452 lines
14 KiB
C
452 lines
14 KiB
C
/* SPDX-FileCopyrightText: 2001-2002 NaN Holding BV. All rights reserved.
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*
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* SPDX-License-Identifier: GPL-2.0-or-later */
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#pragma once
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/** \file
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* \ingroup bli
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*
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* \section mathabbrev Abbreviations
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*
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* - `fl` = `float`.
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* - `db` = `double`.
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* - `v2` = `vec2` = vector 2.
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* - `v3` = `vec3` = vector 3.
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* - `v4` = `vec4` = vector 4.
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* - `vn` = `vec4q = vector N dimensions, *passed as an arg, after the vector*..
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* - `qt` = `quat` = quaternion.
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* - `dq` = `dquat` = dual quaternion.
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* - `m2` = `mat2` = matrix 2x2.
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* - `m3` = `mat3` = matrix 3x3.
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* - `m4` = `mat4` = matrix 4x4.
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* - `eul` = `euler` rotation.
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* - `eulO` = `euler` with order.
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* - `plane` = `plane 4`, (vec3, distance).
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* - `plane3` = `plane 3`, (same as a `plane` with a zero 4th component).
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*
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* \subsection mathabbrev_all Function Type Abbreviations
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*
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* For non float versions of functions (which typically operate on floats),
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* use single suffix abbreviations.
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*
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* - `_d` = double
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* - `_i` = int
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* - `_u` = unsigned int
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* - `_char` = char
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* - `_uchar` = unsigned char
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*
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* \section mathvarnames Variable Names
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*
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* - f = single value
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* - a, b, c = vectors
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* - r = result vector
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* - A, B, C = matrices
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* - R = result matrix
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*/
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#if defined(_MSC_VER) && !defined(_USE_MATH_DEFINES)
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# define _USE_MATH_DEFINES
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#endif
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#include "BLI_assert.h"
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#include "BLI_math_inline.h"
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#include "BLI_sys_types.h"
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#include <math.h>
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#ifndef M_PI
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# define M_PI 3.14159265358979323846 /* pi */
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#endif
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#ifndef M_PI_2
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# define M_PI_2 1.57079632679489661923 /* pi/2 */
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#endif
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#ifndef M_PI_4
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# define M_PI_4 0.78539816339744830962 /* pi/4 */
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#endif
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#ifndef M_SQRT2
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# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
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#endif
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#ifndef M_SQRT1_2
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# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
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#endif
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#ifndef M_SQRT3
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# define M_SQRT3 1.73205080756887729352 /* sqrt(3) */
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#endif
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#ifndef M_SQRT1_3
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# define M_SQRT1_3 0.57735026918962576450 /* 1/sqrt(3) */
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#endif
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#ifndef M_1_PI
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# define M_1_PI 0.318309886183790671538 /* 1/pi */
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#endif
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#ifndef M_E
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# define M_E 2.7182818284590452354 /* e */
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#endif
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#ifndef M_LOG2E
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# define M_LOG2E 1.4426950408889634074 /* log_2 e */
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#endif
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#ifndef M_LOG10E
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# define M_LOG10E 0.43429448190325182765 /* log_10 e */
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#endif
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#ifndef M_LN2
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# define M_LN2 0.69314718055994530942 /* log_e 2 */
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#endif
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#ifndef M_LN10
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# define M_LN10 2.30258509299404568402 /* log_e 10 */
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#endif
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#if defined(__GNUC__)
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# define NAN_FLT __builtin_nanf("")
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#else /* evil quiet NaN definition */
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static const int NAN_INT = 0x7FC00000;
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# define NAN_FLT (*((float *)(&NAN_INT)))
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#endif
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#if BLI_MATH_DO_INLINE
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# include "intern/math_base_inline.c"
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#endif
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#ifdef BLI_MATH_GCC_WARN_PRAGMA
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# pragma GCC diagnostic push
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# pragma GCC diagnostic ignored "-Wredundant-decls"
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#endif
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#ifdef __cplusplus
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extern "C" {
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#endif
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/******************************* Float ******************************/
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/* `powf` is really slow for raising to integer powers. */
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MINLINE float pow2f(float x);
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MINLINE float pow3f(float x);
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MINLINE float pow4f(float x);
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MINLINE float pow7f(float x);
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MINLINE float sqrt3f(float f);
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MINLINE double sqrt3d(double d);
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MINLINE float sqrtf_signed(float f);
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MINLINE float saacosf(float f);
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MINLINE float saasinf(float f);
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MINLINE float sasqrtf(float f);
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MINLINE float saacos(float fac);
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MINLINE float saasin(float fac);
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MINLINE float sasqrt(float fac);
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/* Compute linear interpolation (lerp) between origin and target. */
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MINLINE float interpf(float target, float origin, float t);
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MINLINE double interpd(double target, double origin, double t);
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MINLINE float ratiof(float min, float max, float pos);
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MINLINE double ratiod(double min, double max, double pos);
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/**
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* Map a normalized value, i.e. from interval [0, 1] to interval [a, b].
