+++ /dev/null
-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 # 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
-//
-
-module testbench;
-
-reg [15:0] sqr;
-
-//Verilog function to find square root of a 32 bit number.
-//The output is 16 bit.
-function [15:0] sqrt;
- input [31:0] num; //declare input
- //intermediate signals.
- reg [31:0] a;
- reg [15:0] q;
- reg [17:0] left,right,r;
- integer i;
-begin
- //initialize all the variables.
- a = num;
- q = 0;
- i = 0;
- left = 0; //input to adder/sub
- right = 0; //input to adder/sub
- r = 0; //remainder
- //run the calculations for 16 iterations.
- 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.
- if (r[17] == 1) //add if r is negative
- r = left + right;
- else //subtract if r is positive
- r = left - right;
- 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;
-}
-
-"""
--- /dev/null
+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 # 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
+//
+
+module testbench;
+
+reg [15:0] sqr;
+
+//Verilog function to find square root of a 32 bit number.
+//The output is 16 bit.
+function [15:0] sqrt;
+ input [31:0] num; //declare input
+ //intermediate signals.
+ reg [31:0] a;
+ reg [15:0] q;
+ reg [17:0] left,right,r;
+ integer i;
+begin
+ //initialize all the variables.
+ a = num;
+ q = 0;
+ i = 0;
+ left = 0; //input to adder/sub
+ right = 0; //input to adder/sub
+ r = 0; //remainder
+ //run the calculations for 16 iterations.
+ 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.
+ if (r[17] == 1) //add if r is negative
+ r = left + right;
+ else //subtract if r is positive
+ r = left - right;
+ 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;
+}
+
+"""
projects / ieee754fpu.git / commitdiff