/*      $NetBSD: catrigf.c,v 1.2 2022/04/19 20:32:16 rillig Exp $       */
/*-
* Copyright (c) 2012 Stephen Montgomery-Smith <[email protected]>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
*    notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
*    notice, this list of conditions and the following disclaimer in the
*    documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/

/*
* The algorithm is very close to that in "Implementing the complex arcsine
* and arccosine functions using exception handling" by T. E. Hull, Thomas F.
* Fairgrieve, and Ping Tak Peter Tang, published in ACM Transactions on
* Mathematical Software, Volume 23 Issue 3, 1997, Pages 299-335,
* http://dl.acm.org/citation.cfm?id=275324.
*
* See catrig.c for complete comments.
*
* XXX comments were removed automatically, and even short ones on the right
* of statements were removed (all of them), contrary to normal style.  Only
* a few comments on the right of declarations remain.
*/

#include <sys/cdefs.h>
#if 0
__FBSDID("$FreeBSD: head/lib/msun/src/catrigf.c 275819 2014-12-16 09:21:56Z ed $");
#endif
__RCSID("$NetBSD: catrigf.c,v 1.2 2022/04/19 20:32:16 rillig Exp $");

#include "namespace.h"
#ifdef __weak_alias
__weak_alias(casinf, _casinf)
#endif
#ifdef __weak_alias
__weak_alias(catanf, _catanf)
#endif


#include <complex.h>
#include <float.h>

#include "math.h"
#include "math_private.h"

#undef isinf
#define isinf(x)        (fabsf(x) == INFINITY)
#undef isnan
#define isnan(x)        ((x) != (x))
#define raise_inexact() do { volatile float junk __unused = /*LINTED*/1 + tiny; } while (0)
#undef signbit
#define signbit(x)      (__builtin_signbitf(x))

static const float
A_crossover =           10,
B_crossover =           0.6417,
FOUR_SQRT_MIN =         0x1p-61,
QUARTER_SQRT_MAX =      0x1p61,
m_e =                   2.7182818285e0,         /*  0xadf854.0p-22 */
m_ln2 =                 6.9314718056e-1,        /*  0xb17218.0p-24 */
pio2_hi =               1.5707962513e0,         /*  0xc90fda.0p-23 */
RECIP_EPSILON =         1 / FLT_EPSILON,
SQRT_3_EPSILON =        5.9801995673e-4,        /*  0x9cc471.0p-34 */
SQRT_6_EPSILON =        8.4572793338e-4,        /*  0xddb3d7.0p-34 */
SQRT_MIN =              0x1p-63;

static const volatile float
pio2_lo =               7.5497899549e-8,        /*  0xa22169.0p-47 */
tiny =                  0x1p-100;

static float complex clog_for_large_values(float complex z);

static inline float
f(float a, float b, float hypot_a_b)
{
       if (b < 0)
               return ((hypot_a_b - b) / 2);
       if (b == 0)
               return (a / 2);
       return (a * a / (hypot_a_b + b) / 2);
}

static inline void
do_hard_work(float x, float y, float *rx, int *B_is_usable, float *B,
   float *sqrt_A2my2, float *new_y)
{
       float R, S, A;
       float Am1, Amy;

       R = hypotf(x, y + 1);
       S = hypotf(x, y - 1);

       A = (R + S) / 2;
       if (A < 1)
               A = 1;

       if (A < A_crossover) {
               if (y == 1 && x < FLT_EPSILON * FLT_EPSILON / 128) {
                       *rx = sqrtf(x);
               } else if (x >= FLT_EPSILON * fabsf(y - 1)) {
                       Am1 = f(x, 1 + y, R) + f(x, 1 - y, S);
                       *rx = log1pf(Am1 + sqrtf(Am1 * (A + 1)));
               } else if (y < 1) {
                       *rx = x / sqrtf((1 - y) * (1 + y));
               } else {
                       *rx = log1pf((y - 1) + sqrtf((y - 1) * (y + 1)));
               }
       } else {
               *rx = logf(A + sqrtf(A * A - 1));
       }

