common/complex/csqrtl.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 __csqrtl = csqrtl
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "libm.h"       /* fabsl/isinfl/sqrtl */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "complex_wrapper.h"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "longdouble.h"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* INDENT OFF */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisstatic const long double
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    twom9001 = 2.6854002716003034957421765100615693043656e-2710L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    twom4500 = 2.3174987687592429423263242862381544149252e-1355L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    two8999 = 9.3095991180122343502582347372163290310934e+2708L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    two4500 = 4.3149968987270974283777803545571722250806e+1354L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    zero = 0.0L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    half = 0.5L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    two = 2.0L;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* INDENT ON */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisldcomplex
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtiscsqrtl(ldcomplex z) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    ldcomplex ans;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    long double x, y, t, ax, ay;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    int n, ix, iy, hx, hy;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    x = LD_RE(z);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    y = LD_IM(z);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    hx = HI_XWORD(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    hy = HI_XWORD(y);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    ix = hx & 0x7fffffff;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    iy = hy & 0x7fffffff;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    ay = fabsl(y);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    ax = fabsl(x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (ix >= 0x7fff0000 || iy >= 0x7fff0000) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        /* x or y is Inf or NaN */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (isinfl(y))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_IM(ans) = LD_RE(ans) = ay;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        else if (isinfl(x)) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            if (hx > 0) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                LD_RE(ans) = ax;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                LD_IM(ans) = ay * zero;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                LD_RE(ans) = ay * zero;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                LD_IM(ans) = ax;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_IM(ans) = LD_RE(ans) = ax + ay;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    } else if (y == zero) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (hx >= 0) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_RE(ans) = sqrtl(ax);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_IM(ans) = zero;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_IM(ans) = sqrtl(ax);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_RE(ans) = zero;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    } else if (ix >= iy) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        n = (ix - iy) >> 16;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#if defined(__x86)      /* 64 significant bits */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (n >= 35)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#else               /* 113 significant bits  */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (n >= 60)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#endif
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            t = sqrtl(ax);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        else if (ix >= 0x5f3f0000) {    /* x > 2**8000 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            ax *= twom9001;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            y *= twom9001;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            t = two4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else if (iy <= 0x20bf0000) {  /* y < 2**-8000 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            ax *= two8999;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            y *= two8999;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            t = twom4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            t = sqrtl(half * (ax + sqrtl(ax * ax + y * y)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (hx >= 0) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_RE(ans) = t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_IM(ans) = ay / (t + t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_IM(ans) = t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_RE(ans) = ay / (t + t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        n = (iy - ix) >> 16;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#if defined(__x86)      /* 64 significant bits */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (n >= 35) {  /* } */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#else               /* 113 significant bits  */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (n >= 60) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#endif
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            if (n >= 120)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                t = sqrtl(half * ay);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            else if (iy >= 0x7ffe0000)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                t = sqrtl(half * ay + half * ax);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            else if (ix <= 0x00010000)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                t = half * (sqrtl(two * (ax + ay)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis                t = sqrtl(half * (ax + ay));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else if (iy >= 0x5f3f0000) {  /* y > 2**8000 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            ax *= twom9001;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            y *= twom9001;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            t = two4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else if (ix <= 0x20bf0000) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            ax *= two8999;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            y *= two8999;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            t = twom4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            t = sqrtl(half * (ax + sqrtl(ax * ax + y * y)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        if (hx >= 0) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_RE(ans) = t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_IM(ans) = ay / (t + t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_IM(ans) = t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis            LD_RE(ans) = ay / (t + t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    if (hy < 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis        LD_IM(ans) = -LD_IM(ans);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis    return (ans);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis}