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/* Copyright (C) 2009 Free Software Foundation, Inc.
This file is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 2 of the License, or (at your option)
any later version.
This file is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with this file; see the file COPYING. If not, write to the Free
Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA. */
/* As a special exception, if you link this library with files compiled with
GCC to produce an executable, this does not cause the resulting executable
to be covered by the GNU General Public License. The exception does not
however invalidate any other reasons why the executable file might be covered
by the GNU General Public License. */
#include <spu_intrinsics.h>
vector double __divv2df3 (vector double a_in, vector double b_in);
/* __divv2df3 divides the vector dividend a by the vector divisor b and
returns the resulting vector quotient. Maximum error about 0.5 ulp
over entire double range including denorms, compared to true result
in round-to-nearest rounding mode. Handles Inf or NaN operands and
results correctly. */
vector double
__divv2df3 (vector double a_in, vector double b_in)
{
/* Variables */
vec_int4 exp, exp_bias;
vec_uint4 no_underflow, overflow;
vec_float4 mant_bf, inv_bf;
vec_ullong2 exp_a, exp_b;
vec_ullong2 a_nan, a_zero, a_inf, a_denorm, a_denorm0;
vec_ullong2 b_nan, b_zero, b_inf, b_denorm, b_denorm0;
vec_ullong2 nan;
vec_uint4 a_exp, b_exp;
vec_ullong2 a_mant_0, b_mant_0;
vec_ullong2 a_exp_1s, b_exp_1s;
vec_ullong2 sign_exp_mask;
vec_double2 a, b;
vec_double2 mant_a, mant_b, inv_b, q0, q1, q2, mult;
/* Constants */
vec_uint4 exp_mask_u32 = spu_splats((unsigned int)0x7FF00000);
vec_uchar16 splat_hi = (vec_uchar16){0,1,2,3, 0,1,2,3, 8, 9,10,11, 8,9,10,11};
vec_uchar16 swap_32 = (vec_uchar16){4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11};
vec_ullong2 exp_mask = spu_splats(0x7FF0000000000000ULL);
vec_ullong2 sign_mask = spu_splats(0x8000000000000000ULL);
vec_float4 onef = spu_splats(1.0f);
vec_double2 one = spu_splats(1.0);
vec_double2 exp_53 = (vec_double2)spu_splats(0x0350000000000000ULL);
sign_exp_mask = spu_or(sign_mask, exp_mask);
/* Extract the floating point components from each of the operands including
* exponent and mantissa.
*/
a_exp = (vec_uint4)spu_and((vec_uint4)a_in, exp_mask_u32);
a_exp = spu_shuffle(a_exp, a_exp, splat_hi);
b_exp = (vec_uint4)spu_and((vec_uint4)b_in, exp_mask_u32);
b_exp = spu_shuffle(b_exp, b_exp, splat_hi);
a_mant_0 = (vec_ullong2)spu_cmpeq((vec_uint4)spu_andc((vec_ullong2)a_in, sign_exp_mask), 0);
a_mant_0 = spu_and(a_mant_0, spu_shuffle(a_mant_0, a_mant_0, swap_32));
b_mant_0 = (vec_ullong2)spu_cmpeq((vec_uint4)spu_andc((vec_ullong2)b_in, sign_exp_mask), 0);
b_mant_0 = spu_and(b_mant_0, spu_shuffle(b_mant_0, b_mant_0, swap_32));
a_exp_1s = (vec_ullong2)spu_cmpeq(a_exp, exp_mask_u32);
b_exp_1s = (vec_ullong2)spu_cmpeq(b_exp, exp_mask_u32);
/* Identify all possible special values that must be accomodated including:
* +-denorm, +-0, +-infinity, and NaNs.
*/
a_denorm0= (vec_ullong2)spu_cmpeq(a_exp, 0);
a_nan = spu_andc(a_exp_1s, a_mant_0);
a_zero = spu_and (a_denorm0, a_mant_0);
a_inf = spu_and (a_exp_1s, a_mant_0);
a_denorm = spu_andc(a_denorm0, a_zero);
b_denorm0= (vec_ullong2)spu_cmpeq(b_exp, 0);
b_nan = spu_andc(b_exp_1s, b_mant_0);
b_zero = spu_and (b_denorm0, b_mant_0);
b_inf = spu_and (b_exp_1s, b_mant_0);
b_denorm = spu_andc(b_denorm0, b_zero);
/* Scale denorm inputs to into normalized numbers by conditionally scaling the
* input parameters.
