src/math/sqrtf.c

   1 #include <stdint.h>
   2 #include <math.h>
   3 #include "libm.h"
   4 #include "sqrt_data.h"
   5
   6 #define FENV_SUPPORT 1
   7
   8 static inline uint32_t mul32(uint32_t a, uint32_t b)
   9 {
  10         return (uint64_t)a*b >> 32;
  11 }
  12
  13 /* see sqrt.c for more detailed comments.  */
  14
  15 float sqrtf(float x)
  16 {
  17         uint32_t ix, m, m1, m0, even, ey;
  18
  19         ix = asuint(x);
  20         if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
  21                 /* x < 0x1p-126 or inf or nan.  */
  22                 if (ix * 2 == 0)
  23                         return x;
  24                 if (ix == 0x7f800000)
  25                         return x;
  26                 if (ix > 0x7f800000)
  27                         return __math_invalidf(x);
  28                 /* x is subnormal, normalize it.  */
  29                 ix = asuint(x * 0x1p23f);
  30                 ix -= 23 << 23;
  31         }
  32
  33         /* x = 4^e m; with int e and m in [1, 4).  */
  34         even = ix & 0x00800000;
  35         m1 = (ix << 8) | 0x80000000;
  36         m0 = (ix << 7) & 0x7fffffff;
  37         m = even ? m0 : m1;
  38
  39         /* 2^e is the exponent part of the return value.  */
  40         ey = ix >> 1;
  41         ey += 0x3f800000 >> 1;
  42         ey &= 0x7f800000;
  43
  44         /* compute r ~ 1/sqrt(m), s ~ sqrt(m) with 2 goldschmidt iterations.  */
  45         static const uint32_t three = 0xc0000000;
  46         uint32_t r, s, d, u, i;
  47         i = (ix >> 17) % 128;
  48         r = (uint32_t)__rsqrt_tab[i] << 16;
  49         /* |r*sqrt(m) - 1| < 0x1p-8 */
  50         s = mul32(m, r);
  51         /* |s/sqrt(m) - 1| < 0x1p-8 */
  52         d = mul32(s, r);
  53         u = three - d;
  54         r = mul32(r, u) << 1;
  55         /* |r*sqrt(m) - 1| < 0x1.7bp-16 */
  56         s = mul32(s, u) << 1;
  57         /* |s/sqrt(m) - 1| < 0x1.7bp-16 */
  58         d = mul32(s, r);
  59         u = three - d;
  60         s = mul32(s, u);
  61         /* -0x1.03p-28 < s/sqrt(m) - 1 < 0x1.fp-31 */
  62         s = (s - 1)>>6;
  63         /* s < sqrt(m) < s + 0x1.08p-23 */
  64
  65         /* compute nearest rounded result.  */
  66         uint32_t d0, d1, d2;
  67         float y, t;
  68         d0 = (m << 16) - s*s;
  69         d1 = s - d0;
  70         d2 = d1 + s + 1;
  71         s += d1 >> 31;
  72         s &= 0x007fffff;
  73         s |= ey;
  74         y = asfloat(s);
  75         if (FENV_SUPPORT) {
  76                 /* handle rounding and inexact exception. */
  77                 uint32_t tiny = predict_false(d2==0) ? 0 : 0x01000000;
  78                 tiny |= (d1^d2) & 0x80000000;
  79                 t = asfloat(tiny);
  80                 y = eval_as_float(y + t);
  81         }
  82         return y;
  83 }