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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 0.5 ULPS for
* normalized results, 1ulp for denorm results, 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, vector double b)
{
/* Variables
*/
vec_float4 inv_bf, mant_bf;
vec_double2 mant_a, mant_b, inv_b, q0, q1, q2, mult;
vec_int4 exp, tmp;
vec_uint4 exp_a, exp_b, exp_q1, overflow, nounderflow, normal, utmp,
sign_a, sign_b, a_frac, b_frac, a_frac_0, b_frac_0, a_exp_0, b_exp_0,
a_exp_ones, b_exp_ones, a_nan, b_nan, a_inf, b_inf, a_zero, b_zero,
res_nan, sign_res;
/* Constants
*/
vec_float4 onef = spu_splats(1.0f);
vec_double2 one = spu_splats(1.0);
vec_uint4 exp_mask = (vec_uint4) { 0x7FF00000, 0, 0x7FF00000, 0 };
vec_uint4 sign_mask = (vec_uint4) { 0x80000000, 0, 0x80000000, 0};
vec_uint4 sign_exp_mask = (vec_uint4) { 0xFFF00000, 0, 0xFFF00000,0};
vec_uint4 frac_mask =(vec_uint4) { 0x000FFFFF, 0xFFFFFFFF, 0x000FFFFF, 0xFFFFFFFF };
vec_uchar16 swap32 = (vec_uchar16) ((vec_uint4) { 0x04050607, 0x00010203, 0x0C0D0E0F, 0x08090A0B} );
vec_uint4 zero = (vec_uint4) { 0, 0, 0, 0 };
vec_int4 e1022 = (vec_int4) { 0x000003FE, 0, 0x000003FE, 0 };
vec_int4 emax = (vec_int4) { 0x000007FE, 0, 0x000007FE, 0 };
vec_int4 e1 = (vec_int4) { 0x00000001, 0, 0x00000001, 0 };
vec_uint4 nan = (vec_uint4) { 0x7FF80000, 0, 0x7FF80000, 0};
/* Extract exponents and underflow denorm arguments to signed zero.
*/
exp_a = spu_and((vec_uint4)a, exp_mask);
exp_b = spu_and((vec_uint4)b, exp_mask);
sign_a = spu_and((vec_uint4)a, sign_mask);
sign_b = spu_and((vec_uint4)b, sign_mask);
a_exp_0 = spu_cmpeq (exp_a, 0);
utmp = spu_shuffle (a_exp_0, a_exp_0, swap32);
a_exp_0 = spu_and (a_exp_0, utmp);
b_exp_0 = spu_cmpeq (exp_b, 0);
utmp = spu_shuffle (b_exp_0, b_exp_0, swap32);
b_exp_0 = spu_and (b_exp_0, utmp);
a = spu_sel(a, (vec_double2)sign_a, (vec_ullong2)a_exp_0);
b = spu_sel(b, (vec_double2)sign_b, (vec_ullong2)b_exp_0);
/* Force the divisor and dividend into the range [1.0,2.0).
(Unless they're zero.)
*/
mant_a = spu_sel(a, one, (vec_ullong2)sign_exp_mask);
mant_b = spu_sel(b, one, (vec_ullong2)sign_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.
*/
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);
/* Compute the quotient's expected exponent. If the exponent
* is out of range, then force the resulting exponent to 0.
* (1023 with the bias). We correct for the out of range
* values by computing a multiplier (mult) that will force the
* result to the correct out of range value and set the
* correct exception flag (UNF, OVF, or neither).
*/
exp_q1 = spu_and((vec_uint4)q1, exp_mask);
exp = spu_sub((vec_int4)exp_a, (vec_int4)exp_b);
exp = spu_rlmaska(exp, -20); // shift right to allow enough bits for working
tmp = spu_rlmaska((vec_int4)exp_q1, -20);
exp = spu_add(exp, tmp); // biased exponent of result (right justified)
/* The default multiplier is 1.0. If an underflow is detected (the computed
* exponent is less than or equal to a biased 0), force the multiplier to 0.0.
