b5 */
+invln2  = 1.4426950216e+0f,  /* 0x3fb8aa3b */
-ln2HI[2]   = { 6.9314575195e-01,  /* 0x3f317200 */
-              -6.9314575195e-01,},/* 0xbf317200 */
-ln2LO[2]   = { 1.4286067653e-06,  /* 0x35bfbe8e */
-              -1.4286067653e-06,},/* 0xb5bfbe8e */
-invln2 = 1.4426950216e+00,        /* 0x3fb8aa3b */
 /*
  * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
  * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
  */
-P1 =  1.6666625440e-1, /*  0xaaaa8f.0p-26 */
+P1 =  1.6666625440e-1f, /*  0xaaaa8f.0p-26 */
-P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */
+P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
-
-static const volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
 
 float expf(float x)
 {
-	float y,hi=0.0,lo=0.0,c,t,twopk;
+	float hi, lo, c, xx;
-	int32_t k=0,xsb;
+	int k, sign;
 	uint32_t hx;
 
 	GET_FLOAT_WORD(hx, x);
-	xsb = (hx>>31)&1;  /* sign bit of x */
+	sign = hx >> 31;   /* sign bit of x */
 	hx &= 0x7fffffff;  /* high word of |x| */
 
-	/* filter out non-finite argument */
+	/* special cases */
-	if (hx >= 0x42b17218) {  /* if |x|>=88.721... */
+	if (hx >= 0x42b17218) {  /* if |x| >= 88.722839f or NaN */
 		if (hx > 0x7f800000)  /* NaN */
-			return x+x;
+			return x;
-		if (hx == 0x7f800000)  /* exp(+-inf)={inf,0} */
+		if (!sign) {
-			return xsb==0 ? x : 0.0;
+			/* overflow if x!=inf */
-		if (x > o_threshold)
+			STRICT_ASSIGN(float, x, x * 0x1p127f);
-			return huge*huge; /* overflow */
+			return x;
-		if (x < u_threshold)
+		}
-			return twom100*twom100; /* underflow */
+		if (hx == 0x7f800000)  /* -inf */
+			return 0;
+		if (hx >= 0x42cff1b5) { /* x <= -103.972084f */
+			/* underflow */
+			STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f);
+			return x;
+		}
 	}
 
 	/* argument reduction */
 	if (hx > 0x3eb17218) {  /* if |x| > 0.5 ln2 */
-		if (hx < 0x3F851592) {  /* and |x| < 1.5 ln2 */
+		if (hx > 0x3f851592)  /* if |x| > 1.5 ln2 */
-			hi = x-ln2HI[xsb];
+			k = invln2*x + half[sign];
-			lo = ln2LO[xsb];
+		else
-			k = 1 - xsb - xsb;
+			k = 1 - sign - sign;
-		} else {
+		hi = x - k*ln2hi;  /* k*ln2hi is exact here */
-			k  = invln2*x + halF[xsb];
+		lo = k*ln2lo;
-			t  = k;
-			hi = x - t*ln2HI[0];  /* t*ln2HI is exact here */
-			lo = t*ln2LO[0];
-		}
 		STRICT_ASSIGN(float, x, hi - lo);
-	} else if(hx < 0x39000000)  {  /* |x|<2**-14 */
+	} else if (hx > 0x39000000) {  /* |x| > 2**-14 */
-		/* raise inexact */
-		if (huge+x > 1.0f)
-			return 1.0f + x;
-	} else
 		k = 0;
+		hi = x;
+		lo = 0;
+	} else {
+		/* raise inexact */
+		FORCE_EVAL(0x1p127f + x);
+		return 1 + x;
+	}
 
 	/* x is now in primary range */
-	t = x*x;
+	xx = x*x;
-	if (k >= -125)
+	c = x - xx*(P1+xx*P2);
-		SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));
+	x = 1 + (x*c/(2-c) - lo + hi);
-	else
-		SET_FLOAT_WORD(twopk, 0x3f800000+((k+100)<<23));
-	c  = x - t*(P1+t*P2);
 	if (k == 0)
-		return 1.0f - ((x*c)/(c - 2.0f) - x);
+		return x;
-	y = 1.0f - ((lo - (x*c)/(2.0f - c)) - hi);
+	return scalbnf(x, k);
-	if (k < -125)
-		return y*twopk*twom100;
-	if (k == 128)
-		return y*2.0f*0x1p127f;
-	return y*twopk;
 }