1 /////////////////////////////////////////////////////////////////
4 // Routines for doing math operations in MSAPROBS
5 /////////////////////////////////////////////////////////////////
15 typedef float ScoreType;
17 const float LOG_ZERO = -2e20;
18 const float LOG_ONE = 0.0;
20 /////////////////////////////////////////////////////////////////
23 // Compute the logarithm of x.
24 /////////////////////////////////////////////////////////////////
26 inline ScoreType LOG(ScoreType x) {
30 /////////////////////////////////////////////////////////////////
34 /////////////////////////////////////////////////////////////////
36 inline ScoreType EXP(ScoreType x) {
42 return (((0.03254409303190190000 * x + 0.16280432765779600000) * x
43 + 0.49929760485974900000) * x + 0.99995149601363700000) * x
44 + 0.99999925508501600000;
47 return (((0.01973899026052090000 * x + 0.13822379685007000000) * x
48 + 0.48056651562365000000) * x + 0.99326940370383500000) * x
49 + 0.99906756856399500000;
50 return (((0.00940528203591384000 * x + 0.09414963667859410000) * x
51 + 0.40825793595877300000) * x + 0.93933625499130400000) * x
52 + 0.98369508190545300000;
56 return (((0.00217245711583303000 * x + 0.03484829428350620000) * x
57 + 0.22118199801337800000) * x + 0.67049462206469500000) * x
58 + 0.83556950223398500000;
59 return (((0.00012398771025456900 * x + 0.00349155785951272000) * x
60 + 0.03727721426017900000) * x + 0.17974997741536900000) * x
61 + 0.33249299994217400000;
64 return (((0.00000051741713416603 * x + 0.00002721456879608080) * x
65 + 0.00053418601865636800) * x + 0.00464101989351936000) * x
66 + 0.01507447981459420000;
71 /////////////////////////////////////////////////////////////////
74 // Computes log (exp (x) + 1), for 0 <= x <= 7.5.
75 /////////////////////////////////////////////////////////////////
77 inline ScoreType LOOKUP (ScoreType x){
78 //return log (exp(x) + 1);
82 return log (exp(x) + 1);
83 return (((-0.00486373205785640000*x - 0.00020245408813934800)*x + 0.12504222666029800000)*x + 0.49999685320563000000)*x + 0.69314723138948900000;
86 return (((-0.00278634205460548000*x - 0.00458097251248546000)*x + 0.12865849880472500000)*x + 0.49862228499205200000)*x + 0.69334810088688000000;
87 return (((0.00059633755154209200*x - 0.01918996666063320000)*x + 0.15288232492093800000)*x + 0.48039958825756900000)*x + 0.69857578503189200000;
91 return (((0.00135958539181047000*x - 0.02329807659316430000)*x + 0.15885799609532100000)*x + 0.48167498563270800000)*x + 0.69276185058669200000;
92 return (((0.00011992394456683500*x - 0.00338464503306568000)*x + 0.03622746366545470000)*x + 0.82481250248383700000)*x + 0.32507892994863100000;
95 return (((0.00000051726300753785*x - 0.00002720671238876090)*x + 0.00053403733818413500)*x + 0.99536021775747900000)*x + 0.01507065715532010000;
99 /////////////////////////////////////////////////////////////////
102 // Computes log (exp (x) + 1).
103 /////////////////////////////////////////////////////////////////
105 inline ScoreType LOOKUP_SLOW (ScoreType x){
106 return log (exp (x) + 1);
109 /////////////////////////////////////////////////////////////////
112 // Compute max of three numbers
113 /////////////////////////////////////////////////////////////////
115 inline ScoreType MAX (ScoreType x, ScoreType y, ScoreType z){
126 /////////////////////////////////////////////////////////////////
129 // Add two log probabilities and store in the first argument
130 /////////////////////////////////////////////////////////////////
132 inline void LOG_PLUS_EQUALS (ScoreType &x, ScoreType y){
134 x = (x <= LOG_ZERO) ? y : LOOKUP(y-x) + x;
136 x = (y <= LOG_ZERO) ? x : LOOKUP(x-y) + y;
139 /////////////////////////////////////////////////////////////////
140 // LOG_PLUS_EQUALS_SLOW()
142 // Add two log probabilities and store in the first argument
143 /////////////////////////////////////////////////////////////////
145 inline void LOG_PLUS_EQUALS_SLOW (ScoreType &x, ScoreType y){
147 x = (x <= LOG_ZERO) ? y : LOOKUP_SLOW(y-x) + x;
149 x = (y <= LOG_ZERO) ? x : LOOKUP_SLOW(x-y) + y;
152 /////////////////////////////////////////////////////////////////
155 // Add two log probabilities
156 /////////////////////////////////////////////////////////////////
158 inline ScoreType LOG_ADD (ScoreType x, ScoreType y){
159 if (x < y) return (x <= LOG_ZERO) ? y : LOOKUP(y-x) + x;
160 return (y <= LOG_ZERO) ? x : LOOKUP(x-y) + y;
165 /////////////////////////////////////////////////////////////////
168 // Compute the logarithm of x.
169 /////////////////////////////////////////////////////////////////
171 inline float LOG (float x){
175 /////////////////////////////////////////////////////////////////
178 // Computes exp(x), fr -4.6 <= x <= 0.
