libgcc/config/spu/divv2df3.c

   1 /* Copyright (C) 2009-2015 Free Software Foundation, Inc.
   2
   3    This file is free software; you can redistribute it and/or modify it under
   4    the terms of the GNU General Public License as published by the Free
   5    Software Foundation; either version 3 of the License, or (at your option)
   6    any later version.
   7
   8    This file is distributed in the hope that it will be useful, but WITHOUT
   9    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  10    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  11    for more details.
  12
  13    Under Section 7 of GPL version 3, you are granted additional
  14    permissions described in the GCC Runtime Library Exception, version
  15    3.1, as published by the Free Software Foundation.
  16
  17    You should have received a copy of the GNU General Public License and
  18    a copy of the GCC Runtime Library Exception along with this program;
  19    see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  20    <http://www.gnu.org/licenses/>.  */
  21
  22 #include <spu_intrinsics.h>
  23
  24 vector double __divv2df3 (vector double a_in, vector double b_in);
  25
  26 /* __divv2df3 divides the vector dividend a by the vector divisor b and
  27    returns the resulting vector quotient.  Maximum error about 0.5 ulp
  28    over entire double range including denorms, compared to true result
  29    in round-to-nearest rounding mode.  Handles Inf or NaN operands and
  30    results correctly.  */
  31
  32 vector double
  33 __divv2df3 (vector double a_in, vector double b_in)
  34 {
  35   /* Variables */
  36   vec_int4    exp, exp_bias;
  37   vec_uint4   no_underflow, overflow;
  38   vec_float4  mant_bf, inv_bf;
  39   vec_ullong2 exp_a, exp_b;
  40   vec_ullong2 a_nan, a_zero, a_inf, a_denorm, a_denorm0;
  41   vec_ullong2 b_nan, b_zero, b_inf, b_denorm, b_denorm0;
  42   vec_ullong2 nan;
  43   vec_uint4   a_exp, b_exp;
  44   vec_ullong2 a_mant_0, b_mant_0;
  45   vec_ullong2 a_exp_1s, b_exp_1s;
  46   vec_ullong2 sign_exp_mask;
  47
  48   vec_double2 a, b;
  49   vec_double2 mant_a, mant_b, inv_b, q0, q1, q2, mult;
  50
  51   /* Constants */
  52   vec_uint4   exp_mask_u32 = spu_splats((unsigned int)0x7FF00000);
  53   vec_uchar16 splat_hi = (vec_uchar16){0,1,2,3, 0,1,2,3,  8, 9,10,11, 8,9,10,11};
  54   vec_uchar16 swap_32 = (vec_uchar16){4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11};
  55   vec_ullong2 exp_mask = spu_splats(0x7FF0000000000000ULL);
  56   vec_ullong2 sign_mask = spu_splats(0x8000000000000000ULL);
  57   vec_float4  onef = spu_splats(1.0f);
  58   vec_double2 one = spu_splats(1.0);
  59   vec_double2 exp_53 = (vec_double2)spu_splats(0x0350000000000000ULL);
  60
  61   sign_exp_mask = spu_or(sign_mask, exp_mask);
  62
  63   /* Extract the floating point components from each of the operands including
  64    * exponent and mantissa.
  65    */
  66   a_exp = (vec_uint4)spu_and((vec_uint4)a_in, exp_mask_u32);
  67   a_exp = spu_shuffle(a_exp, a_exp, splat_hi);
  68   b_exp = (vec_uint4)spu_and((vec_uint4)b_in, exp_mask_u32);
  69   b_exp = spu_shuffle(b_exp, b_exp, splat_hi);
  70
  71   a_mant_0 = (vec_ullong2)spu_cmpeq((vec_uint4)spu_andc((vec_ullong2)a_in, sign_exp_mask), 0);
  72   a_mant_0 = spu_and(a_mant_0, spu_shuffle(a_mant_0, a_mant_0, swap_32));
  73
  74   b_mant_0 = (vec_ullong2)spu_cmpeq((vec_uint4)spu_andc((vec_ullong2)b_in, sign_exp_mask), 0);
  75   b_mant_0 = spu_and(b_mant_0, spu_shuffle(b_mant_0, b_mant_0, swap_32));
  76
  77   a_exp_1s = (vec_ullong2)spu_cmpeq(a_exp, exp_mask_u32);
  78   b_exp_1s = (vec_ullong2)spu_cmpeq(b_exp, exp_mask_u32);
  79
  80   /* Identify all possible special values that must be accommodated including:
  81    * +-denorm, +-0, +-infinity, and NaNs.
  82    */
  83   a_denorm0= (vec_ullong2)spu_cmpeq(a_exp, 0);
  84   a_nan    = spu_andc(a_exp_1s, a_mant_0);
  85   a_zero   = spu_and (a_denorm0, a_mant_0);
  86   a_inf    = spu_and (a_exp_1s, a_mant_0);
  87   a_denorm = spu_andc(a_denorm0, a_zero);
  88
  89   b_denorm0= (vec_ullong2)spu_cmpeq(b_exp, 0);
  90   b_nan    = spu_andc(b_exp_1s, b_mant_0);
  91   b_zero   = spu_and (b_denorm0, b_mant_0);
  92   b_inf    = spu_and (b_exp_1s, b_mant_0);
  93   b_denorm = spu_andc(b_denorm0, b_zero);
  94
  95   /* Scale denorm inputs to into normalized numbers by conditionally scaling the
  96    * input parameters.
