src/common/RTMath.h

/***************************************************************************
 *                                                                         *
 *   LinuxSampler - modular, streaming capable sampler                     *
 *                                                                         *
 *   Copyright (C) 2003, 2004 by Benno Senoner and Christian Schoenebeck   *
 *   Copyright (C) 2005 - 2016 Christian Schoenebeck                       *
 *                                                                         *
 *   This program is free software; you can redistribute it and/or modify  *
 *   it under the terms of the GNU General Public License as published by  *
 *   the Free Software Foundation; either version 2 of the License, or     *
 *   (at your option) any later version.                                   *
 *                                                                         *
 *   This program is distributed in the hope that it will be useful,       *
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
 *   GNU General Public License for more details.                          *
 *                                                                         *
 *   You should have received a copy of the GNU General Public License     *
 *   along with this program; if not, write to the Free Software           *
 *   Foundation, Inc., 59 Temple Place, Suite 330, Boston,                 *
 *   MA  02111-1307  USA                                                   *
 ***************************************************************************/

#ifndef __RT_MATH_H__
#define __RT_MATH_H__

#include <math.h>
#include <stdint.h>
#include "global_private.h"

/// Needed for calculating frequency ratio used to pitch a sample
#define TWELVEHUNDREDTH_ROOT_OF_TWO     1.000577789506555

enum implementation_t {
    CPP,
    ASM_X86_MMX_SSE
};

/** @brief Real Time Math Base Class
 *
 * Math functions for real time operation. This base class contains all
 * non-template methods.
 */
class RTMathBase {
    public:
        /**
         * High resolution time stamp.
         */
        typedef uint32_t time_stamp_t;

        typedef uint64_t usecs_t;

        /**
         * We read the processor's cycle count register as a reference
         * for the real time. These are of course only abstract values
         * with arbitrary time entity, but that's not a problem as long
         * as we calculate relatively.
         *
         * @see unsafeMicroSeconds()
         */
        static time_stamp_t CreateTimeStamp();

        /**
         * Calculates the frequency ratio for a pitch value given in cents
         * (assuming equal tempered scale of course, divided into 12
         * semitones per octave and 100 cents per semitone).
         *
         * Note: CONFIG_MAX_PITCH (defined in config.h) has to be defined to an
         * appropriate value, otherwise the behavior of this function is
         * undefined, but most probably if CONFIG_MAX_PITCH is too small, the
         * application will crash due to segmentation fault here.
         *
         * @param cents - pitch value in cents (+1200 cents means +1 octave)
         * @returns  frequency ratio (e.g. +2.0 for +1 octave)
         */
        inline static double CentsToFreqRatio(double Cents) {
            int   index_int   = (int) (Cents);      // integer index
            float index_fract = Cents - index_int;  // fractional part of index
            return pCentsToFreqTable[index_int] + index_fract * (pCentsToFreqTable[index_int+1] - pCentsToFreqTable[index_int]);
        }

        /**
         * Slower version of CentsToFreqRatio, for big values.
         *
         * @param cents - pitch value in cents (+1200 cents means +1 octave)
         * @returns  frequency ratio (e.g. +2.0 for +1 octave)
         */
        static double CentsToFreqRatioUnlimited(double Cents) {
            int octaves = int(Cents / 1200);
            double x = CentsToFreqRatio(Cents - octaves * 1200);
            return  octaves < 0 ? x / (1 << -octaves) : x * (1 << octaves);
        }

        /**
         * Inverse function to CentsToFreqRatio(). This function is a bit
         * slow, so it should not be called too frequently.
         */
        static double FreqRatioToCents(double FreqRatio) {
            return log(FreqRatio) / log(TWELVEHUNDREDTH_ROOT_OF_TWO);
        }

        /**
         * Calculates the line ratio value representation (linear scale)
         * of the @a decibel value provided (exponential scale).
         *
         * The context of audio acoustic sound pressure levels is assumed, and
         * hence the field version of the dB unit is used here (which uses a
         * linear factor of 20). This function is a bit slow, so it should
         * not be called too frequently.
         *
         * @param decibel - sound pressure level in dB
         * @returns linear ratio of the supplied dB value
         */
        static float DecibelToLinRatio(float decibel) {
            return powf(10.f, decibel / 20.f);
        }

