math_base_inline.cc

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/* SPDX-FileCopyrightText: 2001-2002 NaN Holding BV. All rights reserved.
 *
 * SPDX-License-Identifier: GPL-2.0-or-later */

 
#ifndef __MATH_BASE_INLINE_C__
#define __MATH_BASE_INLINE_C__
 
#include <float.h>
#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
 
#include "BLI_assert.h"
#include "BLI_math_inline.h"
#include "BLI_sys_types.h"
 
/* copied from BLI_utildefines.h */
#ifdef __GNUC__
#  define UNLIKELY(x) __builtin_expect(!!(x), 0)
#else
#  define UNLIKELY(x) (x)
#endif
 
MINLINE float pow2f(float x)
{
  return x * x;
}
MINLINE float pow3f(float x)
{
  return pow2f(x) * x;
}
MINLINE float pow4f(float x)
{
  return pow2f(pow2f(x));
}
MINLINE float pow5f(float x)
{
  return pow4f(x) * x;
}
MINLINE float pow7f(float x)
{
  return pow2f(pow3f(x)) * x;
}
 
MINLINE float sqrt3f(float f)
{
  if (UNLIKELY(f == 0.0f)) {
    return 0.0f;
  }
  if (UNLIKELY(f < 0.0f)) {
    return -(float)(exp(log(-f) / 3.0));
  }
  return (float)(exp(log(f) / 3.0));
}
 
MINLINE double sqrt3d(double d)
{
  if (UNLIKELY(d == 0.0)) {
    return 0.0;
  }
  if (UNLIKELY(d < 0.0)) {
    return -exp(log(-d) / 3.0);
  }
  return exp(log(d) / 3.0);
}
 
MINLINE float sqrtf_signed(float f)
{
  return (f >= 0.0f) ? sqrtf(f) : -sqrtf(-f);
}
 
MINLINE float interpf(float target, float origin, float fac)
{
  return (fac * target) + (1.0f - fac) * origin;
}
 
MINLINE double interpd(double target, double origin, double fac)
{
  return (fac * target) + (1.0f - fac) * origin;
}
 
MINLINE float ratiof(float min, float max, float pos)
{
  float range = max - min;
  return range == 0 ? 0 : ((pos - min) / range);
}
 
MINLINE double ratiod(double min, double max, double pos)
{
  double range = max - min;
  return range == 0 ? 0 : ((pos - min) / range);
}
 
MINLINE float power_of_2(float val)
{
  return (float)pow(2.0, ceil(log((double)val) / M_LN2));
}
 
MINLINE int is_power_of_2_i(int n)
{
  return (n & (n - 1)) == 0;
}
 
MINLINE int power_of_2_max_i(int n)
{
  if (is_power_of_2_i(n)) {
    return n;
  }
 
  do {
    n = n & (n - 1);
  } while (!is_power_of_2_i(n));
 
  return n * 2;
}
 
MINLINE int power_of_2_min_i(int n)
{
  while (!is_power_of_2_i(n)) {
    n = n & (n - 1);
  }
 
  return n;
}
 
MINLINE unsigned int power_of_2_max_u(unsigned int x)
{
  x -= 1;
  x |= (x >> 1);
  x |= (x >> 2);
  x |= (x >> 4);
  x |= (x >> 8);
  x |= (x >> 16);
  return x + 1;
}
 
MINLINE unsigned int log2_floor_u(unsigned int x)
{
  return x <= 1 ? 0 : 1 + log2_floor_u(x >> 1);
}
 
MINLINE unsigned int log2_ceil_u(unsigned int x)
{
  if (is_power_of_2_i((int)x)) {
    return log2_floor_u(x);
  }
  return log2_floor_u(x) + 1;
}
 
/* rounding and clamping */
 
#define _round_clamp_fl_impl(arg, ty, min, max) \
  { \
    float r = floorf(arg + 0.5f); \
    if (UNLIKELY(r <= (float)min)) { \
      return (ty)min; \
    } \
    if (UNLIKELY(r >= (float)max)) { \
      return (ty)max; \
    } \
    return (ty)r; \
  }
 
#define _round_clamp_db_impl(arg, ty, min, max) \
  { \
    double r = floor(arg + 0.5); \
    if (UNLIKELY(r <= (double)min)) { \
      return (ty)min; \
    } \
    if (UNLIKELY(r >= (double)max)) { \
      return (ty)max; \
    } \
    return (ty)r; \
  }
 
