X-Git-Url: https://git.libre-soc.org/?a=blobdiff_plain;f=src%2Fadd%2Ffsqrt.py;h=a87af61db4ded516df1f93d6cb3af933d6318af3;hb=7541ca979084de96ebdf292e1baa0a03af64d3fc;hp=6b233779d22e4c55a67f01ee82c52c9dc03b057f;hpb=a298ae5ded7672c5c913d1f1ef044a4b38bd0dfe;p=ieee754fpu.git

diff --git a/src/add/fsqrt.py b/src/add/fsqrt.py
index 6b233779..a87af61d 100644
--- a/src/add/fsqrt.py
+++ b/src/add/fsqrt.py
@@ -1,6 +1,150 @@
+from sfpy import Float32
 
 
+# XXX DO NOT USE, fails on num=65536.  wark-wark...
+def sqrtsimple(num):
+    res = 0
+    bit = 1
+
+    while (bit < num):
+        bit <<= 2
+
+    while (bit != 0):
+        if (num >= res + bit):
+            num -= res + bit
+            res = (res >> 1) + bit
+        else:
+            res >>= 1
+        bit >>= 2
+
+    return res
+
+
+def sqrt(num):
+    D = num # D is input (from num)
+    Q = 0
+    R = 0 # remainder
+    for i in range(64, -1, -1): # negative ranges are weird...
+
+        R = (R<<2)|((D>>(i+i))&3)
+
+        if R >= 0:
+            R -= ((Q<<2)|1) # -Q01
+        else:
+            R += ((Q<<2)|3) # +Q11
+
+        Q <<= 1
+        if R >= 0:
+            Q |= 1 # new Q
+
+    if R < 0:
+        R = R + ((Q<<1)|1)
+
+    return Q, R
+
+
+# grabbed these from unit_test_single (convenience, this is just experimenting)
+
+def get_mantissa(x):
+    return 0x7fffff & x
+
+def get_exponent(x):
+    return ((x & 0x7f800000) >> 23) - 127
+
+def set_exponent(x, e):
+    return (x & ~0x7f800000) | ((e+127) << 23)
+
+def get_sign(x):
+    return ((x & 0x80000000) >> 31)
+
+# convert FP32 to s/e/m
+def create_fp32(s, e, m):
+    """ receive sign, exponent, mantissa, return FP32 """
+    return set_exponent((s << 31) | get_mantissa(m))
+
+# convert s/e/m to FP32
+def decode_fp32(x):
+    """ receive FP32, return sign, exponent, mantissa """
+    return get_sign(x), get_exponent(x), get_mantissa(x)
+
+
+# main function, takes mantissa and exponent as separate arguments
+# returns a tuple, sqrt'd mantissa, sqrt'd exponent
+
+def main(mantissa, exponent):
+    if exponent & 1 != 0:
+        # shift mantissa up, subtract 1 from exp to compensate
+        mantissa <<= 1
+        exponent -= 1
+    m, r = sqrt(mantissa)
+    return m, r, exponent >> 1
+
+
+def fsqrt_test(x):
+
+    xbits = x.bits
+    print ("x", x, type(x))
+    sq_test = x.sqrt()
+    print ("sqrt", sq_test)
+
+    print (xbits, type(xbits))
+    s, e, m = decode_fp32(xbits)
+    print("x decode", s, e, m, hex(m))
+
+    m |= 1<<23 # set top bit (the missing "1" from mantissa)
+    m <<= 27
+
+    sm, sr, se = main(m, e)
+    lowbits = sm & 0x3
+    sm >>= 2
+    sm = get_mantissa(sm)
+    #sm += 2
+    print("our  sqrt", s, se, sm, hex(sm), bin(sm), "lowbits", lowbits,
+                                                    "rem", hex(sr))
+    if lowbits >= 2:
+        print ("probably needs rounding (+1 on mantissa)")
+
+    sq_xbits = sq_test.bits
+    s, e, m = decode_fp32(sq_xbits)
+    print ("sf32 sqrt", s, e, m, hex(m), bin(m))
+    print ()
+
+if __name__ == '__main__':
+
+    # quick test up to 1000 of two sqrt functions
+    for Q in range(1, int(1e4)):
+        print(Q, sqrt(Q), sqrtsimple(Q), int(Q**0.5))
+        assert int(Q**0.5) == sqrtsimple(Q), "Q sqrtsimpl fail %d" % Q
+        assert int(Q**0.5) == sqrt(Q)[0], "Q sqrt fail %d" % Q
+
+    # quick mantissa/exponent demo
+    for e in range(26):
+        for m in range(26):
+            ms, mr, es = main(m, e)
+            print("m:%d e:%d sqrt: m:%d-%d e:%d" % (m, e, ms, mr, es))
+
+    x = Float32(1234.123456789)
+    fsqrt_test(x)
+    x = Float32(32.1)
+    fsqrt_test(x)
+    x = Float32(16.0)
+    fsqrt_test(x)
+    x = Float32(8.0)
+    fsqrt_test(x)
+    x = Float32(8.5)
+    fsqrt_test(x)
+    x = Float32(3.14159265358979323)
+    fsqrt_test(x)
+    x = Float32(12.99392923123123)
+    fsqrt_test(x)
+    x = Float32(0.123456)
+    fsqrt_test(x)
+
 """
+
+Notes:
+https://pdfs.semanticscholar.org/5060/4e9aff0e37089c4ab9a376c3f35761ffe28b.pdf
+
 //This is the main code of integer sqrt function found here:http://verilogcodes.blogspot.com/2017/11/a-verilog-function-for-finding-square-root.html
 //
 
