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1.1 root 1:
2: /*============================================================================
3:
4: This C source file is an extension to the SoftFloat IEC/IEEE Floating-point
5: Arithmetic Package, Release 2a.
6:
7: Written by Andreas Grabher for Previous, NeXT Computer Emulator.
8:
9: =============================================================================*/
10:
11: #include <stdint.h>
12: #include <stdlib.h>
13:
14: #include "softfloat.h"
15: #include "softfloat-specialize.h"
16: #include "softfloat_fpsp_tables.h"
17:
18:
19: /*----------------------------------------------------------------------------
20: | Algorithms for transcendental functions supported by MC68881 and MC68882
21: | mathematical coprocessors. The functions are derived from FPSP library.
22: *----------------------------------------------------------------------------*/
23:
24: #define pi_sig LIT64(0xc90fdaa22168c235)
25: #define pi_sig0 LIT64(0xc90fdaa22168c234)
26: #define pi_sig1 LIT64(0xc4c6628b80dc1cd1)
27:
28: #define pi_exp 0x4000
29: #define piby2_exp 0x3FFF
30: #define piby4_exp 0x3FFE
31:
32: #define one_exp 0x3FFF
33: #define one_sig LIT64(0x8000000000000000)
34:
35: #define SET_PREC \
36: int8_t user_rnd_mode, user_rnd_prec; \
37: user_rnd_mode = status->float_rounding_mode; \
38: user_rnd_prec = status->floatx80_rounding_precision; \
39: status->float_rounding_mode = float_round_nearest_even; \
40: status->floatx80_rounding_precision = 80
41:
42: #define RESET_PREC \
43: status->float_rounding_mode = user_rnd_mode; \
44: status->floatx80_rounding_precision = user_rnd_prec
45:
46: /*----------------------------------------------------------------------------
47: | Function for compactifying extended double-precision floating point values.
48: *----------------------------------------------------------------------------*/
49:
50: static int32_t floatx80_make_compact(int32_t aExp, uint64_t aSig)
51: {
52: return (aExp<<16)|(aSig>>48);
53: }
54:
55:
56: /*----------------------------------------------------------------------------
57: | Arc cosine
58: *----------------------------------------------------------------------------*/
59:
60: floatx80 floatx80_acos(floatx80 a, float_status *status)
61: {
62: flag aSign;
63: int32_t aExp;
64: uint64_t aSig;
65:
66:
67: int32_t compact;
68: floatx80 fp0, fp1, one;
69:
70: aSig = extractFloatx80Frac(a);
71: aExp = extractFloatx80Exp(a);
72: aSign = extractFloatx80Sign(a);
73:
74: if (aExp == 0x7FFF && (uint64_t) (aSig<<1)) {
75: return propagateFloatx80NaNOneArg(a, status);
76: }
77: if (aExp == 0 && aSig == 0) {
78: float_raise(float_flag_inexact, status);
79: return roundAndPackFloatx80(status->floatx80_rounding_precision, 0, piby2_exp, pi_sig, 0, status);
80: }
81:
82: compact = floatx80_make_compact(aExp, aSig);
83:
84: if (compact >= 0x3FFF8000) { // |X| >= 1
85: if (aExp == one_exp && aSig == one_sig) { // |X| == 1
86: if (aSign) { // X == -1
87: a = packFloatx80(0, pi_exp, pi_sig);
88: float_raise(float_flag_inexact, status);
89: return floatx80_move(a, status);
90: } else { // X == +1
91: return packFloatx80(0, 0, 0);
92: }
93: } else { // |X| > 1
94: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 95: return floatx80_default_nan(status);
1.1 root 96: }
97: } // |X| < 1
98:
99: SET_PREC;
100:
101: one = packFloatx80(0, one_exp, one_sig);
102: fp0 = a;
103:
104: fp1 = floatx80_add(one, fp0, status); // 1 + X
105: fp0 = floatx80_sub(one, fp0, status); // 1 - X
106: fp0 = floatx80_div(fp0, fp1, status); // (1-X)/(1+X)
107: fp0 = floatx80_sqrt(fp0, status); // SQRT((1-X)/(1+X))
108: fp0 = floatx80_atan(fp0, status); // ATAN(SQRT((1-X)/(1+X)))
109:
110: RESET_PREC;
111:
112: a = floatx80_add(fp0, fp0, status); // 2 * ATAN(SQRT((1-X)/(1+X)))
113:
114: float_raise(float_flag_inexact, status);
115:
116: return a;
117: }
118:
119: /*----------------------------------------------------------------------------
120: | Arc sine
121: *----------------------------------------------------------------------------*/
122:
123: floatx80 floatx80_asin(floatx80 a, float_status *status)
124: {
125: flag aSign;
126: int32_t aExp;
127: uint64_t aSig;
128:
129: int32_t compact;
130: floatx80 fp0, fp1, fp2, one;
131:
132: aSig = extractFloatx80Frac(a);
133: aExp = extractFloatx80Exp(a);
134: aSign = extractFloatx80Sign(a);
135:
136: if (aExp == 0x7FFF && (uint64_t) (aSig<<1)) {
137: return propagateFloatx80NaNOneArg(a, status);
138: }
139:
140: if (aExp == 0 && aSig == 0) {
141: return packFloatx80(aSign, 0, 0);
142: }
143:
144: compact = floatx80_make_compact(aExp, aSig);
145:
146: if (compact >= 0x3FFF8000) { // |X| >= 1
147: if (aExp == one_exp && aSig == one_sig) { // |X| == 1
148: float_raise(float_flag_inexact, status);
149: a = packFloatx80(aSign, piby2_exp, pi_sig);
150: return floatx80_move(a, status);
151: } else { // |X| > 1
152: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 153: return floatx80_default_nan(status);
1.1 root 154: }
155:
156: } // |X| < 1
157:
158: SET_PREC;
159:
160: one = packFloatx80(0, one_exp, one_sig);
161: fp0 = a;
162:
163: fp1 = floatx80_sub(one, fp0, status); // 1 - X
164: fp2 = floatx80_add(one, fp0, status); // 1 + X
165: fp1 = floatx80_mul(fp2, fp1, status); // (1+X)*(1-X)
166: fp1 = floatx80_sqrt(fp1, status); // SQRT((1+X)*(1-X))
167: fp0 = floatx80_div(fp0, fp1, status); // X/SQRT((1+X)*(1-X))
168:
169: RESET_PREC;
170:
171: a = floatx80_atan(fp0, status); // ATAN(X/SQRT((1+X)*(1-X)))
172:
173: float_raise(float_flag_inexact, status);
174:
175: return a;
176: }
177:
178: /*----------------------------------------------------------------------------
179: | Arc tangent
180: *----------------------------------------------------------------------------*/
181:
182: floatx80 floatx80_atan(floatx80 a, float_status *status)
183: {
184: flag aSign;
185: int32_t aExp;
186: uint64_t aSig;
187:
188: int32_t compact, tbl_index;
189: floatx80 fp0, fp1, fp2, fp3, xsave;
190:
191: aSig = extractFloatx80Frac(a);
192: aExp = extractFloatx80Exp(a);
193: aSign = extractFloatx80Sign(a);
194:
195: if (aExp == 0x7FFF) {
196: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
197: a = packFloatx80(aSign, piby2_exp, pi_sig);
198: float_raise(float_flag_inexact, status);
199: return floatx80_move(a, status);
200: }
201:
202: if (aExp == 0 && aSig == 0) {
203: return packFloatx80(aSign, 0, 0);
204: }
205:
206: compact = floatx80_make_compact(aExp, aSig);
207:
208: SET_PREC;
209:
210: if (compact < 0x3FFB8000 || compact > 0x4002FFFF) { // |X| >= 16 or |X| < 1/16
211: if (compact > 0x3FFF8000) { // |X| >= 16
212: if (compact > 0x40638000) { // |X| > 2^(100)
213: fp0 = packFloatx80(aSign, piby2_exp, pi_sig);
214: fp1 = packFloatx80(aSign, 0x0001, one_sig);
215:
216: RESET_PREC;
217:
218: a = floatx80_sub(fp0, fp1, status);
219:
220: float_raise(float_flag_inexact, status);
221:
222: return a;
223: } else {
224: fp0 = a;
225: fp1 = packFloatx80(1, one_exp, one_sig); // -1
226: fp1 = floatx80_div(fp1, fp0, status); // X' = -1/X
227: xsave = fp1;
228: fp0 = floatx80_mul(fp1, fp1, status); // Y = X'*X'
229: fp1 = floatx80_mul(fp0, fp0, status); // Z = Y*Y
230: fp3 = float64_to_floatx80(LIT64(0xBFB70BF398539E6A), status); // C5
231: fp2 = float64_to_floatx80(LIT64(0x3FBC7187962D1D7D), status); // C4
232: fp3 = floatx80_mul(fp3, fp1, status); // Z*C5
233: fp2 = floatx80_mul(fp2, fp1, status); // Z*C4
234: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0xBFC24924827107B8), status), status); // C3+Z*C5
235: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FC999999996263E), status), status); // C2+Z*C4
236: fp1 = floatx80_mul(fp1, fp3, status); // Z*(C3+Z*C5)
237: fp2 = floatx80_mul(fp2, fp0, status); // Y*(C2+Z*C4)
238: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0xBFD5555555555536), status), status); // C1+Z*(C3+Z*C5)
239: fp0 = floatx80_mul(fp0, xsave, status); // X'*Y
240: fp1 = floatx80_add(fp1, fp2, status); // [Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
241: fp0 = floatx80_mul(fp0, fp1, status); // X'*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) ??