#define _round_fl_impl(arg, ty) \
  { \
    return (ty)floorf(arg + 0.5f); \
  }
#define _round_db_impl(arg, ty) \
  { \
    return (ty)floor(arg + 0.5); \
  }
 
MINLINE unsigned char round_fl_to_uchar(float a){_round_fl_impl(a, unsigned char)} MINLINE
    short round_fl_to_short(float a){_round_fl_impl(a, short)} MINLINE
    int round_fl_to_int(float a){_round_fl_impl(a, int)} MINLINE
    unsigned int round_fl_to_uint(float a){_round_fl_impl(a, unsigned int)}
 
MINLINE int round_db_to_int(double a){_round_db_impl(a, int)}
 
#undef _round_fl_impl
#undef _round_db_impl
 
MINLINE unsigned char round_fl_to_uchar_clamp(float a){
    _round_clamp_fl_impl(a, unsigned char, 0, UCHAR_MAX)} MINLINE
    int round_fl_to_int_clamp(float a){_round_clamp_fl_impl(a, int, INT_MIN, INT_MAX)}
 
MINLINE unsigned char round_db_to_uchar_clamp(double a){
    _round_clamp_db_impl(a, unsigned char, 0, UCHAR_MAX)} MINLINE
    short round_db_to_short_clamp(double a){
        _round_clamp_db_impl(a, short, SHRT_MIN, SHRT_MAX)} MINLINE
    int round_db_to_int_clamp(double a){_round_clamp_db_impl(a, int, INT_MIN, INT_MAX)}
 
#undef _round_clamp_fl_impl
#undef _round_clamp_db_impl
 
MINLINE float round_to_even(float f)
{
  return roundf(f * 0.5f) * 2.0f;
}
 
MINLINE int divide_round_i(int a, int b)
{
  return (2 * a + b) / (2 * b);
}

MINLINE int divide_floor_i(int a, int b)
{
  int d = a / b;
  int r = a % b; /* Optimizes into a single division. */
  return r ? d - ((a < 0) ^ (b < 0)) : d;
}
 
MINLINE uint divide_ceil_u(uint a, uint b)
{
  return (a + b - 1) / b;
}
 
MINLINE uint64_t divide_ceil_ul(uint64_t a, uint64_t b)
{
  return (a + b - 1) / b;
}
 
MINLINE uint ceil_to_multiple_u(uint a, uint b)
{
  return divide_ceil_u(a, b) * b;
}
 
MINLINE uint64_t ceil_to_multiple_ul(uint64_t a, uint64_t b)
{
  return divide_ceil_ul(a, b) * b;
}
 
MINLINE int mod_i(int i, int n)
{
  return (i % n + n) % n;
}
 
MINLINE float floored_fmod(const float f, const float n)
{
  return f - n * floorf(f / n);
}
 
MINLINE float fractf(float a)
{
  return a - floorf(a);
}
 
/* Adapted from `godot-engine` math_funcs.h. */
MINLINE float wrapf(float value, float max, float min)
{
  float range = max - min;
  return (range != 0.0f) ? value - (range * floorf((value - min) / range)) : min;
}
 
MINLINE float pingpongf(float value, float scale)
{
  if (scale == 0.0f) {
    return 0.0f;
  }
  return fabsf(fractf((value - scale) / (scale * 2.0f)) * scale * 2.0f - scale);
}
 
/* Square. */
 
MINLINE int square_s(short a)
{
  return a * a;
}
 
MINLINE int square_i(int a)
{
  return a * a;
}
 
MINLINE unsigned int square_uint(unsigned int a)
{
  return a * a;
}
 
MINLINE float square_f(float a)
{
  return a * a;
}
 
/* Cube. */
 
MINLINE int cube_i(int a)
{
  return a * a * a;
}
 
MINLINE float cube_f(float a)
{
  return a * a * a;
}
 
/* Min/max */
 
MINLINE float min_ff(float a, float b)
{
  return (a < b) ? a : b;
}
MINLINE float max_ff(float a, float b)
{
  return (a > b) ? a : b;
}
/* See: https://www.iquilezles.org/www/articles/smin/smin.htm. */
MINLINE float smoothminf(float a, float b, float c)
{
  if (c != 0.0f) {
    float h = max_ff(c - fabsf(a - b), 0.0f) / c;
    return min_ff(a, b) - h * h * h * c * (1.0f / 6.0f);
  }
  return min_ff(a, b);
}
 