        /**
         * Calculates the relatively summed average of a set of values.
         *
         * @param current - the current avaerage value of all previously summed values
         * @param sample - new value to be applied as summed average to the existing values
         * @param n - amount of sample values applied so far
         * @returns new average value of all summed values (including the new @a sample)
         */
        inline static float RelativeSummedAvg(float current, float sample, int n) {
            return current + (sample - current) / float(n);
        }

        /**
         * Clock source to use for getting the current time.
         */
        enum clock_source_t {
            real_clock,    ///< Use this to measure time that passed in reality (no matter if process got suspended).
            process_clock, ///< Use this to measure only the CPU execution time of the current process (if the process got suspended, the clock is paused as well).
            thread_clock,  ///< Use this to measure only the CPU execution time of the current thread (if the process got suspended or another thread is executed, the clock is paused as well).
        };

        /**
         * Returns a time stamp of the current time in microseconds (in
         * probably real-time @b unsafe way). There is no guarantee about
         * what the returned amount of microseconds relates to (i.e.
         * microseconds since epoch, microseconds since system uptime, ...).
         * So you should only use it to calculate time differences between
         * values taken with this method.
         *
         * @b CAUTION: This method may not @b NOT be real-time safe! On some
         * systems it could be RT safe, but there is no guarantee whatsoever!
         * So this method should only be used for debugging, benchmarking and
         * other developing purposes !
         *
         * For creating time stamps in real-time context, use
         * CreateTimeStamp() instead.
         *
         * @param source - the actual clock to use for getting the current
         *                 time, note that the various clock sources may not
         *                 be implemented on all systems
         * @returns time stamp in microseconds
         *
         * @see CreateTimeStamp()
         */
        static usecs_t unsafeMicroSeconds(clock_source_t source);

    private:
        static float* pCentsToFreqTable;

        static float* InitCentsToFreqTable();
};

/** @brief Real Time Math
 *
 * This is a template which provides customized methods for the desired low
 * level implementation. The ASM_X86_MMX_SSE implementation of each method
 * for example doesn't use 387 FPU instruction. This is needed for MMX
 * algorithms which do not allow mixed MMX and 387 instructions.
 */
template<implementation_t IMPL = CPP>
class __RTMath : public RTMathBase {
    public:
        // conversion using truncate
        inline static int Int(const float a) {
            switch (IMPL) {
                #if CONFIG_ASM && ARCH_X86
                case ASM_X86_MMX_SSE: {
                    int ret;
                    asm (
                        "cvttss2si %1, %0  # convert to int\n\t"
                        : "=r" (ret)
                        : "m" (a)
                    );
                    return ret;
                }
                #endif // CONFIG_ASM && ARCH_X86
                default: {
                    return (int) a;
                }
            }
        }

        //for doubles and everything else except floats
        template<class T_a> inline static int Int(const T_a a) {
            return (int) a;
        }

        inline static float Float(const int a) {
            switch (IMPL) {
                #if CONFIG_ASM && ARCH_X86
                case ASM_X86_MMX_SSE: {
                    float ret;
                    asm (
                        "cvtsi2ss %1, %%xmm0  # convert to float\n\t"
                        "movss    %%xmm0,%0   # output\n\t"
                        : "=m" (ret)
                        : "r" (a)
                    );
                    return ret;
                }
                #endif // CONFIG_ASM && ARCH_X86
                default: {
                    return (float) a;
                }
            }
        }

#if 0
        //for everything except ints
        template<class T_a> inline static float Float(T_a a) {
            return (float) a;
        }
#endif

        inline static float Sum(const float& a, const float& b) {
            switch (IMPL) {
                #if CONFIG_ASM && ARCH_X86
                case ASM_X86_MMX_SSE: {
                    float ret;
                    asm (
                        "movss    %1, %%xmm0  # load a\n\t"
                        "addss    %2, %%xmm0  # a + b\n\t"
                        "movss    %%xmm0, %0  # output\n\t"
                        : "=m" (ret)
                        : "m" (a), "m" (b)
                    );
                    return ret;
                }
                #endif // CONFIG_ASM && ARCH_X86
                default: {
                    return (a + b);
                }
            }
        }

        template<class T_a, class T_b> inline static T_a Sum(const T_a a, const T_b b) {
            return (a + b);
        }

        inline static float Sub(const float& a, const float& b) {
            switch (IMPL) {
                #if CONFIG_ASM && ARCH_X86
                case ASM_X86_MMX_SSE: {
                    float ret;
                    asm (
                        "movss    %1, %%xmm0  # load a\n\t"
                        "subss    %2, %%xmm0  # a - b\n\t"
                        "movss    %%xmm0, %0  # output\n\t"
                        : "=m" (ret)
                        : "m" (a), "m" (b)
                    );
                    return ret;
                }
                #endif // CONFIG_ASM && ARCH_X86
                default: {
                    return (a - b);
                }
            }
        }

        template<class T_a, class T_b> inline static T_a Sub(const T_a a, const T_b b) {
            return (a - b);
        }

        inline static float Mul(const float a, const float b) {
            switch (IMPL) {
                #if CONFIG_ASM && ARCH_X86
                case ASM_X86_MMX_SSE: {
                    float ret;
                    asm (
                        "movss    %1, %%xmm0  # load a\n\t"
                        "mulss    %2, %%xmm0  # a * b\n\t"
                        "movss    %%xmm0, %0  # output\n\t"
                        : "=m" (ret)
                        : "m" (a), "m" (b)
                    );
                    return ret;
                }
                #endif // CONFIG_ASM && ARCH_X86
                default: {
                    return (a * b);
                }
            }
        }

        template<class T_a, class T_b> inline static T_a Mul(const T_a a, const T_b b) {
            return (a * b);
        }

        inline static float Div(const float a, const float b) {
            switch (IMPL) {
                #if CONFIG_ASM && ARCH_X86
                case ASM_X86_MMX_SSE: {
                    float ret;
                    asm (
                        "movss    %1, %%xmm0  # load a\n\t"
                        "divss    %2, %%xmm0  # a / b\n\t"
                        "movss    %%xmm0, %0  # output\n\t"
                        : "=m" (ret)
                        : "m" (a), "m" (b)
                    );
                    return ret;
                }
                #endif // CONFIG_ASM && ARCH_X86
                default: {
                    return (a / b);
                }
            }
        }

        template<class T_a, class T_b> inline static T_a Div(const T_a a, const T_b b) {
            return (a / b);
        }

        inline static float Min(const float a, const float b) {
            switch (IMPL) {
                #if CONFIG_ASM && ARCH_X86
                case ASM_X86_MMX_SSE: {
                    float ret;
                    asm (
                        "movss    %1, %%xmm0  # load a\n\t"
                        "minss    %2, %%xmm0  # Minimum(a, b)\n\t"
                        "movss    %%xmm0, %0  # output\n\t"
                        : "=m" (ret)
                        : "m" (a), "m" (b)
                    );
                    return ret;
                }
                #endif // CONFIG_ASM && ARCH_X86
                default: {
                    return std::min(a, b);
                }
            }
        }

        template<class T_a, class T_b> inline static T_a Min(const T_a a, const T_b b) {
            return (b < a) ? b : a;
        }

        inline static float Max(const float a, const float b) {
            switch (IMPL) {
                #if CONFIG_ASM && ARCH_X86
                case ASM_X86_MMX_SSE: {
                    float ret;
                    asm (
                        "movss    %1, %%xmm0  # load a\n\t"
                        "maxss    %2, %%xmm0  # Maximum(a, b)\n\t"
                        "movss    %%xmm0, %0  # output\n\t"
                        : "=m" (ret)
                        : "m" (a), "m" (b)
                    );
                    return ret;
                }
                #endif // CONFIG_ASM && ARCH_X86
                default: {
                    return std::max(a, b);
                }
            }
        }

