233 lines
9.7 KiB
C
233 lines
9.7 KiB
C
/* -------------------------------------------------------------- */
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/* (C)Copyright 2001,2008, */
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/* International Business Machines Corporation, */
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/* Sony Computer Entertainment, Incorporated, */
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/* Toshiba Corporation, */
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/* */
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/* All Rights Reserved. */
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/* */
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/* Redistribution and use in source and binary forms, with or */
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/* without modification, are permitted provided that the */
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/* following conditions are met: */
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/* */
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/* - Redistributions of source code must retain the above copyright*/
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/* notice, this list of conditions and the following disclaimer. */
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/* */
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/* - Redistributions in binary form must reproduce the above */
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/* copyright notice, this list of conditions and the following */
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/* disclaimer in the documentation and/or other materials */
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/* provided with the distribution. */
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/* */
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/* - Neither the name of IBM Corporation nor the names of its */
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/* contributors may be used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* */
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/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
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/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
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/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
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/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
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/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
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/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
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/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
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/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
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/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
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/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
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/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
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/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
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/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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/* -------------------------------------------------------------- */
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/* PROLOG END TAG zYx */
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#ifdef __SPU__
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#ifndef _DIVD2_H_
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#define _DIVD2_H_ 1
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#include <spu_intrinsics.h>
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/*
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* FUNCTION
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* vector double _divd2(vector double a, vector double b)
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*
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* DESCRIPTION
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* _divd2 divides the vector dividend a by the vector divisor b and
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* returns the resulting vector quotient. Maximum error 0.5 ULPS for
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* normalized results, 1ulp for denorm results, over entire double
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* range including denorms, compared to true result in round-to-nearest
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* rounding mode. Handles Inf or NaN operands and results correctly.
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*/
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static __inline vector double _divd2(vector double a, vector double b)
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{
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/* Variables
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*/
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vec_float4 inv_bf, mant_bf;
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vec_double2 mant_a, mant_b, inv_b, q0, q1, q2, mult;
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vec_int4 exp, tmp;
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vec_uint4 exp_a, exp_b, exp_q1, overflow, nounderflow, normal, utmp,
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sign_a, sign_b, a_frac, b_frac, a_frac_0, b_frac_0, a_exp_0, b_exp_0,
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a_exp_ones, b_exp_ones, a_nan, b_nan, a_inf, b_inf, a_zero, b_zero,
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res_nan, sign_res;
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/* Constants
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*/
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vec_float4 onef = spu_splats(1.0f);
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vec_double2 one = spu_splats(1.0);
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vec_uint4 exp_mask = (vec_uint4) { 0x7FF00000, 0, 0x7FF00000, 0 };
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vec_uint4 sign_mask = (vec_uint4) { 0x80000000, 0, 0x80000000, 0};
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vec_uint4 sign_exp_mask = (vec_uint4) { 0xFFF00000, 0, 0xFFF00000,0};
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vec_uint4 frac_mask =(vec_uint4) { 0x000FFFFF, 0xFFFFFFFF, 0x000FFFFF, 0xFFFFFFFF };
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vec_uchar16 swap32 = (vec_uchar16) ((vec_uint4) { 0x04050607, 0x00010203, 0x0C0D0E0F, 0x08090A0B} );
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vec_uint4 zero = (vec_uint4) { 0, 0, 0, 0 };
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vec_int4 e1022 = (vec_int4) { 0x000003FE, 0, 0x000003FE, 0 };
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vec_int4 emax = (vec_int4) { 0x000007FE, 0, 0x000007FE, 0 };
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vec_int4 e1 = (vec_int4) { 0x00000001, 0, 0x00000001, 0 };
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vec_uint4 nan = (vec_uint4) { 0x7FF80000, 0, 0x7FF80000, 0};
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/* Extract exponents and underflow denorm arguments to signed zero.
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*/
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exp_a = spu_and((vec_uint4)a, exp_mask);
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exp_b = spu_and((vec_uint4)b, exp_mask);
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sign_a = spu_and((vec_uint4)a, sign_mask);
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sign_b = spu_and((vec_uint4)b, sign_mask);
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a_exp_0 = spu_cmpeq (exp_a, 0);
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utmp = spu_shuffle (a_exp_0, a_exp_0, swap32);
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a_exp_0 = spu_and (a_exp_0, utmp);
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b_exp_0 = spu_cmpeq (exp_b, 0);
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utmp = spu_shuffle (b_exp_0, b_exp_0, swap32);
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b_exp_0 = spu_and (b_exp_0, utmp);
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a = spu_sel(a, (vec_double2)sign_a, (vec_ullong2)a_exp_0);
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b = spu_sel(b, (vec_double2)sign_b, (vec_ullong2)b_exp_0);
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/* Force the divisor and dividend into the range [1.0,2.0).
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(Unless they're zero.)
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*/
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mant_a = spu_sel(a, one, (vec_ullong2)sign_exp_mask);
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mant_b = spu_sel(b, one, (vec_ullong2)sign_exp_mask);
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/* Approximate the single reciprocal of b by using
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* the single precision reciprocal estimate followed by one
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* single precision iteration of Newton-Raphson.
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*/
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mant_bf = spu_roundtf(mant_b);
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inv_bf = spu_re(mant_bf);
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inv_bf = spu_madd(spu_nmsub(mant_bf, inv_bf, onef), inv_bf, inv_bf);
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/* Perform 2 more Newton-Raphson iterations in double precision.
