math: cleanup exp2.c exp2f.c and exp2l.c

* old code relied on sign extension on right shift
* exp2l ld64 wrapper was wrong
* use scalbn instead of bithacks

src/math/exp2.c

@@ -27,11 +27,9 @@
 
 #include "libm.h"
 
-#define TBLBITS 8
+#define TBLSIZE 256
-#define TBLSIZE (1 << TBLBITS)
 
 static const double
-huge  = 0x1p1000,
 redux = 0x1.8p52 / TBLSIZE,
 P1    = 0x1.62e42fefa39efp-1,
 P2    = 0x1.ebfbdff82c575p-3,
@@ -39,8 +37,6 @@ P3    = 0x1.c6b08d704a0a6p-5,
 P4    = 0x1.3b2ab88f70400p-7,
 P5    = 0x1.5d88003875c74p-10;
 
-static const volatile double twom1000 = 0x1p-1000;
-
 static const double tbl[TBLSIZE * 2] = {
 /*  exp2(z + eps)          eps     */
   0x1.6a09e667f3d5dp-1,  0x1.9880p-44,
@@ -334,25 +330,28 @@ static const double tbl[TBLSIZE * 2] = {
  */
 double exp2(double x)
 {
-	double r, t, twopk, twopkp1000, z;
+	double r, t, z;
-	uint32_t hx, ix, lx, i0;
+	uint32_t hx, ix, i0;
-	int k;
+	union {uint32_t u; int32_t i;} k;
 
 	/* Filter out exceptional cases. */
 	GET_HIGH_WORD(hx, x);
 	ix = hx & 0x7fffffff;
 	if (ix >= 0x40900000) {        /* |x| >= 1024 */
 		if (ix >= 0x7ff00000) {
-			GET_LOW_WORD(lx, x);
+			GET_LOW_WORD(ix, x);
-			if (((ix & 0xfffff) | lx) != 0 || (hx & 0x80000000) == 0)
+			if (hx == 0xfff00000 && ix == 0) /* -inf */
-				return x + x; /* x is NaN or +Inf */
+				return 0;
-			else
+			return x;
-				return 0.0;   /* x is -Inf */
+		}
+		if (x >= 1024) {
+			STRICT_ASSIGN(double, x, x * 0x1p1023);
+			return x;
+		}
+		if (x <= -1075) {
+			STRICT_ASSIGN(double, x, 0x1p-1000*0x1p-1000);
+			return x;
 		}
-		if (x >= 0x1.0p10)
-			return huge * huge; /* overflow */
-		if (x <= -0x1.0ccp10)
-			return twom1000 * twom1000; /* underflow */
 	} else if (ix < 0x3c900000) {  /* |x| < 0x1p-54 */
 		return 1.0 + x;
 	}
@@ -361,24 +360,16 @@ double exp2(double x)
 	STRICT_ASSIGN(double, t, x + redux);
 	GET_LOW_WORD(i0, t);
 	i0 += TBLSIZE / 2;
-	k = (i0 >> TBLBITS) << 20;
+	k.u = i0 / TBLSIZE * TBLSIZE;
-	i0 = (i0 & (TBLSIZE - 1)) << 1;
+	k.i /= TBLSIZE;
+	i0 %= TBLSIZE;
 	t -= redux;
 	z = x - t;
 
 	/* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
-	t = tbl[i0];       /* exp2t[i0] */
+	t = tbl[2*i0];       /* exp2t[i0] */
-	z -= tbl[i0 + 1];  /* eps[i0]   */
+	z -= tbl[2*i0 + 1];  /* eps[i0]   */
-	if (k >= -1021 << 20)
-		INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
-	else
-		INSERT_WORDS(twopkp1000, 0x3ff00000 + k + (1000 << 20), 0);
 	r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5))));
 
-	/* Scale by 2**(k>>20). */
+	return scalbn(r, k.i);
-	if (k < -1021 << 20)
-		return r * twopkp1000 * twom1000;
-	if (k == 1024 << 20)
-		return r * 2.0 * 0x1p1023;
-	return r * twopk;
 }

src/math/exp2f.c

@@ -27,19 +27,15 @@
 
 #include "libm.h"
 
-#define TBLBITS 4
+#define TBLSIZE 16
-#define TBLSIZE (1 << TBLBITS)
 
 static const float
-huge  = 0x1p100f,
 redux = 0x1.8p23f / TBLSIZE,
 P1    = 0x1.62e430p-1f,
 P2    = 0x1.ebfbe0p-3f,
 P3    = 0x1.c6b348p-5f,
 P4    = 0x1.3b2c9cp-7f;
 
-static const volatile float twom100 = 0x1p-100f;
-
 static const double exp2ft[TBLSIZE] = {
   0x1.6a09e667f3bcdp-1,
   0x1.7a11473eb0187p-1,
@@ -89,23 +85,25 @@ float exp2f(float x)
 {
 	double tv, twopk, u, z;
 	float t;
-	uint32_t hx, ix, i0;
+	uint32_t hx, ix, i0, k;
-	int32_t k;
 
