/***************************************************************************/ /* */ /* fttrigon.c */ /* */ /* FreeType trigonometric functions (body). */ /* */ /* Copyright 2001-2005, 2012-2013 by */ /* David Turner, Robert Wilhelm, and Werner Lemberg. */ /* */ /* This file is part of the FreeType project, and may only be used, */ /* modified, and distributed under the terms of the FreeType project */ /* license, LICENSE.TXT. By continuing to use, modify, or distribute */ /* this file you indicate that you have read the license and */ /* understand and accept it fully. */ /* */ /***************************************************************************/ #include "sw_ft_math.h" #include //form https://github.com/chromium/chromium/blob/59afd8336009c9d97c22854c52e0382b62b3aa5e/third_party/abseil-cpp/absl/base/internal/bits.h #if defined(_MSC_VER) #include static unsigned int __inline clz(unsigned int x) { unsigned long r = 0; if (x != 0) { _BitScanReverse(&r, x); } return r; } #define SW_FT_MSB(x) (clz(x)) #elif defined(__GNUC__) #define SW_FT_MSB(x) (31 - __builtin_clz(x)) #else static unsigned int __inline clz(unsigned int x) { int c = 31; x &= ~x + 1; if (n & 0x0000FFFF) c -= 16; if (n & 0x00FF00FF) c -= 8; if (n & 0x0F0F0F0F) c -= 4; if (n & 0x33333333) c -= 2; if (n & 0x55555555) c -= 1; return c; } #define SW_FT_MSB(x) (clz(x)) #endif #define SW_FT_PAD_FLOOR(x, n) ((x) & ~((n)-1)) #define SW_FT_PAD_ROUND(x, n) SW_FT_PAD_FLOOR((x) + ((n) / 2), n) #define SW_FT_PAD_CEIL(x, n) SW_FT_PAD_FLOOR((x) + ((n)-1), n) #define SW_FT_BEGIN_STMNT do { #define SW_FT_END_STMNT \ } \ while (0) /* transfer sign leaving a positive number */ #define SW_FT_MOVE_SIGN(x, s) \ SW_FT_BEGIN_STMNT \ if (x < 0) { \ x = -x; \ s = -s; \ } \ SW_FT_END_STMNT SW_FT_Long SW_FT_MulFix(SW_FT_Long a, SW_FT_Long b) { SW_FT_Int s = 1; SW_FT_Long c; SW_FT_MOVE_SIGN(a, s); SW_FT_MOVE_SIGN(b, s); c = (SW_FT_Long)(((SW_FT_Int64)a * b + 0x8000L) >> 16); return (s > 0) ? c : -c; } SW_FT_Long SW_FT_MulDiv(SW_FT_Long a, SW_FT_Long b, SW_FT_Long c) { SW_FT_Int s = 1; SW_FT_Long d; SW_FT_MOVE_SIGN(a, s); SW_FT_MOVE_SIGN(b, s); SW_FT_MOVE_SIGN(c, s); d = (SW_FT_Long)(c > 0 ? ((SW_FT_Int64)a * b + (c >> 1)) / c : 0x7FFFFFFFL); return (s > 0) ? d : -d; } SW_FT_Long SW_FT_DivFix(SW_FT_Long a, SW_FT_Long b) { SW_FT_Int s = 1; SW_FT_Long q; SW_FT_MOVE_SIGN(a, s); SW_FT_MOVE_SIGN(b, s); q = (SW_FT_Long)(b > 0 ? (((SW_FT_UInt64)a << 16) + (b >> 1)) / b : 0x7FFFFFFFL); return (s < 0 ? -q : q); } /*************************************************************************/ /* */ /* This is a fixed-point CORDIC implementation of trigonometric */ /* functions as well as transformations between Cartesian and polar */ /* coordinates. The angles are represented as 16.16 fixed-point values */ /* in degrees, i.e., the angular resolution is 2^-16 degrees. Note that */ /* only vectors longer than 2^16*180/pi (or at least 22 bits) on a */ /* discrete Cartesian grid can have the same or better angular */ /* resolution. Therefore, to maintain this precision, some functions */ /* require an interim upscaling of the vectors, whereas others operate */ /* with 24-bit long vectors directly. */ /* */ /*************************************************************************/ /* the Cordic shrink factor 0.858785336480436 * 2^32 */ #define SW_FT_TRIG_SCALE 0xDBD95B16UL /* the highest bit in overflow-safe vector components, */ /* MSB of 0.858785336480436 * sqrt(0.5) * 2^30 */ #define SW_FT_TRIG_SAFE_MSB 29 /* this table was generated for SW_FT_PI = 180L << 16, i.e. degrees */ #define SW_FT_TRIG_MAX_ITERS 23 static const SW_FT_Fixed ft_trig_arctan_table[] = { 1740967L, 919879L, 466945L, 234379L, 117304L, 58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L, 57L, 29L, 14L, 7L, 4L, 2L, 1L}; /* multiply a given value by the CORDIC shrink factor */ static SW_FT_Fixed ft_trig_downscale(SW_FT_Fixed val) { SW_FT_Fixed s; SW_FT_Int64 v; s = val; val = SW_FT_ABS(val); v = (val * (SW_FT_Int64)SW_FT_TRIG_SCALE) + 0x100000000UL; val = (SW_FT_Fixed)(v >> 32); return (s >= 0) ? val : -val; } /* undefined and never called for zero vector */ static SW_FT_Int ft_trig_prenorm(SW_FT_Vector* vec) { SW_FT_Pos x, y; SW_FT_Int shift; x = vec->x; y = vec->y; shift = SW_FT_MSB(SW_FT_ABS(x) | SW_FT_ABS(y)); if (shift <= SW_FT_TRIG_SAFE_MSB) { shift = SW_FT_TRIG_SAFE_MSB - shift; vec->x = (SW_FT_Pos)((SW_FT_ULong)x << shift); vec->y = (SW_FT_Pos)((SW_FT_ULong)y << shift); } else { shift -= SW_FT_TRIG_SAFE_MSB; vec->x = x >> shift; vec->y = y >> shift; shift = -shift; } return shift; } static void ft_trig_pseudo_rotate(SW_FT_Vector* vec, SW_FT_Angle theta) { SW_FT_Int i; SW_FT_Fixed x, y, xtemp, b; const SW_FT_Fixed* arctanptr; x = vec->x; y = vec->y; /* Rotate inside [-PI/4,PI/4] sector */ while (theta < -SW_FT_ANGLE_PI4) { xtemp = y; y = -x; x = xtemp; theta += SW_FT_ANGLE_PI2; } while (theta > SW_FT_ANGLE_PI4) { xtemp = -y; y = x; x = xtemp; theta -= SW_FT_ANGLE_PI2; } arctanptr = ft_trig_arctan_table; /* Pseudorotations, with right shifts */ for (i = 1, b = 1; i < SW_FT_TRIG_MAX_ITERS; b <<= 1, i++) { SW_FT_Fixed v1 = ((y + b) >> i); SW_FT_Fixed v2 = ((x + b) >> i); if (theta < 0) { xtemp = x + v1; y = y - v2; x = xtemp; theta += *arctanptr++; } else { xtemp = x - v1; y = y + v2; x = xtemp; theta -= *arctanptr++; } } vec->x = x; vec->y = y; } static void ft_trig_pseudo_polarize(SW_FT_Vector* vec) { SW_FT_Angle theta; SW_FT_Int i; SW_FT_Fixed x, y, xtemp, b; const SW_FT_Fixed* arctanptr; x = vec->x; y = vec->y; /* Get the vector into [-PI/4,PI/4] sector */ if (y > x) { if (y > -x) { theta = SW_FT_ANGLE_PI2; xtemp = y; y = -x; x = xtemp; } else { theta = y > 0 ? SW_FT_ANGLE_PI : -SW_FT_ANGLE_PI; x = -x; y = -y; } } else { if (y < -x) { theta = -SW_FT_ANGLE_PI2; xtemp = -y; y = x; x = xtemp; } else { theta = 0; } } arctanptr = ft_trig_arctan_table; /* Pseudorotations, with right shifts */ for (i = 1, b = 1; i < SW_FT_TRIG_MAX_ITERS; b <<= 1, i++) { SW_FT_Fixed v1 = ((y + b) >> i); SW_FT_Fixed v2 = ((x + b) >> i); if (y > 0) { xtemp = x + v1; y = y - v2; x = xtemp; theta += *arctanptr++; } else { xtemp = x - v1; y = y + v2; x = xtemp; theta -= *arctanptr++; } } /* round theta */ if (theta >= 0) theta = SW_FT_PAD_ROUND(theta, 32); else theta = -SW_FT_PAD_ROUND(-theta, 32); vec->x = x; vec->y = theta; } /* documentation is in fttrigon.h */ SW_FT_Fixed SW_FT_Cos(SW_FT_Angle