  97    */
  98   a = spu_sub(spu_or(a_in, exp_53), spu_sel(exp_53, a_in, sign_mask));
  99   a = spu_sel(a_in, a, a_denorm);
 100
 101   b = spu_sub(spu_or(b_in, exp_53), spu_sel(exp_53, b_in, sign_mask));
 102   b = spu_sel(b_in, b, b_denorm);
 103
 104   /* Extract the divisor and dividend exponent and force parameters into the signed
 105    * range [1.0,2.0) or [-1.0,2.0).
 106    */
 107   exp_a = spu_and((vec_ullong2)a, exp_mask);
 108   exp_b = spu_and((vec_ullong2)b, exp_mask);
 109
 110   mant_a = spu_sel(a, one, (vec_ullong2)exp_mask);
 111   mant_b = spu_sel(b, one, (vec_ullong2)exp_mask);
 112
 113   /* Approximate the single reciprocal of b by using
 114    * the single precision reciprocal estimate followed by one
 115    * single precision iteration of Newton-Raphson.
 116    */
 117   mant_bf = spu_roundtf(mant_b);
 118   inv_bf = spu_re(mant_bf);
 119   inv_bf = spu_madd(spu_nmsub(mant_bf, inv_bf, onef), inv_bf, inv_bf);
 120
 121   /* Perform 2 more Newton-Raphson iterations in double precision. The
 122    * result (q1) is in the range (0.5, 2.0).
 123    */
 124   inv_b = spu_extend(inv_bf);
 125   inv_b = spu_madd(spu_nmsub(mant_b, inv_b, one), inv_b, inv_b);
 126   q0 = spu_mul(mant_a, inv_b);
 127   q1 = spu_madd(spu_nmsub(mant_b, q0, mant_a), inv_b, q0);
 128
 129   /* Determine the exponent correction factor that must be applied
 130    * to q1 by taking into account the exponent of the normalized inputs
 131    * and the scale factors that were applied to normalize them.
 132    */
 133   exp = spu_rlmaska(spu_sub((vec_int4)exp_a, (vec_int4)exp_b), -20);
 134   exp = spu_add(exp, (vec_int4)spu_add(spu_and((vec_int4)a_denorm, -0x34), spu_and((vec_int4)b_denorm, 0x34)));
 135
 136   /* Bias the quotient exponent depending on the sign of the exponent correction
 137    * factor so that a single multiplier will ensure the entire double precision
 138    * domain (including denorms) can be achieved.
 139    *
 140    *    exp            bias q1     adjust exp
 141    *   =====           ========    ==========
 142    *   positive         2^+65         -65
 143    *   negative         2^-64         +64
 144    */
 145   exp_bias = spu_xor(spu_rlmaska(exp, -31), 64);
 146   exp = spu_sub(exp, exp_bias);
 147
 148   q1 = spu_sel(q1, (vec_double2)spu_add((vec_int4)q1, spu_sl(exp_bias, 20)), exp_mask);
 149
 150   /* Compute a multiplier (mult) to applied to the quotient (q1) to produce the
 151    * expected result. On overflow, clamp the multiplier to the maximum non-infinite
 152    * number in case the rounding mode is not round-to-nearest.
 153    */
 154   exp = spu_add(exp, 0x3FF);
 155   no_underflow = spu_cmpgt(exp, 0);
 156   overflow = spu_cmpgt(exp, 0x7FE);
 157   exp = spu_and(spu_sl(exp, 20), (vec_int4)no_underflow);
 158   exp = spu_and(exp, (vec_int4)exp_mask);
 159
 160   mult = spu_sel((vec_double2)exp, (vec_double2)(spu_add((vec_uint4)exp_mask, -1)), (vec_ullong2)overflow);
 161
 162   /* Handle special value conditions. These include:
 163    *
 164    * 1) IF either operand is a NaN OR both operands are 0 or INFINITY THEN a NaN
 165    *    results.
 166    * 2) ELSE IF the dividend is an INFINITY OR the divisor is 0 THEN a INFINITY results.
 167    * 3) ELSE IF the dividend is 0 OR the divisor is INFINITY THEN a 0 results.
 168    */
 169   mult = spu_andc(mult, (vec_double2)spu_or(a_zero, b_inf));
 170   mult = spu_sel(mult, (vec_double2)exp_mask, spu_or(a_inf, b_zero));
 171
 172   nan = spu_or(a_nan, b_nan);
 173   nan = spu_or(nan, spu_and(a_zero, b_zero));
 174   nan = spu_or(nan, spu_and(a_inf, b_inf));
 175
 176   mult = spu_or(mult, (vec_double2)nan);
 177
 178   /* Scale the final quotient */
 179
 180   q2 = spu_mul(q1, mult);
 181
 182   return (q2);
 183 }
 184
 185
 186 /* We use the same function for vector and scalar division.  Provide the
 187    scalar entry point as an alias.  */
 188 double __divdf3 (double a, double b)
 189   __attribute__ ((__alias__ ("__divv2df3")));
 190
 191 /* Some toolchain builds used the __fast_divdf3 name for this helper function.
 192    Provide this as another alternate entry point for compatibility.  */
 193 double __fast_divdf3 (double a, double b)
 194   __attribute__ ((__alias__ ("__divv2df3")));
 195