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*/
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inv_b = spu_extend(inv_bf);
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inv_b = spu_madd(spu_nmsub(mant_b, inv_b, one), inv_b, inv_b);
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q0 = spu_mul(mant_a, inv_b);
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q1 = spu_madd(spu_nmsub(mant_b, q0, mant_a), inv_b, q0);
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/* Compute the quotient's expected exponent. If the exponent
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* is out of range, then force the resulting exponent to 0.
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* (1023 with the bias). We correct for the out of range
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* values by computing a multiplier (mult) that will force the
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* result to the correct out of range value and set the
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* correct exception flag (UNF, OVF, or neither).
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*/
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exp_q1 = spu_and((vec_uint4)q1, exp_mask);
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exp = spu_sub((vec_int4)exp_a, (vec_int4)exp_b);
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exp = spu_rlmaska(exp, -20); // shift right to allow enough bits for working
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tmp = spu_rlmaska((vec_int4)exp_q1, -20);
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exp = spu_add(exp, tmp); // biased exponent of result (right justified)
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/* The default multiplier is 1.0. If an underflow is detected (the computed
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* exponent is less than or equal to a biased 0), force the multiplier to 0.0.
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* If exp<=0 set mult = 2**(unbiased exp + 1022) and unbiased exp = -1022
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* = biased 1, the smallest normalized exponent. If exp<-51 set
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* mult = 2**(-1074) to ensure underflowing result. Otherwise mult=1.
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*/
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normal = spu_cmpgt(exp, 0);
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nounderflow = spu_cmpgt(exp, -52);
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tmp = spu_add(exp, e1022);
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mult = (vec_double2)spu_sl(tmp, 20);
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mult = spu_sel(mult, one, (vec_ullong2)normal);
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mult = spu_sel((vec_double2)e1, mult, (vec_ullong2)nounderflow);
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exp = spu_sel(e1, exp, normal); // unbiased -1022 is biased 1
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/* Force the multiplier to positive infinity (exp_mask) and the biased
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* exponent to 1022, if the computed biased exponent is > emax.
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*/
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overflow = spu_cmpgt(exp, (vec_int4)emax);
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exp = spu_sel(exp, (vec_int4)e1022, overflow);
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mult = spu_sel(mult, (vec_double2)exp_mask, (vec_ullong2)overflow);
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/* Determine if a, b are Inf, NaN, or zero.
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* Since these are rare, it would improve speed if these could be detected
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* quickly and a branch used to avoid slowing down the main path. However
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* most of the work seems to be in the detection.
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*/
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a_exp_ones = spu_cmpeq (exp_a, exp_mask);
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utmp = spu_shuffle (a_exp_ones, a_exp_ones, swap32);
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a_exp_ones = spu_and (a_exp_ones, utmp);
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a_frac = spu_and ((vec_uint4)a, frac_mask);
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a_frac_0 = spu_cmpeq (a_frac, 0);
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utmp = spu_shuffle (a_frac_0, a_frac_0, swap32);
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a_frac_0 = spu_and (a_frac_0, utmp);
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a_zero = spu_and (a_exp_0, a_frac_0);
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a_inf = spu_and (a_exp_ones, a_frac_0);
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a_nan = spu_andc (a_exp_ones, a_frac_0);
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b_exp_ones = spu_cmpeq (exp_b, exp_mask);
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utmp = spu_shuffle (b_exp_ones, b_exp_ones, swap32);
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b_exp_ones = spu_and (b_exp_ones, utmp);
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b_frac = spu_and ((vec_uint4)b, frac_mask);
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b_frac_0 = spu_cmpeq (b_frac, 0);
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utmp = spu_shuffle (b_frac_0, b_frac_0, swap32);
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b_frac_0 = spu_and (b_frac_0, utmp);
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b_zero = spu_and (b_exp_0, b_frac_0);
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b_inf = spu_and (b_exp_ones, b_frac_0);
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b_nan = spu_andc (b_exp_ones, b_frac_0);
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/* Handle exception cases */
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/* Result is 0 for 0/x, x!=0, or x/Inf, x!=Inf.
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* Set mult=0 for 0/0 or Inf/Inf now, since it will be replaced
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* with NaN later.
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*/
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utmp = spu_or (a_zero, b_inf);
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mult = spu_sel(mult, (vec_double2)zero, (vec_ullong2)utmp);
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/* Result is Inf for x/0, x!=0. Set mult=Inf for 0/0 now, since it
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* will be replaced with NaN later.
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*/
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mult = spu_sel(mult, (vec_double2)exp_mask, (vec_ullong2)b_zero);
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/* Result is NaN if either operand is, or Inf/Inf, or 0/0.
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*/
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res_nan = spu_or (a_nan, b_nan);
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utmp = spu_and (a_inf, b_inf);
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res_nan = spu_or (res_nan, utmp);
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utmp = spu_and (a_zero, b_zero);
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res_nan = spu_or (res_nan, utmp);
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mult = spu_sel(mult, (vec_double2)nan, (vec_ullong2)res_nan);
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/* Insert sign of result into mult.
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*/
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sign_res = spu_xor (sign_a, sign_b);
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mult = spu_or (mult, (vec_double2)sign_res);
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/* Insert the sign and exponent into the result and perform the
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* final multiplication.
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*/
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exp = spu_sl(exp, 20);
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q2 = spu_sel(q1, (vec_double2)exp, (vec_ullong2)exp_mask);
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q2 = spu_mul(q2, mult);
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return (q2);
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}
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#endif /* _DIVD2_H_ */
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#endif /* __SPU__ */
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