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-/*
- * OpenCL library for double word floating point calculation using compensated arithmetics
- *
- * The theoritical basis can be found in Valentina Popescu's PhD thesis:
- * Towards fast and certified multi-precision libraries
- * Reference LYSEN036
- * http://www.theses.fr/2017LYSEN036
- * All page number and equation number are refering to this document. 
- * 
- * The precision of the calculation (bounds) is provided in ULP (smallest possible mantissa) 
- * and come from the table 2.2 (page 68 of the thesis).
- * The number of equivalent FLOP is taken from the table 2.3 (page 69 the thesis). 
- * Note that FLOP are not all equal: a division is much more expensive than an addition.
- */
-
-//This library can be expanded to double-double by redefining fp, fp2 and one to double, double2 and 1.0.
-#ifdef DOUBLEDOUBLE
-#define fp double
-#define fp2 double2
-#define one 1.0
-#else
-#define fp float
-#define fp2 float2
-#define one 1.0f
-#endif
-
-/* Nota: i386 computer use x87 registers which are larger than the 32bits precision
- * which can invalidate the error compensation mechanism.
- *
- * We use the trick to declare some variable "volatile" to enforce the actual
- * precision reduction of those variables.
-*/
-
-#ifndef X87_VOLATILE
-# define X87_VOLATILE
-#endif
-
-//Algorithm 1, p23, theorem 1.1.12. Requires e_x > e_y, valid if |x| > |y| 
-inline fp2 fast_fp_plus_fp(fp x, fp y){
-    X87_VOLATILE fp s = x + y;
-    X87_VOLATILE fp z = s - x;
-    fp e = y - z;
-    return (fp2)(s, e);
-}
-
-//Algorithm 2, p24, same as fast_fp_plus_fp without the condition on e_x and e_y
-inline fp2 fp_plus_fp(fp x, fp y){
-    X87_VOLATILE fp s = x + y;
-    X87_VOLATILE fp xp = s - y;
-    X87_VOLATILE fp yp = s - xp;
-    X87_VOLATILE fp dx = x - xp;
-    X87_VOLATILE fp dy = y - yp;
-    return (fp2)(s, dx+dy);  
-}
-
-//Algorithm 3, p24: multiplication with a FMA
-inline fp2 fp_times_fp(fp x, fp y){
-    fp p = x * y;
-    fp e = fma(x, y, -p);
-    return (fp2)(p, e);  
-}
-
-//Algorithm 7, p38: Addition of a FP to a DW. 10flop bounds:2u²+5u³
-inline fp2 dw_plus_fp(fp2 x, fp y){
-    fp2 s = fp_plus_fp(x.s0, y);
-    X87_VOLATILE fp v = x.s1 + s.s1;
-    return fast_fp_plus_fp(s.s0, v);
-}
-
-//Algorithm 9, p40: addition of two DW: 20flop bounds:3u²+13u³
-inline fp2 dw_plus_dw(fp2 x, fp2 y){
-    fp2 s = fp_plus_fp(x.s0, y.s0);
-    fp2 t = fp_plus_fp(x.s1, y.s1);
-    fp2 v = fast_fp_plus_fp(s.s0, s.s1 + t.s0);
-    return fast_fp_plus_fp(v.s0, t.s1 + v.s1);
-}
-
-//Algorithm 12, p49: Multiplication FP*DW: 6flops bounds:2u²
-inline fp2 dw_times_fp(fp2 x, fp y){
-    fp2 c = fp_times_fp(x.s0, y);
-    return fast_fp_plus_fp(c.s0, fma(x.s1, y, c.s1));
-}
-
-//Algorithm 14, p52: Multiplication DW*DW, 8 flops bounds:6u²
-inline fp2 dw_times_dw(fp2 x, fp2 y){
-    fp2 c = fp_times_fp(x.s0, y.s0);
-    X87_VOLATILE fp l = fma(x.s1, y.s0, x.s0 * y.s1);
-    return fast_fp_plus_fp(c.s0, c.s1 + l);
-}
-
-//Algorithm 17, p55: Division DW / FP, 10flops bounds: 3.5u²
-inline fp2 dw_div_fp(fp2 x, fp y){
-    X87_VOLATILE fp th = x.s0 / y;
-    fp2 pi = fp_times_fp(th, y);
-    fp2 d = x - pi;
-    X87_VOLATILE fp delta = d.s0 + d.s1;
-    X87_VOLATILE fp tl = delta/y; 
-    return fast_fp_plus_fp(th, tl);
-}
-
-//Derived from algorithm 20, p64: Inversion 1/ DW, 22 flops
-inline fp2 inv_dw(fp2 y){
-    X87_VOLATILE fp th = one/y.s0;
-    X87_VOLATILE fp rh = fma(-y.s0, th, one);
-    X87_VOLATILE fp rl = -y.s1 * th;
-    fp2 e = fast_fp_plus_fp(rh, rl);
-    fp2 delta = dw_times_fp(e, th);
-    return dw_plus_fp(delta, th);
-}
-    
-//Algorithm 20, p64: Division DW / DW, 30 flops: bounds:9.8u²
-inline fp2 dw_div_dw(fp2 x, fp2 y){
-    return dw_times_dw(x, inv_dw(y));
-}
-