242: fp0 = floatx80_add(fp0, xsave, status);
243: fp1 = packFloatx80(aSign, piby2_exp, pi_sig);
244:
245: RESET_PREC;
246:
247: a = floatx80_add(fp0, fp1, status);
248:
249: float_raise(float_flag_inexact, status);
250:
251: return a;
252: }
253: } else { // |X| < 1/16
254: if (compact < 0x3FD78000) { // |X| < 2^(-40)
255: RESET_PREC;
256:
257: a = floatx80_move(a, status);
258:
259: float_raise(float_flag_inexact, status);
260:
261: return a;
262: } else {
263: fp0 = a;
264: xsave = a;
265: fp0 = floatx80_mul(fp0, fp0, status); // Y = X*X
266: fp1 = floatx80_mul(fp0, fp0, status); // Z = Y*Y
267: fp2 = float64_to_floatx80(LIT64(0x3FB344447F876989), status); // B6
268: fp3 = float64_to_floatx80(LIT64(0xBFB744EE7FAF45DB), status); // B5
269: fp2 = floatx80_mul(fp2, fp1, status); // Z*B6
270: fp3 = floatx80_mul(fp3, fp1, status); // Z*B5
271: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FBC71C646940220), status), status); // B4+Z*B6
272: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0xBFC24924921872F9), status), status); // B3+Z*B5
273: fp2 = floatx80_mul(fp2, fp1, status); // Z*(B4+Z*B6)
274: fp1 = floatx80_mul(fp1, fp3, status); // Z*(B3+Z*B5)
275: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FC9999999998FA9), status), status); // B2+Z*(B4+Z*B6)
276: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0xBFD5555555555555), status), status); // B1+Z*(B3+Z*B5)
277: fp2 = floatx80_mul(fp2, fp0, status); // Y*(B2+Z*(B4+Z*B6))
278: fp0 = floatx80_mul(fp0, xsave, status); // X*Y
279: fp1 = floatx80_add(fp1, fp2, status); // [B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
280: fp0 = floatx80_mul(fp0, fp1, status); // X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
281:
282: RESET_PREC;
283:
284: a = floatx80_add(fp0, xsave, status);
285:
286: float_raise(float_flag_inexact, status);
287:
288: return a;
289: }
290: }
291: } else {
292: aSig &= LIT64(0xF800000000000000);
293: aSig |= LIT64(0x0400000000000000);
294: xsave = packFloatx80(aSign, aExp, aSig); // F
295: fp0 = a;
296: fp1 = a; // X
297: fp2 = packFloatx80(0, one_exp, one_sig); // 1
298: fp1 = floatx80_mul(fp1, xsave, status); // X*F
299: fp0 = floatx80_sub(fp0, xsave, status); // X-F
300: fp1 = floatx80_add(fp1, fp2, status); // 1 + X*F
301: fp0 = floatx80_div(fp0, fp1, status); // U = (X-F)/(1+X*F)
302:
303: tbl_index = compact;
304:
305: tbl_index &= 0x7FFF0000;
306: tbl_index -= 0x3FFB0000;
307: tbl_index >>= 1;
308: tbl_index += compact&0x00007800;
309: tbl_index >>= 11;
310:
311: fp3 = atan_tbl[tbl_index];
312:
313: fp3.high |= aSign ? 0x8000 : 0; // ATAN(F)
314:
315: fp1 = floatx80_mul(fp0, fp0, status); // V = U*U
316: fp2 = float64_to_floatx80(LIT64(0xBFF6687E314987D8), status); // A3
317: fp2 = floatx80_add(fp2, fp1, status); // A3+V
318: fp2 = floatx80_mul(fp2, fp1, status); // V*(A3+V)
319: fp1 = floatx80_mul(fp1, fp0, status); // U*V
320: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x4002AC6934A26DB3), status), status); // A2+V*(A3+V)
321: fp1 = floatx80_mul(fp1, float64_to_floatx80(LIT64(0xBFC2476F4E1DA28E), status), status); // A1+U*V
322: fp1 = floatx80_mul(fp1, fp2, status); // A1*U*V*(A2+V*(A3+V))
323: fp0 = floatx80_add(fp0, fp1, status); // ATAN(U)
324:
325: RESET_PREC;
326:
327: a = floatx80_add(fp0, fp3, status); // ATAN(X)
328:
329: float_raise(float_flag_inexact, status);
330:
331: return a;
332: }
333: }
334:
335: /*----------------------------------------------------------------------------
336: | Hyperbolic arc tangent
337: *----------------------------------------------------------------------------*/
338:
339: floatx80 floatx80_atanh(floatx80 a, float_status *status)
340: {
341: flag aSign;
342: int32_t aExp;
343: uint64_t aSig;
344:
345: int32_t compact;
346: floatx80 fp0, fp1, fp2, one;
347:
348: aSig = extractFloatx80Frac(a);
349: aExp = extractFloatx80Exp(a);
350: aSign = extractFloatx80Sign(a);
351:
352: if (aExp == 0x7FFF && (uint64_t) (aSig<<1)) {
353: return propagateFloatx80NaNOneArg(a, status);
354: }
355:
356: if (aExp == 0 && aSig == 0) {
357: return packFloatx80(aSign, 0, 0);
358: }
359:
360: compact = floatx80_make_compact(aExp, aSig);
361:
362: if (compact >= 0x3FFF8000) { // |X| >= 1
363: if (aExp == one_exp && aSig == one_sig) { // |X| == 1
364: float_raise(float_flag_divbyzero, status);
365: return packFloatx80(aSign, 0x7FFF, floatx80_default_infinity_low);
366: } else { // |X| > 1
367: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 368: return floatx80_default_nan(status);
1.1 root 369: }
370: } // |X| < 1
371:
372: SET_PREC;
373:
374: one = packFloatx80(0, one_exp, one_sig);
375: fp2 = packFloatx80(aSign, 0x3FFE, one_sig); // SIGN(X) * (1/2)
376: fp0 = packFloatx80(0, aExp, aSig); // Y = |X|
377: fp1 = packFloatx80(1, aExp, aSig); // -Y
378: fp0 = floatx80_add(fp0, fp0, status); // 2Y
379: fp1 = floatx80_add(fp1, one, status); // 1-Y
380: fp0 = floatx80_div(fp0, fp1, status); // Z = 2Y/(1-Y)
381: fp0 = floatx80_lognp1(fp0, status); // LOG1P(Z)
382:
383: RESET_PREC;
384:
385: a = floatx80_mul(fp0, fp2, status); // ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z)
386:
387: float_raise(float_flag_inexact, status);
388:
389: return a;
390: }
391:
392: /*----------------------------------------------------------------------------
393: | Cosine
394: *----------------------------------------------------------------------------*/
395:
396: floatx80 floatx80_cos(floatx80 a, float_status *status)
397: {
398: flag aSign, xSign;
399: int32_t aExp, xExp;
400: uint64_t aSig, xSig;
401:
402: int32_t compact, l, n, j;
403: floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2;
404: float32 posneg1, twoto63;
405: flag adjn, endflag;
406:
407: aSig = extractFloatx80Frac(a);
408: aExp = extractFloatx80Exp(a);
409: aSign = extractFloatx80Sign(a);
410:
411: if (aExp == 0x7FFF) {
412: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
413: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 414: return floatx80_default_nan(status);
1.1 root 415: }
416:
417: if (aExp == 0 && aSig == 0) {
418: return packFloatx80(0, one_exp, one_sig);
419: }
420:
421: adjn = 1;
422:
423: SET_PREC;
424:
425: compact = floatx80_make_compact(aExp, aSig);
426:
427: fp0 = a;
428:
429: if (compact < 0x3FD78000 || compact > 0x4004BC7E) { // 2^(-40) > |X| > 15 PI
430: if (compact > 0x3FFF8000) { // |X| >= 15 PI
431: // REDUCEX
432: fp1 = packFloatx80(0, 0, 0);
433: if (compact == 0x7FFEFFFF) {
434: twopi1 = packFloatx80(aSign ^ 1, 0x7FFE, LIT64(0xC90FDAA200000000));
435: twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, LIT64(0x85A308D300000000));
436: fp0 = floatx80_add(fp0, twopi1, status);
437: fp1 = fp0;
438: fp0 = floatx80_add(fp0, twopi2, status);
439: fp1 = floatx80_sub(fp1, fp0, status);
440: fp1 = floatx80_add(fp1, twopi2, status);
441: }
442: loop:
443: xSign = extractFloatx80Sign(fp0);
444: xExp = extractFloatx80Exp(fp0);
445: xExp -= 0x3FFF;
446: if (xExp <= 28) {
447: l = 0;
448: endflag = 1;
449: } else {
450: l = xExp - 27;
