Changeset 816

Timestamp:

Apr 28, 2016, 1:12:20 PM (9 years ago)

Author:

cfuguet

Message:

Add a software integer version of the libmath/sqrt function.

Also a flag to enable/disable the use of hard FPU instructions is
add into the giet_config.h file.

Location:

soft/giet_vm

Files:

• giet_config.h (modified) (1 diff)
• giet_libs/math/sqrt.c (modified) (1 diff)

soft/giet_vm/giet_config.h

@@ -61 +61 @@
 #define GIET_SDC_PERIOD           2            /* number of cycles in SDC period */
 #define GIET_SR_INIT_VALUE        0x2000FF13   /* SR initial value (before eret) */
+#define GIET_USE_HARD_FLOAT       0            /* hard float supported */
 
 #endif

soft/giet_vm/giet_libs/math/sqrt.c

@@ +1 @@
+#include "../math.h"
+#include "math_private.h"
+
+static const double one = 1.0, tiny = 1.0e-300;
+
+/* this function was taken from the uCLibc library
+ * Return correctly rounded sqrt.
+ * Method:
+ *   Bit by bit method using integer arithmetic. (Slow, but portable)
+ *   1. Normalization
+ *      Scale x to y in [1,4) with even powers of 2:
+ *      find an integer k such that  1 <= (y=x*2^(2k)) < 4, then
+ *              sqrt(x) = 2^k * sqrt(y)
+ *   2. Bit by bit computation
+ *      Let q  = sqrt(y) truncated to i bit after binary point (q = 1),
+ *           i                                                   0
+ *                                     i+1         2
+ *          s  = 2*q , and      y  =  2   * ( y - q  ).         (1)
+ *           i      i            i                 i
+ *
+ *      To compute q    from q , one checks whether
+ *                  i+1       i
+ *
+ *                            -(i+1) 2
+ *                      (q + 2      ) <= y.                     (2)
+ *                        i
+ *                                                            -(i+1)
+ *      If (2) is false, then q   = q ; otherwise q   = q  + 2      .
+ *                             i+1   i             i+1   i
+ *
+ *      With some algebric manipulation, it is not difficult to see
+ *      that (2) is equivalent to
+ *                             -(i+1)
+ *                      s  +  2       <= y                      (3)
+ *                       i                i
+ *
+ *      The advantage of (3) is that s  and y  can be computed by
+ *                                    i      i
+ *      the following recurrence formula:
+ *          if (3) is false
+ *
+ *          s     =  s  ,       y    = y   ;                    (4)
+ *           i+1      i          i+1    i
+ *
+ *          otherwise,
+ *                         -i                     -(i+1)
+ *          s     =  s  + 2  ,  y    = y  -  s  - 2             (5)
+ *           i+1      i          i+1    i     i
+ *
+ *      One may easily use induction to prove (4) and (5).
+ *      Note. Since the left hand side of (3) contain only i+2 bits,
+ *            it does not necessary to do a full (53-bit) comparison
+ *            in (3).
+ *   3. Final rounding
+ *      After generating the 53 bits result, we compute one more bit.
+ *      Together with the remainder, we can decide whether the
+ *      result is exact, bigger than 1/2ulp, or less than 1/2ulp
+ *      (it will never equal to 1/2ulp).
+ *      The rounding mode can be detected by checking whether
+ *      huge + tiny is equal to huge, and whether huge - tiny is
+ *      equal to huge for some floating point number "huge" and "tiny".
+ *
+ * Special cases:
+ *      sqrt(+-0) = +-0         ... exact
+ *      sqrt(inf) = inf
+ *      sqrt(-ve) = NaN         ... with invalid signal
+ *      sqrt(NaN) = NaN         ... with invalid signal for signaling NaN
+ *
+ * Other methods : see the appended file at the end of the program below.
+ *---------------
+ */
+static double __ieee754_sqrt(double x)
+{
+    double z;
+    int32_t sign = (int)0x80000000;
+    int32_t ix0,s0,q,m,t,i;
+    uint32_t r,t1,s1,ix1,q1;
+
+    EXTRACT_WORDS(ix0,ix1,x);
+
+    /* take care of Inf and NaN */
+    if((ix0&0x7ff00000)==0x7ff00000) {
+        return x*x+x;           /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
+                               sqrt(-inf)=sNaN */
+    }
+    /* take care of zero */
+    if(ix0<=0) {
+        if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
+        else if(ix0<0)
+            return (x-x)/(x-x);         /* sqrt(-ve) = sNaN */
+    }
+    /* normalize x */
+    m = (ix0>>20);
+    if(m==0) {                          /* subnormal x */
+        while(ix0==0) {
+            m -= 21;
+            ix0 |= (ix1>>11); ix1 <<= 21;
+        }
+        for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
+        m -= i-1;
+        ix0 |= (ix1>>(32-i));
+        ix1 <<= i;
+    }
+    m -= 1023;  /* unbias exponent */
+    ix0 = (ix0&0x000fffff)|0x00100000;
+    if(m&1){    /* odd m, double x to make it even */
+        ix0 += ix0 + ((ix1&sign)>>31);
+        ix1 += ix1;
+    }
+    m >>= 1;    /* m = [m/2] */
+
+    /* generate sqrt(x) bit by bit */
+    ix0 += ix0 + ((ix1&sign)>>31);
+    ix1 += ix1;
+    q = q1 = s0 = s1 = 0;       /* [q,q1] = sqrt(x) */
+    r = 0x00200000;             /* r = moving bit from right to left */
+
+    while(r!=0) {
+        t = s0+r;
+        if(t<=ix0) {
+            s0   = t+r;
+            ix0 -= t;
+            q   += r;
+        }
+        ix0 += ix0 + ((ix1&sign)>>31);
+        ix1 += ix1;
+        r>>=1;
+    }
+
+    r = sign;
+    while(r!=0) {
+        t1 = s1+r;
+        t  = s0;
+        if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
+            s1  = t1+r;
+            if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
+            ix0 -= t;
+            if (ix1 < t1) ix0 -= 1;
+            ix1 -= t1;
+            q1  += r;
+        }
+        ix0 += ix0 + ((ix1&sign)>>31);
+        ix1 += ix1;
+        r>>=1;
+    }
+
+    /* use floating add to find out rounding direction */
+    if((ix0|ix1)!=0) {
+        z = one-tiny; /* trigger inexact flag */
+        if (z>=one) {
+            z = one+tiny;
+            if (q1==(uint32_t)0xffffffff) { q1=0; q += 1;}
+            else if (z>one) {
+                if (q1==(uint32_t)0xfffffffe) q+=1;
+                q1+=2;
+            } else
+                q1 += (q1&1);
+        }
+    }
+    ix0 = (q>>1)+0x3fe00000;
+    ix1 =  q1>>1;
+    if ((q&1)==1) ix1 |= sign;
+    ix0 += (m <<20);
+    INSERT_WORDS(z,ix0,ix1);
+    return z;
+}
 
 double sqrt(double x)
 {
-  double z;
-  __asm__ ("sqrt.d %0,%1" : "=f" (z) : "f" (x));
-  return z;
+#if GIET_USE_HARD_FLOAT
+    double z;
+    __asm__ ("sqrt.d %0,%1" : "=f" (z) : "f" (x));
+    return z;
+#else
+    return __ieee754_sqrt(x);
+#endif
 }
 
+/*
+ * vim: ts=4 : sts=4 : sw=4 : et
+ */