1 /****************************************************************************
2 *
3 * ftcalc.h
4 *
5 * Arithmetic computations (specification).
6 *
7 * Copyright (C) 1996-2019 by
8 * David Turner, Robert Wilhelm, and Werner Lemberg.
9 *
10 * This file is part of the FreeType project, and may only be used,
11 * modified, and distributed under the terms of the FreeType project
12 * license, LICENSE.TXT. By continuing to use, modify, or distribute
13 * this file you indicate that you have read the license and
14 * understand and accept it fully.
15 *
16 */
17
18
19 #ifndef FTCALC_H_
20 #define FTCALC_H_
21
22
23 #include <ft2build.h>
24 #include FT_FREETYPE_H
25
26
27 FT_BEGIN_HEADER
28
29
30 /**************************************************************************
31 *
32 * FT_MulDiv() and FT_MulFix() are declared in freetype.h.
33 *
34 */
35
36 #ifndef FT_CONFIG_OPTION_NO_ASSEMBLER
37 /* Provide assembler fragments for performance-critical functions. */
38 /* These must be defined `static __inline__' with GCC. */
39
40 #if defined( __CC_ARM ) || defined( __ARMCC__ ) /* RVCT */
41
42 #define FT_MULFIX_ASSEMBLER FT_MulFix_arm
43
44 /* documentation is in freetype.h */
45
46 static __inline FT_Int32
47 FT_MulFix_arm( FT_Int32 a,
48 FT_Int32 b )
49 {
50 FT_Int32 t, t2;
51
52
53 __asm
54 {
55 smull t2, t, b, a /* (lo=t2,hi=t) = a*b */
56 mov a, t, asr #31 /* a = (hi >> 31) */
57 add a, a, #0x8000 /* a += 0x8000 */
58 adds t2, t2, a /* t2 += a */
59 adc t, t, #0 /* t += carry */
60 mov a, t2, lsr #16 /* a = t2 >> 16 */
61 orr a, a, t, lsl #16 /* a |= t << 16 */
62 }
63 return a;
64 }
65
66 #endif /* __CC_ARM || __ARMCC__ */
67
68
69 #ifdef __GNUC__
70
71 #if defined( __arm__ ) && \
72 ( !defined( __thumb__ ) || defined( __thumb2__ ) ) && \
73 !( defined( __CC_ARM ) || defined( __ARMCC__ ) )
74
75 #define FT_MULFIX_ASSEMBLER FT_MulFix_arm
76
77 /* documentation is in freetype.h */
78
79 static __inline__ FT_Int32
80 FT_MulFix_arm( FT_Int32 a,
81 FT_Int32 b )
82 {
83 FT_Int32 t, t2;
84
85
86 __asm__ __volatile__ (
87 "smull %1, %2, %4, %3\n\t" /* (lo=%1,hi=%2) = a*b */
88 "mov %0, %2, asr #31\n\t" /* %0 = (hi >> 31) */
89 #if defined( __clang__ ) && defined( __thumb2__ )
90 "add.w %0, %0, #0x8000\n\t" /* %0 += 0x8000 */
91 #else
92 "add %0, %0, #0x8000\n\t" /* %0 += 0x8000 */
93 #endif
94 "adds %1, %1, %0\n\t" /* %1 += %0 */
95 "adc %2, %2, #0\n\t" /* %2 += carry */
96 "mov %0, %1, lsr #16\n\t" /* %0 = %1 >> 16 */
97 "orr %0, %0, %2, lsl #16\n\t" /* %0 |= %2 << 16 */
98 : "=r"(a), "=&r"(t2), "=&r"(t)
99 : "r"(a), "r"(b)
100 : "cc" );
101 return a;
102 }
103
104 #endif /* __arm__ && */
105 /* ( __thumb2__ || !__thumb__ ) && */
106 /* !( __CC_ARM || __ARMCC__ ) */
107
108
109 #if defined( __i386__ )
110
111 #define FT_MULFIX_ASSEMBLER FT_MulFix_i386
112
113 /* documentation is in freetype.h */
114
115 static __inline__ FT_Int32
116 FT_MulFix_i386( FT_Int32 a,
117 FT_Int32 b )
118 {
119 FT_Int32 result;
120
121
122 __asm__ __volatile__ (
123 "imul %%edx\n"
124 "movl %%edx, %%ecx\n"
125 "sarl $31, %%ecx\n"
126 "addl $0x8000, %%ecx\n"
127 "addl %%ecx, %%eax\n"
128 "adcl $0, %%edx\n"
129 "shrl $16, %%eax\n"
130 "shll $16, %%edx\n"
131 "addl %%edx, %%eax\n"
132 : "=a"(result), "=d"(b)
