various fixes detected with -Wdouble-promotion

Changes with respect to v1:
- added comment in e_j1f.c to explain the use of float is enough
Reviewed-by: Adhemerval Zanella  <adhemerval.zanella@linaro.org>

diff --git a/math/w_jnf_compat.c b/math/w_jnf_compat.c
index 8f465cee6e529f636a54df2f7839a732db61ec8f..4732d96bd5aa096f0548e6d226021528f3f93a98 100644 (file)
--- a/math/w_jnf_compat.c
+++ b/math/w_jnf_compat.c
@@ -52,7 +52,7 @@ __ynf (int n, float x)
          feraiseexcept (FE_INVALID);
          return __kernel_standard_f (n, x, 113);
        }
-      else if (x == 0.0)
+      else if (x == 0.0f)
        {
          /* d = -one/(x-x) */
          feraiseexcept (FE_DIVBYZERO);

diff --git a/math/w_log2f_compat.c b/math/w_log2f_compat.c
index f26a97531d0d4bee6cfeb8acb3b2041e30c34edb..e6a4658aa73415b397839e82a4f07f72cb3dd89e 100644 (file)
--- a/math/w_log2f_compat.c
+++ b/math/w_log2f_compat.c
@@ -29,7 +29,7 @@ __log2f_compat (float x)
 {
   if (__builtin_expect (islessequal (x, 0.0f), 0) && _LIB_VERSION != _IEEE_)
     {
-      if (x == 0.0)
+      if (x == 0.0f)
        {
          feraiseexcept (FE_DIVBYZERO);
          return __kernel_standard_f (x, x, 148); /* log2(0) */

diff --git a/math/w_tgammaf_compat.c b/math/w_tgammaf_compat.c
index addbdb1109457452336d18a62b6267315428716a..253d0c8b6634154e7cffd4e86e82fae3d6159d70 100644 (file)
--- a/math/w_tgammaf_compat.c
+++ b/math/w_tgammaf_compat.c
@@ -26,7 +26,7 @@ __tgammaf(float x)
        float y = __ieee754_gammaf_r(x, NULL);
 
        if(__glibc_unlikely (!isfinite (y) || y == 0)
-          && (isfinite (x) || (isinf (x) && x < 0.0))
+          && (isfinite (x) || (isinf (x) && x < 0.0f))
           && _LIB_VERSION != _IEEE_) {
          if (x == (float)0.0)
            /* tgammaf pole */

diff --git a/sysdeps/ieee754/dbl-64/s_fmaf.c b/sysdeps/ieee754/dbl-64/s_fmaf.c
index 375bd13e0b5287f37f1fbc66d8674aaeab3c194d..7bf9941dd8895dd6fd5c2b55c753429339bafc3e 100644 (file)
--- a/sysdeps/ieee754/dbl-64/s_fmaf.c
+++ b/sysdeps/ieee754/dbl-64/s_fmaf.c
@@ -45,7 +45,7 @@ __fmaf (float x, float y, float z)
 
   /* Ensure correct sign of an exact zero result by performing the
      addition in the original rounding mode in that case.  */
-  if (temp == -z)
+  if (temp == (double) -z)
     return (float) temp + z;
 
   union ieee754_double u;

diff --git a/sysdeps/ieee754/flt-32/e_acosf.c b/sysdeps/ieee754/flt-32/e_acosf.c
index 820e9298646152d06e49ac7cc06ca92aa9f3a880..929ad38342f36e3714133ad55e3c842e5cc62b9d 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_acosf.c
+++ b/sysdeps/ieee754/flt-32/e_acosf.c
@@ -112,9 +112,9 @@ __ieee754_acosf (float x)
   if (ax < (0x7eu << 24))
     {
       if (t == 0x328885a3u)
-       return 0x1.921fb6p+0f + 0x1p-25;
+       return 0x1.921fb6p+0f + 0x1p-25f;
       if (t == 0x39826222u)
-       return 0x1.920f6ap+0f + 0x1p-25;
+       return 0x1.920f6ap+0f + 0x1p-25f;
       double x2 = xs * xs;
       r = (pi2 - xs) - (xs * x2) * poly12 (x2, C0);
     }

