/* -------------------------------------------------------------- */ /* (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 /* * 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__ */