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