diff --git a/sysdeps/ieee754/flt-32/e_atan2f.c b/sysdeps/ieee754/flt-32/e_atan2f.c
index 82a0151293cda9cf89d6a18b6f8b35d4fdaeddd4..1c72845c7c8df79bfea07a65bb1798e22de1f260 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_atan2f.c
+++ b/sysdeps/ieee754/flt-32/e_atan2f.c
@@ -73,7 +73,7 @@ cr_atan2f_tiny (float y, float x)
   static const double c = -0x1.5555555555555p-2; /* -1/3 rounded to nearest */
   double zz = z * z;
   double cz = c * z;
-  e = e / x + cz * zz;
+  e = e / dx + cz * zz;
   uint64_t t = asuint64 (z);
   if ((t & UINT64_C(0xfffffff)) == 0) /* boundary case */
     {
@@ -139,7 +139,7 @@ __ieee754_atan2f (float y, float x)
          if (ux >> 31)
            return pi * sgn[uy >> 31];
          else
-           return 0.0f * sgn[uy >> 31];
+           return 0.0 * sgn[uy >> 31];
        }
       if (yinf)
        return pi2 * sgn[uy >> 31];
@@ -155,7 +155,7 @@ __ieee754_atan2f (float y, float x)
            return off[i];
        }
       if (!(ux >> 31))
-       return 0.0f * sgn[uy >> 31];
+       return 0.0 * sgn[uy >> 31];
     }
   uint32_t gt = ay > ax;
   uint32_t i = (uy >> 31) * 4 + (ux >> 31) * 2 + gt;

diff --git a/sysdeps/ieee754/flt-32/e_coshf.c b/sysdeps/ieee754/flt-32/e_coshf.c
index 382cd55cdf0ed01102eed04e51992234beccf483..c6c0392dab0cac474765fe1e2b595592f7400ce0 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_coshf.c
+++ b/sysdeps/ieee754/flt-32/e_coshf.c
@@ -77,7 +77,7 @@ __ieee754_coshf (float x)
   double rm = sm * (te - h * to);
   double r = rp + rm;
   float ub = r;
-  double lb = r - 1.45e-10 * r;
+  float lb = r - 1.45e-10 * r;
   if (__glibc_unlikely (ub != lb))
     {
       const double iln2h = 0x1.7154765p+5;

diff --git a/sysdeps/ieee754/flt-32/e_exp10f.c b/sysdeps/ieee754/flt-32/e_exp10f.c
index 10e3b885231c4139046ccd7394dfb902dd69db80..aface56ff25c9453e1c5c81757cc9ee869665831 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_exp10f.c
+++ b/sysdeps/ieee754/flt-32/e_exp10f.c
@@ -163,7 +163,7 @@ __exp10f (float x)
       if (x < -0x2d.278d4p0f)
         return __math_uflowf (0);
 #if WANT_ERRNO_UFLOW
-      if (x < -0x2c.da7cfp0)
+      if (x < -0x2c.da7cfp0f)
         return __math_may_uflowf (0);
 #endif
       /* the smallest value such that 10^x >= 2^-126 (normal range)

diff --git a/sysdeps/ieee754/flt-32/e_j0f.c b/sysdeps/ieee754/flt-32/e_j0f.c
index 9ae91a9dccc07f33951c518f97611d03c5a6d387..c800acd3cb8a716712c6c9a4ce0c9af414310d7e 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_j0f.c
+++ b/sysdeps/ieee754/flt-32/e_j0f.c
@@ -203,7 +203,7 @@ j0f_asympt (float x)
     return 0xf.47039p-28f;
   double y = 1.0 / (double) x;
   double y2 = y * y;
-  double beta0 = 1.0f + y2 * (-0x1p-4f + 0x1.a8p-4 * y2);
+  double beta0 = 1.0 + y2 * (-0x1p-4 + 0x1.a8p-4 * y2);
   double alpha0 = y * (0x2p-4 - 0x1.0aaaaap-4 * y2);
   double h;
   int n;
@@ -484,7 +484,7 @@ y0f_asympt (float x)
     return 0x1.a48974p-40f;
   double y = 1.0 / (double) x;
   double y2 = y * y;
-  double beta0 = 1.0f + y2 * (-0x1p-4f + 0x1.a8p-4 * y2);
+  double beta0 = 1.0 + y2 * (-0x1p-4 + 0x1.a8p-4 * y2);
   double alpha0 = y * (0x2p-4 - 0x1.0aaaaap-4 * y2);
   double h;
   int n;
@@ -529,7 +529,7 @@ y0f_near_root (float x, float z)
   /* For degree 0 use a degree-5 polynomial, where the coefficients of
      degree 4 and 5 are hard-coded.  */
   float p6 = (index > 0) ? p[6]
-    : p[6] + y * (-0x3.a46c9p-4 + y * 0x3.735478p-4);
+    : p[6] + y * (-0x3.a46c9p-4f + y * 0x3.735478p-4f);
   float res = p[3] + y * (p[4] + y * (p[5] + y * p6));
   return res;
 }