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*/
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MINLINE float scalenorm(float a, float b, float x);
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/**
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* Map a normalized value, i.e. from interval [0, 1] to interval [a, b].
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*/
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MINLINE double scalenormd(double a, double b, double x);
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/* NOTE: Compilers will up-cast all types smaller than int to int when performing arithmetic
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* operation. */
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MINLINE int square_s(short a);
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MINLINE int square_uchar(unsigned char a);
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MINLINE int cube_s(short a);
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MINLINE int cube_uchar(unsigned char a);
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MINLINE int square_i(int a);
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MINLINE unsigned int square_uint(unsigned int a);
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MINLINE float square_f(float a);
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MINLINE double square_d(double a);
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MINLINE int cube_i(int a);
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MINLINE unsigned int cube_uint(unsigned int a);
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MINLINE float cube_f(float a);
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MINLINE double cube_d(double a);
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MINLINE float min_ff(float a, float b);
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MINLINE float max_ff(float a, float b);
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MINLINE float min_fff(float a, float b, float c);
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MINLINE float max_fff(float a, float b, float c);
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MINLINE float min_ffff(float a, float b, float c, float d);
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MINLINE float max_ffff(float a, float b, float c, float d);
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MINLINE double min_dd(double a, double b);
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MINLINE double max_dd(double a, double b);
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MINLINE double min_ddd(double a, double b, double c);
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MINLINE double max_ddd(double a, double b, double c);
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MINLINE int min_ii(int a, int b);
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MINLINE int max_ii(int a, int b);
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MINLINE int min_iii(int a, int b, int c);
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MINLINE int max_iii(int a, int b, int c);
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MINLINE int min_iiii(int a, int b, int c, int d);
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MINLINE int max_iiii(int a, int b, int c, int d);
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MINLINE uint min_uu(uint a, uint b);
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MINLINE uint max_uu(uint a, uint b);
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MINLINE size_t min_zz(size_t a, size_t b);
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MINLINE size_t max_zz(size_t a, size_t b);
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MINLINE char min_cc(char a, char b);
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MINLINE char max_cc(char a, char b);
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MINLINE int clamp_i(int value, int min, int max);
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MINLINE float clamp_f(float value, float min, float max);
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MINLINE size_t clamp_z(size_t value, size_t min, size_t max);
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/**
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* Almost-equal for IEEE floats, using absolute difference method.
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*
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* \param max_diff: the maximum absolute difference.
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*/
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MINLINE int compare_ff(float a, float b, float max_diff);
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/**
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* Computes the distance between two floats in ulps.
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*
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* In other words, returns zero if the floats are exactly equal, and
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* otherwise returns 1 plus the number of (unique) representable floats
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* between `a` and `b` on the number line.
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*
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* Notes:
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* - The order of `a` and `b` doesn't matter. The returned value is the
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* absolute difference.
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* - Unlike many ulp difference functions, this function handles the
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* difference between positive and negative floats in a meaningful way.
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* It returns the number (plus 1) of representable floats between those
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* two values as they would be arranged on a number line.
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* - Zero and negative zero are *not* considered unique from each other.
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* They are counted together as a single float in the difference.
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* - NaNs are not handled meaningfully. If either number is NaN, this
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* function returns uint max (0xffffffff).
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*/
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MINLINE uint ulp_diff_ff(float a, float b);
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/**
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* Almost-equal for IEEE floats, using their integer representation
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* (mixing ULP and absolute difference methods).
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*
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* \param max_diff: is the maximum absolute difference (allows to take care of the near-zero area,
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* where relative difference methods cannot really work).
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* \param max_ulps: is the 'maximum number of floats + 1'
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* allowed between \a a and \a b to consider them equal.