179 /////////////////////////////////////////////////////////////////
181 inline float EXP (float x){
183 if (x < EXP_UNDERFLOW_THRESHOLD) return 0.0f;
184 return (((0.006349841068584 * x + 0.080775412572352) * x + 0.397982026296272) * x + 0.95279335963787f) * x + 0.995176455837312f;
185 //return (((0.00681169825657f * x + 0.08386267698832f) * x + 0.40413983195844f) * x + 0.95656674979767f) * x + 0.99556744049130f;
189 const float EXP_UNDERFLOW_THRESHOLD = -4.6;
190 const float LOG_UNDERFLOW_THRESHOLD = 7.5;
192 /////////////////////////////////////////////////////////////////
195 // Computes log (exp (x) + 1), for 0 <= x <= 7.5.
196 /////////////////////////////////////////////////////////////////
198 inline float LOOKUP(float x) {
200 assert(x <= LOG_UNDERFLOW_THRESHOLD);
201 //return ((-0.00653779113685f * x + 0.09537236626558f) * x + 0.55317574459331f) * x + 0.68672959851568f;
203 return ((-0.009350833524763f * x + 0.130659527668286f) * x
204 + 0.498799810682272f) * x + 0.693203116424741f;
206 return ((-0.014532321752540f * x + 0.139942324101744f) * x
207 + 0.495635523139337f) * x + 0.692140569840976f;
209 return ((-0.004605031767994f * x + 0.063427417320019f) * x
210 + 0.695956496475118f) * x + 0.514272634594009f;
211 assert(x <= LOG_UNDERFLOW_THRESHOLD);
212 return ((-0.000458661602210f * x + 0.009695946122598f) * x
213 + 0.930734667215156f) * x + 0.168037164329057f;
215 //return (((0.00089738532761f * x - 0.01859488697982f) * x + 0.14415772028626f) * x + 0.49515490689159f) * x + 0.69311928966454f;
218 /////////////////////////////////////////////////////////////////
221 // Computes log (exp (x) + 1).
222 /////////////////////////////////////////////////////////////////
224 inline float LOOKUP_SLOW(float x) {
225 return log(exp(x) + 1);
228 /////////////////////////////////////////////////////////////////
231 // Compute max of three numbers
232 /////////////////////////////////////////////////////////////////
234 inline float MAX(float x, float y, float z) {
245 /////////////////////////////////////////////////////////////////
248 // Add two log probabilities and store in the first argument
249 /////////////////////////////////////////////////////////////////
251 inline void LOG_PLUS_EQUALS(float &x, float y) {
253 x = (x == LOG_ZERO || y - x >= LOG_UNDERFLOW_THRESHOLD) ?
254 y : LOOKUP(y - x) + x;
256 x = (y == LOG_ZERO || x - y >= LOG_UNDERFLOW_THRESHOLD) ?
257 x : LOOKUP(x - y) + y;
260 /////////////////////////////////////////////////////////////////
261 // LOG_PLUS_EQUALS_SLOW()
263 // Add two log probabilities and store in the first argument
264 /////////////////////////////////////////////////////////////////
266 inline void LOG_PLUS_EQUALS_SLOW(float &x, float y) {
268 x = (x == LOG_ZERO) ? y : LOOKUP_SLOW(y - x) + x;
270 x = (y == LOG_ZERO) ? x : LOOKUP_SLOW(x - y) + y;
273 /////////////////////////////////////////////////////////////////
276 // Add two log probabilities
277 /////////////////////////////////////////////////////////////////
279 inline float LOG_ADD(float x, float y) {
281 return (x == LOG_ZERO || y - x >= LOG_UNDERFLOW_THRESHOLD) ?
282 y : LOOKUP(y - x) + x;
283 return (y == LOG_ZERO || x - y >= LOG_UNDERFLOW_THRESHOLD) ?
284 x : LOOKUP(x - y) + y;
287 /////////////////////////////////////////////////////////////////
290 // Add three log probabilities
291 /////////////////////////////////////////////////////////////////
293 inline float LOG_ADD(float x1, float x2, float x3) {
294 return LOG_ADD(x1, LOG_ADD(x2, x3));
297 /////////////////////////////////////////////////////////////////
300 // Add four log probabilities
301 /////////////////////////////////////////////////////////////////
303 inline float LOG_ADD(float x1, float x2, float x3, float x4) {
304 return LOG_ADD(x1, LOG_ADD(x2, LOG_ADD(x3, x4)));
307 /////////////////////////////////////////////////////////////////
310 // Add five log probabilities
311 /////////////////////////////////////////////////////////////////
313 inline float LOG_ADD(float x1, float x2, float x3, float x4, float x5) {
314 return LOG_ADD(x1, LOG_ADD(x2, LOG_ADD(x3, LOG_ADD(x4, x5))));
317 /////////////////////////////////////////////////////////////////
320 // Add siz log probabilities
321 /////////////////////////////////////////////////////////////////
323 inline float LOG_ADD(float x1, float x2, float x3, float x4, float x5,
325 return LOG_ADD(x1, LOG_ADD(x2, LOG_ADD(x3, LOG_ADD(x4, LOG_ADD(x5, x6)))));
328 /////////////////////////////////////////////////////////////////
331 // Add seven log probabilities
332 /////////////////////////////////////////////////////////////////
334 inline float LOG_ADD(float x1, float x2, float x3, float x4, float x5, float x6,
337 LOG_ADD(x2, LOG_ADD(x3, LOG_ADD(x4, LOG_ADD(x5, LOG_ADD(x6, x7))))));
340 /////////////////////////////////////////////////////////////////
341 // ChooseBestOfThree()
343 // Store the largest of three values x1, x2, and x3 in *x. Also
344 // if xi is the largest value, then store bi in *b.
345 /////////////////////////////////////////////////////////////////
347 inline void ChooseBestOfThree(float x1, float x2, float x3, char b1, char b2,
348 char b3, float *x, char *b) {