        template<class T_a, class T_b> inline static T_a Max(const T_a a, const T_b b) {
            return (b > a) ? b : a;
        }

        inline static float Fmodf(const float &a, const float &b) {
            switch (IMPL) {
                #if CONFIG_ASM && ARCH_X86
                case ASM_X86_MMX_SSE: {
                    float ret;
                    asm (
                        "movss    %1, %%xmm0  # load a\n\t"
                        "movss    %2, %%xmm1  # load b\n\t"
                        "movss    %%xmm0,%%xmm2\n\t"
                        "divss    %%xmm1, %%xmm2  # xmm2 = a / b\n\t"
                        "cvttss2si %%xmm2, %%ecx  #convert to int\n\t"
                        "cvtsi2ss %%ecx, %%xmm2  #convert back to float\n\t"
                        "mulss    %%xmm1, %%xmm2  # xmm2 = b * int(a/b)\n\t"
                        "subss    %%xmm2, %%xmm0  #sub a\n\t"
                        "movss    %%xmm0, %0  # output\n\t"
                        : "=m" (ret)
                        : "m" (a), "m" (b)
                        : "%ecx"
                    );
                    return ret;
                }
                #endif // CONFIG_ASM && ARCH_X86
                default: {
                    return fmodf(a, b);
                }
            }
        }
};

/// convenience typedef for using the default implementation (which is CPP)
typedef __RTMath<> RTMath;