diff --git a/sysdeps/ieee754/flt-32/e_j1f.c b/sysdeps/ieee754/flt-32/e_j1f.c
index ade10402fdb64aaf100d781bfd0c3a7e9d19d501..52d52814959e42033f577da5863a8250e8e44232 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_j1f.c
+++ b/sysdeps/ieee754/flt-32/e_j1f.c
@@ -207,7 +207,7 @@ j1f_asympt (float x)
     }
   double y = 1.0 / (double) x;
   double y2 = y * y;
-  double beta1 = 1.0f + y2 * (0x3p-4 - 0x3.18p-4 * y2);
+  double beta1 = 1.0 + y2 * (0x3p-4 - 0x3.18p-4 * y2);
   double alpha1;
   alpha1 = y * (-0x6p-4 + y2 * (0x2.ap-4 - 0x5.ef33333333334p-4 * y2));
   double h;
@@ -494,7 +494,7 @@ y1f_asympt (float x)
   float cst = 0xc.c422ap-4; /* sqrt(2/pi) rounded to nearest  */
   double y = 1.0 / (double) x;
   double y2 = y * y;
-  double beta1 = 1.0f + y2 * (0x3p-4 - 0x3.18p-4 * y2);
+  double beta1 = 1.0 + y2 * (0x3p-4 - 0x3.18p-4 * y2);
   double alpha1;
   alpha1 = y * (-0x6p-4 + y2 * (0x2.ap-4 - 0x5.ef33333333334p-4 * y2));
   double h;
@@ -537,10 +537,12 @@ y1f_near_root (float x, float z)
     return z;
   float xmid = p[1];
   float y = x - xmid, p6;
+  /* Using float rather than double in the constants below is enough to get
+     the desired accuracy (at most 9 ulps).  */
   if (index == 0)
-    p6 = p[6] + y * (-0x1.28043p-8 + y * 0x2.50e83p-8);
+    p6 = p[6] + y * (-0x1.28043p-8f + y * 0x2.50e83p-8f);
   else if (index == 1)
-    p6 = p[6] + y * -0xf.ff6b8p-12;
+    p6 = p[6] + y * -0xf.ff6b8p-12f;
   else
     p6 = p[6];
   return p[3] + y * (p[4] + y * (p[5] + y * p6));

diff --git a/sysdeps/ieee754/flt-32/e_jnf.c b/sysdeps/ieee754/flt-32/e_jnf.c
index ff0a9d7c6349ca20b94debaacbc11996a470969e..9d3e0aaaa3be3d25bcfc6fcfb168fc5d440c605c 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_jnf.c
+++ b/sysdeps/ieee754/flt-32/e_jnf.c
@@ -61,7 +61,8 @@ __ieee754_jnf(int n, float x)
            b = __ieee754_j1f(x);
            for(i=1;i<n;i++){
                temp = b;
-               b = b*((double)(i+i)/x) - a; /* avoid underflow */
+                /* the following computation should be done in double precision */
+               b = (double)b*((double)(i+i)/(double)x) - (double)a; /* avoid underflow */
                a = temp;
            }
        } else {
@@ -219,7 +220,8 @@ __ieee754_ynf(int n, float x)
        GET_FLOAT_WORD(ib,b);
        for(i=1;i<n&&ib!=0xff800000;i++){
            temp = b;
-           b = ((double)(i+i)/x)*b - a;
+            /* the following computation should be done in double precision */
+           b = ((double)(i+i)/(double)x)*(double)b - (double)a;
            GET_FLOAT_WORD(ib,b);
            a = temp;
        }