* If exp<=0 set mult = 2**(unbiased exp + 1022) and unbiased exp = -1022
* = biased 1, the smallest normalized exponent. If exp<-51 set
* mult = 2**(-1074) to ensure underflowing result. Otherwise mult=1.
*/
normal = spu_cmpgt(exp, 0);
nounderflow = spu_cmpgt(exp, -52);
tmp = spu_add(exp, e1022);
mult = (vec_double2)spu_sl(tmp, 20);
mult = spu_sel(mult, one, (vec_ullong2)normal);
mult = spu_sel((vec_double2)e1, mult, (vec_ullong2)nounderflow);
exp = spu_sel(e1, exp, normal); // unbiased -1022 is biased 1
/* Force the multiplier to positive infinity (exp_mask) and the biased
* exponent to 1022, if the computed biased exponent is > emax.
*/
overflow = spu_cmpgt(exp, (vec_int4)emax);
exp = spu_sel(exp, (vec_int4)e1022, overflow);
mult = spu_sel(mult, (vec_double2)exp_mask, (vec_ullong2)overflow);
/* Determine if a, b are Inf, NaN, or zero.
* Since these are rare, it would improve speed if these could be detected
* quickly and a branch used to avoid slowing down the main path. However
* most of the work seems to be in the detection.
*/
a_exp_ones = spu_cmpeq (exp_a, exp_mask);
utmp = spu_shuffle (a_exp_ones, a_exp_ones, swap32);
a_exp_ones = spu_and (a_exp_ones, utmp);
a_frac = spu_and ((vec_uint4)a, frac_mask);
a_frac_0 = spu_cmpeq (a_frac, 0);
utmp = spu_shuffle (a_frac_0, a_frac_0, swap32);
a_frac_0 = spu_and (a_frac_0, utmp);
a_zero = spu_and (a_exp_0, a_frac_0);
a_inf = spu_and (a_exp_ones, a_frac_0);
a_nan = spu_andc (a_exp_ones, a_frac_0);
b_exp_ones = spu_cmpeq (exp_b, exp_mask);
utmp = spu_shuffle (b_exp_ones, b_exp_ones, swap32);
b_exp_ones = spu_and (b_exp_ones, utmp);
b_frac = spu_and ((vec_uint4)b, frac_mask);
b_frac_0 = spu_cmpeq (b_frac, 0);
utmp = spu_shuffle (b_frac_0, b_frac_0, swap32);
b_frac_0 = spu_and (b_frac_0, utmp);
b_zero = spu_and (b_exp_0, b_frac_0);
b_inf = spu_and (b_exp_ones, b_frac_0);
b_nan = spu_andc (b_exp_ones, b_frac_0);
/* Handle exception cases */
/* Result is 0 for 0/x, x!=0, or x/Inf, x!=Inf.
* Set mult=0 for 0/0 or Inf/Inf now, since it will be replaced
* with NaN later.
*/
utmp = spu_or (a_zero, b_inf);
mult = spu_sel(mult, (vec_double2)zero, (vec_ullong2)utmp);
/* Result is Inf for x/0, x!=0. Set mult=Inf for 0/0 now, since it
* will be replaced with NaN later.
*/
mult = spu_sel(mult, (vec_double2)exp_mask, (vec_ullong2)b_zero);
/* Result is NaN if either operand is, or Inf/Inf, or 0/0.
*/
res_nan = spu_or (a_nan, b_nan);
utmp = spu_and (a_inf, b_inf);
res_nan = spu_or (res_nan, utmp);
utmp = spu_and (a_zero, b_zero);
res_nan = spu_or (res_nan, utmp);
mult = spu_sel(mult, (vec_double2)nan, (vec_ullong2)res_nan);
/* Insert sign of result into mult.
*/
sign_res = spu_xor (sign_a, sign_b);
mult = spu_or (mult, (vec_double2)sign_res);
/* Insert the sign and exponent into the result and perform the
* final multiplication.
*/
exp = spu_sl(exp, 20);
q2 = spu_sel(q1, (vec_double2)exp, (vec_ullong2)exp_mask);
q2 = spu_mul(q2, mult);
return (q2);
}
#endif /* _DIVD2_H_ */
#endif /* __SPU__ */
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