MINLINE float smoothstep(float edge0, float edge1, float x)
{
  float result;
  if (x < edge0) {
    result = 0.0f;
  }
  else if (x >= edge1) {
    result = 1.0f;
  }
  else {
    float t = (x - edge0) / (edge1 - edge0);
    result = (3.0f - 2.0f * t) * (t * t);
  }
  return result;
}
 
MINLINE double min_dd(double a, double b)
{
  return (a < b) ? a : b;
}
MINLINE double max_dd(double a, double b)
{
  return (a > b) ? a : b;
}
 
MINLINE int min_ii(int a, int b)
{
  return (a < b) ? a : b;
}
MINLINE int max_ii(int a, int b)
{
  return (b < a) ? a : b;
}
 
MINLINE uint min_uu(uint a, uint b)
{
  return (a < b) ? a : b;
}
MINLINE uint max_uu(uint a, uint b)
{
  return (b < a) ? a : b;
}
 
MINLINE unsigned long long min_ulul(unsigned long long a, unsigned long long b)
{
  return (a < b) ? a : b;
}
MINLINE unsigned long long max_ulul(unsigned long long a, unsigned long long b)
{
  return (b < a) ? a : b;
}
 
MINLINE double max_ddd(double a, double b, double c)
{
  return max_dd(max_dd(a, b), c);
}
 
MINLINE float min_fff(float a, float b, float c)
{
  return min_ff(min_ff(a, b), c);
}
MINLINE float max_fff(float a, float b, float c)
{
  return max_ff(max_ff(a, b), c);
}
 
MINLINE int min_iii(int a, int b, int c)
{
  return min_ii(min_ii(a, b), c);
}
MINLINE int max_iii(int a, int b, int c)
{
  return max_ii(max_ii(a, b), c);
}
 
MINLINE float min_ffff(float a, float b, float c, float d)
{
  return min_ff(min_fff(a, b, c), d);
}
MINLINE float max_ffff(float a, float b, float c, float d)
{
  return max_ff(max_fff(a, b, c), d);
}
 
MINLINE int min_iiii(int a, int b, int c, int d)
{
  return min_ii(min_iii(a, b, c), d);
}
MINLINE int max_iiii(int a, int b, int c, int d)
{
  return max_ii(max_iii(a, b, c), d);
}
 
MINLINE size_t min_zz(size_t a, size_t b)
{
  return (a < b) ? a : b;
}
MINLINE size_t max_zz(size_t a, size_t b)
{
  return (b < a) ? a : b;
}
 
MINLINE int clamp_i(int value, int min, int max)
{
  return min_ii(max_ii(value, min), max);
}
 
MINLINE float clamp_f(float value, float min, float max)
{
  if (value > max) {
    return max;
  }
  if (value < min) {
    return min;
  }
  return value;
}
 
MINLINE int compare_ff(float a, float b, const float max_diff)
{
  return fabsf(a - b) <= max_diff;
}
 
MINLINE uint ulp_diff_ff(float a, float b)
{
  BLI_assert(sizeof(float) == sizeof(uint));
 
  const uint sign_bit = 0x80000000;
  const uint infinity = 0x7f800000;
 
  union {
    float f;
    uint i;
  } ua, ub;
  ua.f = a;
  ub.f = b;
 
  const uint a_sign = ua.i & sign_bit;
  const uint b_sign = ub.i & sign_bit;
  const uint a_abs = ua.i & ~sign_bit;
  const uint b_abs = ub.i & ~sign_bit;
 
  if (a_abs > infinity || b_abs > infinity) {
    /* NaNs always return maximum ulps apart. */
    return 0xffffffff;
  }
  if (a_sign == b_sign) {
    const uint min_abs = a_abs < b_abs ? a_abs : b_abs;
    const uint max_abs = a_abs > b_abs ? a_abs : b_abs;
    return max_abs - min_abs;
  }
  return a_abs + b_abs;
}
 
