211 lines
3.9 KiB
C
211 lines
3.9 KiB
C
#include "quadmath-imp.h"
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#define REALPART(z) (__real__(z))
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#define IMAGPART(z) (__imag__(z))
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#define COMPLEX_ASSIGN(z_, r_, i_) {__real__(z_) = (r_); __imag__(z_) = (i_);}
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// Horrible... GCC doesn't know how to multiply or divide these
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// __complex128 things. We have to do it on our own.
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// Protect it around macros so, some day, we can switch it on
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#if 0
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# define C128_MULT(x,y) ((x)*(y))
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# define C128_DIV(x,y) ((x)/(y))
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#else
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#define C128_MULT(x,y) mult_c128(x,y)
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#define C128_DIV(x,y) div_c128(x,y)
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static inline __complex128 mult_c128 (__complex128 x, __complex128 y)
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{
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__float128 r1 = REALPART(x), i1 = IMAGPART(x);
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__float128 r2 = REALPART(y), i2 = IMAGPART(y);
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__complex128 res;
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COMPLEX_ASSIGN(res, r1*r2 - i1*i2, i2*r1 + i1*r2);
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return res;
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}
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// Careful: the algorithm for the division sucks. A lot.
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static inline __complex128 div_c128 (__complex128 x, __complex128 y)
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{
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__float128 n = hypotq (REALPART (y), IMAGPART (y));
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__float128 r1 = REALPART(x), i1 = IMAGPART(x);
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__float128 r2 = REALPART(y), i2 = IMAGPART(y);
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__complex128 res;
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COMPLEX_ASSIGN(res, r1*r2 + i1*i2, i1*r2 - i2*r1);
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return res / n;
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}
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#endif
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__float128
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cabsq (__complex128 z)
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{
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return hypotq (REALPART (z), IMAGPART (z));
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}
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__complex128
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cexpq (__complex128 z)
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{
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__float128 a, b;
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__complex128 v;
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a = REALPART (z);
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b = IMAGPART (z);
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COMPLEX_ASSIGN (v, cosq (b), sinq (b));
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return expq (a) * v;
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}
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__complex128
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cexpiq (__float128 x)
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{
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__complex128 v;
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COMPLEX_ASSIGN (v, cosq (x), sinq (x));
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return v;
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}
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__float128
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cargq (__complex128 z)
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{
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return atan2q (IMAGPART (z), REALPART (z));
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}
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__complex128
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clogq (__complex128 z)
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{
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__complex128 v;
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COMPLEX_ASSIGN (v, logq (cabsq (z)), cargq (z));
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return v;
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}
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__complex128
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clog10q (__complex128 z)
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{
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__complex128 v;
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COMPLEX_ASSIGN (v, log10q (cabsq (z)), cargq (z));
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return v;
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}
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__complex128
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cpowq (__complex128 base, __complex128 power)
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{
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return cexpq (C128_MULT(power, clogq (base)));
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}
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__complex128
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csinq (__complex128 a)
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{
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__float128 r = REALPART (a), i = IMAGPART (a);
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__complex128 v;
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COMPLEX_ASSIGN (v, sinq (r) * coshq (i), cosq (r) * sinhq (i));
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return v;
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}
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__complex128
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csinhq (__complex128 a)
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{
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__float128 r = REALPART (a), i = IMAGPART (a);
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__complex128 v;
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COMPLEX_ASSIGN (v, sinhq (r) * cosq (i), coshq (r) * sinq (i));
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return v;
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}
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__complex128
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ccosq (__complex128 a)
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{
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__float128 r = REALPART (a), i = IMAGPART (a);
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__complex128 v;
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COMPLEX_ASSIGN (v, cosq (r) * coshq (i), - (sinq (r) * sinhq (i)));
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return v;
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}
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__complex128
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ccoshq (__complex128 a)
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{
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__float128 r = REALPART (a), i = IMAGPART (a);
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__complex128 v;
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COMPLEX_ASSIGN (v, coshq (r) * cosq (i), sinhq (r) * sinq (i));
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return v;
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}
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__complex128
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ctanq (__complex128 a)
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{
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__float128 rt = tanq (REALPART (a)), it = tanhq (IMAGPART (a));
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__complex128 n, d;
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COMPLEX_ASSIGN (n, rt, it);
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COMPLEX_ASSIGN (d, 1, - (rt * it));
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return C128_DIV(n,d);
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}
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__complex128
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ctanhq (__complex128 a)
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{
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__float128 rt = tanhq (REALPART (a)), it = tanq (IMAGPART (a));
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__complex128 n, d;
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COMPLEX_ASSIGN (n, rt, it);
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COMPLEX_ASSIGN (d, 1, rt * it);
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return C128_DIV(n,d);
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}
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/* Square root algorithm from glibc. */
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__complex128
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csqrtq (__complex128 z)
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{
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__float128 re = REALPART(z), im = IMAGPART(z);
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__complex128 v;
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if (im == 0)
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{
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if (re < 0)
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{
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COMPLEX_ASSIGN (v, 0, copysignq (sqrtq (-re), im));
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}
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else
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{
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COMPLEX_ASSIGN (v, fabsq (sqrtq (re)), copysignq (0, im));
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}
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}
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else if (re == 0)
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{
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__float128 r = sqrtq (0.5 * fabsq (im));
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COMPLEX_ASSIGN (v, r, copysignq (r, im));
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}
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else
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{
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__float128 d = hypotq (re, im);
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__float128 r, s;
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/* Use the identity 2 Re res Im res = Im x
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to avoid cancellation error in d +/- Re x. */
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if (re > 0)
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r = sqrtq (0.5 * d + 0.5 * re), s = (0.5 * im) / r;
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else
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s = sqrtq (0.5 * d - 0.5 * re), r = fabsq ((0.5 * im) / s);
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COMPLEX_ASSIGN (v, r, copysignq (s, im));
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}
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return v;
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}
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