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*
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* \see https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
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*/
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MINLINE int compare_ff_relative(float a, float b, float max_diff, int max_ulps);
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MINLINE bool compare_threshold_relative(float value1, float value2, float thresh);
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MINLINE float signf(float f);
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MINLINE int signum_i_ex(float a, float eps);
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MINLINE int signum_i(float a);
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/**
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* Used for zoom values.
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*/
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MINLINE float power_of_2(float f);
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/**
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* Returns number of (base ten) *significant* digits of integer part of given float
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* (negative in case of decimal-only floats, 0.01 returns -1 e.g.).
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*/
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MINLINE int integer_digits_f(float f);
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/**
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* Returns number of (base ten) *significant* digits of integer part of given double
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* (negative in case of decimal-only floats, 0.01 returns -1 e.g.).
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*/
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MINLINE int integer_digits_d(double d);
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MINLINE int integer_digits_i(int i);
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/* These don't really fit anywhere but were being copied about a lot. */
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MINLINE int is_power_of_2_i(int n);
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MINLINE unsigned int log2_floor_u(unsigned int x);
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MINLINE unsigned int log2_ceil_u(unsigned int x);
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/**
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* Returns next (or previous) power of 2 or the input number if it is already a power of 2.
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*/
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MINLINE int power_of_2_max_i(int n);
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MINLINE int power_of_2_min_i(int n);
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MINLINE unsigned int power_of_2_max_u(unsigned int x);
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MINLINE unsigned int power_of_2_min_u(unsigned int x);
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/**
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* Integer division that rounds 0.5 up, particularly useful for color blending
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* with integers, to avoid gradual darkening when rounding down.
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*/
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MINLINE int divide_round_i(int a, int b);
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/**
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* Integer division that returns the ceiling, instead of flooring like normal C division.
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*/
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MINLINE uint divide_ceil_u(uint a, uint b);
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MINLINE uint64_t divide_ceil_ul(uint64_t a, uint64_t b);
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/**
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* Returns \a a if it is a multiple of \a b or the next multiple or \a b after \b a .
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*/
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MINLINE uint ceil_to_multiple_u(uint a, uint b);
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MINLINE uint64_t ceil_to_multiple_ul(uint64_t a, uint64_t b);
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/**
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* modulo that handles negative numbers, works the same as Python's.
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*/
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MINLINE int mod_i(int i, int n);
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/**
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* Modulo that returns a positive result, regardless of the sign of \a f.
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*
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* For example, mod_f_positive(-0.1, 1.0) => 0.9.
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*
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* \returns a float in the interval [0, n).
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*/
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MINLINE float mod_f_positive(float f, float n);
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/**
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* Round to closest even number, halfway cases are rounded away from zero.
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*/
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MINLINE float round_to_even(float f);
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MINLINE signed char round_fl_to_char(float a);
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MINLINE unsigned char round_fl_to_uchar(float a);
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MINLINE short round_fl_to_short(float a);
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MINLINE unsigned short round_fl_to_ushort(float a);
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MINLINE int round_fl_to_int(float a);
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MINLINE unsigned int round_fl_to_uint(float a);
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MINLINE signed char round_db_to_char(double a);
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MINLINE unsigned char round_db_to_uchar(double a);
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MINLINE short round_db_to_short(double a);
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MINLINE unsigned short round_db_to_ushort(double a);
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MINLINE int round_db_to_int(double a);
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MINLINE unsigned int round_db_to_uint(double a);
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MINLINE signed char round_fl_to_char_clamp(float a);
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MINLINE unsigned char round_fl_to_uchar_clamp(float a);
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MINLINE short round_fl_to_short_clamp(float a);
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MINLINE unsigned short round_fl_to_ushort_clamp(float a);
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MINLINE int round_fl_to_int_clamp(float a);
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MINLINE unsigned int round_fl_to_uint_clamp(float a);
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MINLINE signed char round_db_to_char_clamp(double a);
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MINLINE unsigned char round_db_to_uchar_clamp(double a);
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MINLINE short round_db_to_short_clamp(double a);
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MINLINE unsigned short round_db_to_ushort_clamp(double a);
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MINLINE int round_db_to_int_clamp(double a);
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MINLINE unsigned int round_db_to_uint_clamp(double a);
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int pow_i(int base, int exp);
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/**
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* \param ndigits: must be between 0 and 21.