451: endflag = 0;
452: }
453: invtwopi = packFloatx80(0, 0x3FFE - l, LIT64(0xA2F9836E4E44152A)); // INVTWOPI
454: twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000));
455: twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(0x85A308D300000000));
456:
457: twoto63 = 0x5F000000;
458: twoto63 |= xSign ? 0x80000000 : 0x00000000; // SIGN(INARG)*2^63 IN SGL
459:
460: fp2 = floatx80_mul(fp0, invtwopi, status);
461: fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), status); // THE FRACTIONAL PART OF FP2 IS ROUNDED
462: fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status), status); // FP2 is N
463: fp4 = floatx80_mul(twopi1, fp2, status); // W = N*P1
464: fp5 = floatx80_mul(twopi2, fp2, status); // w = N*P2
465: fp3 = floatx80_add(fp4, fp5, status); // FP3 is P
466: fp4 = floatx80_sub(fp4, fp3, status); // W-P
467: fp0 = floatx80_sub(fp0, fp3, status); // FP0 is A := R - P
468: fp4 = floatx80_add(fp4, fp5, status); // FP4 is p = (W-P)+w
469: fp3 = fp0; // FP3 is A
470: fp1 = floatx80_sub(fp1, fp4, status); // FP1 is a := r - p
471: fp0 = floatx80_add(fp0, fp1, status); // FP0 is R := A+a
472:
473: if (endflag > 0) {
474: n = floatx80_to_int32(fp2, status);
475: goto sincont;
476: }
477: fp3 = floatx80_sub(fp3, fp0, status); // A-R
478: fp1 = floatx80_add(fp1, fp3, status); // FP1 is r := (A-R)+a
479: goto loop;
480: } else {
481: // SINSM
482: fp0 = float32_to_floatx80(0x3F800000, status); // 1
483:
484: RESET_PREC;
485:
486: if (adjn) {
487: // COSTINY
488: a = floatx80_sub(fp0, float32_to_floatx80(0x00800000, status), status);
489: } else {
490: // SINTINY
491: a = floatx80_move(a, status);
492: }
493: float_raise(float_flag_inexact, status);
494:
495: return a;
496: }
497: } else {
498: fp1 = floatx80_mul(fp0, float64_to_floatx80(LIT64(0x3FE45F306DC9C883), status), status); // X*2/PI
499:
500: n = floatx80_to_int32(fp1, status);
501: j = 32 + n;
502:
503: fp0 = floatx80_sub(fp0, pi_tbl[j], status); // X-Y1
504: fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status), status); // FP0 IS R = (X-Y1)-Y2
505:
506: sincont:
507: if ((n + adjn) & 1) {
508: // COSPOLY
509: fp0 = floatx80_mul(fp0, fp0, status); // FP0 IS S
510: fp1 = floatx80_mul(fp0, fp0, status); // FP1 IS T
511: fp2 = float64_to_floatx80(LIT64(0x3D2AC4D0D6011EE3), status); // B8
512: fp3 = float64_to_floatx80(LIT64(0xBDA9396F9F45AC19), status); // B7
513:
514: xSign = extractFloatx80Sign(fp0); // X IS S
515: xExp = extractFloatx80Exp(fp0);
516: xSig = extractFloatx80Frac(fp0);
517:
518: if (((n + adjn) >> 1) & 1) {
519: xSign ^= 1;
520: posneg1 = 0xBF800000; // -1
521: } else {
522: xSign ^= 0;
523: posneg1 = 0x3F800000; // 1
524: } // X IS NOW R'= SGN*R
525:
526: fp2 = floatx80_mul(fp2, fp1, status); // TB8
527: fp3 = floatx80_mul(fp3, fp1, status); // TB7
528: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3E21EED90612C972), status), status); // B6+TB8
529: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0xBE927E4FB79D9FCF), status), status); // B5+TB7
530: fp2 = floatx80_mul(fp2, fp1, status); // T(B6+TB8)
531: fp3 = floatx80_mul(fp3, fp1, status); // T(B5+TB7)
532: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3EFA01A01A01D423), status), status); // B4+T(B6+TB8)
533: fp4 = packFloatx80(1, 0x3FF5, LIT64(0xB60B60B60B61D438));
534: fp3 = floatx80_add(fp3, fp4, status); // B3+T(B5+TB7)
535: fp2 = floatx80_mul(fp2, fp1, status); // T(B4+T(B6+TB8))
536: fp1 = floatx80_mul(fp1, fp3, status); // T(B3+T(B5+TB7))
537: fp4 = packFloatx80(0, 0x3FFA, LIT64(0xAAAAAAAAAAAAAB5E));
538: fp2 = floatx80_add(fp2, fp4, status); // B2+T(B4+T(B6+TB8))
539: fp1 = floatx80_add(fp1, float32_to_floatx80(0xBF000000, status), status); // B1+T(B3+T(B5+TB7))
540: fp0 = floatx80_mul(fp0, fp2, status); // S(B2+T(B4+T(B6+TB8)))
541: fp0 = floatx80_add(fp0, fp1, status); // [B1+T(B3+T(B5+TB7))]+[S(B2+T(B4+T(B6+TB8)))]
542:
543: x = packFloatx80(xSign, xExp, xSig);
544: fp0 = floatx80_mul(fp0, x, status);
545:
546: RESET_PREC;
547:
548: a = floatx80_add(fp0, float32_to_floatx80(posneg1, status), status);
549:
550: float_raise(float_flag_inexact, status);
551:
552: return a;
553: } else {
554: // SINPOLY
555: xSign = extractFloatx80Sign(fp0); // X IS R
556: xExp = extractFloatx80Exp(fp0);
557: xSig = extractFloatx80Frac(fp0);
558:
559: xSign ^= ((n + adjn) >> 1) & 1; // X IS NOW R'= SGN*R
560:
561: fp0 = floatx80_mul(fp0, fp0, status); // FP0 IS S
562: fp1 = floatx80_mul(fp0, fp0, status); // FP1 IS T
563: fp3 = float64_to_floatx80(LIT64(0xBD6AAA77CCC994F5), status); // A7
564: fp2 = float64_to_floatx80(LIT64(0x3DE612097AAE8DA1), status); // A6
565: fp3 = floatx80_mul(fp3, fp1, status); // T*A7
566: fp2 = floatx80_mul(fp2, fp1, status); // T*A6
567: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0xBE5AE6452A118AE4), status), status); // A5+T*A7
568: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3EC71DE3A5341531), status), status); // A4+T*A6
569: fp3 = floatx80_mul(fp3, fp1, status); // T(A5+TA7)
570: fp2 = floatx80_mul(fp2, fp1, status); // T(A4+TA6)
571: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0xBF2A01A01A018B59), status), status); // A3+T(A5+TA7)
572: fp4 = packFloatx80(0, 0x3FF8, LIT64(0x88888888888859AF));
573: fp2 = floatx80_add(fp2, fp4, status); // A2+T(A4+TA6)
574: fp1 = floatx80_mul(fp1, fp3, status); // T(A3+T(A5+TA7))
575: fp2 = floatx80_mul(fp2, fp0, status); // S(A2+T(A4+TA6))
576: fp4 = packFloatx80(1, 0x3FFC, LIT64(0xAAAAAAAAAAAAAA99));
577: fp1 = floatx80_add(fp1, fp4, status); // A1+T(A3+T(A5+TA7))
578: fp1 = floatx80_add(fp1, fp2, status); // [A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))]
579:
580: x = packFloatx80(xSign, xExp, xSig);
581: fp0 = floatx80_mul(fp0, x, status); // R'*S
582: fp0 = floatx80_mul(fp0, fp1, status); // SIN(R')-R'
583:
584: RESET_PREC;
585:
586: a = floatx80_add(fp0, x, status);
587:
588: float_raise(float_flag_inexact, status);
589:
590: return a;
591: }
592: }
593: }
594:
595: /*----------------------------------------------------------------------------
596: | Hyperbolic cosine
597: *----------------------------------------------------------------------------*/
598:
599: floatx80 floatx80_cosh(floatx80 a, float_status *status)
600: {
601: flag aSign;
602: int32_t aExp;
603: uint64_t aSig;
604:
605: int32_t compact;
606: floatx80 fp0, fp1;
607:
608: aSig = extractFloatx80Frac(a);
609: aExp = extractFloatx80Exp(a);
610: aSign = extractFloatx80Sign(a);
611:
612: if (aExp == 0x7FFF) {
613: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
1.1.1.2 ! root 614: return packFloatx80(0, aExp, aSig);
1.1 root 615: }
616:
617: if (aExp == 0 && aSig == 0) {
618: return packFloatx80(0, one_exp, one_sig);
619: }
620:
621: SET_PREC;
622:
623: compact = floatx80_make_compact(aExp, aSig);
624:
625: if (compact > 0x400CB167) {
626: if (compact > 0x400CB2B3) {
627: RESET_PREC;
628: return roundAndPackFloatx80(status->floatx80_rounding_precision, 0, 0x8000, one_sig, 0, status);
629: } else {
630: fp0 = packFloatx80(0, aExp, aSig);
