long double cleanup, initial commit

new ldshape union, ld128 support is kept, code that used the old
ldshape union was rewritten (IEEEl2bits union of freebsd libm is
not touched yet)

ld80 __fpclassifyl no longer tries to handle invalid representation

src/internal/libm.h

@@ -17,6 +17,7 @@
 #include <float.h>
 #include <math.h>
 #include <complex.h>
+#include <endian.h>
 
 #include "longdbl.h"
 
@@ -32,6 +33,33 @@ union dshape {
 	uint64_t bits;
 };
 
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __LITTLE_ENDIAN
+union ldshape {
+	long double f;
+	struct {
+		uint64_t m;
+		uint16_t se;
+	} i;
+};
+#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __LITTLE_ENDIAN
+union ldshape {
+	long double f;
+	struct {
+		uint64_t lo;
+		uint32_t mid;
+		uint16_t top;
+		uint16_t se;
+	} i;
+	struct {
+		uint64_t lo;
+		uint64_t hi;
+	} i2;
+};
+#else
+#error Unsupported long double representation
+#endif
+
 #define FORCE_EVAL(x) do {                          \
 	if (sizeof(x) == sizeof(float)) {           \
 		volatile float __x;                 \

src/internal/longdbl.h

@@ -4,32 +4,6 @@
 #include <float.h>
 #include <stdint.h>
 
-#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
-#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-union ldshape {
-	long double value;
-	struct {
-		uint64_t m;
-		uint16_t exp:15;
-		uint16_t sign:1;
-		uint16_t pad;
-	} bits;
-};
-#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
-union ldshape {
-	long double value;
-	struct {
-		uint64_t mlo;
-		uint64_t mhi:48;
-		uint16_t exp:15;
-		uint16_t sign:1;
-	} bits;
-};
-#else
-#error Unsupported long double representation
-#endif
-
-
 // FIXME: hacks to make freebsd+openbsd long double code happy
 
 // union and macros for freebsd

src/math/__fpclassifyl.c

@@ -3,28 +3,28 @@
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
 
 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+/* invalid representations (top bit of u.i.m is wrong) are not handled */
 int __fpclassifyl(long double x)
 {
-	union ldshape u = { x };
-	int e = u.bits.exp;
-	if (!e) {
-		if (u.bits.m >> 63) return FP_NAN;
-		else if (u.bits.m) return FP_SUBNORMAL;
-		else return FP_ZERO;
-	}
+	union ldshape u = {x};
+	int e = u.i.se & 0x7fff;
+	if (!e)
+		return u.i.m ? FP_SUBNORMAL : FP_ZERO;
 	if (e == 0x7fff)
-		return u.bits.m & (uint64_t)-1>>1 ? FP_NAN : FP_INFINITE;
-	return u.bits.m & (uint64_t)1<<63 ? FP_NORMAL : FP_NAN;
+		return u.i.m << 1 ? FP_NAN : FP_INFINITE;
+	return FP_NORMAL;
 }
 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
 int __fpclassifyl(long double x)
 {
-	union ldshape u = { x };
-	int e = u.bits.exp;
+	union ldshape u = {x};
+	int e = u.i.se & 0x7fff;
 	if (!e)
-		return u.bits.mlo | u.bits.mhi ? FP_SUBNORMAL : FP_ZERO;
-	if (e == 0x7fff)
-		return u.bits.mlo | u.bits.mhi ? FP_NAN : FP_INFINITE;
+		return u.i2.lo | u.i2.hi ? FP_SUBNORMAL : FP_ZERO;
+	if (e == 0x7fff) {
+		u.i.se = 0;
+		return u.i2.lo | u.i2.hi ? FP_NAN : FP_INFINITE;
+	}
 	return FP_NORMAL;
 }
 #endif

src/math/__signbitl.c

@@ -1,11 +1,9 @@
 #include "libm.h"
 
-// FIXME: should be a macro
 #if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
 int __signbitl(long double x)
 {
 	union ldshape u = {x};
-
-	return u.bits.sign;
+	return u.i.se >> 15;
 }
 #endif

src/math/copysignl.c

@@ -9,8 +9,8 @@ long double copysignl(long double x, long double y)
 long double copysignl(long double x, long double y)
 {
 	union ldshape ux = {x}, uy = {y};
-
-	ux.bits.sign = uy.bits.sign;
-	return ux.value;
+	ux.i.se &= 0x7fff;
+	ux.i.se |= uy.i.se & 0x8000;
+	return ux.f;
 }
 #endif

src/math/fabsl.c

@@ -9,7 +9,7 @@ long double fabsl(long double x)
 {
 	union ldshape u = {x};
 