#endif // __RT_MATH_H__
1	/***************************************************************************
2	* *
3	* LinuxSampler - modular, streaming capable sampler *
4	* *
5	* Copyright (C) 2003, 2004 by Benno Senoner and Christian Schoenebeck *
6	* Copyright (C) 2005 - 2016 Christian Schoenebeck *
7	* *
8	* This program is free software; you can redistribute it and/or modify *
9	* it under the terms of the GNU General Public License as published by *
10	* the Free Software Foundation; either version 2 of the License, or *
11	* (at your option) any later version. *
12	* *
13	* This program is distributed in the hope that it will be useful, *
14	* but WITHOUT ANY WARRANTY; without even the implied warranty of *
15	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
16	* GNU General Public License for more details. *
17	* *
18	* You should have received a copy of the GNU General Public License *
19	* along with this program; if not, write to the Free Software *
20	* Foundation, Inc., 59 Temple Place, Suite 330, Boston, *
21	* MA 02111-1307 USA *
22	***************************************************************************/
23
24	#ifndef __RT_MATH_H__
25	#define __RT_MATH_H__
26
27	#include <math.h>
28	#include <stdint.h>
29	#include "global_private.h"
30
31	/// Needed for calculating frequency ratio used to pitch a sample
32	#define TWELVEHUNDREDTH_ROOT_OF_TWO 1.000577789506555
33
34	enum implementation_t {
35	CPP,
36	ASM_X86_MMX_SSE
37	};
38
39	/** @brief Real Time Math Base Class
40	*
41	* Math functions for real time operation. This base class contains all
42	* non-template methods.
43	*/
44	class RTMathBase {
45	public:
46	/**
47	* High resolution time stamp.
48	*/
49	typedef uint32_t time_stamp_t;
50
51	typedef uint64_t usecs_t;
52
53	/**
54	* We read the processor's cycle count register as a reference
55	* for the real time. These are of course only abstract values
56	* with arbitrary time entity, but that's not a problem as long
57	* as we calculate relatively.
58	*
59	* @see unsafeMicroSeconds()
60	*/
61	static time_stamp_t CreateTimeStamp();
62
63	/**
64	* Calculates the frequency ratio for a pitch value given in cents
65	* (assuming equal tempered scale of course, divided into 12
66	* semitones per octave and 100 cents per semitone).
67	*
68	* Note: CONFIG_MAX_PITCH (defined in config.h) has to be defined to an
69	* appropriate value, otherwise the behavior of this function is
70	* undefined, but most probably if CONFIG_MAX_PITCH is too small, the
71	* application will crash due to segmentation fault here.
72	*
73	* @param cents - pitch value in cents (+1200 cents means +1 octave)
74	* @returns frequency ratio (e.g. +2.0 for +1 octave)
75	*/
76	inline static double CentsToFreqRatio(double Cents) {
77	int index_int = (int) (Cents); // integer index
78	float index_fract = Cents - index_int; // fractional part of index
79	return pCentsToFreqTable[index_int] + index_fract * (pCentsToFreqTable[index_int+1] - pCentsToFreqTable[index_int]);
80	}
81
82	/**
83	* Slower version of CentsToFreqRatio, for big values.
84	*
85	* @param cents - pitch value in cents (+1200 cents means +1 octave)
86	* @returns frequency ratio (e.g. +2.0 for +1 octave)
87	*/
88	static double CentsToFreqRatioUnlimited(double Cents) {
89	int octaves = int(Cents / 1200);
90	double x = CentsToFreqRatio(Cents - octaves * 1200);
91	return octaves < 0 ? x / (1 << -octaves) : x * (1 << octaves);
92	}
93
94	/**
95	* Inverse function to CentsToFreqRatio(). This function is a bit
96	* slow, so it should not be called too frequently.
97	*/
98	static double FreqRatioToCents(double FreqRatio) {
99	return log(FreqRatio) / log(TWELVEHUNDREDTH_ROOT_OF_TWO);
100	}
101
102	/**
103	* Calculates the line ratio value representation (linear scale)
104	* of the @a decibel value provided (exponential scale).
105	*
106	* The context of audio acoustic sound pressure levels is assumed, and
107	* hence the field version of the dB unit is used here (which uses a
108	* linear factor of 20). This function is a bit slow, so it should
109	* not be called too frequently.
110	*