631: fp0 = floatx80_sub(fp0, float64_to_floatx80(LIT64(0x40C62D38D3D64634), status), status);
632: fp0 = floatx80_sub(fp0, float64_to_floatx80(LIT64(0x3D6F90AEB1E75CC7), status), status);
633: fp0 = floatx80_etox(fp0, status);
634: fp1 = packFloatx80(0, 0x7FFB, one_sig);
635:
636: RESET_PREC;
637:
638: a = floatx80_mul(fp0, fp1, status);
639:
640: float_raise(float_flag_inexact, status);
641:
642: return a;
643: }
644: }
645:
646: fp0 = packFloatx80(0, aExp, aSig); // |X|
647: fp0 = floatx80_etox(fp0, status); // EXP(|X|)
648: fp0 = floatx80_mul(fp0, float32_to_floatx80(0x3F000000, status), status); // (1/2)*EXP(|X|)
649: fp1 = float32_to_floatx80(0x3E800000, status); // 1/4
650: fp1 = floatx80_div(fp1, fp0, status); // 1/(2*EXP(|X|))
651:
652: RESET_PREC;
653:
654: a = floatx80_add(fp0, fp1, status);
655:
656: float_raise(float_flag_inexact, status);
657:
658: return a;
659: }
660:
661: /*----------------------------------------------------------------------------
662: | e to x
663: *----------------------------------------------------------------------------*/
664:
665: floatx80 floatx80_etox(floatx80 a, float_status *status)
666: {
667: flag aSign;
668: int32_t aExp;
669: uint64_t aSig;
670:
671: int32_t compact, n, j, k, m, m1;
672: floatx80 fp0, fp1, fp2, fp3, l2, scale, adjscale;
673: flag adjflag;
674:
675: aSig = extractFloatx80Frac(a);
676: aExp = extractFloatx80Exp(a);
677: aSign = extractFloatx80Sign(a);
678:
679: if (aExp == 0x7FFF) {
680: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
681: if (aSign) return packFloatx80(0, 0, 0);
1.1.1.2 ! root 682: return a;
1.1 root 683: }
684:
685: if (aExp == 0 && aSig == 0) {
686: return packFloatx80(0, one_exp, one_sig);
687: }
688:
689: SET_PREC;
690:
691: adjflag = 0;
692:
693: if (aExp >= 0x3FBE) { // |X| >= 2^(-65)
694: compact = floatx80_make_compact(aExp, aSig);
695:
696: if (compact < 0x400CB167) { // |X| < 16380 log2
697: fp0 = a;
698: fp1 = a;
699: fp0 = floatx80_mul(fp0, float32_to_floatx80(0x42B8AA3B, status), status); // 64/log2 * X
700: adjflag = 0;
701: n = floatx80_to_int32(fp0, status); // int(64/log2*X)
702: fp0 = int32_to_floatx80(n);
703:
704: j = n & 0x3F; // J = N mod 64
705: m = n / 64; // NOTE: this is really arithmetic right shift by 6
706: if (n < 0 && j) { // arithmetic right shift is division and round towards minus infinity
707: m--;
708: }
709: m += 0x3FFF; // biased exponent of 2^(M)
710:
711: expcont1:
712: fp2 = fp0; // N
713: fp0 = floatx80_mul(fp0, float32_to_floatx80(0xBC317218, status), status); // N * L1, L1 = lead(-log2/64)
714: l2 = packFloatx80(0, 0x3FDC, LIT64(0x82E308654361C4C6));
715: fp2 = floatx80_mul(fp2, l2, status); // N * L2, L1+L2 = -log2/64
716: fp0 = floatx80_add(fp0, fp1, status); // X + N*L1
717: fp0 = floatx80_add(fp0, fp2, status); // R
718:
719: fp1 = floatx80_mul(fp0, fp0, status); // S = R*R
720: fp2 = float32_to_floatx80(0x3AB60B70, status); // A5
721: fp2 = floatx80_mul(fp2, fp1, status); // fp2 is S*A5
722: fp3 = floatx80_mul(float32_to_floatx80(0x3C088895, status), fp1, status); // fp3 is S*A4
723: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FA5555555554431), status), status); // fp2 is A3+S*A5
724: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0x3FC5555555554018), status), status); // fp3 is A2+S*A4
725: fp2 = floatx80_mul(fp2, fp1, status); // fp2 is S*(A3+S*A5)
726: fp3 = floatx80_mul(fp3, fp1, status); // fp3 is S*(A2+S*A4)
727: fp2 = floatx80_add(fp2, float32_to_floatx80(0x3F000000, status), status); // fp2 is A1+S*(A3+S*A5)
728: fp3 = floatx80_mul(fp3, fp0, status); // fp3 IS R*S*(A2+S*A4)
729: fp2 = floatx80_mul(fp2, fp1, status); // fp2 IS S*(A1+S*(A3+S*A5))
730: fp0 = floatx80_add(fp0, fp3, status); // fp0 IS R+R*S*(A2+S*A4)
731: fp0 = floatx80_add(fp0, fp2, status); // fp0 IS EXP(R) - 1
732:
733: fp1 = exp_tbl[j];
734: fp0 = floatx80_mul(fp0, fp1, status); // 2^(J/64)*(Exp(R)-1)
735: fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status), status); // accurate 2^(J/64)
736: fp0 = floatx80_add(fp0, fp1, status); // 2^(J/64) + 2^(J/64)*(Exp(R)-1)
737:
738: scale = packFloatx80(0, m, one_sig);
739: if (adjflag) {
740: adjscale = packFloatx80(0, m1, one_sig);
741: fp0 = floatx80_mul(fp0, adjscale, status);
742: }
743:
744: RESET_PREC;
745:
746: a = floatx80_mul(fp0, scale, status);
747:
748: float_raise(float_flag_inexact, status);
749:
750: return a;
751: } else { // |X| >= 16380 log2
752: if (compact > 0x400CB27C) { // |X| >= 16480 log2
753: RESET_PREC;
754: if (aSign) {
755: a = roundAndPackFloatx80(status->floatx80_rounding_precision, 0, -0x1000, aSig, 0, status);
756: } else {
757: a = roundAndPackFloatx80(status->floatx80_rounding_precision, 0, 0x8000, aSig, 0, status);
758: }
759: float_raise(float_flag_inexact, status);
760:
761: return a;
762: } else {
763: fp0 = a;
764: fp1 = a;
765: fp0 = floatx80_mul(fp0, float32_to_floatx80(0x42B8AA3B, status), status); // 64/log2 * X
766: adjflag = 1;
767: n = floatx80_to_int32(fp0, status); // int(64/log2*X)
768: fp0 = int32_to_floatx80(n);
769:
770: j = n & 0x3F; // J = N mod 64
771: k = n / 64; // NOTE: this is really arithmetic right shift by 6
772: if (n < 0 && j) { // arithmetic right shift is division and round towards minus infinity
773: k--;
774: }
775: m1 = k / 2; // NOTE: this is really arithmetic right shift by 1
776: if (k < 0 && (k & 1)) { // arithmetic right shift is division and round towards minus infinity
777: m1--;
778: }
779: m = k - m1;
780: m1 += 0x3FFF; // biased exponent of 2^(M1)
781: m += 0x3FFF; // biased exponent of 2^(M)
782:
783: goto expcont1;
784: }
785: }
786: } else { // |X| < 2^(-65)
787: RESET_PREC;
788:
789: a = floatx80_add(a, float32_to_floatx80(0x3F800000, status), status); // 1 + X
790:
791: float_raise(float_flag_inexact, status);
792:
793: return a;
794: }
795: }
796:
797: /*----------------------------------------------------------------------------
798: | e to x minus 1
799: *----------------------------------------------------------------------------*/
800:
801: floatx80 floatx80_etoxm1(floatx80 a, float_status *status)
802: {
803: flag aSign;
804: int32_t aExp;
805: uint64_t aSig;
806:
807: int32_t compact, n, j, m, m1;
808: floatx80 fp0, fp1, fp2, fp3, l2, sc, onebysc;
809:
810: aSig = extractFloatx80Frac(a);
811: aExp = extractFloatx80Exp(a);
812: aSign = extractFloatx80Sign(a);
813:
814: if (aExp == 0x7FFF) {
815: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
816: if (aSign) return packFloatx80(aSign, one_exp, one_sig);
1.1.1.2 ! root 817: return a;
1.1 root 818: }
819:
820: if (aExp == 0 && aSig == 0) {
821: return packFloatx80(aSign, 0, 0);
822: }
823:
824: SET_PREC;
825:
826: if (aExp >= 0x3FFD) { // |X| >= 1/4
827: compact = floatx80_make_compact(aExp, aSig);
828:
829: if (compact <= 0x4004C215) { // |X| <= 70 log2
830: fp0 = a;
831: fp1 = a;
832: fp0 = floatx80_mul(fp0, float32_to_floatx80(0x42B8AA3B, status), status); // 64/log2 * X
833: n = floatx80_to_int32(fp0, status); // int(64/log2*X)
