math: clean up atan2.c

* remove volatile hacks
* don't care about inexact flag for now (removed all the +-tiny)
* fix atanl to raise underflow properly
* remove signed int arithmetics
* use pi/2 instead of pi_o_2 (gcc generates the same code, which is not
correct, but it does not matter: we mainly care about nearest rounding)

diff --git a/src/math/atan2.c b/src/math/atan2.c
index 825a38f..5a1903c 100644 (file)
--- a/src/math/atan2.c
+++ b/src/math/atan2.c
@@ -39,75 +39,63 @@
 
 #include "libm.h"
 
-// FIXME
-static const volatile double
-tiny  = 1.0e-300;
 static const double
-pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
-pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
-pi     = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
-static const volatile double
+pi     = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
 pi_lo  = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
 
 double atan2(double y, double x)
 {
        double z;
-       int32_t k,m,hx,hy,ix,iy;
-       uint32_t lx,ly;
+       uint32_t m,lx,ly,ix,iy;
 
-       EXTRACT_WORDS(hx, lx, x);
-       ix = hx & 0x7fffffff;
-       EXTRACT_WORDS(hy, ly, y);
-       iy = hy & 0x7fffffff;
-       if ((ix|((lx|-lx)>>31)) > 0x7ff00000 ||
-           (iy|((ly|-ly)>>31)) > 0x7ff00000)  /* x or y is NaN */
+       if (isnan(x) || isnan(y))
                return x+y;
-       if ((hx-0x3ff00000 | lx) == 0)  /* x = 1.0 */
+       EXTRACT_WORDS(ix, lx, x);
+       EXTRACT_WORDS(iy, ly, y);
+       if ((ix-0x3ff00000 | lx) == 0)  /* x = 1.0 */
                return atan(y);
-       m = ((hy>>31)&1) | ((hx>>30)&2);  /* 2*sign(x)+sign(y) */
+       m = ((iy>>31)&1) | ((ix>>30)&2);  /* 2*sign(x)+sign(y) */
+       ix = ix & 0x7fffffff;
+       iy = iy & 0x7fffffff;
 
        /* when y = 0 */
        if ((iy|ly) == 0) {
                switch(m) {
                case 0:
-               case 1: return y;        /* atan(+-0,+anything)=+-0 */
-               case 2: return  pi+tiny; /* atan(+0,-anything) = pi */
-               case 3: return -pi-tiny; /* atan(-0,-anything) =-pi */
+               case 1: return y;   /* atan(+-0,+anything)=+-0 */
+               case 2: return  pi; /* atan(+0,-anything) = pi */
+               case 3: return -pi; /* atan(-0,-anything) =-pi */
                }
        }
        /* when x = 0 */
        if ((ix|lx) == 0)
-               return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
+               return m&1 ? -pi/2 : pi/2;
        /* when x is INF */
        if (ix == 0x7ff00000) {
                if (iy == 0x7ff00000) {
                        switch(m) {
-                       case 0: return  pi_o_4+tiny; /* atan(+INF,+INF) */
-                       case 1: return -pi_o_4-tiny; /* atan(-INF,+INF) */
-                       case 2: return  3.0*pi_o_4+tiny; /* atan(+INF,-INF) */
-                       case 3: return -3.0*pi_o_4-tiny; /* atan(-INF,-INF) */
+                       case 0: return  pi/4;   /* atan(+INF,+INF) */
+                       case 1: return -pi/4;   /* atan(-INF,+INF) */
+                       case 2: return  3*pi/4; /* atan(+INF,-INF) */
+                       case 3: return -3*pi/4; /* atan(-INF,-INF) */
                        }
                } else {
                        switch(m) {
-                       case 0: return  0.0;     /* atan(+...,+INF) */
-                       case 1: return -0.0;     /* atan(-...,+INF) */
-                       case 2: return  pi+tiny; /* atan(+...,-INF) */
-                       case 3: return -pi-tiny; /* atan(-...,-INF) */
+                       case 0: return  0.0; /* atan(+...,+INF) */
+                       case 1: return -0.0; /* atan(-...,+INF) */
+                       case 2: return  pi;  /* atan(+...,-INF) */
+                       case 3: return -pi;  /* atan(-...,-INF) */
                        }
                }
        }
-       /* when y is INF */
-       if (iy == 0x7ff00000)
-               return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
+       /* |y/x| > 0x1p64 */
+       if (ix+(64<<20) < iy || iy == 0x7ff00000)
+               return m&1 ? -pi/2 : pi/2;
 