 	/* Filter out exceptional cases. */
 	GET_FLOAT_WORD(hx, x);
 	ix = hx & 0x7fffffff;
 	if (ix >= 0x43000000) {  /* |x| >= 128 */
 		if (ix >= 0x7f800000) {
-			if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0)
+			if (hx == 0xff800000) /* -inf */
-				return x + x; /* x is NaN or +Inf */
+				return 0;
-			else
+			return x;
-				return 0.0;   /* x is -Inf */
+		}
+		if (x >= 128) {
+			STRICT_ASSIGN(float, x, x * 0x1p127);
+			return x;
+		}
+		if (x <= -150) {
+			STRICT_ASSIGN(float, x, 0x1p-100*0x1p-100);
+			return x;
 		}
-		if (x >= 0x1.0p7f)
-			return huge * huge;   /* overflow */
-		if (x <= -0x1.2cp7f)
-			return twom100 * twom100; /* underflow */
 	} else if (ix <= 0x33000000) {  /* |x| <= 0x1p-25 */
 		return 1.0f + x;
 	}
@@ -114,7 +112,7 @@ float exp2f(float x)
 	STRICT_ASSIGN(float, t, x + redux);
 	GET_FLOAT_WORD(i0, t);
 	i0 += TBLSIZE / 2;
-	k = (i0 >> TBLBITS) << 20;
+	k = (i0 / TBLSIZE) << 20;
 	i0 &= TBLSIZE - 1;
 	t -= redux;
 	z = x - t;

src/math/exp2l.c

@@ -30,7 +30,7 @@
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
 long double exp2l(long double x)
 {
-	return exp2l(x);
+	return exp2(x);
 }
 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
 
@@ -40,10 +40,6 @@ long double exp2l(long double x)
 #define BIAS    (LDBL_MAX_EXP - 1)
 #define EXPMASK (BIAS + LDBL_MAX_EXP)
 
-static const long double huge = 0x1p10000L;
-/* XXX Prevent gcc from erroneously constant folding this. */
-static const volatile long double twom10000 = 0x1p-10000L;
-
 static const double
 redux = 0x1.8p63 / TBLSIZE,
 P1    = 0x1.62e42fefa39efp-1,
@@ -208,27 +204,28 @@ static const double tbl[TBLSIZE * 2] = {
 long double exp2l(long double x)
 {
 	union IEEEl2bits u, v;
-	long double r, twopk, twopkp10000, z;
+	long double r, z;
 	uint32_t hx, ix, i0;
-	int k;
+	union {uint32_t u; int32_t i;} k;
 
 	/* Filter out exceptional cases. */
 	u.e = x;
 	hx = u.xbits.expsign;
 	ix = hx & EXPMASK;
 	if (ix >= BIAS + 14) {  /* |x| >= 16384 or x is NaN */
-		if (ix == BIAS + LDBL_MAX_EXP) {
+		if (ix == EXPMASK) {
-			if (u.xbits.man != 1ULL << 63 || (hx & 0x8000) == 0)
+			if (u.xbits.man == 1ULL << 63 && hx == 0xffff) /* -inf */
-				return x + x;  /* x is +Inf or NaN */
+				return 0;
-			return 0.0;  /* x is -Inf */
+			return x;
+		}
+		if (x >= 16384) {
+			x *= 0x1p16383L;
+			return x;
 		}
-		if (x >= 16384)
-			return huge * huge;  /* overflow */
 		if (x <= -16446)
-			return twom10000 * twom10000;  /* underflow */
+			return 0x1p-10000L*0x1p-10000L;
-	} else if (ix <= BIAS - 66) {  /* |x| < 0x1p-66 */
+	} else if (ix < BIAS - 64)  /* |x| < 0x1p-64 */
-		return 1.0 + x;
+		return 1 + x;
-	}
 
 	/*
 	 * Reduce x, computing z, i0, and k. The low bits of x + redux
@@ -240,38 +237,22 @@ long double exp2l(long double x)
 	 * Then the low-order word of x + redux is 0x000abc12,
 	 * We split this into k = 0xabc and i0 = 0x12 (adjusted to
 	 * index into the table), then we compute z = 0x0.003456p0.
-	 *
-	 * XXX If the exponent is negative, the computation of k depends on
-	 *     '>>' doing sign extension.
 	 */
 	u.e = x + redux;
 	i0 = u.bits.manl + TBLSIZE / 2;
-	k = (int)i0 >> TBLBITS;
+	k.u = i0 / TBLSIZE * TBLSIZE;
-	i0 = (i0 & (TBLSIZE - 1)) << 1;
+	k.i /= TBLSIZE;
+	i0 %= TBLSIZE;
 	u.e -= redux;
 	z = x - u.e;
-	v.xbits.man = 1ULL << 63;
-	if (k >= LDBL_MIN_EXP) {
-		v.xbits.expsign = LDBL_MAX_EXP - 1 + k;
-		twopk = v.e;
-	} else {
-		v.xbits.expsign = LDBL_MAX_EXP - 1 + k + 10000;
-		twopkp10000 = v.e;
-	}
 
 	/* Compute r = exp2l(y) = exp2lt[i0] * p(z). */
-	long double t_hi = tbl[i0];
+	long double t_hi = tbl[2*i0];
-	long double t_lo = tbl[i0 + 1];
+	long double t_lo = tbl[2*i0 + 1];
 	/* XXX This gives > 1 ulp errors outside of FE_TONEAREST mode */
 	r = t_lo + (t_hi + t_lo) * z * (P1 + z * (P2 + z * (P3 + z * (P4
 	     + z * (P5 + z * P6))))) + t_hi;
 
-	/* Scale by 2**k. */
+	return scalbnl(r, k.i);
-	if (k >= LDBL_MIN_EXP) {
-		if (k == LDBL_MAX_EXP)
-			return r * 2.0 * 0x1p16383L;
-		return r * twopk;
-	}
-	return r * twopkp10000 * twom10000;
 }
 #endif