834: fp0 = int32_to_floatx80(n);
835:
836: j = n & 0x3F; // J = N mod 64
837: m = n / 64; // NOTE: this is really arithmetic right shift by 6
838: if (n < 0 && j) { // arithmetic right shift is division and round towards minus infinity
839: m--;
840: }
841: m1 = -m;
842: //m += 0x3FFF; // biased exponent of 2^(M)
843: //m1 += 0x3FFF; // biased exponent of -2^(-M)
844:
845: fp2 = fp0; // N
846: fp0 = floatx80_mul(fp0, float32_to_floatx80(0xBC317218, status), status); // N * L1, L1 = lead(-log2/64)
847: l2 = packFloatx80(0, 0x3FDC, LIT64(0x82E308654361C4C6));
848: fp2 = floatx80_mul(fp2, l2, status); // N * L2, L1+L2 = -log2/64
849: fp0 = floatx80_add(fp0, fp1, status); // X + N*L1
850: fp0 = floatx80_add(fp0, fp2, status); // R
851:
852: fp1 = floatx80_mul(fp0, fp0, status); // S = R*R
853: fp2 = float32_to_floatx80(0x3950097B, status); // A6
854: fp2 = floatx80_mul(fp2, fp1, status); // fp2 is S*A6
855: fp3 = floatx80_mul(float32_to_floatx80(0x3AB60B6A, status), fp1, status); // fp3 is S*A5
856: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3F81111111174385), status), status); // fp2 IS A4+S*A6
857: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0x3FA5555555554F5A), status), status); // fp3 is A3+S*A5
858: fp2 = floatx80_mul(fp2, fp1, status); // fp2 IS S*(A4+S*A6)
859: fp3 = floatx80_mul(fp3, fp1, status); // fp3 IS S*(A3+S*A5)
860: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FC5555555555555), status), status); // fp2 IS A2+S*(A4+S*A6)
861: fp3 = floatx80_add(fp3, float32_to_floatx80(0x3F000000, status), status); // fp3 IS A1+S*(A3+S*A5)
862: fp2 = floatx80_mul(fp2, fp1, status); // fp2 IS S*(A2+S*(A4+S*A6))
863: fp1 = floatx80_mul(fp1, fp3, status); // fp1 IS S*(A1+S*(A3+S*A5))
864: fp2 = floatx80_mul(fp2, fp0, status); // fp2 IS R*S*(A2+S*(A4+S*A6))
865: fp0 = floatx80_add(fp0, fp1, status); // fp0 IS R+S*(A1+S*(A3+S*A5))
866: fp0 = floatx80_add(fp0, fp2, status); // fp0 IS EXP(R) - 1
867:
868: fp0 = floatx80_mul(fp0, exp_tbl[j], status); // 2^(J/64)*(Exp(R)-1)
869:
870: if (m >= 64) {
871: fp1 = float32_to_floatx80(exp_tbl2[j], status);
872: onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); // -2^(-M)
873: fp1 = floatx80_add(fp1, onebysc, status);
874: fp0 = floatx80_add(fp0, fp1, status);
875: fp0 = floatx80_add(fp0, exp_tbl[j], status);
876: } else if (m < -3) {
877: fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status), status);
878: fp0 = floatx80_add(fp0, exp_tbl[j], status);
879: onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); // -2^(-M)
880: fp0 = floatx80_add(fp0, onebysc, status);
881: } else { // -3 <= m <= 63
882: fp1 = exp_tbl[j];
883: fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status), status);
884: onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); // -2^(-M)
885: fp1 = floatx80_add(fp1, onebysc, status);
886: fp0 = floatx80_add(fp0, fp1, status);
887: }
888:
889: sc = packFloatx80(0, m + 0x3FFF, one_sig);
890:
891: RESET_PREC;
892:
893: a = floatx80_mul(fp0, sc, status);
894:
895: float_raise(float_flag_inexact, status);
896:
897: return a;
898: } else { // |X| > 70 log2
899: if (aSign) {
900: fp0 = float32_to_floatx80(0xBF800000, status); // -1
901:
902: RESET_PREC;
903:
904: a = floatx80_add(fp0, float32_to_floatx80(0x00800000, status), status); // -1 + 2^(-126)
905:
906: float_raise(float_flag_inexact, status);
907:
908: return a;
909: } else {
910: RESET_PREC;
911:
912: return floatx80_etox(a, status);
913: }
914: }
915: } else { // |X| < 1/4
916: if (aExp >= 0x3FBE) {
917: fp0 = a;
918: fp0 = floatx80_mul(fp0, fp0, status); // S = X*X
919: fp1 = float32_to_floatx80(0x2F30CAA8, status); // B12
920: fp1 = floatx80_mul(fp1, fp0, status); // S * B12
921: fp2 = float32_to_floatx80(0x310F8290, status); // B11
922: fp1 = floatx80_add(fp1, float32_to_floatx80(0x32D73220, status), status); // B10
923: fp2 = floatx80_mul(fp2, fp0, status);
924: fp1 = floatx80_mul(fp1, fp0, status);
925: fp2 = floatx80_add(fp2, float32_to_floatx80(0x3493F281, status), status); // B9
926: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3EC71DE3A5774682), status), status); // B8
927: fp2 = floatx80_mul(fp2, fp0, status);
928: fp1 = floatx80_mul(fp1, fp0, status);
929: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3EFA01A019D7CB68), status), status); // B7
930: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3F2A01A01A019DF3), status), status); // B6
931: fp2 = floatx80_mul(fp2, fp0, status);
932: fp1 = floatx80_mul(fp1, fp0, status);
933: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3F56C16C16C170E2), status), status); // B5
934: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3F81111111111111), status), status); // B4
935: fp2 = floatx80_mul(fp2, fp0, status);
936: fp1 = floatx80_mul(fp1, fp0, status);
937: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FA5555555555555), status), status); // B3
938: fp3 = packFloatx80(0, 0x3FFC, LIT64(0xAAAAAAAAAAAAAAAB));
939: fp1 = floatx80_add(fp1, fp3, status); // B2
940: fp2 = floatx80_mul(fp2, fp0, status);
941: fp1 = floatx80_mul(fp1, fp0, status);
942:
943: fp2 = floatx80_mul(fp2, fp0, status);
944: fp1 = floatx80_mul(fp1, a, status);
945:
946: fp0 = floatx80_mul(fp0, float32_to_floatx80(0x3F000000, status), status); // S*B1
947: fp1 = floatx80_add(fp1, fp2, status); // Q
948: fp0 = floatx80_add(fp0, fp1, status); // S*B1+Q
949:
950: RESET_PREC;
951:
952: a = floatx80_add(fp0, a, status);
953:
954: float_raise(float_flag_inexact, status);
955:
956: return a;
957: } else { // |X| < 2^(-65)
958: sc = packFloatx80(1, 1, one_sig);
959: fp0 = a;
960:
961: if (aExp < 0x0033) { // |X| < 2^(-16382)
962: fp0 = floatx80_mul(fp0, float64_to_floatx80(LIT64(0x48B0000000000000), status), status);
963: fp0 = floatx80_add(fp0, sc, status);
964:
965: RESET_PREC;
966:
967: a = floatx80_mul(fp0, float64_to_floatx80(LIT64(0x3730000000000000), status), status);
968: } else {
969: RESET_PREC;
970:
971: a = floatx80_add(fp0, sc, status);
972: }
973:
974: float_raise(float_flag_inexact, status);
975:
976: return a;
977: }
978: }
979: }
980:
981: /*----------------------------------------------------------------------------
982: | Log base 10
983: *----------------------------------------------------------------------------*/
984:
985: floatx80 floatx80_log10(floatx80 a, float_status *status)
986: {
987: flag aSign;
988: int32_t aExp;
989: uint64_t aSig;
990:
991: floatx80 fp0, fp1;
992:
993: aSig = extractFloatx80Frac(a);
994: aExp = extractFloatx80Exp(a);
995: aSign = extractFloatx80Sign(a);
996:
997: if (aExp == 0x7FFF) {
1.1.1.2 ! root 998: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
1.1 root 999: if (aSign == 0)
1.1.1.2 ! root 1000: return a;
1.1 root 1001: }
1002:
1003: if (aExp == 0 && aSig == 0) {
1004: float_raise(float_flag_divbyzero, status);
1005: return packFloatx80(1, 0x7FFF, floatx80_default_infinity_low);
1006: }
1007:
1008: if (aSign) {
1009: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 1010: return floatx80_default_nan(status);
1.1 root 1011: }