111	* @param decibel - sound pressure level in dB
112	* @returns linear ratio of the supplied dB value
113	*/
114	static float DecibelToLinRatio(float decibel) {
115	return powf(10.f, decibel / 20.f);
116	}
117
118	/**
119	* Calculates the relatively summed average of a set of values.
120	*
121	* @param current - the current avaerage value of all previously summed values
122	* @param sample - new value to be applied as summed average to the existing values
123	* @param n - amount of sample values applied so far
124	* @returns new average value of all summed values (including the new @a sample)
125	*/
126	inline static float RelativeSummedAvg(float current, float sample, int n) {
127	return current + (sample - current) / float(n);
128	}
129
130	/**
131	* Clock source to use for getting the current time.
132	*/
133	enum clock_source_t {
134	real_clock, ///< Use this to measure time that passed in reality (no matter if process got suspended).
135	process_clock, ///< Use this to measure only the CPU execution time of the current process (if the process got suspended, the clock is paused as well).
136	thread_clock, ///< Use this to measure only the CPU execution time of the current thread (if the process got suspended or another thread is executed, the clock is paused as well).
137	};
138
139	/**
140	* Returns a time stamp of the current time in microseconds (in
141	* probably real-time @b unsafe way). There is no guarantee about
142	* what the returned amount of microseconds relates to (i.e.
143	* microseconds since epoch, microseconds since system uptime, ...).
144	* So you should only use it to calculate time differences between
145	* values taken with this method.
146	*
147	* @b CAUTION: This method may not @b NOT be real-time safe! On some
148	* systems it could be RT safe, but there is no guarantee whatsoever!
149	* So this method should only be used for debugging, benchmarking and
150	* other developing purposes !
151	*
152	* For creating time stamps in real-time context, use
153	* CreateTimeStamp() instead.
154	*
155	* @param source - the actual clock to use for getting the current
156	* time, note that the various clock sources may not
157	* be implemented on all systems
158	* @returns time stamp in microseconds
159	*
160	* @see CreateTimeStamp()
161	*/
162	static usecs_t unsafeMicroSeconds(clock_source_t source);
163
164	private:
165	static float* pCentsToFreqTable;
166
167	static float* InitCentsToFreqTable();
168	};
169
170	/** @brief Real Time Math
171	*
172	* This is a template which provides customized methods for the desired low
173	* level implementation. The ASM_X86_MMX_SSE implementation of each method
174	* for example doesn't use 387 FPU instruction. This is needed for MMX
175	* algorithms which do not allow mixed MMX and 387 instructions.
176	*/
177	template<implementation_t IMPL = CPP>
178	class __RTMath : public RTMathBase {
179	public:
180	// conversion using truncate
181	inline static int Int(const float a) {
182	switch (IMPL) {
183	#if CONFIG_ASM && ARCH_X86
184	case ASM_X86_MMX_SSE: {
185	int ret;
186	asm (
187	"cvttss2si %1, %0 # convert to int\n\t"
188	: "=r" (ret)
189	: "m" (a)
190	);
191	return ret;
192	}
193	#endif // CONFIG_ASM && ARCH_X86
194	default: {
195	return (int) a;
196	}
197	}
198	}
199
200	//for doubles and everything else except floats
201	template<class T_a> inline static int Int(const T_a a) {
202	return (int) a;
203	}
204
205	inline static float Float(const int a) {
206	switch (IMPL) {
207	#if CONFIG_ASM && ARCH_X86
208	case ASM_X86_MMX_SSE: {
209	float ret;
210	asm (
211	"cvtsi2ss %1, %%xmm0 # convert to float\n\t"
212	"movss %%xmm0,%0 # output\n\t"
213	: "=m" (ret)
214	: "r" (a)
215	);
216	return ret;
217	}
218	#endif // CONFIG_ASM && ARCH_X86
219	default: {
220	return (float) a;
221	}
222	}
223	}
224
225	#if 0
226	//for everything except ints
227	template<class T_a> inline static float Float(T_a a) {
228	return (float) a;
229	}
230	#endif
231
232	inline static float Sum(const float& a, const float& b) {
233	switch (IMPL) {
234	#if CONFIG_ASM && ARCH_X86
235	case ASM_X86_MMX_SSE: {