133 : "a"(a), "d"(b)
134 : "%ecx", "cc" );
135 return result;
136 }
137
138 #endif /* i386 */
139
140 #endif /* __GNUC__ */
141
142
143 #ifdef _MSC_VER /* Visual C++ */
144
145 #ifdef _M_IX86
146
147 #define FT_MULFIX_ASSEMBLER FT_MulFix_i386
148
149 /* documentation is in freetype.h */
150
151 static __inline FT_Int32
152 FT_MulFix_i386( FT_Int32 a,
153 FT_Int32 b )
154 {
155 FT_Int32 result;
156
157 __asm
158 {
159 mov eax, a
160 mov edx, b
161 imul edx
162 mov ecx, edx
163 sar ecx, 31
164 add ecx, 8000h
165 add eax, ecx
166 adc edx, 0
167 shr eax, 16
168 shl edx, 16
169 add eax, edx
170 mov result, eax
171 }
172 return result;
173 }
174
175 #endif /* _M_IX86 */
176
177 #endif /* _MSC_VER */
178
179
180 #if defined( __GNUC__ ) && defined( __x86_64__ )
181
182 #define FT_MULFIX_ASSEMBLER FT_MulFix_x86_64
183
184 static __inline__ FT_Int32
185 FT_MulFix_x86_64( FT_Int32 a,
186 FT_Int32 b )
187 {
188 /* Temporarily disable the warning that C90 doesn't support */
189 /* `long long'. */
190 #if __GNUC__ > 4 || ( __GNUC__ == 4 && __GNUC_MINOR__ >= 6 )
191 #pragma GCC diagnostic push
192 #pragma GCC diagnostic ignored "-Wlong-long"
193 #endif
194
195 #if 1
196 /* Technically not an assembly fragment, but GCC does a really good */
197 /* job at inlining it and generating good machine code for it. */
198 long long ret, tmp;
199
200
201 ret = (long long)a * b;
202 tmp = ret >> 63;
203 ret += 0x8000 + tmp;
204
205 return (FT_Int32)( ret >> 16 );
206 #else
207
208 /* For some reason, GCC 4.6 on Ubuntu 12.04 generates invalid machine */
209 /* code from the lines below. The main issue is that `wide_a' is not */
210 /* properly initialized by sign-extending `a'. Instead, the generated */
211 /* machine code assumes that the register that contains `a' on input */
212 /* can be used directly as a 64-bit value, which is wrong most of the */
213 /* time. */
214 long long wide_a = (long long)a;
215 long long wide_b = (long long)b;
216 long long result;
217
218
219 __asm__ __volatile__ (
220 "imul %2, %1\n"
221 "mov %1, %0\n"
222 "sar $63, %0\n"
223 "lea 0x8000(%1, %0), %0\n"
224 "sar $16, %0\n"
225 : "=&r"(result), "=&r"(wide_a)
226 : "r"(wide_b)
227 : "cc" );
228
229 return (FT_Int32)result;
230 #endif
231
232 #if __GNUC__ > 4 || ( __GNUC__ == 4 && __GNUC_MINOR__ >= 6 )
233 #pragma GCC diagnostic pop
234 #endif
235 }
236
237 #endif /* __GNUC__ && __x86_64__ */
238
239 #endif /* !FT_CONFIG_OPTION_NO_ASSEMBLER */
240
241
242 #ifdef FT_CONFIG_OPTION_INLINE_MULFIX
243 #ifdef FT_MULFIX_ASSEMBLER
244 #define FT_MulFix( a, b ) FT_MULFIX_ASSEMBLER( (FT_Int32)(a), (FT_Int32)(b) )
245 #endif
246 #endif
247
248
249 /**************************************************************************
250 *
251 * @function:
252 * FT_MulDiv_No_Round
253 *
254 * @description:
255 * A very simple function used to perform the computation '(a*b)/c'
256 * (without rounding) with maximum accuracy (it uses a 64-bit
257 * intermediate integer whenever necessary).
258 *
259 * This function isn't necessarily as fast as some processor-specific
260 * operations, but is at least completely portable.
261 *
262 * @input:
263 * a ::
264 * The first multiplier.
265 * b ::
266 * The second multiplier.
267 * c ::
268 * The divisor.