1012:
1013: SET_PREC;
1014:
1015: fp0 = floatx80_logn(a, status);
1016: fp1 = packFloatx80(0, 0x3FFD, LIT64(0xDE5BD8A937287195)); // INV_L10
1017:
1018: RESET_PREC;
1019:
1020: a = floatx80_mul(fp0, fp1, status); // LOGN(X)*INV_L10
1021:
1022: float_raise(float_flag_inexact, status);
1023:
1024: return a;
1025: }
1026:
1027: /*----------------------------------------------------------------------------
1028: | Log base 2
1029: *----------------------------------------------------------------------------*/
1030:
1031: floatx80 floatx80_log2(floatx80 a, float_status *status)
1032: {
1033: flag aSign;
1034: int32_t aExp;
1035: uint64_t aSig;
1036:
1037: floatx80 fp0, fp1;
1038:
1039: aSig = extractFloatx80Frac(a);
1040: aExp = extractFloatx80Exp(a);
1041: aSign = extractFloatx80Sign(a);
1042:
1043: if (aExp == 0x7FFF) {
1.1.1.2 ! root 1044: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
1.1 root 1045: if (aSign == 0)
1.1.1.2 ! root 1046: return a;
1.1 root 1047: }
1048:
1049: if (aExp == 0) {
1050: if (aSig == 0) {
1051: float_raise(float_flag_divbyzero, status);
1052: return packFloatx80(1, 0x7FFF, floatx80_default_infinity_low);
1053: }
1054: normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
1055: }
1056:
1057: if (aSign) {
1058: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 1059: return floatx80_default_nan(status);
1.1 root 1060: }
1061:
1062: SET_PREC;
1063:
1064: if (aSig == one_sig) { // X is 2^k
1065: RESET_PREC;
1066:
1067: a = int32_to_floatx80(aExp-0x3FFF);
1068: } else {
1069: fp0 = floatx80_logn(a, status);
1070: fp1 = packFloatx80(0, 0x3FFF, LIT64(0xB8AA3B295C17F0BC)); // INV_L2
1071:
1072: RESET_PREC;
1073:
1074: a = floatx80_mul(fp0, fp1, status); // LOGN(X)*INV_L2
1075: }
1076:
1077: float_raise(float_flag_inexact, status);
1078:
1079: return a;
1080: }
1081:
1082: /*----------------------------------------------------------------------------
1083: | Log base e
1084: *----------------------------------------------------------------------------*/
1085:
1086: floatx80 floatx80_logn(floatx80 a, float_status *status)
1087: {
1088: flag aSign;
1089: int32_t aExp;
1090: uint64_t aSig, fSig;
1091:
1092: int32_t compact, j, k, adjk;
1093: floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu;
1094:
1095: aSig = extractFloatx80Frac(a);
1096: aExp = extractFloatx80Exp(a);
1097: aSign = extractFloatx80Sign(a);
1098:
1099: if (aExp == 0x7FFF) {
1.1.1.2 ! root 1100: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
1.1 root 1101: if (aSign == 0)
1.1.1.2 ! root 1102: return a;
1.1 root 1103: }
1104:
1105: adjk = 0;
1106:
1107: if (aExp == 0) {
1108: if (aSig == 0) { // zero
1109: float_raise(float_flag_divbyzero, status);
1110: return packFloatx80(1, 0x7FFF, floatx80_default_infinity_low);
1111: }
1112: #if 1
1113: if ((aSig & one_sig) == 0) { // denormal
1114: normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
1115: adjk = -100;
1116: aExp += 100;
1117: a = packFloatx80(aSign, aExp, aSig);
1118: }
1119: #else
1120: normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
1121: #endif
1122: }
1123:
1124: if (aSign) {
1125: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 1126: return floatx80_default_nan(status);
1.1 root 1127: }
1128:
1129: SET_PREC;
1130:
1131: compact = floatx80_make_compact(aExp, aSig);
1132:
1133: if (compact < 0x3FFEF07D || compact > 0x3FFF8841) { // |X| < 15/16 or |X| > 17/16
1134: k = aExp - 0x3FFF;
1135: k += adjk;
1136: fp1 = int32_to_floatx80(k);
1137:
1138: fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000);
1139: j = (fSig >> 56) & 0x7E; // DISPLACEMENT FOR 1/F
1140:
1141: f = packFloatx80(0, 0x3FFF, fSig); // F
1142: fp0 = packFloatx80(0, 0x3FFF, aSig); // Y
1143:
1144: fp0 = floatx80_sub(fp0, f, status); // Y-F
1145:
1146: // LP1CONT1
1147: fp0 = floatx80_mul(fp0, log_tbl[j], status); // FP0 IS U = (Y-F)/F
1148: logof2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC));
1149: klog2 = floatx80_mul(fp1, logof2, status); // FP1 IS K*LOG2
1150: fp2 = floatx80_mul(fp0, fp0, status); // FP2 IS V=U*U
1151:
1152: fp3 = fp2;
1153: fp1 = fp2;
1154:
1155: fp1 = floatx80_mul(fp1, float64_to_floatx80(LIT64(0x3FC2499AB5E4040B), status), status); // V*A6
1156: fp2 = floatx80_mul(fp2, float64_to_floatx80(LIT64(0xBFC555B5848CB7DB), status), status); // V*A5
1157: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3FC99999987D8730), status), status); // A4+V*A6
1158: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0xBFCFFFFFFF6F7E97), status), status); // A3+V*A5
1159: fp1 = floatx80_mul(fp1, fp3, status); // V*(A4+V*A6)
1160: fp2 = floatx80_mul(fp2, fp3, status); // V*(A3+V*A5)
1161: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3FD55555555555A4), status), status); // A2+V*(A4+V*A6)
1162: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0xBFE0000000000008), status), status); // A1+V*(A3+V*A5)
1163: fp1 = floatx80_mul(fp1, fp3, status); // V*(A2+V*(A4+V*A6))
1164: fp2 = floatx80_mul(fp2, fp3, status); // V*(A1+V*(A3+V*A5))
1165: fp1 = floatx80_mul(fp1, fp0, status); // U*V*(A2+V*(A4+V*A6))
1166: fp0 = floatx80_add(fp0, fp2, status); // U+V*(A1+V*(A3+V*A5))
1167:
1168: fp1 = floatx80_add(fp1, log_tbl[j+1], status); // LOG(F)+U*V*(A2+V*(A4+V*A6))
1169: fp0 = floatx80_add(fp0, fp1, status); // FP0 IS LOG(F) + LOG(1+U)
1170:
1171: RESET_PREC;
1172:
1173: a = floatx80_add(fp0, klog2, status);
1174:
1175: float_raise(float_flag_inexact, status);
1176:
1177: return a;
1178: } else { // |X-1| >= 1/16
1179: fp0 = a;
1180: fp1 = a;
1181: fp1 = floatx80_sub(fp1, float32_to_floatx80(0x3F800000, status), status); // FP1 IS X-1
1182: fp0 = floatx80_add(fp0, float32_to_floatx80(0x3F800000, status), status); // FP0 IS X+1
1183: fp1 = floatx80_add(fp1, fp1, status); // FP1 IS 2(X-1)
1184:
1185: // LP1CONT2
1186: fp1 = floatx80_div(fp1, fp0, status); // U
1187: saveu = fp1;
1188: fp0 = floatx80_mul(fp1, fp1, status); // FP0 IS V = U*U
1189: fp1 = floatx80_mul(fp0, fp0, status); // FP1 IS W = V*V
1190:
1191: fp3 = float64_to_floatx80(LIT64(0x3F175496ADD7DAD6), status); // B5
1192: fp2 = float64_to_floatx80(LIT64(0x3F3C71C2FE80C7E0), status); // B4
1193: fp3 = floatx80_mul(fp3, fp1, status); // W*B5
1194: fp2 = floatx80_mul(fp2, fp1, status); // W*B4
1195: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0x3F624924928BCCFF), status), status); // B3+W*B5
1196: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3F899999999995EC), status), status); // B2+W*B4
1197: fp1 = floatx80_mul(fp1, fp3, status); // W*(B3+W*B5)
1198: fp2 = floatx80_mul(fp2, fp0, status); // V*(B2+W*B4)
1199: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3FB5555555555555), status), status); // B1+W*(B3+W*B5)
1200:
1201: fp0 = floatx80_mul(fp0, saveu, status); // FP0 IS U*V
1202: fp1 = floatx80_add(fp1, fp2, status); // B1+W*(B3+W*B5) + V*(B2+W*B4)
1203: fp0 = floatx80_mul(fp0, fp1, status); // U*V*( [B1+W*(B3+W*B5)] + [V*(B2+W*B4)] )
1204:
1205: RESET_PREC;
1206:
1207: a = floatx80_add(fp0, saveu, status);
1208:
