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/* Copyright (C) 2009-2015 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 3 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.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
#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 accommodated 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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