269 *
270 * @return:
271 * The result of '(a*b)/c'. This function never traps when trying to
272 * divide by zero; it simply returns 'MaxInt' or 'MinInt' depending on
273 * the signs of 'a' and 'b'.
274 */
275 FT_BASE( FT_Long )
276 FT_MulDiv_No_Round( FT_Long a,
277 FT_Long b,
278 FT_Long c );
279
280
281 /*
282 * A variant of FT_Matrix_Multiply which scales its result afterwards. The
283 * idea is that both `a' and `b' are scaled by factors of 10 so that the
284 * values are as precise as possible to get a correct result during the
285 * 64bit multiplication. Let `sa' and `sb' be the scaling factors of `a'
286 * and `b', respectively, then the scaling factor of the result is `sa*sb'.
287 */
288 FT_BASE( void )
289 FT_Matrix_Multiply_Scaled( const FT_Matrix* a,
290 FT_Matrix *b,
291 FT_Long scaling );
292
293
294 /*
295 * Check a matrix. If the transformation would lead to extreme shear or
296 * extreme scaling, for example, return 0. If everything is OK, return 1.
297 *
298 * Based on geometric considerations we use the following inequality to
299 * identify a degenerate matrix.
300 *
301 * 50 * abs(xx*yy - xy*yx) < xx^2 + xy^2 + yx^2 + yy^2
302 *
303 * Value 50 is heuristic.
304 */
305 FT_BASE( FT_Bool )
306 FT_Matrix_Check( const FT_Matrix* matrix );
307
308
309 /*
310 * A variant of FT_Vector_Transform. See comments for
311 * FT_Matrix_Multiply_Scaled.
312 */
313 FT_BASE( void )
314 FT_Vector_Transform_Scaled( FT_Vector* vector,
315 const FT_Matrix* matrix,
316 FT_Long scaling );
317
318
319 /*
320 * This function normalizes a vector and returns its original length. The
321 * normalized vector is a 16.16 fixed-point unit vector with length close
322 * to 0x10000. The accuracy of the returned length is limited to 16 bits
323 * also. The function utilizes quick inverse square root approximation
324 * without divisions and square roots relying on Newton's iterations
325 * instead.
326 */
327 FT_BASE( FT_UInt32 )
328 FT_Vector_NormLen( FT_Vector* vector );
329
330
331 /*
332 * Return -1, 0, or +1, depending on the orientation of a given corner. We
333 * use the Cartesian coordinate system, with positive vertical values going
334 * upwards. The function returns +1 if the corner turns to the left, -1 to
335 * the right, and 0 for undecidable cases.
336 */
337 FT_BASE( FT_Int )
338 ft_corner_orientation( FT_Pos in_x,
339 FT_Pos in_y,
340 FT_Pos out_x,
341 FT_Pos out_y );
342
343
344 /*
345 * Return TRUE if a corner is flat or nearly flat. This is equivalent to
346 * saying that the corner point is close to its neighbors, or inside an
347 * ellipse defined by the neighbor focal points to be more precise.
348 */
349 FT_BASE( FT_Int )
350 ft_corner_is_flat( FT_Pos in_x,
351 FT_Pos in_y,
352 FT_Pos out_x,
353 FT_Pos out_y );
354
355
356 /*
357 * Return the most significant bit index.
358 */
359
360 #ifndef FT_CONFIG_OPTION_NO_ASSEMBLER
361
362 #if defined( __GNUC__ ) && \
363 ( __GNUC__ > 3 || ( __GNUC__ == 3 && __GNUC_MINOR__ >= 4 ) )
364
365 #if FT_SIZEOF_INT == 4
366
367 #define FT_MSB( x ) ( 31 - __builtin_clz( x ) )
368
369 #elif FT_SIZEOF_LONG == 4
370
371 #define FT_MSB( x ) ( 31 - __builtin_clzl( x ) )
372
373 #endif /* __GNUC__ */
374
375
376 #elif defined( _MSC_VER ) && ( _MSC_VER >= 1400 )
377
378 #if FT_SIZEOF_INT == 4
379
380 #include <intrin.h>
381 #pragma intrinsic( _BitScanReverse )
382
383 static __inline FT_Int32
384 FT_MSB_i386( FT_UInt32 x )
385 {
386 unsigned long where;
387
388
389 _BitScanReverse( &where, x );
390
391 return (FT_Int32)where;
392 }
393
394 #define FT_MSB( x ) ( FT_MSB_i386( x ) )
395
396 #endif
397
398 #endif /* _MSC_VER */
399
400
401 #endif /* !FT_CONFIG_OPTION_NO_ASSEMBLER */
402
403 #ifndef FT_MSB
404
405 FT_BASE( FT_Int )
406 FT_MSB( FT_UInt32 z );
407
408 #endif
409
410
411 /*
412 * Return sqrt(x*x+y*y), which is the same as `FT_Vector_Length' but uses
413 * two fixed-point arguments instead.
