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Diffstat (limited to 'newlib/libm/machine/spu/headers/divd2.h')
| -rw-r--r-- | newlib/libm/machine/spu/headers/divd2.h | 244 |
1 files changed, 244 insertions, 0 deletions
diff --git a/newlib/libm/machine/spu/headers/divd2.h b/newlib/libm/machine/spu/headers/divd2.h new file mode 100644 index 000000000..b04d3c592 --- /dev/null +++ b/newlib/libm/machine/spu/headers/divd2.h @@ -0,0 +1,244 @@ +/* -------------------------------------------------------------- */ +/* (C)Copyright 2006,2007, */ +/* 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. */ +/* 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__ */ |