ARM Architecture Reference Manual ARMv7-A and ARMv7-R edition

Application Level Programmers’ Model
// Underflow occurs if exponent is too small before rounding, and result is inexact or
// the Underflow exception is trapped.
if biased_exp == 0 && (error != 0.0 || fpscr_val == ‘1’) then
FPProcessException(FPExc_Underflow, fpscr_val);
// Round result according to rounding mode.
case fpscr_val of
when ‘00’ // Round to Nearest (rounding to even if exactly halfway)
round_up = (error > 0.5 || (error == 0.5 && int_mant == ‘1’));
overflow_to_inf = TRUE;
when ‘01’ // Round towards Plus Infinity
round_up = (error != 0.0 && sign == ‘0’);
overflow_to_inf = (sign == ‘0’);
when ‘10’ // Round towards Minus Infinity
round_up = (error != 0.0 && sign == ‘1’);
overflow_to_inf = (sign == ‘1’);
when ‘11’ // Round towards Zero
round_up = FALSE;
overflow_to_inf = FALSE;
if round_up then
int_mant = int_mant + 1;
if int_mant == 2^F then // Rounded up from denormalized to normalized
biased_exp = 1;
if int_mant == 2^(F+1) then // Rounded up to next exponent
biased_exp = biased_exp + 1; int_mant = int_mant DIV 2;
// Deal with overflow and generate result.
if N != 16 || fpscr_val == ‘0’ then // Single, double or IEEE half precision
if biased_exp >= 2^E - 1 then
result = if overflow_to_inf then FPInfinity(sign, N) else FPMaxNormal(sign, N);
FPProcessException(FPExc_Overflow, fpscr_val);
else
result = sign : biased_exp : int_mant;
else // Alternative half precision
if biased_exp >= 2^E then
result = sign : Ones(15);
FPProcessException(FPExc_InvalidOp, fpscr_val);
error = 0.0; // avoid an Inexact exception
else
result = sign : biased_exp : int_mant;
// Deal with Inexact exception.
if error != 0 then
FPProcessException(FPExc_Inexact, fpscr_val);
return result;
Selection of ARM standard floating-point arithmetic
StandardFPSCRValue is an FPSCR value that selects ARM standard floating-point arithmetic. Most of the
arithmetic functions have a boolean fpscr_controlled argument that is TRUE for VFP operations and FALSE
for Advanced SIMD operations, and that selects between using the real FPSCR value and this value.
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