MINLINE int compare_ff_relative(float a, float b, const float max_diff, const int max_ulps)
{
  BLI_assert(max_ulps >= 0 && max_ulps < (1 << 22));
 
  if (fabsf(a - b) <= max_diff) {
    return 1;
  }
 
  return (ulp_diff_ff(a, b) <= (uint)max_ulps) ? 1 : 0;
}
 
MINLINE bool compare_threshold_relative(const float value1, const float value2, const float thresh)
{
  const float abs_diff = fabsf(value1 - value2);
  /* Avoid letting the threshold get too small just because the values happen to be close to zero.
   */
  if (fabsf(value2) < 1) {
    return abs_diff > thresh;
  }
  /* Using relative threshold in general. */
  return abs_diff > thresh * fabsf(value2);
}
 
MINLINE float increment_ulp(const float value)
{
  if (!isfinite(value)) {
    return value;
  }
 
  union {
    float f;
    uint i;
  } v;
  v.f = value;
 
  if (v.f > 0.0f) {
    v.i += 1;
  }
  else if (v.f < -0.0f) {
    v.i -= 1;
  }
  else {
    v.i = 0x00000001;
  }
 
  return v.f;
}
 
MINLINE float decrement_ulp(const float value)
{
  if (!isfinite(value)) {
    return value;
  }
 
  union {
    float f;
    uint i;
  } v;
  v.f = value;
 
  if (v.f > 0.0f) {
    v.i -= 1;
  }
  else if (v.f < -0.0f) {
    v.i += 1;
  }
  else {
    v.i = 0x80000001;
  }
 
  return v.f;
}
 
MINLINE float signf(float f)
{
  return (f < 0.0f) ? -1.0f : 1.0f;
}
 
MINLINE float compatible_signf(float f)
{
  if (f > 0.0f) {
    return 1.0f;
  }
  if (f < 0.0f) {
    return -1.0f;
  }
  return 0.0f;
}
 
MINLINE int signum_i_ex(float a, float eps)
{
  if (a > eps) {
    return 1;
  }
  if (a < -eps) {
    return -1;
  }
  return 0;
}
 
MINLINE int signum_i(float a)
{
  if (a > 0.0f) {
    return 1;
  }
  if (a < 0.0f) {
    return -1;
  }
  return 0;
}
 
MINLINE int integer_digits_f(const float f)
{
  return (f == 0.0f) ? 0 : (int)floor(log10(fabs(f))) + 1;
}
 
MINLINE int integer_digits_d(const double d)
{
  return (d == 0.0) ? 0 : (int)floor(log10(fabs(d))) + 1;
}
 
MINLINE int integer_digits_i(const int i)
{
  return (int)log10((double)i) + 1;
}
 
/* Low level conversion functions */
MINLINE unsigned char unit_float_to_uchar_clamp(float val)
{
  return (unsigned char)((
      (val <= 0.0f) ? 0 : ((val > (1.0f - 0.5f / 255.0f)) ? 255 : ((255.0f * val) + 0.5f))));
}
 
MINLINE unsigned short unit_float_to_ushort_clamp(float val)
{
  return (unsigned short)((val >= 1.0f - 0.5f / 65535) ? 65535 :
                          (val <= 0.0f)                ? 0 :
                                                         (val * 65535.0f + 0.5f));
}
 
MINLINE unsigned char unit_ushort_to_uchar(unsigned short val)
{
  return (unsigned char)(((val) >= 65535 - 128) ? 255 : ((val) + 128) >> 8);
}
 
#define unit_float_to_uchar_clamp_v3(v1, v2) \
  { \
    (v1)[0] = unit_float_to_uchar_clamp((v2[0])); \
    (v1)[1] = unit_float_to_uchar_clamp((v2[1])); \
    (v1)[2] = unit_float_to_uchar_clamp((v2[2])); \
  } \
  ((void)0)
#define unit_float_to_uchar_clamp_v4(v1, v2) \
  { \
    (v1)[0] = unit_float_to_uchar_clamp((v2[0])); \
    (v1)[1] = unit_float_to_uchar_clamp((v2[1])); \
    (v1)[2] = unit_float_to_uchar_clamp((v2[2])); \
    (v1)[3] = unit_float_to_uchar_clamp((v2[3])); \
  } \
  ((void)0)
 
#endif /* __MATH_BASE_INLINE_C__ */