@@ -15,7 +159,7 @@ function [15:0] sqrt;
     //intermediate signals.
     reg [31:0] a;
     reg [15:0] q;
-    reg [17:0] left,right,r;    
+    reg [17:0] left,right,r;
     integer i;
 begin
     //initialize all the variables.
@@ -26,7 +170,7 @@ begin
     right = 0;  //input to adder/sub
     r = 0;  //remainder
     //run the calculations for 16 iterations.
-    for(i=0;i<16;i=i+1) begin 
+    for(i=0;i<16;i=i+1) begin
         right = {q,r[17],1'b1};
         left = {r[15:0],a[31:30]};
         a = {a[29:0],2'b00};    //left shift by 2 bits.
@@ -34,10 +178,64 @@ begin
             r = left + right;
         else    //subtract if r is positive
             r = left - right;
-        q = {q[14:0],!r[17]};       
+        q = {q[14:0],!r[17]};
     end
     sqrt = q;   //final assignment of output.
 end
 endfunction //end of Function
 
+
+c version (from paper linked from URL)
+
+unsigned squart(D, r) /*Non-Restoring sqrt*/
+    unsigned D; /*D:32-bit unsigned integer to be square rooted */
+    int *r;
+{
+    unsigned Q = 0; /*Q:16-bit unsigned integer (root)*/
+    int R = 0; /*R:17-bit integer (remainder)*/
+    int i;
+    for (i = 15;i>=0;i--) /*for each root bit*/
+    {
+        if (R>=0)
+        { /*new remainder:*/
+            R = R<<2)|((D>>(i+i))&3);
+            R = R-((Q<<2)|1); /*-Q01*/
+        }
+        else
+        { /*new remainder:*/
+            R = R<<2)|((D>>(i+i))&3);
+            R = R+((Q<<2)|3); /*+Q11*/
+        }
+        if (R>=0) Q = Q<<1)|1; /*new Q:*/
+        else Q = Q<<1)|0; /*new Q:*/
+    }
+
+    /*remainder adjusting*/
+    if (R<0) R = R+((Q<<1)|1);
+    *r = R; /*return remainder*/
+    return(Q); /*return root*/
+}
+
+From wikipedia page:
+
+short isqrt(short num) {
+    short res = 0;
+    short bit = 1 << 14; // The second-to-top bit is set: 1 << 30 for 32 bits
+
+    // "bit" starts at the highest power of four <= the argument.
+    while (bit > num)
+        bit >>= 2;
+
+    while (bit != 0) {
+        if (num >= res + bit) {
+            num -= res + bit;
+            res = (res >> 1) + bit;
+        }
+        else
+            res >>= 1;
+        bit >>= 2;
+    }
+    return res;
+}
+
 """