       *new_y = y;

       if (y < FOUR_SQRT_MIN) {
               *B_is_usable = 0;
               *sqrt_A2my2 = A * (2 / FLT_EPSILON);
               *new_y = y * (2 / FLT_EPSILON);
               return;
       }

       *B = y / A;
       *B_is_usable = 1;

       if (*B > B_crossover) {
               *B_is_usable = 0;
               if (y == 1 && x < FLT_EPSILON / 128) {
                       *sqrt_A2my2 = sqrtf(x) * sqrtf((A + y) / 2);
               } else if (x >= FLT_EPSILON * fabsf(y - 1)) {
                       Amy = f(x, y + 1, R) + f(x, y - 1, S);
                       *sqrt_A2my2 = sqrtf(Amy * (A + y));
               } else if (y > 1) {
                       *sqrt_A2my2 = x * (4 / FLT_EPSILON / FLT_EPSILON) * y /
                           sqrtf((y + 1) * (y - 1));
                       *new_y = y * (4 / FLT_EPSILON / FLT_EPSILON);
               } else {
                       *sqrt_A2my2 = sqrtf((1 - y) * (1 + y));
               }
       }
}

float complex
casinhf(float complex z)
{
       float x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y;
       int B_is_usable;
       float complex w;

       x = crealf(z);
       y = cimagf(z);
       ax = fabsf(x);
       ay = fabsf(y);

       if (isnan(x) || isnan(y)) {
               if (isinf(x))
                       return (CMPLXF(x, y + y));
               if (isinf(y))
                       return (CMPLXF(y, x + x));
               if (y == 0)
                       return (CMPLXF(x + x, y));
               return (CMPLXF(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
       }

       if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
               if (signbit(x) == 0)
                       w = clog_for_large_values(z) + m_ln2;
               else
                       w = clog_for_large_values(-z) + m_ln2;
               return (CMPLXF(copysignf(crealf(w), x),
                   copysignf(cimagf(w), y)));
       }

       if (x == 0 && y == 0)
               return (z);

       raise_inexact();

       if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
               return (z);

       do_hard_work(ax, ay, &rx, &B_is_usable, &B, &sqrt_A2my2, &new_y);
       if (B_is_usable)
               ry = asinf(B);
       else
               ry = atan2f(new_y, sqrt_A2my2);
       return (CMPLXF(copysignf(rx, x), copysignf(ry, y)));
}

float complex
casinf(float complex z)
{
       float complex w = casinhf(CMPLXF(cimagf(z), crealf(z)));

       return (CMPLXF(cimagf(w), crealf(w)));
}

float complex
cacosf(float complex z)
{
       float x, y, ax, ay, rx, ry, B, sqrt_A2mx2, new_x;
       int sx, sy;
       int B_is_usable;
       float complex w;

       x = crealf(z);
       y = cimagf(z);
       sx = signbit(x);
       sy = signbit(y);
       ax = fabsf(x);
       ay = fabsf(y);

       if (isnan(x) || isnan(y)) {
               if (isinf(x))
                       return (CMPLXF(y + y, -INFINITY));
               if (isinf(y))
                       return (CMPLXF(x + x, -y));
               if (x == 0)
                       return (CMPLXF(pio2_hi + pio2_lo, y + y));
               return (CMPLXF(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
       }

       if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
               w = clog_for_large_values(z);
               rx = fabsf(cimagf(w));
               ry = crealf(w) + m_ln2;
               if (sy == 0)
                       ry = -ry;
               return (CMPLXF(rx, ry));
       }

       if (x == 1 && y == 0)
               return (CMPLXF(0, -y));

       raise_inexact();

       if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
               return (CMPLXF(pio2_hi - (x - pio2_lo), -y));

       do_hard_work(ay, ax, &ry, &B_is_usable, &B, &sqrt_A2mx2, &new_x);
       if (B_is_usable) {
               if (sx == 0)
                       rx = acosf(B);
               else
                       rx = acosf(-B);
       } else {
               if (sx == 0)
                       rx = atan2f(sqrt_A2mx2, new_x);
               else
                       rx = atan2f(sqrt_A2mx2, -new_x);
       }
       if (sy == 0)
               ry = -ry;
       return (CMPLXF(rx, ry));
}

