math: nextafter and nexttoward cleanup

make nexttoward, nexttowardf independent of long double representation.
fix nextafterl: it did not raise underflow flag when the result was 0.

diff --git a/src/math/nextafter.c b/src/math/nextafter.c
index 5e53654..d9e2923 100644 (file)
--- a/src/math/nextafter.c
+++ b/src/math/nextafter.c
@@ -1,79 +1,36 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_nextafter.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-/* IEEE functions
- *      nextafter(x,y)
- *      return the next machine floating-point number of x in the
- *      direction toward y.
- *   Special cases:
- */
-
 #include "libm.h"
 
+#define SIGN ((uint64_t)1<<63)
+
 double nextafter(double x, double y)
 {
-       volatile double t;
-       int32_t hx,hy,ix,iy;
-       uint32_t lx,ly;
-
-       EXTRACT_WORDS(hx, lx, x);
-       EXTRACT_WORDS(hy, ly, y);
-       ix = hx & 0x7fffffff;  /* |x| */
-       iy = hy & 0x7fffffff;  /* |y| */
+       union dshape ux, uy;
+       uint64_t ax, ay;
+       int e;
 
-       if ((ix >= 0x7ff00000 && (ix-0x7ff00000)|lx) != 0 ||   /* x is nan */
-           (iy >= 0x7ff00000 && (iy-0x7ff00000)|ly) != 0)     /* y is nan */
-               return x+y;
-       if (x == y)          /* x == y */
+       if (isnan(x) || isnan(y))
+               return x + y;
+       ux.value = x;
+       uy.value = y;
+       if (ux.bits == uy.bits)
                return y;
-       if ((ix|lx) == 0) {  /* x == 0 */
-               INSERT_WORDS(x, hy&0x80000000, 1);  /* return +-minsubnormal */
-               /* raise underflow flag */
-               t = x*x;
-               if (t == x)
-                       return t;
-               return x;
-       }
-       if (hx >= 0) {  /* x > 0 */
-               if (hx > hy || (hx == hy && lx > ly)) {  /* x > y, x -= ulp */
-                       if (lx == 0)
-                               hx--;
-                       lx--;
-               } else {                                 /* x < y, x += ulp */
-                       lx++;
-                       if (lx == 0)
-                               hx++;
-               }
-       } else {        /* x < 0 */
-               if (hy >= 0 || hx > hy || (hx == hy && lx > ly)) { /* x < y, x -= ulp */
-                       if (lx == 0)
-                               hx--;
-                       lx--;
-               } else {                                 /* x > y, x += ulp */
-                       lx++;
-                       if (lx == 0)
-                               hx++;
-               }
-       }
-       hy = hx & 0x7ff00000;
-       if (hy >= 0x7ff00000)  /* overflow  */
-               return x+x;
-       if (hy < 0x00100000) { /* underflow */
-               /* raise underflow flag */
-               t = x*x;
-               if (t != x) {
-                       INSERT_WORDS(y, hx, lx);
+       ax = ux.bits & ~SIGN;
+       ay = uy.bits & ~SIGN;
+       if (ax == 0) {
+               if (ay == 0)
                        return y;
-               }
+               ux.bits = (uy.bits & SIGN) | 1;
+       } else if (ax > ay || ((ux.bits ^ uy.bits) & SIGN))
+               ux.bits--;
+       else
+               ux.bits++;
+       e = ux.bits >> 52 & 0x7ff;
+       /* raise overflow if ux.value is infinite and x is finite */
+       if (e == 0x7ff)
+               return x + x;
+       /* raise underflow if ux.value is subnormal or zero */
+       if (e == 0) {
+               volatile double z = x*x + ux.value*ux.value;
        }
-       INSERT_WORDS(x, hx, lx);
-       return x;
+       return ux.value;
 }

diff --git a/src/math/nextafterf.c b/src/math/nextafterf.c
index bdc88ca..4727f7b 100644 (file)
--- a/src/math/nextafterf.c
+++ b/src/math/nextafterf.c
@@ -1,67 +1,35 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_nextafterf.c */
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
 #include "libm.h"
 