angle) { SW_FT_Vector v; v.x = SW_FT_TRIG_SCALE >> 8; v.y = 0; ft_trig_pseudo_rotate(&v, angle); return (v.x + 0x80L) >> 8; } /* documentation is in fttrigon.h */ SW_FT_Fixed SW_FT_Sin(SW_FT_Angle angle) { return SW_FT_Cos(SW_FT_ANGLE_PI2 - angle); } /* documentation is in fttrigon.h */ SW_FT_Fixed SW_FT_Tan(SW_FT_Angle angle) { SW_FT_Vector v; v.x = SW_FT_TRIG_SCALE >> 8; v.y = 0; ft_trig_pseudo_rotate(&v, angle); return SW_FT_DivFix(v.y, v.x); } /* documentation is in fttrigon.h */ SW_FT_Angle SW_FT_Atan2(SW_FT_Fixed dx, SW_FT_Fixed dy) { SW_FT_Vector v; if (dx == 0 && dy == 0) return 0; v.x = dx; v.y = dy; ft_trig_prenorm(&v); ft_trig_pseudo_polarize(&v); return v.y; } /* documentation is in fttrigon.h */ void SW_FT_Vector_Unit(SW_FT_Vector* vec, SW_FT_Angle angle) { vec->x = SW_FT_TRIG_SCALE >> 8; vec->y = 0; ft_trig_pseudo_rotate(vec, angle); vec->x = (vec->x + 0x80L) >> 8; vec->y = (vec->y + 0x80L) >> 8; } /* these macros return 0 for positive numbers, and -1 for negative ones */ #define SW_FT_SIGN_LONG(x) ((x) >> (SW_FT_SIZEOF_LONG * 8 - 1)) #define SW_FT_SIGN_INT(x) ((x) >> (SW_FT_SIZEOF_INT * 8 - 1)) #define SW_FT_SIGN_INT32(x) ((x) >> 31) #define SW_FT_SIGN_INT16(x) ((x) >> 15) /* documentation is in fttrigon.h */ void SW_FT_Vector_Rotate(SW_FT_Vector* vec, SW_FT_Angle angle) { SW_FT_Int shift; SW_FT_Vector v; v.x = vec->x; v.y = vec->y; if (angle && (v.x != 0 || v.y != 0)) { shift = ft_trig_prenorm(&v); ft_trig_pseudo_rotate(&v, angle); v.x = ft_trig_downscale(v.x); v.y = ft_trig_downscale(v.y); if (shift > 0) { SW_FT_Int32 half = (SW_FT_Int32)1L << (shift - 1); vec->x = (v.x + half + SW_FT_SIGN_LONG(v.x)) >> shift; vec->y = (v.y + half + SW_FT_SIGN_LONG(v.y)) >> shift; } else { shift = -shift; vec->x = (SW_FT_Pos)((SW_FT_ULong)v.x << shift); vec->y = (SW_FT_Pos)((SW_FT_ULong)v.y << shift); } } } /* documentation is in fttrigon.h */ SW_FT_Fixed SW_FT_Vector_Length(SW_FT_Vector* vec) { SW_FT_Int shift; SW_FT_Vector v; v = *vec; /* handle trivial cases */ if (v.x == 0) { return SW_FT_ABS(v.y); } else if (v.y == 0) { return SW_FT_ABS(v.x); } /* general case */ shift = ft_trig_prenorm(&v); ft_trig_pseudo_polarize(&v); v.x = ft_trig_downscale(v.x); if (shift > 0) return (v.x + (1 << (shift - 1))) >> shift; return (SW_FT_Fixed)((SW_FT_UInt32)v.x << -shift); } /* documentation is in fttrigon.h */ void SW_FT_Vector_Polarize(SW_FT_Vector* vec, SW_FT_Fixed* length, SW_FT_Angle* angle) { SW_FT_Int shift; SW_FT_Vector v; v = *vec; if (v.x == 0 && v.y == 0) return; shift = ft_trig_prenorm(&v); ft_trig_pseudo_polarize(&v); v.x = ft_trig_downscale(v.x); *length = (shift >= 0) ? (v.x >> shift) : (SW_FT_Fixed)((SW_FT_UInt32)v.x << -shift); *angle = v.y; } /* documentation is in fttrigon.h */ void SW_FT_Vector_From_Polar(SW_FT_Vector* vec, SW_FT_Fixed length, SW_FT_Angle angle) { vec->x = length; vec->y = 0; SW_FT_Vector_Rotate(vec, angle); } /* documentation is in fttrigon.h */ SW_FT_Angle SW_FT_Angle_Diff( SW_FT_Angle angle1, SW_FT_Angle angle2 ) { SW_FT_Angle delta = angle2 - angle1; while ( delta <= -SW_FT_ANGLE_PI ) delta += SW_FT_ANGLE_2PI; while ( delta > SW_FT_ANGLE_PI ) delta -= SW_FT_ANGLE_2PI; return delta; } /* END */