diff --git a/sysdeps/ieee754/flt-32/e_lgammaf_r.c b/sysdeps/ieee754/flt-32/e_lgammaf_r.c
index cd87248ffe0a39eee3b134b566e8539d13220444..059afa86c617ab6c1cef7257d0e0822dcef465b4 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_lgammaf_r.c
+++ b/sysdeps/ieee754/flt-32/e_lgammaf_r.c
@@ -181,6 +181,7 @@ __ieee754_lgammaf_r (float x, int *signgamp)
     *signgamp = 1 - ((((int) fx) & 1) << 1);
 
   double z = ax, f;
+  double s = x;
   if (__glibc_unlikely (ax < 0x1.52p-1f))
     {
       static const double rn[] =
@@ -198,7 +199,6 @@ __ieee754_lgammaf_r (float x, int *signgamp)
          -0x1.7dd25af0b83d4p+0, -0x1.36bf1880125fcp+0,
          -0x1.1379fc8023d9cp+0, -0x1.03712e41525d2p+0
        };
-      double s = x;
       f = (c0 * s) * as_r8 (s, rn) / as_r8 (s, rd) - as_ln (z);
     }
   else
@@ -208,7 +208,7 @@ __ieee754_lgammaf_r (float x, int *signgamp)
          if (__glibc_unlikely (x > 0x1.895f1cp+121f))
            return math_narrow_eval (0x1p127f * 0x1p127f);
          /* |x|>=2**23, must be -integer */
-         if (__glibc_unlikely (x < 0.0f && ax > 0x1p+23))
+         if (__glibc_unlikely (x < 0.0f && ax > 0x1p+23f))
            return ax / 0.0f;
          double lz = as_ln (z);
          f = (z - 0.5) * (lz - 1) + 0x1.acfe390c97d69p-2;
@@ -286,7 +286,7 @@ __ieee754_lgammaf_r (float x, int *signgamp)
            {
              if (__glibc_unlikely (t < 0x40301b93u && t > 0x402f95c2u))
                {
-                 double h = (x + 0x1.5fb410a1bd901p+1)
+                 double h = (s + 0x1.5fb410a1bd901p+1)
                    - 0x1.a19a96d2e6f85p-54;
                  double h2 = h * h;
                  double h4 = h2 * h2;
@@ -302,7 +302,7 @@ __ieee754_lgammaf_r (float x, int *signgamp)
                }
              else if (__glibc_unlikely (t > 0x401ceccbu && t < 0x401d95cau))
                {
-                 double h = (x + 0x1.3a7fc9600f86cp+1)
+                 double h = (s + 0x1.3a7fc9600f86cp+1)
                    + 0x1.55f64f98af8dp-55;
                  double h2 = h * h;
                  double h4 = h2 * h2;
@@ -319,7 +319,7 @@ __ieee754_lgammaf_r (float x, int *signgamp)
                }
              else if (__glibc_unlikely (t > 0x40492009u && t < 0x404940efu))
                {
-                 double h = (x + 0x1.9260dbc9e59afp+1)
+                 double h = (s + 0x1.9260dbc9e59afp+1)
                    + 0x1.f717cd335a7b3p-53;
                  double h2 = h * h;
                  double h4 = h2 * h2;

diff --git a/sysdeps/ieee754/flt-32/e_powf.c b/sysdeps/ieee754/flt-32/e_powf.c
index ae3af360db0ddd5ce93211190d358ed17a6c561d..06587140fbbf47291fae86566efc7946f49ad466 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_powf.c
+++ b/sysdeps/ieee754/flt-32/e_powf.c
@@ -203,7 +203,7 @@ __powf (float x, float y)
        }
     }
   double_t logx = log2_inline (ix);
-  double_t ylogx = y * logx; /* Note: cannot overflow, y is single prec.  */
+  double_t ylogx = (double) y * logx; /* Note: cannot overflow, y is single prec.  */
   if (__glibc_unlikely ((asuint64 (ylogx) >> 47 & 0xffff)
                        >= asuint64 (126.0 * POWF_SCALE) >> 47))
     {

