void fp2inv_mont(f2elm_t *a)
{// GF(p^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2).
f2elm_t t1;
fpsqr_mont(a->e[0], t1.e[0]); // t10 = a0^2
fpsqr_mont(a->e[1], t1.e[1]); // t11 = a1^2
fpadd(t1.e[0], t1.e[1], t1.e[0]); // t10 = a0^2+a1^2
fpinv_mont(t1.e[0]); // t10 = (a0^2+a1^2)^-1
fpneg(a->e[1]); // a = a0-i*a1
fpmul_mont(a->e[0], t1.e[0], a->e[0]);
fpmul_mont(a->e[1], t1.e[0], a->e[1]); // a = (a0-i*a1)*(a0^2+a1^2)^-1
}
enum RPNError rpn_run(byte *rpnExpr, word rpnLen, Float *yValue, Float *xValue)
{
rpnStackIndex = 0;
word reader = 0;
while (reader < rpnLen)
{
byte op = rpnExpr[reader++];
switch (op)
{
case RPN_VAR: // put a copy of the independent variable's value on rpnStack
if (rpnStackIndex == RPN_STACK_SIZE)
return RPN_ERR_OVERFLOW;
rpn_push(xValue);
break;
case RPN_FUNC:
{
if (rpnStackIndex < 1)
return RPN_ERR_UNDERFLOW;
fp0load(rpn_get(rpnStackIndex - 1));
byte funcIndex = rpnExpr[reader++];
if (funcIndex == UNKNOWN_FUNCTION_INDEX)
{
--reader;
return RPN_ERR_INVALID_FUNC;
}
// Check the argument (FP0).
void *check = knownFunctions[funcIndex].checkArgFuncPtr;
if (check)
{
enum RPNError e = (*check)(); // check FP0
if (e != RPN_ERR_NONE)
return e;
}
// Argument (FP0) is valid. Apply the function to it.
(*knownFunctions[funcIndex].evalFuncPtr)();
--rpnStackIndex;
rpn_push(FP0ADDR); // push the result
break;
}
case RPN_NUM: // put FP that follows on rpnStack
if (rpnStackIndex == RPN_STACK_SIZE)
return RPN_ERR_OVERFLOW;
rpn_push((Float *) (rpnExpr + reader)); // push 6-byte accumulator
reader += sizeof(Float);
break;
case RPN_ADD:
case RPN_SUB:
case RPN_MUL:
if (rpnStackIndex < 2)
return RPN_ERR_UNDERFLOW;
fp0load(rpn_get(rpnStackIndex - 2));
fp1load(rpn_get(rpnStackIndex - 1));
switch (op)
{
case RPN_ADD: fpadd(); break;
case RPN_SUB: fpsub(); break;
case RPN_MUL: fpmul(); break;
}
rpnStackIndex -= 2;
rpn_push(FP0ADDR); // push the result
break;
case RPN_DIV:
{
if (rpnStackIndex < 2)
return RPN_ERR_UNDERFLOW;
// Check if the divisor is too close to zero
Float *divisor = rpn_get(rpnStackIndex - 1);
fp0load(divisor);
fpabs();
if (fpcmp(&verySmall) < 0) // if abs(divisor) too small
return RPN_ERR_DIV_BY_ZERO; // avoid enormous (and unusable) quotient
fp0load(divisor);
fp1load(rpn_get(rpnStackIndex - 2)); // dividend
fpdiv();
rpnStackIndex -= 2;
rpn_push(FP0ADDR); // push the result
break;
}
case RPN_NEG:
if (rpnStackIndex < 1)
return RPN_ERR_UNDERFLOW;
fp0load(rpn_get(rpnStackIndex - 1));
fpneg();
--rpnStackIndex;
rpn_push(FP0ADDR); // push the result
break;
case RPN_POW:
if (rpnStackIndex < 2)
return RPN_ERR_UNDERFLOW;
fp0load(rpn_get(rpnStackIndex - 1)); // power
fp1load(rpn_get(rpnStackIndex - 2)); // base
if (fp1sgn() < 0 && ! fpisint()) // if negative base and non-int power
return RPN_ERR_POW_OF_NEG;
fppow();
rpnStackIndex -= 2;
rpn_push(FP0ADDR); // push the result
break;
default:
--reader;
return RPN_ERR_UNEXPECTED;
}
}
if (rpnStackIndex != 1)
return RPN_ERR_INVALID_EXPR;
#if 0
fp0load(rpn_get(0));
char buf[FPSTRBUFSIZ];
char *decimalResult = fpstr(buf);
printf("Result: [%s]\n", decimalResult);
#endif
fpcpy(yValue, rpn_get(0));
return RPN_ERR_NONE;
}
void fp2neg(f2elm_t *a)
{ // GF(p^2) negation, a = -a in GF(p^2).
fpneg(a->e[0]);
fpneg(a->e[1]);
}