-       /* compute y/x */
-       k = (iy-ix)>>20;
-       if (k > 60) {                  /* |y/x| >  2**60 */
-               z = pi_o_2+0.5*pi_lo;
-               m &= 1;
-       } else if (hx < 0 && k < -60)  /* 0 > |y|/x > -2**-60 */
-               z = 0.0;
-       else                           /* safe to do y/x */
+       /* z = atan(|y/x|) without spurious underflow */
+       if ((m&2) && iy+(64<<20) < ix)  /* |y/x| < 0x1p-64, x<0 */
+               z = 0;
+       else
                z = atan(fabs(y/x));
        switch (m) {
        case 0: return z;              /* atan(+,+) */

diff --git a/src/math/atan2f.c b/src/math/atan2f.c
index 96839cb..c634d00 100644 (file)
--- a/src/math/atan2f.c
+++ b/src/math/atan2f.c
@@ -15,72 +15,63 @@
 
 #include "libm.h"
 
-static const volatile float
-tiny = 1.0e-30;
 static const float
-pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
-pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
-pi     = 3.1415927410e+00; /* 0x40490fdb */
-static const volatile float
+pi     = 3.1415927410e+00, /* 0x40490fdb */
 pi_lo  = -8.7422776573e-08; /* 0xb3bbbd2e */
 
 float atan2f(float y, float x)
 {
        float z;
-       int32_t k,m,hx,hy,ix,iy;
+       uint32_t m,ix,iy;
 
-       GET_FLOAT_WORD(hx, x);
-       ix = hx & 0x7fffffff;
-       GET_FLOAT_WORD(hy, y);
-       iy = hy & 0x7fffffff;
-       if (ix > 0x7f800000 || iy > 0x7f800000)  /* x or y is NaN */
+       if (isnan(x) || isnan(y))
                return x+y;
-       if (hx == 0x3f800000)  /* x=1.0 */
+       GET_FLOAT_WORD(ix, x);
+       GET_FLOAT_WORD(iy, y);
+       if (ix == 0x3f800000)  /* x=1.0 */
                return atanf(y);
-       m = ((hy>>31)&1) | ((hx>>30)&2);  /* 2*sign(x)+sign(y) */
+       m = ((iy>>31)&1) | ((ix>>30)&2);  /* 2*sign(x)+sign(y) */
+       ix &= 0x7fffffff;
+       iy &= 0x7fffffff;
 
        /* when y = 0 */
        if (iy == 0) {
                switch (m) {
                case 0:
-               case 1: return y;        /* atan(+-0,+anything)=+-0 */
-               case 2: return  pi+tiny; /* atan(+0,-anything) = pi */
-               case 3: return -pi-tiny; /* atan(-0,-anything) =-pi */
+               case 1: return y;   /* atan(+-0,+anything)=+-0 */
+               case 2: return  pi; /* atan(+0,-anything) = pi */
+               case 3: return -pi; /* atan(-0,-anything) =-pi */
                }
        }
        /* when x = 0 */
        if (ix == 0)
-               return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
+               return m&1 ? -pi/2 : pi/2;
        /* when x is INF */
        if (ix == 0x7f800000) {
                if (iy == 0x7f800000) {
                        switch (m) {
-                       case 0: return  pi_o_4+tiny; /* atan(+INF,+INF) */
-                       case 1: return -pi_o_4-tiny; /* atan(-INF,+INF) */
-                       case 2: return 3.0f*pi_o_4+tiny;  /*atan(+INF,-INF)*/
-                       case 3: return -3.0f*pi_o_4-tiny; /*atan(-INF,-INF)*/
+                       case 0: return  pi/4; /* atan(+INF,+INF) */
+                       case 1: return -pi/4; /* atan(-INF,+INF) */
+                       case 2: return 3*pi/4;  /*atan(+INF,-INF)*/
+                       case 3: return -3*pi/4; /*atan(-INF,-INF)*/
                        }
                } else {
                        switch (m) {
                        case 0: return  0.0f;    /* atan(+...,+INF) */
                        case 1: return -0.0f;    /* atan(-...,+INF) */
-                       case 2: return  pi+tiny; /* atan(+...,-INF) */
-                       case 3: return -pi-tiny; /* atan(-...,-INF) */
+                       case 2: return  pi; /* atan(+...,-INF) */
+                       case 3: return -pi; /* atan(-...,-INF) */
                        }
                }
        }
-       /* when y is INF */
-       if (iy == 0x7f800000)
-               return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
+       /* |y/x| > 0x1p26 */
+       if (ix+(26<<23) < iy || iy == 0x7f800000)
+               return m&1 ? -pi/2 : pi/2;
 
