common/complex/ctanhf.c

25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Use is subject to license terms.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
ddc0e0b53c661f6e439e3b7072b3ef353eadb4afRichard Lowe#pragma weak __ctanhf = ctanhf
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "libm.h"       /* expf/expm1f/fabsf/sincosf/sinf/tanhf */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "complex_wrapper.h"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* INDENT OFF */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisstatic const float four = 4.0F, two = 2.0F, one = 1.0F, zero = 0.0F;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* INDENT ON */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisfcomplex
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisctanhf(fcomplex z) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    float r, u, v, t, x, y, S, C;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    int hx, ix, hy, iy;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    fcomplex ans;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    x = F_RE(z);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    y = F_IM(z);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    hx = THE_WORD(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    ix = hx & 0x7fffffff;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    hy = THE_WORD(y);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    iy = hy & 0x7fffffff;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    x = fabsf(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    y = fabsf(y);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (iy == 0) {      /* ctanh(x,0) = (x,0) for x = 0 or NaN */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        F_RE(ans) = tanhf(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        F_IM(ans) = zero;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    } else if (iy >= 0x7f800000) {  /* y is inf or NaN */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (ix < 0x7f800000)    /* catanh(finite x,inf/nan) is nan */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            F_RE(ans) = F_IM(ans) = y - y;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        else if (ix == 0x7f800000) {    /* x is inf */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            F_RE(ans) = one;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            F_IM(ans) = zero;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            F_RE(ans) = x + y;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            F_IM(ans) = y - y;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    } else if (ix >= 0x41600000) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        /*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * |x| > 14 = prec/2 (14,28,34,60)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         * ctanh z ~ 1 + i (sin2y)/(exp(2x))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        F_RE(ans) = one;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (iy < 0x7f000000)    /* t = sin(2y) */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            S = sinf(y + y);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            (void) sincosf(y, &S, &C);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            S = (S + S) * C;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (ix >= 0x7f000000) { /* |x| > max/2 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            if (ix >= 0x7f800000) { /* |x| is inf or NaN */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                if (ix > 0x7f800000)    /* x is NaN */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                    F_RE(ans) = F_IM(ans) = x + y;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                    F_IM(ans) = zero * S;   /* x is inf */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            } else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                F_IM(ans) = S * expf(-x);   /* underflow */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            F_IM(ans) = (S + S) * expf(-(x + x));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                            /* 2 sin 2y / exp(2x) */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        /* INDENT OFF */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        /*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *                        t*t+2t
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *    ctanh z = ---------------------------
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *               t*t+[4(t+1)(cos y)](cos y)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *                  [4(t+1)(cos y)]*(sin y)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *              i --------------------------
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         *                t*t+[4(t+1)(cos y)](cos y)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis         */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        /* INDENT ON */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        (void) sincosf(y, &S, &C);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        t = expm1f(x + x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        r = (four * C) * (t + one);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        u = t * t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        v = one / (u + r * C);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        F_RE(ans) = (u + two * t) * v;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        F_IM(ans) = (r * S) * v;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (hx < 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        F_RE(ans) = -F_RE(ans);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (hy < 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        F_IM(ans) = -F_IM(ans);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    return (ans);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis}