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/* -------------------------------------------------------------- */
/* (C)Copyright 2001,2008, */
/* International Business Machines Corporation, */
/* Sony Computer Entertainment, Incorporated, */
/* Toshiba Corporation, */
/* */
/* All Rights Reserved. */
/* */
/* Redistribution and use in source and binary forms, with or */
/* without modification, are permitted provided that the */
/* following conditions are met: */
/* */
/* - Redistributions of source code must retain the above copyright*/
/* notice, this list of conditions and the following disclaimer. */
/* */
/* - Redistributions in binary form must reproduce the above */
/* copyright notice, this list of conditions and the following */
/* disclaimer in the documentation and/or other materials */
/* provided with the distribution. */
/* */
/* - Neither the name of IBM Corporation nor the names of its */
/* contributors may be used to endorse or promote products */
/* derived from this software without specific prior written */
/* permission. */
/* */
/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
/* -------------------------------------------------------------- */
/* PROLOG END TAG zYx */
#ifdef __SPU__
#ifndef _DIVD2_H_
#define _DIVD2_H_ 1
#include <spu_intrinsics.h>
/*
* FUNCTION
* vector double _divd2(vector double a, vector double b)
*
* DESCRIPTION
* _divd2 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.
*/
static __inline vector double _divd2(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;
vec_ullong2 b_nan, b_zero, b_inf, b_denorm;
vec_ullong2 nan;
vec_double2 a, b;
vec_double2 mant_a, mant_b, inv_b, q0, q1, q2, mult;
/* Constants */
vec_float4 onef = spu_splats(1.0f);
vec_ullong2 exp_mask = spu_splats(0x7FF0000000000000ULL);
vec_double2 one = spu_splats(1.0);
#ifdef __SPU_EDP__
vec_double2 denorm_scale = (vec_double2)spu_splats(0x4330000000000000ULL);
/* Identify all possible special values that must be accomodated including:
* +-0, +-infinity, +-denorm, and NaNs.
*/
a_nan = spu_testsv(a_in, (SPU_SV_NAN));
a_zero = spu_testsv(a_in, (SPU_SV_NEG_ZERO | SPU_SV_POS_ZERO));
a_inf = spu_testsv(a_in, (SPU_SV_NEG_INFINITY | SPU_SV_POS_INFINITY));
a_denorm = spu_testsv(a_in, (SPU_SV_NEG_DENORM | SPU_SV_POS_DENORM));
b_nan = spu_testsv(b_in, (SPU_SV_NAN));
b_zero = spu_testsv(b_in, (SPU_SV_NEG_ZERO | SPU_SV_POS_ZERO));
b_inf = spu_testsv(b_in, (SPU_SV_NEG_INFINITY | SPU_SV_POS_INFINITY));
b_denorm = spu_testsv(b_in, (SPU_SV_NEG_DENORM | SPU_SV_POS_DENORM));
/* Scale denorm inputs to into normalized numbers by conditionally scaling the
* input parameters.
*/
a = spu_sel(a_in, spu_mul(a_in, denorm_scale), a_denorm);
b = spu_sel(b_in, spu_mul(b_in, denorm_scale), b_denorm);
#else /* !__SPU_EDP__ */
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_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 sign_mask = spu_splats(0x8000000000000000ULL);
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_denorm = (vec_ullong2)spu_cmpeq(a_exp, 0); /* really is a_exp_0 */
a_nan = spu_andc(a_exp_1s, a_mant_0);
a_zero = spu_and (a_denorm, a_mant_0);
a_inf = spu_and (a_exp_1s, a_mant_0);
b_denorm = (vec_ullong2)spu_cmpeq(b_exp, 0); /* really is b_exp_0 */
b_nan = spu_andc(b_exp_1s, b_mant_0);
b_zero = spu_and (b_denorm, b_mant_0);
b_inf = spu_and (b_exp_1s, b_mant_0);
/* 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);
#endif /* __SPU_EDP__ */
/* 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.
*/
exp = spu_add(exp, 0x3FF);
no_underflow = spu_cmpgt(exp, 0);
overflow = spu_cmpgt(exp, 0x7FF);
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)exp_mask, (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);
}
#endif /* _DIVD2_H_ */
#endif /* __SPU__ */
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