236	float ret;
237	asm (
238	"movss %1, %%xmm0 # load a\n\t"
239	"addss %2, %%xmm0 # a + b\n\t"
240	"movss %%xmm0, %0 # output\n\t"
241	: "=m" (ret)
242	: "m" (a), "m" (b)
243	);
244	return ret;
245	}
246	#endif // CONFIG_ASM && ARCH_X86
247	default: {
248	return (a + b);
249	}
250	}
251	}
252
253	template<class T_a, class T_b> inline static T_a Sum(const T_a a, const T_b b) {
254	return (a + b);
255	}
256
257	inline static float Sub(const float& a, const float& b) {
258	switch (IMPL) {
259	#if CONFIG_ASM && ARCH_X86
260	case ASM_X86_MMX_SSE: {
261	float ret;
262	asm (
263	"movss %1, %%xmm0 # load a\n\t"
264	"subss %2, %%xmm0 # a - b\n\t"
265	"movss %%xmm0, %0 # output\n\t"
266	: "=m" (ret)
267	: "m" (a), "m" (b)
268	);
269	return ret;
270	}
271	#endif // CONFIG_ASM && ARCH_X86
272	default: {
273	return (a - b);
274	}
275	}
276	}
277
278	template<class T_a, class T_b> inline static T_a Sub(const T_a a, const T_b b) {
279	return (a - b);
280	}
281
282	inline static float Mul(const float a, const float b) {
283	switch (IMPL) {
284	#if CONFIG_ASM && ARCH_X86
285	case ASM_X86_MMX_SSE: {
286	float ret;
287	asm (
288	"movss %1, %%xmm0 # load a\n\t"
289	"mulss %2, %%xmm0 # a * b\n\t"
290	"movss %%xmm0, %0 # output\n\t"
291	: "=m" (ret)
292	: "m" (a), "m" (b)
293	);
294	return ret;
295	}
296	#endif // CONFIG_ASM && ARCH_X86
297	default: {
298	return (a * b);
299	}
300	}
301	}
302
303	template<class T_a, class T_b> inline static T_a Mul(const T_a a, const T_b b) {
304	return (a * b);
305	}
306
307	inline static float Div(const float a, const float b) {
308	switch (IMPL) {
309	#if CONFIG_ASM && ARCH_X86
310	case ASM_X86_MMX_SSE: {
311	float ret;
312	asm (
313	"movss %1, %%xmm0 # load a\n\t"
314	"divss %2, %%xmm0 # a / b\n\t"
315	"movss %%xmm0, %0 # output\n\t"
316	: "=m" (ret)
317	: "m" (a), "m" (b)
318	);
319	return ret;
320	}
321	#endif // CONFIG_ASM && ARCH_X86
322	default: {
323	return (a / b);
324	}
325	}
326	}
327
328	template<class T_a, class T_b> inline static T_a Div(const T_a a, const T_b b) {
329	return (a / b);
330	}
331
332	inline static float Min(const float a, const float b) {
333	switch (IMPL) {
334	#if CONFIG_ASM && ARCH_X86
335	case ASM_X86_MMX_SSE: {
336	float ret;
337	asm (
338	"movss %1, %%xmm0 # load a\n\t"
339	"minss %2, %%xmm0 # Minimum(a, b)\n\t"
340	"movss %%xmm0, %0 # output\n\t"
341	: "=m" (ret)
342	: "m" (a), "m" (b)
343	);
344	return ret;
345	}
346	#endif // CONFIG_ASM && ARCH_X86
347	default: {
348	return std::min(a, b);
349	}
350	}
351	}
352
353	template<class T_a, class T_b> inline static T_a Min(const T_a a, const T_b b) {
354	return (b < a) ? b : a;
355	}
356
357	inline static float Max(const float a, const float b) {
358	switch (IMPL) {
359	#if CONFIG_ASM && ARCH_X86
360	case ASM_X86_MMX_SSE: {
361	float ret;
362	asm (
363	"movss %1, %%xmm0 # load a\n\t"
364	"maxss %2, %%xmm0 # Maximum(a, b)\n\t"
365	"movss %%xmm0, %0 # output\n\t"
366	: "=m" (ret)
367	: "m" (a), "m" (b)
368	);
369	return ret;
370	}
371	#endif // CONFIG_ASM && ARCH_X86
372	default: {
373	return std::max(a, b);
374	}
375	}
376	}
377
378	template<class T_a, class T_b> inline static T_a Max(const T_a a, const T_b b) {
379	return (b > a) ? b : a;
380	}
381
382	inline static float Fmodf(const float &a, const float &b) {
383	switch (IMPL) {
384	#if CONFIG_ASM && ARCH_X86
385	case ASM_X86_MMX_SSE: {
386	float ret;
387	asm (
388	"movss %1, %%xmm0 # load a\n\t"
389	"movss %2, %%xmm1 # load b\n\t"
390	"movss %%xmm0,%%xmm2\n\t"
391	"divss %%xmm1, %%xmm2 # xmm2 = a / b\n\t"
392	"cvttss2si %%xmm2, %%ecx #convert to int\n\t"
393	"cvtsi2ss %%ecx, %%xmm2 #convert back to float\n\t"
394	"mulss %%xmm1, %%xmm2 # xmm2 = b * int(a/b)\n\t"
395	"subss %%xmm2, %%xmm0 #sub a\n\t"
396	"movss %%xmm0, %0 # output\n\t"
397	: "=m" (ret)
398	: "m" (a), "m" (b)
399	: "%ecx"
400	);
401	return ret;
402	}
403	#endif // CONFIG_ASM && ARCH_X86
404	default: {
405	return fmodf(a, b);
406	}
407	}
408	}
409	};
410
411	/// convenience typedef for using the default implementation (which is CPP)
412	typedef __RTMath<> RTMath;
413
414	#endif // __RT_MATH_H__