-       /* compute y/x */
-       k = (iy-ix)>>23;
-       if (k > 26) {                  /* |y/x| >  2**26 */
-               z = pi_o_2 + 0.5f*pi_lo;
-               m &= 1;
-       } else if (k < -26 && hx < 0)  /* 0 > |y|/x > -2**-26 */
+       /* z = atan(|y/x|) with correct underflow */
+       if ((m&2) && iy+(26<<23) < ix)  /*|y/x| < 0x1p-26, x < 0 */
                z = 0.0;
-       else                           /* safe to do y/x */
+       else
                z = atanf(fabsf(y/x));
        switch (m) {
        case 0: return z;              /* atan(+,+) */

diff --git a/src/math/atan2l.c b/src/math/atan2l.c
index 7cb42c2..e0167d0 100644 (file)
--- a/src/math/atan2l.c
+++ b/src/math/atan2l.c
@@ -29,26 +29,22 @@ long double atan2l(long double y, long double x)
 {
        union IEEEl2bits ux, uy;
        long double z;
-       int32_t k,m;
-       int16_t exptx, expsignx, expty, expsigny;
+       int m;
+       uint16_t exptx, expsignx, expty, expsigny;
 
+       if (isnan(x) || isnan(y))
+               return x+y;
+       if (x == 1)
+               return atanl(y);
        uy.e = y;
        expsigny = uy.xbits.expsign;
        expty = expsigny & 0x7fff;
        ux.e = x;
        expsignx = ux.xbits.expsign;
        exptx = expsignx & 0x7fff;
-       if ((exptx==0x7fff &&
-            ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
-           (expty==0x7fff &&
-            ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0))   /* y is NaN */
-               return x+y;
-       if (expsignx==0x3fff && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
-               return atanl(y);
        m = ((expsigny>>15)&1) | ((expsignx>>14)&2);  /* 2*sign(x)+sign(y) */
 
-       /* when y = 0 */
-       if (expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
+       if (y == 0) {
                switch(m) {
                case 0:
                case 1: return y;           /* atan(+-0,+anything)=+-0 */
@@ -56,9 +52,8 @@ long double atan2l(long double y, long double x)
                case 3: return -2*pio2_hi-0x1p-120f; /* atan(-0,-anything) =-pi */
                }
        }
-       /* when x = 0 */
-       if (exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
-               return expsigny < 0 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
+       if (x == 0)
+               return m&1 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
        /* when x is INF */
        if (exptx == 0x7fff) {
                if (expty == 0x7fff) {
@@ -78,17 +73,12 @@ long double atan2l(long double y, long double x)
                }
        }
        /* when y is INF */
-       if (expty == 0x7fff)
-               return expsigny < 0 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
+       if (exptx+120 < expty || expty == 0x7fff)
+               return m&1 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
 
-       /* compute y/x */
-       k = expty-exptx;
-       if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
-               z = pio2_hi+0x1p-120f;
-               m &= 1;
-       } else if (expsignx < 0 && k < -LDBL_MANT_DIG-2) /* |y/x| tiny, x<0 */
+       if ((m&2) && expty+120 < exptx) /* |y/x| tiny, x<0 */
                z = 0.0;
-       else                     /* safe to do y/x */
+       else
                z = atanl(fabsl(y/x));
        switch (m) {
        case 0: return z;               /* atan(+,+) */

diff --git a/src/math/atanl.c b/src/math/atanl.c
index e76693e..d29e631 100644 (file)
--- a/src/math/atanl.c
+++ b/src/math/atanl.c
@@ -70,8 +70,8 @@ long double atanl(long double x)
        union IEEEl2bits u;
        long double w,s1,s2,z;
        int id;
-       int16_t expsign, expt;
-       int32_t expman;
+       uint16_t expsign, expt;
+       uint32_t expman;
 
        u.e = x;
        expsign = u.xbits.expsign;
@@ -81,15 +81,16 @@ long double atanl(long double x)
                    ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)  /* NaN */
                        return x+x;
                z = atanhi[3] + 0x1p-120f;
-               return expsign < 0 ? -z : z;
+               return expsign>>15 ? -z : z;
        }
        /* Extract the exponent and the first few bits of the mantissa. */
        /* XXX There should be a more convenient way to do this. */
        expman = (expt << 8) | ((u.bits.manh >> (LDBL_MANH_SIZE - 9)) & 0xff);
        if (expman < ((0x3fff - 2) << 8) + 0xc0) {  /* |x| < 0.4375 */
                if (expt < 0x3fff - 32) {   /* if |x| is small, atanl(x)~=x */
-                       /* raise inexact if x!=0 */
-                       FORCE_EVAL(x + 0x1p120f);
+                       /* raise underflow if subnormal */
+                       if (expt == 0)
+                               FORCE_EVAL((float)x);
                        return x;
                }
                id = -1;
@@ -122,6 +123,6 @@ long double atanl(long double x)
        if (id < 0)
                return x - x*(s1+s2);
        z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
-       return expsign < 0 ? -z : z;
+       return expsign>>15 ? -z : z;
 }
 #endif