-	u.bits.sign = 0;
-	return u.value;
+	u.i.se &= 0x7fff;
+	return u.f;
 }
 #endif

src/math/ilogbl.c

@@ -10,12 +10,12 @@ int ilogbl(long double x)
 int ilogbl(long double x)
 {
 	union ldshape u = {x};
-	uint64_t m = u.bits.m;
-	int e = u.bits.exp;
+	uint64_t m = u.i.m;
+	int e = u.i.se & 0x7fff;
 
 	if (!e) {
 		if (m == 0) {
-			FORCE_EVAL(0/0.0f);
+			FORCE_EVAL(x/x);
 			return FP_ILOGB0;
 		}
 		/* subnormal x */
@@ -25,7 +25,7 @@ int ilogbl(long double x)
 	if (e == 0x7fff) {
 		FORCE_EVAL(0/0.0f);
 		/* in ld80 msb is set in inf */
-		return m & (uint64_t)-1>>1 ? FP_ILOGBNAN : INT_MAX;
+		return m << 1 ? FP_ILOGBNAN : INT_MAX;
 	}
 	return e - 0x3fff;
 }

src/math/nextafterl.c

@@ -6,7 +6,6 @@ long double nextafterl(long double x, long double y)
 	return nextafter(x, y);
 }
 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-#define MSB ((uint64_t)1<<63)
 long double nextafterl(long double x, long double y)
 {
 	union ldshape ux, uy;
@@ -15,32 +14,32 @@ long double nextafterl(long double x, long double y)
 		return x + y;
 	if (x == y)
 		return y;
-	ux.value = x;
+	ux.f = x;
 	if (x == 0) {
-		uy.value = y;
-		ux.bits.m = 1;
-		ux.bits.sign = uy.bits.sign;
-	} else if (x < y ^ ux.bits.sign) {
-		ux.bits.m++;
-		if ((ux.bits.m & ~MSB) == 0) {
-			ux.bits.m = MSB;
-			ux.bits.exp++;
+		uy.f = y;
+		ux.i.m = 1;
+		ux.i.se = uy.i.se & 0x8000;
+	} else if ((x < y) == !(ux.i.se & 0x8000)) {
+		ux.i.m++;
+		if (ux.i.m << 1 == 0) {
+			ux.i.m = 1ULL << 63;
+			ux.i.se++;
 		}
 	} else {
-		if ((ux.bits.m & ~MSB) == 0) {
-			ux.bits.exp--;
-			if (ux.bits.exp)
-				ux.bits.m = 0;
+		if (ux.i.m << 1 == 0) {
+			ux.i.se--;
+			if (ux.i.se)
+				ux.i.m = 0;
 		}
-		ux.bits.m--;
+		ux.i.m--;
 	}
-	/* raise overflow if ux.value is infinite and x is finite */
-	if (ux.bits.exp == 0x7fff)
+	/* raise overflow if ux is infinite and x is finite */
+	if ((ux.i.se & 0x7fff) == 0x7fff)
 		return x + x;
-	/* raise underflow if ux.value is subnormal or zero */
-	if (ux.bits.exp == 0)
-		FORCE_EVAL(x*x + ux.value*ux.value);
-	return ux.value;
+	/* raise underflow if ux is subnormal or zero */
+	if ((ux.i.se & 0x7fff) == 0)
+		FORCE_EVAL(x*x + ux.f*ux.f);
+	return ux.f;
 }
 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
 long double nextafterl(long double x, long double y)
@@ -51,32 +50,26 @@ long double nextafterl(long double x, long double y)
 		return x + y;
 	if (x == y)
 		return y;
-	ux.value = x;
+	ux.f = x;
 	if (x == 0) {
-		uy.value = y;
-		ux.bits.mlo = 1;
-		ux.bits.sign = uy.bits.sign;
-	} else if (x < y ^ ux.bits.sign) {
-		ux.bits.mlo++;
-		if (ux.bits.mlo == 0) {
-			ux.bits.mhi++;
-			if (ux.bits.mhi == 0)
-				ux.bits.exp++;
-		}
+		uy.f = y;
+		ux.i.lo = 1;
+		ux.i.se = uy.i.se & 0x8000;
+	} else if ((x < y) == !(ux.i.se & 0x8000)) {
+		ux.i2.lo++;
+		if (ux.i2.lo == 0)
+			ux.i2.hi++;
 	} else {
-		if (ux.bits.mlo == 0) {
-			if (ux.bits.mhi == 0)
-				ux.bits.exp--;
-			ux.bits.mhi--;
-		}
-		ux.bits.mlo--;
+		if (ux.i2.lo == 0)
+			ux.i2.hi--;
+		ux.i2.lo--;
 	}
-	/* raise overflow if ux.value is infinite and x is finite */
-	if (ux.bits.exp == 0x7fff)
+	/* raise overflow if ux is infinite and x is finite */
+	if ((ux.i.se & 0x7fff) == 0x7fff)
 		return x + x;
-	/* raise underflow if ux.value is subnormal or zero */
-	if (ux.bits.exp == 0)
-		FORCE_EVAL(x*x + ux.value*ux.value);
-	return ux.value;
+	/* raise underflow if ux is subnormal or zero */
+	if ((ux.i.se & 0x7fff) == 0)
+		FORCE_EVAL(x*x + ux.f*ux.f);
+	return ux.f;
 }
 #endif