1209: float_raise(float_flag_inexact, status);
1210:
1211: return a;
1212: }
1213: }
1214:
1215: /*----------------------------------------------------------------------------
1216: | Log base e of x plus 1
1217: *----------------------------------------------------------------------------*/
1218:
1219: floatx80 floatx80_lognp1(floatx80 a, float_status *status)
1220: {
1221: flag aSign;
1222: int32_t aExp;
1223: uint64_t aSig, fSig;
1224:
1225: int32_t compact, j, k;
1226: floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu;
1227:
1228: aSig = extractFloatx80Frac(a);
1229: aExp = extractFloatx80Exp(a);
1230: aSign = extractFloatx80Sign(a);
1231:
1232: if (aExp == 0x7FFF) {
1.1.1.2 ! root 1233: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
1.1 root 1234: if (aSign) {
1235: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 1236: return floatx80_default_nan(status);
1.1 root 1237: }
1.1.1.2 ! root 1238: return a;
1.1 root 1239: }
1240:
1241: if (aExp == 0 && aSig == 0) {
1242: return packFloatx80(aSign, 0, 0);
1243: }
1244:
1245: if (aSign && aExp >= one_exp) {
1246: if (aExp == one_exp && aSig == one_sig) {
1247: float_raise(float_flag_divbyzero, status);
1.1.1.2 ! root 1248: return packFloatx80(aSign, 0x7FFF, floatx80_default_infinity_low);
1.1 root 1249: }
1250: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 1251: return floatx80_default_nan(status);
1.1 root 1252: }
1253:
1254: if (aExp < 0x3f99 || (aExp == 0x3f99 && aSig == one_sig)) { // <= min threshold
1255: float_raise(float_flag_inexact, status);
1256: return floatx80_move(a, status);
1257: }
1258:
1259: SET_PREC;
1260:
1261: compact = floatx80_make_compact(aExp, aSig);
1262:
1263: fp0 = a; // Z
1264: fp1 = a;
1265:
1266: fp0 = floatx80_add(fp0, float32_to_floatx80(0x3F800000, status), status); // X = (1+Z)
1267:
1268: aExp = extractFloatx80Exp(fp0);
1269: aSig = extractFloatx80Frac(fp0);
1270:
1271: compact = floatx80_make_compact(aExp, aSig);
1272:
1273: if (compact < 0x3FFE8000 || compact > 0x3FFFC000) { // |X| < 1/2 or |X| > 3/2
1274: k = aExp - 0x3FFF;
1275: fp1 = int32_to_floatx80(k);
1276:
1277: fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000);
1278: j = (fSig >> 56) & 0x7E; // DISPLACEMENT FOR 1/F
1279:
1280: f = packFloatx80(0, 0x3FFF, fSig); // F
1281: fp0 = packFloatx80(0, 0x3FFF, aSig); // Y
1282:
1283: fp0 = floatx80_sub(fp0, f, status); // Y-F
1284:
1285: lp1cont1:
1286: // LP1CONT1
1287: fp0 = floatx80_mul(fp0, log_tbl[j], status); // FP0 IS U = (Y-F)/F
1288: logof2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC));
1289: klog2 = floatx80_mul(fp1, logof2, status); // FP1 IS K*LOG2
1290: fp2 = floatx80_mul(fp0, fp0, status); // FP2 IS V=U*U
1291:
1292: fp3 = fp2;
1293: fp1 = fp2;
1294:
1295: fp1 = floatx80_mul(fp1, float64_to_floatx80(LIT64(0x3FC2499AB5E4040B), status), status); // V*A6
1296: fp2 = floatx80_mul(fp2, float64_to_floatx80(LIT64(0xBFC555B5848CB7DB), status), status); // V*A5
1297: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3FC99999987D8730), status), status); // A4+V*A6
1298: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0xBFCFFFFFFF6F7E97), status), status); // A3+V*A5
1299: fp1 = floatx80_mul(fp1, fp3, status); // V*(A4+V*A6)
1300: fp2 = floatx80_mul(fp2, fp3, status); // V*(A3+V*A5)
1301: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3FD55555555555A4), status), status); // A2+V*(A4+V*A6)
1302: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0xBFE0000000000008), status), status); // A1+V*(A3+V*A5)
1303: fp1 = floatx80_mul(fp1, fp3, status); // V*(A2+V*(A4+V*A6))
1304: fp2 = floatx80_mul(fp2, fp3, status); // V*(A1+V*(A3+V*A5))
1305: fp1 = floatx80_mul(fp1, fp0, status); // U*V*(A2+V*(A4+V*A6))
1306: fp0 = floatx80_add(fp0, fp2, status); // U+V*(A1+V*(A3+V*A5))
1307:
1308: fp1 = floatx80_add(fp1, log_tbl[j+1], status); // LOG(F)+U*V*(A2+V*(A4+V*A6))
1309: fp0 = floatx80_add(fp0, fp1, status); // FP0 IS LOG(F) + LOG(1+U)
1310:
1311: RESET_PREC;
1312:
1313: a = floatx80_add(fp0, klog2, status);
1314:
1315: float_raise(float_flag_inexact, status);
1316:
1317: return a;
1318: } else if (compact < 0x3FFEF07D || compact > 0x3FFF8841) { // |X| < 1/16 or |X| > -1/16
1319: // LP1CARE
1320: fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000);
1321: f = packFloatx80(0, 0x3FFF, fSig); // F
1322: j = (fSig >> 56) & 0x7E; // DISPLACEMENT FOR 1/F
1323:
1324: if (compact >= 0x3FFF8000) { // 1+Z >= 1
1325: // KISZERO
1326: fp0 = floatx80_sub(float32_to_floatx80(0x3F800000, status), f, status); // 1-F
1327: fp0 = floatx80_add(fp0, fp1, status); // FP0 IS Y-F = (1-F)+Z
1328: fp1 = packFloatx80(0, 0, 0); // K = 0
1329: } else {
1330: // KISNEG
1331: fp0 = floatx80_sub(float32_to_floatx80(0x40000000, status), f, status); // 2-F
1332: fp1 = floatx80_add(fp1, fp1, status); // 2Z
1333: fp0 = floatx80_add(fp0, fp1, status); // FP0 IS Y-F = (2-F)+2Z
1334: fp1 = packFloatx80(1, one_exp, one_sig); // K = -1
1335: }
1336: goto lp1cont1;
1337: } else {
1338: // LP1ONE16
1339: fp1 = floatx80_add(fp1, fp1, status); // FP1 IS 2Z
1340: fp0 = floatx80_add(fp0, float32_to_floatx80(0x3F800000, status), status); // FP0 IS 1+X
1341:
1342: // LP1CONT2
1343: fp1 = floatx80_div(fp1, fp0, status); // U
1344: saveu = fp1;
1345: fp0 = floatx80_mul(fp1, fp1, status); // FP0 IS V = U*U
1346: fp1 = floatx80_mul(fp0, fp0, status); // FP1 IS W = V*V
1347:
1348: fp3 = float64_to_floatx80(LIT64(0x3F175496ADD7DAD6), status); // B5
1349: fp2 = float64_to_floatx80(LIT64(0x3F3C71C2FE80C7E0), status); // B4
1350: fp3 = floatx80_mul(fp3, fp1, status); // W*B5
1351: fp2 = floatx80_mul(fp2, fp1, status); // W*B4
1352: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0x3F624924928BCCFF), status), status); // B3+W*B5
1353: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3F899999999995EC), status), status); // B2+W*B4
1354: fp1 = floatx80_mul(fp1, fp3, status); // W*(B3+W*B5)
1355: fp2 = floatx80_mul(fp2, fp0, status); // V*(B2+W*B4)
1356: fp1 = floatx80_add(fp1, float64_to_floatx80(LIT64(0x3FB5555555555555), status), status); // B1+W*(B3+W*B5)
1357:
1358: fp0 = floatx80_mul(fp0, saveu, status); // FP0 IS U*V
1359: fp1 = floatx80_add(fp1, fp2, status); // B1+W*(B3+W*B5) + V*(B2+W*B4)
1360: fp0 = floatx80_mul(fp0, fp1, status); // U*V*( [B1+W*(B3+W*B5)] + [V*(B2+W*B4)] )
1361:
1362: RESET_PREC;
1363:
1364: a = floatx80_add(fp0, saveu, status);
1365:
1366: float_raise(float_flag_inexact, status);
1367:
1368: return a;
1369: }
1370: }
1371:
1372: /*----------------------------------------------------------------------------
1373: | Sine
1374: *----------------------------------------------------------------------------*/
1375:
1376: floatx80 floatx80_sin(floatx80 a, float_status *status)
1377: {
1378: flag aSign, xSign;
1379: int32_t aExp, xExp;
1380: uint64_t aSig, xSig;
1381:
1382: int32_t compact, l, n, j;
1383: floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2;
1384: float32 posneg1, twoto63;
1385: flag adjn, endflag;
1386:
1387: aSig = extractFloatx80Frac(a);
