-def sqrt(num):
+from sfpy import Float32
- num = 6
+# XXX DO NOT USE, fails on num=65536. wark-wark...
+def sqrtsimple(num):
res = 0
- bit = 1 << 14
+ bit = 1
- while (bit > num):
- bit >>= 2
+ while (bit < num):
+ bit <<= 2
while (bit != 0):
if (num >= res + bit):
num -= res + bit
res = (res >> 1) + bit
-
else:
- res >>= 1;
- bit >>= 2;
-
+ res >>= 1
+ bit >>= 2
+
return res
+
+def sqrt(num):
+ D = num # D is input (from num)
+ Q = 0 # quotient
+ 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
+
+
+#normalization function
+def normalise(s, m, e, lowbits):
+ if (lowbits >= 2):
+ m += 1
+ if get_mantissa(m) == ((1<<24)-1):
+ e += 1
+ return s, m, e
+
+
+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
+
+ s, sm, se = normalise(s, sm, se, lowbits)
+
+ 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
//
projects / ieee754fpu.git / blobdiff