+#define SIGN 0x80000000
+
 float nextafterf(float x, float y)
 {
-       volatile float t;
-       int32_t hx,hy,ix,iy;
-
-       GET_FLOAT_WORD(hx, x);
-       GET_FLOAT_WORD(hy, y);
-       ix = hx & 0x7fffffff;  /* |x| */
-       iy = hy & 0x7fffffff;  /* |y| */
+       union fshape ux, uy;
+       uint32_t ax, ay, e;
 
-       if (ix > 0x7f800000 || /* x is nan */
-           iy > 0x7f800000)   /* y is nan */
-               return x+y;
-       if (x == y)            /* x == y */
+       if (isnan(x) || isnan(y))
+               return x + y;
+       ux.value = x;
+       uy.value = y;
+       if (ux.bits == uy.bits)
                return y;
-       if (ix == 0) {         /* x == 0 */
-               SET_FLOAT_WORD(x, (hy&0x80000000)|1); /* return +-minsubnormal */
-               /* raise underflow flag */
-               t = x*x;
-               if (t == x)
-                       return t;
-               return x;
-       }
-       if (hx >= 0) {         /* x > 0 */
-               if (hx > hy) {             /* x > y, x -= ulp */
-                       hx--;
-               } else {                   /* x < y, x += ulp */
-                       hx++;
-               }
-       } else {               /* x < 0 */
-               if (hy >= 0 || hx > hy) {  /* x < y, x -= ulp */
-                       hx--;
-               } else {                   /* x > y, x += ulp */
-                       hx++;
-               }
-       }
-       hy = hx & 0x7f800000;
-       if (hy >= 0x7f800000)  /* overflow */
-               return x+x;
-       if (hy < 0x00800000) { /* underflow */
-               /* raise underflow flag */
-               t = x*x;
-               if (t != x) {
-                       SET_FLOAT_WORD(y, hx);
+       ax = ux.bits & ~SIGN;
+       ay = uy.bits & ~SIGN;
+       if (ax == 0) {
+               if (ay == 0)
                        return y;
-               }
+               ux.bits = (uy.bits & SIGN) | 1;
+       } else if (ax > ay || ((ux.bits ^ uy.bits) & SIGN))
+               ux.bits--;
+       else
+               ux.bits++;
+       e = ux.bits & 0x7f800000;
+       /* raise overflow if ux.value is infinite and x is finite */
+       if (e == 0x7f800000)
+               return x + x;
+       /* raise underflow if ux.value is subnormal or zero */
+       if (e == 0) {
+               volatile float z = x*x + ux.value*ux.value;
        }
-       SET_FLOAT_WORD(x, hx);
-       return x;
+       return ux.value;
 }

diff --git a/src/math/nextafterl.c b/src/math/nextafterl.c
index aec8ab4..611ea53 100644 (file)
--- a/src/math/nextafterl.c
+++ b/src/math/nextafterl.c
@@ -1,21 +1,3 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_nextafterl.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-/* IEEE functions
- *      nextafter(x,y)
- *      return the next machine floating-point number of x in the
- *      direction toward y.
- *   Special cases:
- */
-
 #include "libm.h"
 
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -23,55 +5,80 @@ long double nextafterl(long double x, long double y)
 {
        return nextafter(x, y);
 }
-#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+#define MSB ((uint64_t)1<<63)
 long double nextafterl(long double x, long double y)
 {
-       volatile long double t;
-       union IEEEl2bits ux, uy;
-
-       ux.e = x;
-       uy.e = y;
+       union ldshape ux, uy;
 
