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Add fast multiplication for 192-bit and 256-bit curves.

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This commit is contained in:
Ken MacKay
2014-05-07 22:36:06 -07:00
parent 406aef7b89
commit 95becf0327
5 changed files with 7912 additions and 169 deletions
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scripts/mult.py
-162
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@@ -1,162 +0,0 @@
#!/usr/bin/env python
def rx(i):
return i + 2
def ry(i):
return i + 12
def emit(line, *args):
s = '"' + line + r' \n\t"'
print s % args
#### set up registers
emit("adiw r30, 10")
emit("adiw r28, 10")
for i in xrange(10):
emit("ld r%s, x+", rx(i))
for i in xrange(10):
emit("ld r%s, y+", ry(i))
#### first two multiplications of initial block (x = 0-9, y = 10-19)
emit("ldi r25, 0")
print ""
emit("ldi r23, 0")
emit("mul r2, r12")
emit("st z+, r0")
emit("mov r22, r1")
print ""
emit("ldi r24, 0")
emit("mul r2, r13")
emit("add r22, r0")
emit("adc r23, r1")
emit("mul r3, r12")
emit("add r22, r0")
emit("adc r23, r1")
emit("adc r24, r25")
emit("st z+, r22")
print ""
#### rest of initial block, with moving accumulator registers
acc = [23, 24, 22]
for r in xrange(2, 10):
emit("ldi r%s, 0", acc[2])
for i in xrange(0, r+1):
emit("mul r%s, r%s", rx(i), ry(r - i))
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0])
print ""
acc = acc[1:] + acc[:1]
for r in xrange(1, 9):
emit("ldi r%s, 0", acc[2])
for i in xrange(0, 10-r):
emit("mul r%s, r%s", rx(r+i), ry(9 - i))
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0])
print ""
acc = acc[1:] + acc[:1]
emit("mul r%s, r%s", rx(9), ry(9))
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("st z+, r%s", acc[0])
emit("st z+, r%s", acc[1])
print ""
#### reset y and z pointers (x still points to left + 10)
emit("sbiw r30, 30")
emit("sbiw r28, 20")
#### load y registers
for i in xrange(10):
emit("ld r%s, y+", ry(i))
print ""
#### do x = 0-9, y = 0-9 multiplications
emit("ldi r23, 0")
emit("mul r2, r12")
emit("st z+, r0")
emit("mov r22, r1")
print ""
emit("ldi r24, 0")
emit("mul r2, r13")
emit("add r22, r0")
emit("adc r23, r1")
emit("mul r3, r12")
emit("add r22, r0")
emit("adc r23, r1")
emit("adc r24, r25")
emit("st z+, r22")
print ""
acc = [23, 24, 22]
for r in xrange(2, 10):
emit("ldi r%s, 0", acc[2])
for i in xrange(0, r+1):
emit("mul r%s, r%s", rx(i), ry(r - i))
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0])
print ""
acc = acc[1:] + acc[:1]
#### now we need to start shifting x and loading from z
x_regs = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
for r in xrange(0, 10):
x_regs = x_regs[1:] + x_regs[:1]
emit("ld r%s, x+", x_regs[9]) # load next byte of left
emit("ldi r%s, 0", acc[2])
for i in xrange(0, 10):
emit("mul r%s, r%s", x_regs[i], ry(9 - i))
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("ld r0, z") # load stored value from initial block, and add to accumulator (note z does not increment)
emit("add r%s, r0", acc[0])
emit("adc r%s, r25", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0]) # store next byte (z increments)
print ""
acc = acc[1:] + acc[:1]
# done shifting x, start shifting y
y_regs = [12, 13, 14, 15, 16, 17, 18, 19, 20, 21]
for r in xrange(0, 10):
y_regs = y_regs[1:] + y_regs[:1]
emit("ld r%s, y+", y_regs[9]) # load next byte of right
emit("ldi r%s, 0", acc[2])
for i in xrange(0, 10):
emit("mul r%s, r%s", x_regs[i], y_regs[9 -i])
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("ld r0, z") # load stored value from initial block, and add to accumulator (note z does not increment)
emit("add r%s, r0", acc[0])
emit("adc r%s, r25", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0]) # store next byte (z increments)
print ""
acc = acc[1:] + acc[:1]
# done both shifts, do remaining corner
for r in xrange(1, 9):
emit("ldi r%s, 0", acc[2])
for i in xrange(0, 10-r):
emit("mul r%s, r%s", x_regs[r+i], y_regs[9 - i])
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0])
print ""
acc = acc[1:] + acc[:1]
emit("mul r%s, r%s", x_regs[9], y_regs[9])
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("st z+, r%s", acc[0])
emit("st z+, r%s", acc[1])
emit("eor r1, r1")
scripts/mult_avr.py
Executable
+199
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@@ -0,0 +1,199 @@
#!/usr/bin/env python
import sys
if len(sys.argv) < 2:
print "Provide the integer size in bytes"
sys.exit(1)
size = int(sys.argv[1])
full_rows = size // 10
init_size = size % 10
if init_size == 0:
full_rows = full_rows - 1
