derek.holloway
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93 lines
3.1 KiB
Common Lisp
93 lines
3.1 KiB
Common Lisp
/*===--------------------------------------------------------------------------
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* ROCm Device Libraries
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*
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* This file is distributed under the University of Illinois Open Source
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* License. See LICENSE.TXT for details.
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*===------------------------------------------------------------------------*/
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#include "mathD.h"
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#define DOUBLE_SPECIALIZATION
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#include "ep.h"
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#define NOCFLOW
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CONSTATTR double
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MATH_PRIVATE(tanred2)(double x, double xx, int sel)
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{
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#if defined NOCFLOW
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double s = sqr(con(x,xx)).hi;
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double p = s * MATH_MAD(s, MATH_MAD(s, MATH_MAD(s, MATH_MAD(s,
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MATH_MAD(s, MATH_MAD(s, MATH_MAD(s, MATH_MAD(s,
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MATH_MAD(s, MATH_MAD(s, MATH_MAD(s, MATH_MAD(s,
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MATH_MAD(s,
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0x1.5e089c751c08cp-16, -0x1.78809a9a29f71p-15),
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0x1.7746f90a8aaep-14), -0x1.bb44da6fbf144p-16),
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0x1.1e634a7943acfp-13), 0x1.d250fdeb68febp-13),
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0x1.37fd9b58c4d95p-11), 0x1.7d5af15120e2cp-10),
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0x1.d6d93e09491dfp-9), 0x1.226e12033784dp-7),
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0x1.664f49ac36ae2p-6), 0x1.ba1ba1b451c21p-5),
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0x1.11111111185b7p-3), 0x1.55555555554eep-2);
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double2 t = fadd(con(x,xx), mul(x, p));
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double2 tr = frcp(t);
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return sel ? -tr.hi : t.hi;
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#else
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const double piby4_lead = 0x1.921fb54442d18p-1;
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const double piby4_tail = 0x1.1a62633145c06p-55;
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// In order to maintain relative precision transform using the identity:
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// tan(pi/4-x) = (1-tan(x))/(1+tan(x)) for arguments close to pi/4.
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// Similarly use tan(x-pi/4) = (tan(x)-1)/(tan(x)+1) close to -pi/4.
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bool ca = x > 0.68;
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bool cb = x < -0.68;
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double transform = ca ? 1.0 : 0.0;
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transform = cb ? -1.0 : transform;
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double tx = MATH_MAD(-transform, x, piby4_lead) + MATH_MAD(-transform, xx, piby4_tail);
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bool c = ca | cb;
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x = c ? tx : x;
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xx = c ? 0.0 : xx;
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// Core Remez [2,3] approximation to tan(x+xx) on the interval [0,0.68].
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double t1 = x;
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double r = MATH_MAD(x*xx, 2.0, x*x);
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double a = MATH_MAD(r,
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MATH_MAD(r, 0x1.d5daf289c385ap-13, -0x1.77c24c7569abbp-6),
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0x1.7d50f6638564ap-2);
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double b = MATH_MAD(r,
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MATH_MAD(r,
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MATH_MAD(r, -0x1.e7517ef6d98f8p-13, 0x1.ab0f4f80a0acfp-6),
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-0x1.08046499eb90fp-1),
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0x1.1dfcb8caa40b8p+0);
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double t2 = MATH_MAD(MATH_FAST_DIV(a, b), x*r, xx);
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double tp = t1 + t2;
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double ret;
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if (c) {
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if (sel)
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ret = transform * (MATH_FAST_DIV(2.0*tp, tp - 1.0) - 1.0);
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else
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ret = transform * (1.0 - MATH_FAST_DIV(2.0*tp, 1.0 + tp));
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} else {
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if (sel) {
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// Compute -1.0/(t1 + t2) accurately
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double tq = t2 - (tp - t1);
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double tr = -MATH_FAST_RCP(tp);
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double e = MATH_MAD(tr, tq, MATH_MAD(tr, tp, 1.0));
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ret = MATH_MAD(e, tr, tr);
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} else {
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ret = tp;
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}
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}
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return ret;
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#endif
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}
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