-       if ((ux.bits.exp == 0x7fff && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl) != 0) ||
-           (uy.bits.exp == 0x7fff && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0))
-               return x+y;  /* x or y is nan */
+       if (isnan(x) || isnan(y))
+               return x + y;
        if (x == y)
-               return y;    /* x=y, return y */
-       if (x == 0.0) {
-               /* return +-minsubnormal */
-               ux.bits.manh = 0;
-               ux.bits.manl = 1;
+               return y;
+       ux.value = x;
+       if (x == 0) {
+               uy.value = y;
+               ux.bits.m = 1;
                ux.bits.sign = uy.bits.sign;
-               /* raise underflow flag */
-               t = ux.e*ux.e;
-               if (t == ux.e)
-                       return t;
-               return ux.e;
-       }
-       if(x > 0.0 ^ x < y) {  /* x -= ulp */
-               if (ux.bits.manl == 0) {
-                       if ((ux.bits.manh&~LDBL_NBIT) == 0)
-                               ux.bits.exp--;
-                       ux.bits.manh = (ux.bits.manh - 1) | (ux.bits.manh & LDBL_NBIT);
+       } else if (x < y ^ ux.bits.sign) {
+               ux.bits.m++;
+               if ((ux.bits.m & ~MSB) == 0) {
+                       ux.bits.m = MSB;
+                       ux.bits.exp++;
                }
-               ux.bits.manl--;
-       } else {               /* x += ulp */
-               ux.bits.manl++;
-               if (ux.bits.manl == 0) {
-                       ux.bits.manh = (ux.bits.manh + 1) | (ux.bits.manh & LDBL_NBIT);
-                       if ((ux.bits.manh&~LDBL_NBIT)==0)
+       } else {
+               if ((ux.bits.m & ~MSB) == 0) {
+                       ux.bits.exp--;
+                       if (ux.bits.exp)
+                               ux.bits.m = 0;
+               }
+               ux.bits.m--;
+       }
+       /* raise overflow if ux.value is infinite and x is finite */
+       if (ux.bits.exp == 0x7fff)
+               return x + x;
+       /* raise underflow if ux.value is subnormal or zero */
+       if (ux.bits.exp == 0) {
+               volatile float z = x*x + ux.value*ux.value;
+       }
+       return ux.value;
+}
+#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
+long double nextafterl(long double x, long double y)
+{
+       union ldshape ux, uy;
+
+       if (isnan(x) || isnan(y))
+               return x + y;
+       if (x == y)
+               return y;
+       ux.value = 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++;
                }
+       } else {
+               if (ux.bits.mlo == 0) {
+                       if (ux.bits.mhi == 0)
+                               ux.bits.exp--;
+                       ux.bits.mhi--;
+               }
+               ux.bits.mlo--;
        }
-       if (ux.bits.exp == 0x7fff)  /* overflow  */
-               return x+x;
-       if (ux.bits.exp == 0) {     /* underflow */
-               mask_nbit_l(ux);
-               /* raise underflow flag */
-               t = ux.e * ux.e;
-               if (t != ux.e)
-                       return ux.e;
+       /* raise overflow if ux.value is infinite and x is finite */
+       if (ux.bits.exp == 0x7fff)
+               return x + x;
+       /* raise underflow if ux.value is subnormal or zero */
+       if (ux.bits.exp == 0) {
+               volatile float z = x*x + ux.value*ux.value;
        }
-       return ux.e;
+       return ux.value;
 }
 #endif

diff --git a/src/math/nexttoward.c b/src/math/nexttoward.c
index e150eaa..741b6b5 100644 (file)
--- a/src/math/nexttoward.c
+++ b/src/math/nexttoward.c
@@ -1,15 +1,3 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_nexttoward.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
 #include "libm.h"
 
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -17,52 +5,42 @@ double nexttoward(double x, long double y)
 {
        return nextafter(x, y);
 }
-#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#else
+#define SIGN ((uint64_t)1<<63)
+
 double nexttoward(double x, long double y)
 {
-       union IEEEl2bits uy;
-       volatile double t;
-       int32_t hx,ix;
-       uint32_t lx;
+       union dshape ux;
+       int e;
 