414 */
415 FT_BASE( FT_Fixed )
416 FT_Hypot( FT_Fixed x,
417 FT_Fixed y );
418
419
420 #if 0
421
422 /**************************************************************************
423 *
424 * @function:
425 * FT_SqrtFixed
426 *
427 * @description:
428 * Computes the square root of a 16.16 fixed-point value.
429 *
430 * @input:
431 * x ::
432 * The value to compute the root for.
433 *
434 * @return:
435 * The result of 'sqrt(x)'.
436 *
437 * @note:
438 * This function is not very fast.
439 */
440 FT_BASE( FT_Int32 )
441 FT_SqrtFixed( FT_Int32 x );
442
443 #endif /* 0 */
444
445
446 #define INT_TO_F26DOT6( x ) ( (FT_Long)(x) * 64 ) /* << 6 */
447 #define INT_TO_F2DOT14( x ) ( (FT_Long)(x) * 16384 ) /* << 14 */
448 #define INT_TO_FIXED( x ) ( (FT_Long)(x) * 65536 ) /* << 16 */
449 #define F2DOT14_TO_FIXED( x ) ( (FT_Long)(x) * 4 ) /* << 2 */
450 #define FIXED_TO_INT( x ) ( FT_RoundFix( x ) >> 16 )
451
452 #define ROUND_F26DOT6( x ) ( x >= 0 ? ( ( (x) + 32 ) & -64 ) \
453 : ( -( ( 32 - (x) ) & -64 ) ) )
454
455 /*
456 * The following macros have two purposes.
457 *
458 * - Tag places where overflow is expected and harmless.
459 *
460 * - Avoid run-time sanitizer errors.
461 *
462 * Use with care!
463 */
464 #define ADD_INT( a, b ) \
465 (FT_Int)( (FT_UInt)(a) + (FT_UInt)(b) )
466 #define SUB_INT( a, b ) \
467 (FT_Int)( (FT_UInt)(a) - (FT_UInt)(b) )
468 #define MUL_INT( a, b ) \
469 (FT_Int)( (FT_UInt)(a) * (FT_UInt)(b) )
470 #define NEG_INT( a ) \
471 (FT_Int)( (FT_UInt)0 - (FT_UInt)(a) )
472
473 #define ADD_LONG( a, b ) \
474 (FT_Long)( (FT_ULong)(a) + (FT_ULong)(b) )
475 #define SUB_LONG( a, b ) \
476 (FT_Long)( (FT_ULong)(a) - (FT_ULong)(b) )
477 #define MUL_LONG( a, b ) \
478 (FT_Long)( (FT_ULong)(a) * (FT_ULong)(b) )
479 #define NEG_LONG( a ) \
480 (FT_Long)( (FT_ULong)0 - (FT_ULong)(a) )
481
482 #define ADD_INT32( a, b ) \
483 (FT_Int32)( (FT_UInt32)(a) + (FT_UInt32)(b) )
484 #define SUB_INT32( a, b ) \
485 (FT_Int32)( (FT_UInt32)(a) - (FT_UInt32)(b) )
486 #define MUL_INT32( a, b ) \
487 (FT_Int32)( (FT_UInt32)(a) * (FT_UInt32)(b) )
488 #define NEG_INT32( a ) \
489 (FT_Int32)( (FT_UInt32)0 - (FT_UInt32)(a) )
490
491 #ifdef FT_LONG64
492
493 #define ADD_INT64( a, b ) \
494 (FT_Int64)( (FT_UInt64)(a) + (FT_UInt64)(b) )
495 #define SUB_INT64( a, b ) \
496 (FT_Int64)( (FT_UInt64)(a) - (FT_UInt64)(b) )
497 #define MUL_INT64( a, b ) \
498 (FT_Int64)( (FT_UInt64)(a) * (FT_UInt64)(b) )
499 #define NEG_INT64( a ) \
500 (FT_Int64)( (FT_UInt64)0 - (FT_UInt64)(a) )
501
502 #endif /* FT_LONG64 */
503
504
505 FT_END_HEADER
506
507 #endif /* FTCALC_H_ */
508
509
510 /* END */