float complex
cacoshf(float complex z)
{
       float complex w;
       float rx, ry;

       w = cacosf(z);
       rx = crealf(w);
       ry = cimagf(w);
       if (isnan(rx) && isnan(ry))
               return (CMPLXF(ry, rx));
       if (isnan(rx))
               return (CMPLXF(fabsf(ry), rx));
       if (isnan(ry))
               return (CMPLXF(ry, ry));
       return (CMPLXF(fabsf(ry), copysignf(rx, cimagf(z))));
}

static float complex
clog_for_large_values(float complex z)
{
       float x, y;
       float ax, ay, t;

       x = crealf(z);
       y = cimagf(z);
       ax = fabsf(x);
       ay = fabsf(y);
       if (ax < ay) {
               t = ax;
               ax = ay;
               ay = t;
       }

       if (ax > FLT_MAX / 2)
               return (CMPLXF(logf(hypotf(x / m_e, y / m_e)) + 1,
                   atan2f(y, x)));

       if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN)
               return (CMPLXF(logf(hypotf(x, y)), atan2f(y, x)));

       return (CMPLXF(logf(ax * ax + ay * ay) / 2, atan2f(y, x)));
}

static inline float
sum_squares(float x, float y)
{

       if (y < SQRT_MIN)
               return (x * x);

       return (x * x + y * y);
}

static inline float
real_part_reciprocal(float x, float y)
{
       float scale;
       uint32_t hx, hy;
       int32_t ix, iy;

       GET_FLOAT_WORD(hx, x);
       ix = hx & 0x7f800000;
       GET_FLOAT_WORD(hy, y);
       iy = hy & 0x7f800000;
#define BIAS    (FLT_MAX_EXP - 1)
#define CUTOFF  (FLT_MANT_DIG / 2 + 1)
       if (ix - iy >= CUTOFF << 23 || isinf(x))
               return (1 / x);
       if (iy - ix >= CUTOFF << 23)
               return (x / y / y);
       if (ix <= (BIAS + FLT_MAX_EXP / 2 - CUTOFF) << 23)
               return (x / (x * x + y * y));
       SET_FLOAT_WORD(scale, 0x7f800000 - ix);
       x *= scale;
       y *= scale;
       return (x / (x * x + y * y) * scale);
}

float complex
catanhf(float complex z)
{
       float x, y, ax, ay, rx, ry;

       x = crealf(z);
       y = cimagf(z);
       ax = fabsf(x);
       ay = fabsf(y);

       if (y == 0 && ax <= 1)
               return (CMPLXF(atanhf(x), y));

       if (x == 0)
               return (CMPLXF(x, atanf(y)));

       if (isnan(x) || isnan(y)) {
               if (isinf(x))
                       return (CMPLXF(copysignf(0, x), y + y));
               if (isinf(y))
                       return (CMPLXF(copysignf(0, x),
                           copysignf(pio2_hi + pio2_lo, y)));
               return (CMPLXF(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
       }

       if (ax > RECIP_EPSILON || ay > RECIP_EPSILON)
               return (CMPLXF(real_part_reciprocal(x, y),
                   copysignf(pio2_hi + pio2_lo, y)));

       if (ax < SQRT_3_EPSILON / 2 && ay < SQRT_3_EPSILON / 2) {
               raise_inexact();
               return (z);
       }

       if (ax == 1 && ay < FLT_EPSILON)
               rx = (m_ln2 - logf(ay)) / 2;
       else
               rx = log1pf(4 * ax / sum_squares(ax - 1, ay)) / 4;

       if (ax == 1)
               ry = atan2f(2, -ay) / 2;
       else if (ay < FLT_EPSILON)
               ry = atan2f(2 * ay, (1 - ax) * (1 + ax)) / 2;
       else
               ry = atan2f(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2;

       return (CMPLXF(copysignf(rx, x), copysignf(ry, y)));
}

float complex
catanf(float complex z)
{
       float complex w = catanhf(CMPLXF(cimagf(z), crealf(z)));

       return (CMPLXF(cimagf(w), crealf(w)));
}

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