-       EXTRACT_WORDS(hx, lx, x);
-       ix = hx & 0x7fffffff;
-       uy.e = y;
-
-       if ((ix >= 0x7ff00000 && ((ix-0x7ff00000)|lx) != 0) ||
-           (uy.bits.exp == 0x7fff && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0))
-               return x + y;  /* x or y is nan */
+       if (isnan(x) || isnan(y))
+               return x + y;
        if (x == y)
-               return (double)y;
-       if (x == 0.0) {
-               INSERT_WORDS(x, uy.bits.sign<<31, 1);  /* return +-minsubnormal */
-               /* raise underflow */
-               t = x * x;
-               if (t == x)
-                       return t;
-               return x;
-       }
-       if (hx > 0.0 ^ x < y) {  /* x -= ulp */
-               if (lx == 0)
-                       hx--;
-               lx--;
-       } else {                 /* x += ulp */
-               lx++;
-               if (lx == 0)
-                       hx++;
+               return y;
+       ux.value = x;
+       if (x == 0) {
+               ux.bits = 1;
+               if (signbit(y))
+                       ux.bits |= SIGN;
+       } else if (x < y) {
+               if (signbit(x))
+                       ux.bits--;
+               else
+                       ux.bits++;
+       } else {
+               if (signbit(x))
+                       ux.bits++;
+               else
+                       ux.bits--;
        }
-       ix = hx & 0x7ff00000;
-       if (ix >= 0x7ff00000)   /* overflow  */
+       e = ux.bits>>52 & 0x7ff;
+       /* raise overflow if ux.value is infinite and x is finite */
+       if (e == 0x7ff)
                return x + x;
-       if (ix < 0x00100000) {  /* underflow */
-               /* raise underflow flag */
-               t = x * x;
-               if (t != x) {
-                       INSERT_WORDS(x, hx, lx);
-                       return x;
-               }
+       /* raise underflow if ux.value is subnormal or zero */
+       if (e == 0) {
+               volatile float z = x*x + ux.value*ux.value;
        }
-       INSERT_WORDS(x, hx, lx);
-       return x;
+       return ux.value;
 }
 #endif

diff --git a/src/math/nexttowardf.c b/src/math/nexttowardf.c
index c52ef3a..821f72a 100644 (file)
--- a/src/math/nexttowardf.c
+++ b/src/math/nexttowardf.c
@@ -1,62 +1,37 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_nexttowardf.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
 #include "libm.h"
 
-#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
-// FIXME
-#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-#define LDBL_INFNAN_EXP (LDBL_MAX_EXP * 2 - 1)
-
 float nexttowardf(float x, long double y)
 {
-       union IEEEl2bits uy;
-       volatile float t;
-       int32_t hx,ix;
-
-       GET_FLOAT_WORD(hx, x);
-       ix = hx & 0x7fffffff;  /* |x| */
-       uy.e = y;
+       union fshape ux;
+       uint32_t e;
 
-       if (ix > 0x7f800000 ||
-           (uy.bits.exp == LDBL_INFNAN_EXP &&
-            ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0))
-               return x + y;  /* x or y is nan */
+       if (isnan(x) || isnan(y))
+               return x + y;
        if (x == y)
-               return (float)y;  /* x=y, return y */
-       if (ix == 0) {   /* x == 0 */
-               SET_FLOAT_WORD(x, (uy.bits.sign<<31)|1); /* return +-minsubnormal */
-               /* raise underflow flag */
-               t = x*x;
-               if (t == x)
-                       return t;
-               return x;
+               return y;
+       ux.value = x;
+       if (x == 0) {
+               ux.bits = 1;
+               if (signbit(y))
+                       ux.bits |= 0x80000000;
+       } else if (x < y) {
+               if (signbit(x))
+                       ux.bits--;
+               else
+                       ux.bits++;
+       } else {
+               if (signbit(x))
+                       ux.bits++;
+               else
+                       ux.bits--;
        }
-       if (hx >= 0 ^ x < y)  /* x -= ulp */
-               hx--;
-       else                  /* x += ulp */
-               hx++;
-       ix = hx & 0x7f800000;
-       if (ix >= 0x7f800000)  /* overflow  */
-               return x+x;
-       if (ix < 0x00800000) { /* underflow */
-               /* raise underflow flag */
-               t = x*x;
-               if (t != x) {
-                       SET_FLOAT_WORD(x, hx);
-                       return x;
-               }
+       e = ux.bits & 0x7f800000;
+       /* raise overflow if ux.value is infinite and x is finite */
+       if (e == 0x7f800000)
+               return x + x;
+       /* raise underflow if ux.value is subnormal or zero */
+       if (e == 0) {
+               volatile float z = x*x + ux.value*ux.value;
        }
-       SET_FLOAT_WORD(x, hx);
-       return x;
+       return ux.value;
 }
-#endif