diff --git a/sysdeps/ieee754/flt-32/e_remainderf.c b/sysdeps/ieee754/flt-32/e_remainderf.c
index d0f069fbd214176e0346bfc72f5b4021d0d8da70..6e6d687263b0bfbad9c533430f2965c3ae0e43ef 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_remainderf.c
+++ b/sysdeps/ieee754/flt-32/e_remainderf.c
@@ -46,7 +46,7 @@ __ieee754_remainderf(float x, float p)
            x -= p;
          /* Make sure x is not -0. This can occur only when x = p
             and rounding direction is towards negative infinity. */
-         else if (x == 0.0)
+         else if (x == 0.0f)
            x = 0.0;
        }
     }
@@ -63,7 +63,7 @@ __ieee754_remainderf(float x, float p)
          x -= p;
          if (x >= p_half)
            x -= p;
-         else if (x == 0.0)
+         else if (x == 0.0f)
            x = 0.0;
        }
     }

diff --git a/sysdeps/ieee754/flt-32/e_sinhf.c b/sysdeps/ieee754/flt-32/e_sinhf.c
index 6c8c1db404f165ccce8ad03cc1bb20b6fd1aec71..5e812c35afeafc003bf0ada0894a2a95f7e80bbb 100644 (file)
--- a/sysdeps/ieee754/flt-32/e_sinhf.c
+++ b/sysdeps/ieee754/flt-32/e_sinhf.c
@@ -91,7 +91,7 @@ __ieee754_sinhf (float x)
   double rm = sm * (te - h * to);
   double r = rp - rm;
   float ub = r;
-  double lb = r - 1.52e-10 * r;
+  float lb = r - 1.52e-10 * r;
   if (__glibc_unlikely (ub != lb))
     {
       const double iln2h = 0x1.7154765p+5;

diff --git a/sysdeps/ieee754/flt-32/s_asinpif.c b/sysdeps/ieee754/flt-32/s_asinpif.c
index d50de7fcd7a448570415e55d5ab34c289833b1be..8ba3e72a56d0bbca17eb1f735f9cbe91b21faecb 100644 (file)
--- a/sysdeps/ieee754/flt-32/s_asinpif.c
+++ b/sysdeps/ieee754/flt-32/s_asinpif.c
@@ -65,7 +65,7 @@ __asinpif (float x)
       c0 += c2 * z4;
       c4 += c6 * z4;
       c0 += c4 * (z4 * z4);
-      if (__glibc_unlikely (ax != 0.0 && ax <= 0x1.921fb4p-126f))
+      if (__glibc_unlikely (ax != 0.0f && ax <= 0x1.921fb4p-126f))
        __set_errno (ERANGE);
       return z * c0;
     }

diff --git a/sysdeps/ieee754/flt-32/s_atanpif.c b/sysdeps/ieee754/flt-32/s_atanpif.c
index 8d78163418824087e98659edc1d8745b33907e71..0a46a5bcd05c33f1d967feefad072bc97b7bbe2b 100644 (file)
--- a/sysdeps/ieee754/flt-32/s_atanpif.c
+++ b/sysdeps/ieee754/flt-32/s_atanpif.c
@@ -48,7 +48,7 @@ __atanpif (float x)
        }
       /* Warning: 0x1.45f306p-2f / x underflows for |x| >= 0x1.45f306p+124 */
       if (fabsf (x) >= 0x1.45f306p+124f)
-       return f - copysign (0x1p-26f, x);
+       return f - copysignf (0x1p-26f, x);
       else
        return f - 0x1.45f306p-2f / x;
     }
@@ -63,7 +63,7 @@ __atanpif (float x)
            __set_errno (ERANGE);
          return rsx;
        }
-      return sx - (0x1.5555555555555p-2 * sx) * (x * x);
+      return sx - (0x1.5555555555555p-2 * sx) * (z * z);
     }
   uint32_t ax = t & (~0u >> 1);
   if (__glibc_unlikely (ax == 0x3fa267ddu))