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*/
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double double_round(double x, int ndigits);
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/**
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* Floor to the nearest power of 10, e.g.:
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* - 15.0 -> 10.0
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* - 0.015 -> 0.01
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* - 1.0 -> 1.0
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*
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* \param f: Value to floor, must be over 0.0.
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* \note If we wanted to support signed values we could if this becomes necessary.
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*/
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float floor_power_of_10(float f);
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/**
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* Ceiling to the nearest power of 10, e.g.:
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* - 15.0 -> 100.0
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* - 0.015 -> 0.1
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* - 1.0 -> 1.0
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*
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* \param f: Value to ceiling, must be over 0.0.
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* \note If we wanted to support signed values we could if this becomes necessary.
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*/
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float ceil_power_of_10(float f);
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#ifdef BLI_MATH_GCC_WARN_PRAGMA
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# pragma GCC diagnostic pop
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#endif
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/* Asserts, some math functions expect normalized inputs
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* check the vector is unit length, or zero length (which can't be helped in some cases). */
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#ifndef NDEBUG
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/** \note 0.0001 is too small because normals may be converted from short's: see #34322. */
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# define BLI_ASSERT_UNIT_EPSILON 0.0002f
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# define BLI_ASSERT_UNIT_EPSILON_DB 0.0002
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/**
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* \note Checks are flipped so NAN doesn't assert.
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* This is done because we're making sure the value was normalized and in the case we
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* don't want NAN to be raising asserts since there is nothing to be done in that case.
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*/
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# define BLI_ASSERT_UNIT_V3(v) \
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{ \
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const float _test_unit = len_squared_v3(v); \
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BLI_assert(!(fabsf(_test_unit - 1.0f) >= BLI_ASSERT_UNIT_EPSILON) || \
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!(fabsf(_test_unit) >= BLI_ASSERT_UNIT_EPSILON)); \
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} \
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(void)0
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# define BLI_ASSERT_UNIT_V3_DB(v) \
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{ \
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const double _test_unit = len_squared_v3_db(v); \
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BLI_assert(!(fabs(_test_unit - 1.0) >= BLI_ASSERT_UNIT_EPSILON_DB) || \
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!(fabs(_test_unit) >= BLI_ASSERT_UNIT_EPSILON_DB)); \
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} \
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(void)0
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# define BLI_ASSERT_UNIT_V2(v) \
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{ \
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const float _test_unit = len_squared_v2(v); \
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BLI_assert(!(fabsf(_test_unit - 1.0f) >= BLI_ASSERT_UNIT_EPSILON) || \
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!(fabsf(_test_unit) >= BLI_ASSERT_UNIT_EPSILON)); \
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} \
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(void)0
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# define BLI_ASSERT_UNIT_QUAT(q) \
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{ \
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const float _test_unit = dot_qtqt(q, q); \
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BLI_assert(!(fabsf(_test_unit - 1.0f) >= BLI_ASSERT_UNIT_EPSILON * 10) || \
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!(fabsf(_test_unit) >= BLI_ASSERT_UNIT_EPSILON * 10)); \
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} \
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(void)0
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# define BLI_ASSERT_ZERO_M3(m) \
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{ \
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BLI_assert(dot_vn_vn((const float *)m, (const float *)m, 9) != 0.0); \
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} \
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(void)0
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# define BLI_ASSERT_ZERO_M4(m) \
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{ \
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BLI_assert(dot_vn_vn((const float *)m, (const float *)m, 16) != 0.0); \
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} \
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(void)0
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# define BLI_ASSERT_UNIT_M3(m) \
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{ \
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BLI_ASSERT_UNIT_V3((m)[0]); \
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BLI_ASSERT_UNIT_V3((m)[1]); \
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BLI_ASSERT_UNIT_V3((m)[2]); \
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} \
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(void)0
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#else
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# define BLI_ASSERT_UNIT_V2(v) (void)(v)
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# define BLI_ASSERT_UNIT_V3(v) (void)(v)
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# define BLI_ASSERT_UNIT_V3_DB(v) (void)(v)
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# define BLI_ASSERT_UNIT_QUAT(v) (void)(v)
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# define BLI_ASSERT_ZERO_M3(m) (void)(m)
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# define BLI_ASSERT_ZERO_M4(m) (void)(m)
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# define BLI_ASSERT_UNIT_M3(m) (void)(m)
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#endif
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#ifdef __cplusplus
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}
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#endif
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