1 /***************************************************************************/
2 /* */
3 /* ftcalc.h */
4 /* */
5 /* Arithmetic computations (specification). */
6 /* */
7 /* Copyright 1996-2018 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 :: The first multiplier. */
264 /* b :: The second multiplier. */
265 /* c :: The divisor. */
266 /* */
267 /* <Return> */
268 /* The result of `(a*b)/c'. This function never traps when trying to */
269 /* divide by zero; it simply returns `MaxInt' or `MinInt' depending */
270 /* on the signs of `a' and `b'. */
271 /* */
272 FT_BASE( FT_Long )
273 FT_MulDiv_No_Round( FT_Long a,
274 FT_Long b,
275 FT_Long c );
276
277
278 /*
279 * A variant of FT_Matrix_Multiply which scales its result afterwards.
280 * The idea is that both `a' and `b' are scaled by factors of 10 so that
281 * the values are as precise as possible to get a correct result during
282 * the 64bit multiplication. Let `sa' and `sb' be the scaling factors of
283 * `a' and `b', respectively, then the scaling factor of the result is
284 * `sa*sb'.
285 */
286 FT_BASE( void )
287 FT_Matrix_Multiply_Scaled( const FT_Matrix* a,
288 FT_Matrix *b,
289 FT_Long scaling );
290
291
292 /*
293 * A variant of FT_Vector_Transform. See comments for
294 * FT_Matrix_Multiply_Scaled.
295 */
296 FT_BASE( void )
297 FT_Vector_Transform_Scaled( FT_Vector* vector,
298 const FT_Matrix* matrix,
299 FT_Long scaling );
300
301
302 /*
303 * This function normalizes a vector and returns its original length.
304 * The normalized vector is a 16.16 fixed-point unit vector with length
305 * close to 0x10000. The accuracy of the returned length is limited to
306 * 16 bits also. The function utilizes quick inverse square root
307 * approximation without divisions and square roots relying on Newton's
308 * iterations instead.
309 */
310 FT_BASE( FT_UInt32 )
311 FT_Vector_NormLen( FT_Vector* vector );
312
313
314 /*
315 * Return -1, 0, or +1, depending on the orientation of a given corner.
316 * We use the Cartesian coordinate system, with positive vertical values
317 * going upwards. The function returns +1 if the corner turns to the
318 * left, -1 to the right, and 0 for undecidable cases.
319 */
320 FT_BASE( FT_Int )
321 ft_corner_orientation( FT_Pos in_x,
322 FT_Pos in_y,
323 FT_Pos out_x,
324 FT_Pos out_y );
325
326
327 /*
328 * Return TRUE if a corner is flat or nearly flat. This is equivalent to
329 * saying that the corner point is close to its neighbors, or inside an
330 * ellipse defined by the neighbor focal points to be more precise.
331 */
332 FT_BASE( FT_Int )
333 ft_corner_is_flat( FT_Pos in_x,
334 FT_Pos in_y,
335 FT_Pos out_x,
336 FT_Pos out_y );
337
338
339 /*
340 * Return the most significant bit index.
341 */
342
343 #ifndef FT_CONFIG_OPTION_NO_ASSEMBLER
344 #if defined( __GNUC__ ) && \
345 ( __GNUC__ > 3 || ( __GNUC__ == 3 && __GNUC_MINOR__ >= 4 ) )
346
347 #if FT_SIZEOF_INT == 4
348
349 #define FT_MSB( x ) ( 31 - __builtin_clz( x ) )
350
351 #elif FT_SIZEOF_LONG == 4
352
353 #define FT_MSB( x ) ( 31 - __builtin_clzl( x ) )
354
355 #endif
356
357 #endif /* __GNUC__ */
358 #endif /* !FT_CONFIG_OPTION_NO_ASSEMBLER */
359
360 #ifndef FT_MSB
361
362 FT_BASE( FT_Int )
363 FT_MSB( FT_UInt32 z );
364
365 #endif
366
367
368 /*
369 * Return sqrt(x*x+y*y), which is the same as `FT_Vector_Length' but uses
370 * two fixed-point arguments instead.
371 */
372 FT_BASE( FT_Fixed )
373 FT_Hypot( FT_Fixed x,
374 FT_Fixed y );
375
376
377 #if 0
378
379 /*************************************************************************/
380 /* */
381 /* <Function> */
382 /* FT_SqrtFixed */
383 /* */
384 /* <Description> */
385 /* Computes the square root of a 16.16 fixed-point value. */
386 /* */
387 /* <Input> */
388 /* x :: The value to compute the root for. */
389 /* */
390 /* <Return> */
391 /* The result of `sqrt(x)'. */
392 /* */
393 /* <Note> */
394 /* This function is not very fast. */
395 /* */
396 FT_BASE( FT_Int32 )
397 FT_SqrtFixed( FT_Int32 x );
398
399 #endif /* 0 */
400
401
402 #define INT_TO_F26DOT6( x ) ( (FT_Long)(x) * 64 ) /* << 6 */
403 #define INT_TO_F2DOT14( x ) ( (FT_Long)(x) * 16384 ) /* << 14 */
404 #define INT_TO_FIXED( x ) ( (FT_Long)(x) * 65536 ) /* << 16 */
405 #define F2DOT14_TO_FIXED( x ) ( (FT_Long)(x) * 4 ) /* << 2 */
406 #define FIXED_TO_INT( x ) ( FT_RoundFix( x ) >> 16 )
407
408 #define ROUND_F26DOT6( x ) ( x >= 0 ? ( ( (x) + 32 ) & -64 ) \
409 : ( -( ( 32 - (x) ) & -64 ) ) )
410
411 /*
412 * The following macros have two purposes.
413 *
414 * . Tag places where overflow is expected and harmless.
415 *
416 * . Avoid run-time sanitizer errors.
417 *
418 * Use with care!
419 */
420 #define ADD_LONG( a, b ) \
421 (FT_Long)( (FT_ULong)(a) + (FT_ULong)(b) )
422 #define SUB_LONG( a, b ) \
423 (FT_Long)( (FT_ULong)(a) - (FT_ULong)(b) )
424 #define MUL_LONG( a, b ) \
425 (FT_Long)( (FT_ULong)(a) * (FT_ULong)(b) )
426 #define NEG_LONG( a ) \
427 (FT_Long)( (FT_ULong)0 - (FT_ULong)(a) )
428
429 #define ADD_INT32( a, b ) \
430 (FT_Int32)( (FT_UInt32)(a) + (FT_UInt32)(b) )
431 #define SUB_INT32( a, b ) \
432 (FT_Int32)( (FT_UInt32)(a) - (FT_UInt32)(b) )
433 #define MUL_INT32( a, b ) \
434 (FT_Int32)( (FT_UInt32)(a) * (FT_UInt32)(b) )
435 #define NEG_INT32( a ) \
436 (FT_Int32)( (FT_UInt32)0 - (FT_UInt32)(a) )
437
438
439 FT_END_HEADER
440
441 #endif /* FTCALC_H_ */
442
443
444 /* END */