diff --git a/sysdeps/ieee754/flt-32/s_erfcf.c b/sysdeps/ieee754/flt-32/s_erfcf.c
index 7d77eceb9cb17496f4cdb26d9e45bdb640ab1fde..d15d77a38a26689211b100200b63e1248f02c53a 100644 (file)
--- a/sysdeps/ieee754/flt-32/s_erfcf.c
+++ b/sysdeps/ieee754/flt-32/s_erfcf.c
@@ -131,7 +131,7 @@ __erfcf (float xf)
          0x1.20dd750429b6dp+0, -0x1.812746b03610bp-2, 0x1.ce2f218831d2fp-4,
          -0x1.b82c609607dcbp-6, 0x1.553af09b8008ep-8
        };
-      double f0 = xf
+      double f0 = (double) xf
            * (c[0] + x2 * (c[1] + x2 * (c[2] + x2 * (c[3] + x2 * (c[4])))));
       return 1.0 - f0;
     }

diff --git a/sysdeps/ieee754/flt-32/s_log10p1f.c b/sysdeps/ieee754/flt-32/s_log10p1f.c
index 4e11d55d49a5f5e841498f243137eee0cfc254ef..d9e114920164b7c0e13cd61e4f9779904440ed9e 100644 (file)
--- a/sysdeps/ieee754/flt-32/s_log10p1f.c
+++ b/sysdeps/ieee754/flt-32/s_log10p1f.c
@@ -155,7 +155,7 @@ __log10p1f (float x)
              0x1.63c62378fa3dbp-3, 0x1.fca4139a42374p-4
            };
          float ret = z * ((c[0] + z2 * c[1]) + z4 * (c[2] + z2 * c[3]));
-         if (x != 0.0f && ret == 0.0)
+         if (x != 0.0f && ret == 0.0f)
            __set_errno (ERANGE);
          return ret;
        }

diff --git a/sysdeps/ieee754/flt-32/s_log1pf.c b/sysdeps/ieee754/flt-32/s_log1pf.c
index d1686e78aa3053dc2789fc161434cec5f110227e..f03c60df341600b280515068341bc94c332ce130 100644 (file)
--- a/sysdeps/ieee754/flt-32/s_log1pf.c
+++ b/sysdeps/ieee754/flt-32/s_log1pf.c
@@ -154,21 +154,21 @@ __log1pf (float x)
          double tr = rl + Lh;
          if (__glibc_unlikely ((asuint64 (tr) & 0xfffffffll) == 0))
            {
-             if (x == -0x1.247ab0p-6)
+             if (x == -0x1.247ab0p-6f)
                return -0x1.271f0ep-6f - 0x1p-31f;
-             if (x == -0x1.3a415ep-5)
+             if (x == -0x1.3a415ep-5f)
                return -0x1.407112p-5f + 0x1p-30f;
-             if (x == 0x1.fb035ap-2)
+             if (x == 0x1.fb035ap-2f)
                return 0x1.9bddc2p-2f + 0x1p-27f;
              tr += 64 * (rl + (Lh - tr));
            }
          else if (rl + (Lh - tr) == 0.0)
            {
-             if (x == 0x1.b7fd86p-4)
+             if (x == 0x1.b7fd86p-4f)
                return 0x1.a1ece2p-4f + 0x1p-29f;
-             if (x == -0x1.3a415ep-5)
+             if (x == -0x1.3a415ep-5f)
                return -0x1.407112p-5f + 0x1p-30f;
-             if (x == 0x1.43c7e2p-6)
+             if (x == 0x1.43c7e2p-6f)
                return 0x1.409f80p-6f + 0x1p-31f;
            }
          ub = tr;

diff --git a/sysdeps/ieee754/flt-32/s_remquof.c b/sysdeps/ieee754/flt-32/s_remquof.c
index f813da8c91639910d0a3045fe8440c7e9a48c99e..67d301b3e1f25828f2ddc4b69a95b448d91a1ff1 100644 (file)
--- a/sysdeps/ieee754/flt-32/s_remquof.c
+++ b/sysdeps/ieee754/flt-32/s_remquof.c
@@ -85,7 +85,7 @@ __remquof (float x, float y, int *quo)
     }
   else
     {
-      float y_half = 0.5 * y;
+      float y_half = 0.5f * y;
       if (x > y_half)
        {
          x -= y;