init_size = 10
def rx(i):
return i + 2
def ry(i):
return i + 12
def emit(line, *args):
s = '"' + line + r' \n\t"'
print s % args
#### set up registers
emit("adiw r30, %s" % (size - init_size)) # move z
emit("adiw r28, %s" % (size - init_size)) # move y
for i in xrange(init_size):
emit("ld r%s, x+", rx(i))
for i in xrange(init_size):
emit("ld r%s, y+", ry(i))
# note that this code assume that init_size > 1
#### first two multiplications of initial block
emit("ldi r25, 0")
print ""
emit("ldi r23, 0")
emit("mul r2, r12")
emit("st z+, r0")
emit("mov r22, r1")
print ""
emit("ldi r24, 0")
emit("mul r2, r13")
emit("add r22, r0")
emit("adc r23, r1")
emit("mul r3, r12")
emit("add r22, r0")
emit("adc r23, r1")
emit("adc r24, r25")
emit("st z+, r22")
print ""
#### rest of initial block, with moving accumulator registers
acc = [23, 24, 22]
for r in xrange(2, init_size):
emit("ldi r%s, 0", acc[2])
for i in xrange(0, r+1):
emit("mul r%s, r%s", rx(i), ry(r - i))
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0])
print ""
acc = acc[1:] + acc[:1]
for r in xrange(1, init_size-1):
emit("ldi r%s, 0", acc[2])
for i in xrange(0, init_size-r):
emit("mul r%s, r%s", rx(r+i), ry((init_size-1) - i))
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0])
print ""
acc = acc[1:] + acc[:1]
emit("mul r%s, r%s", rx(init_size-1), ry(init_size-1))
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("st z+, r%s", acc[0])
emit("st z+, r%s", acc[1])
print ""
#### reset y and z pointers
emit("sbiw r30, %s" % (2 * init_size + 10))
emit("sbiw r28, %s" % (init_size + 10))
#### load y registers
for i in xrange(10):
emit("ld r%s, y+", ry(i))
#### load additional x registers
for i in xrange(init_size, 10):
emit("ld r%s, x+", rx(i))
print ""
prev_size = init_size
for row in xrange(full_rows):
#### do x = 0-9, y = 0-9 multiplications
emit("ldi r23, 0")
emit("mul r2, r12")
emit("st z+, r0")
emit("mov r22, r1")
print ""
emit("ldi r24, 0")
emit("mul r2, r13")
emit("add r22, r0")
emit("adc r23, r1")
emit("mul r3, r12")
emit("add r22, r0")
emit("adc r23, r1")
emit("adc r24, r25")
emit("st z+, r22")
print ""
acc = [23, 24, 22]
for r in xrange(2, 10):
emit("ldi r%s, 0", acc[2])
for i in xrange(0, r+1):
emit("mul r%s, r%s", rx(i), ry(r - i))
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0])
print ""
acc = acc[1:] + acc[:1]
#### now we need to start shifting x and loading from z
x_regs = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
for r in xrange(0, prev_size):
x_regs = x_regs[1:] + x_regs[:1]
emit("ld r%s, x+", x_regs[9]) # load next byte of left
emit("ldi r%s, 0", acc[2])
for i in xrange(0, 10):
emit("mul r%s, r%s", x_regs[i], ry(9 - i))
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("ld r0, z") # load stored value from initial block, and add to accumulator (note z does not increment)
emit("add r%s, r0", acc[0])
emit("adc r%s, r25", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0]) # store next byte (z increments)
print ""
acc = acc[1:] + acc[:1]
# done shifting x, start shifting y
y_regs = [12, 13, 14, 15, 16, 17, 18, 19, 20, 21]
for r in xrange(0, prev_size):
y_regs = y_regs[1:] + y_regs[:1]
emit("ld r%s, y+", y_regs[9]) # load next byte of right
emit("ldi r%s, 0", acc[2])
for i in xrange(0, 10):
emit("mul r%s, r%s", x_regs[i], y_regs[9 -i])
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("ld r0, z") # load stored value from initial block, and add to accumulator (note z does not increment)
emit("add r%s, r0", acc[0])
emit("adc r%s, r25", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0]) # store next byte (z increments)
print ""
acc = acc[1:] + acc[:1]
# done both shifts, do remaining corner
for r in xrange(1, 9):
emit("ldi r%s, 0", acc[2])
for i in xrange(0, 10-r):
emit("mul r%s, r%s", x_regs[r+i], y_regs[9 - i])
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("adc r%s, r25", acc[2])
emit("st z+, r%s", acc[0])
print ""
acc = acc[1:] + acc[:1]
emit("mul r%s, r%s", x_regs[9], y_regs[9])
emit("add r%s, r0", acc[0])
emit("adc r%s, r1", acc[1])
emit("st z+, r%s", acc[0])
emit("st z+, r%s", acc[1])
print ""
prev_size = prev_size + 10
if row < full_rows - 1:
#### reset x, y and z pointers
emit("sbiw r30, %s" % (2 * prev_size + 10))
emit("sbiw r28, %s" % (prev_size + 10))
emit("sbiw r26, %s" % (prev_size))
#### load x and y registers
for i in xrange(10):
emit("ld r%s, x+", rx(i))
emit("ld r%s, y+", ry(i))
print ""
emit("eor r1, r1")
scripts/square.py → scripts/square_avr.py
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