*/
a = spu_sub(spu_or(a_in, exp_53), spu_sel(exp_53, a_in, sign_mask));
a = spu_sel(a_in, a, a_denorm);
b = spu_sub(spu_or(b_in, exp_53), spu_sel(exp_53, b_in, sign_mask));
b = spu_sel(b_in, b, b_denorm);
/* Extract the divisor and dividend exponent and force parameters into the signed
* range [1.0,2.0) or [-1.0,2.0).
*/
exp_a = spu_and((vec_ullong2)a, exp_mask);
exp_b = spu_and((vec_ullong2)b, exp_mask);
mant_a = spu_sel(a, one, (vec_ullong2)exp_mask);
mant_b = spu_sel(b, one, (vec_ullong2)exp_mask);
/* Approximate the single reciprocal of b by using
* the single precision reciprocal estimate followed by one
* single precision iteration of Newton-Raphson.
*/
mant_bf = spu_roundtf(mant_b);
inv_bf = spu_re(mant_bf);
inv_bf = spu_madd(spu_nmsub(mant_bf, inv_bf, onef), inv_bf, inv_bf);
/* Perform 2 more Newton-Raphson iterations in double precision. The
* result (q1) is in the range (0.5, 2.0).
*/
inv_b = spu_extend(inv_bf);
inv_b = spu_madd(spu_nmsub(mant_b, inv_b, one), inv_b, inv_b);
q0 = spu_mul(mant_a, inv_b);
q1 = spu_madd(spu_nmsub(mant_b, q0, mant_a), inv_b, q0);
/* Determine the exponent correction factor that must be applied
* to q1 by taking into account the exponent of the normalized inputs
* and the scale factors that were applied to normalize them.
*/
exp = spu_rlmaska(spu_sub((vec_int4)exp_a, (vec_int4)exp_b), -20);
exp = spu_add(exp, (vec_int4)spu_add(spu_and((vec_int4)a_denorm, -0x34), spu_and((vec_int4)b_denorm, 0x34)));
/* Bias the quotient exponent depending on the sign of the exponent correction
* factor so that a single multiplier will ensure the entire double precision
* domain (including denorms) can be achieved.
*
* exp bias q1 adjust exp
* ===== ======== ==========
* positive 2^+65 -65
* negative 2^-64 +64
*/
exp_bias = spu_xor(spu_rlmaska(exp, -31), 64);
exp = spu_sub(exp, exp_bias);
q1 = spu_sel(q1, (vec_double2)spu_add((vec_int4)q1, spu_sl(exp_bias, 20)), exp_mask);
/* Compute a multiplier (mult) to applied to the quotient (q1) to produce the
* expected result. On overflow, clamp the multiplier to the maximum non-infinite
* number in case the rounding mode is not round-to-nearest.
*/
exp = spu_add(exp, 0x3FF);
no_underflow = spu_cmpgt(exp, 0);
overflow = spu_cmpgt(exp, 0x7FE);
exp = spu_and(spu_sl(exp, 20), (vec_int4)no_underflow);
exp = spu_and(exp, (vec_int4)exp_mask);
mult = spu_sel((vec_double2)exp, (vec_double2)(spu_add((vec_uint4)exp_mask, -1)), (vec_ullong2)overflow);
/* Handle special value conditions. These include:
*
* 1) IF either operand is a NaN OR both operands are 0 or INFINITY THEN a NaN
* results.
* 2) ELSE IF the dividend is an INFINITY OR the divisor is 0 THEN a INFINITY results.
* 3) ELSE IF the dividend is 0 OR the divisor is INFINITY THEN a 0 results.
*/
mult = spu_andc(mult, (vec_double2)spu_or(a_zero, b_inf));
mult = spu_sel(mult, (vec_double2)exp_mask, spu_or(a_inf, b_zero));
nan = spu_or(a_nan, b_nan);
nan = spu_or(nan, spu_and(a_zero, b_zero));
nan = spu_or(nan, spu_and(a_inf, b_inf));
mult = spu_or(mult, (vec_double2)nan);
/* Scale the final quotient */
q2 = spu_mul(q1, mult);
return (q2);
}
/* We use the same function for vector and scalar division. Provide the
scalar entry point as an alias. */
double __divdf3 (double a, double b)
__attribute__ ((__alias__ ("__divv2df3")));
/* Some toolchain builds used the __fast_divdf3 name for this helper function.
Provide this as another alternate entry point for compatibility. */
double __fast_divdf3 (double a, double b)
__attribute__ ((__alias__ ("__divv2df3")));
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