1388: aExp = extractFloatx80Exp(a);
1389: aSign = extractFloatx80Sign(a);
1390:
1391: if (aExp == 0x7FFF) {
1392: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
1393: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 1394: return floatx80_default_nan(status);
1.1 root 1395: }
1396:
1397: if (aExp == 0 && aSig == 0) {
1398: return packFloatx80(aSign, 0, 0);
1399: }
1400:
1401: adjn = 0;
1402:
1403: SET_PREC;
1404:
1405: compact = floatx80_make_compact(aExp, aSig);
1406:
1407: fp0 = a;
1408:
1409: if (compact < 0x3FD78000 || compact > 0x4004BC7E) { // 2^(-40) > |X| > 15 PI
1410: if (compact > 0x3FFF8000) { // |X| >= 15 PI
1411: // REDUCEX
1412: fp1 = packFloatx80(0, 0, 0);
1413: if (compact == 0x7FFEFFFF) {
1414: twopi1 = packFloatx80(aSign ^ 1, 0x7FFE, LIT64(0xC90FDAA200000000));
1415: twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, LIT64(0x85A308D300000000));
1416: fp0 = floatx80_add(fp0, twopi1, status);
1417: fp1 = fp0;
1418: fp0 = floatx80_add(fp0, twopi2, status);
1419: fp1 = floatx80_sub(fp1, fp0, status);
1420: fp1 = floatx80_add(fp1, twopi2, status);
1421: }
1422: loop:
1423: xSign = extractFloatx80Sign(fp0);
1424: xExp = extractFloatx80Exp(fp0);
1425: xExp -= 0x3FFF;
1426: if (xExp <= 28) {
1427: l = 0;
1428: endflag = 1;
1429: } else {
1430: l = xExp - 27;
1431: endflag = 0;
1432: }
1433: invtwopi = packFloatx80(0, 0x3FFE - l, LIT64(0xA2F9836E4E44152A)); // INVTWOPI
1434: twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000));
1435: twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(0x85A308D300000000));
1436:
1437: twoto63 = 0x5F000000;
1438: twoto63 |= xSign ? 0x80000000 : 0x00000000; // SIGN(INARG)*2^63 IN SGL
1439:
1440: fp2 = floatx80_mul(fp0, invtwopi, status);
1441: fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), status); // THE FRACTIONAL PART OF FP2 IS ROUNDED
1442: fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status), status); // FP2 is N
1443: fp4 = floatx80_mul(twopi1, fp2, status); // W = N*P1
1444: fp5 = floatx80_mul(twopi2, fp2, status); // w = N*P2
1445: fp3 = floatx80_add(fp4, fp5, status); // FP3 is P
1446: fp4 = floatx80_sub(fp4, fp3, status); // W-P
1447: fp0 = floatx80_sub(fp0, fp3, status); // FP0 is A := R - P
1448: fp4 = floatx80_add(fp4, fp5, status); // FP4 is p = (W-P)+w
1449: fp3 = fp0; // FP3 is A
1450: fp1 = floatx80_sub(fp1, fp4, status); // FP1 is a := r - p
1451: fp0 = floatx80_add(fp0, fp1, status); // FP0 is R := A+a
1452:
1453: if (endflag > 0) {
1454: n = floatx80_to_int32(fp2, status);
1455: goto sincont;
1456: }
1457: fp3 = floatx80_sub(fp3, fp0, status); // A-R
1458: fp1 = floatx80_add(fp1, fp3, status); // FP1 is r := (A-R)+a
1459: goto loop;
1460: } else {
1461: // SINSM
1462: fp0 = float32_to_floatx80(0x3F800000, status); // 1
1463:
1464: RESET_PREC;
1465:
1466: if (adjn) {
1467: // COSTINY
1468: a = floatx80_sub(fp0, float32_to_floatx80(0x00800000, status), status);
1469: } else {
1470: // SINTINY
1471: a = floatx80_move(a, status);
1472: }
1473: float_raise(float_flag_inexact, status);
1474:
1475: return a;
1476: }
1477: } else {
1478: fp1 = floatx80_mul(fp0, float64_to_floatx80(LIT64(0x3FE45F306DC9C883), status), status); // X*2/PI
1479:
1480: n = floatx80_to_int32(fp1, status);
1481: j = 32 + n;
1482:
1483: fp0 = floatx80_sub(fp0, pi_tbl[j], status); // X-Y1
1484: fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status), status); // FP0 IS R = (X-Y1)-Y2
1485:
1486: sincont:
1487: if ((n + adjn) & 1) {
1488: // COSPOLY
1489: fp0 = floatx80_mul(fp0, fp0, status); // FP0 IS S
1490: fp1 = floatx80_mul(fp0, fp0, status); // FP1 IS T
1491: fp2 = float64_to_floatx80(LIT64(0x3D2AC4D0D6011EE3), status); // B8
1492: fp3 = float64_to_floatx80(LIT64(0xBDA9396F9F45AC19), status); // B7
1493:
1494: xSign = extractFloatx80Sign(fp0); // X IS S
1495: xExp = extractFloatx80Exp(fp0);
1496: xSig = extractFloatx80Frac(fp0);
1497:
1498: if (((n + adjn) >> 1) & 1) {
1499: xSign ^= 1;
1500: posneg1 = 0xBF800000; // -1
1501: } else {
1502: xSign ^= 0;
1503: posneg1 = 0x3F800000; // 1
1504: } // X IS NOW R'= SGN*R
1505:
1506: fp2 = floatx80_mul(fp2, fp1, status); // TB8
1507: fp3 = floatx80_mul(fp3, fp1, status); // TB7
1508: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3E21EED90612C972), status), status); // B6+TB8
1509: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0xBE927E4FB79D9FCF), status), status); // B5+TB7
1510: fp2 = floatx80_mul(fp2, fp1, status); // T(B6+TB8)
1511: fp3 = floatx80_mul(fp3, fp1, status); // T(B5+TB7)
1512: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3EFA01A01A01D423), status), status); // B4+T(B6+TB8)
1513: fp4 = packFloatx80(1, 0x3FF5, LIT64(0xB60B60B60B61D438));
1514: fp3 = floatx80_add(fp3, fp4, status); // B3+T(B5+TB7)
1515: fp2 = floatx80_mul(fp2, fp1, status); // T(B4+T(B6+TB8))
1516: fp1 = floatx80_mul(fp1, fp3, status); // T(B3+T(B5+TB7))
1517: fp4 = packFloatx80(0, 0x3FFA, LIT64(0xAAAAAAAAAAAAAB5E));
1518: fp2 = floatx80_add(fp2, fp4, status); // B2+T(B4+T(B6+TB8))
1519: fp1 = floatx80_add(fp1, float32_to_floatx80(0xBF000000, status), status); // B1+T(B3+T(B5+TB7))
1520: fp0 = floatx80_mul(fp0, fp2, status); // S(B2+T(B4+T(B6+TB8)))
1521: fp0 = floatx80_add(fp0, fp1, status); // [B1+T(B3+T(B5+TB7))]+[S(B2+T(B4+T(B6+TB8)))]
1522:
1523: x = packFloatx80(xSign, xExp, xSig);
1524: fp0 = floatx80_mul(fp0, x, status);
1525:
1526: RESET_PREC;
1527:
1528: a = floatx80_add(fp0, float32_to_floatx80(posneg1, status), status);
1529:
1530: float_raise(float_flag_inexact, status);
1531:
1532: return a;
1533: } else {
1534: // SINPOLY
1535: xSign = extractFloatx80Sign(fp0); // X IS R
1536: xExp = extractFloatx80Exp(fp0);
1537: xSig = extractFloatx80Frac(fp0);
1538:
1539: xSign ^= ((n + adjn) >> 1) & 1; // X IS NOW R'= SGN*R
1540:
1541: fp0 = floatx80_mul(fp0, fp0, status); // FP0 IS S
1542: fp1 = floatx80_mul(fp0, fp0, status); // FP1 IS T
1543: fp3 = float64_to_floatx80(LIT64(0xBD6AAA77CCC994F5), status); // A7
1544: fp2 = float64_to_floatx80(LIT64(0x3DE612097AAE8DA1), status); // A6
1545: fp3 = floatx80_mul(fp3, fp1, status); // T*A7
1546: fp2 = floatx80_mul(fp2, fp1, status); // T*A6
1547: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0xBE5AE6452A118AE4), status), status); // A5+T*A7
1548: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3EC71DE3A5341531), status), status); // A4+T*A6
1549: fp3 = floatx80_mul(fp3, fp1, status); // T(A5+TA7)
1550: fp2 = floatx80_mul(fp2, fp1, status); // T(A4+TA6)
1551: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0xBF2A01A01A018B59), status), status); // A3+T(A5+TA7)
1552: fp4 = packFloatx80(0, 0x3FF8, LIT64(0x88888888888859AF));
1553: fp2 = floatx80_add(fp2, fp4, status); // A2+T(A4+TA6)
1554: fp1 = floatx80_mul(fp1, fp3, status); // T(A3+T(A5+TA7))
1555: fp2 = floatx80_mul(fp2, fp0, status); // S(A2+T(A4+TA6))
1556: fp4 = packFloatx80(1, 0x3FFC, LIT64(0xAAAAAAAAAAAAAA99));
1557: fp1 = floatx80_add(fp1, fp4, status); // A1+T(A3+T(A5+TA7))
1558: fp1 = floatx80_add(fp1, fp2, status); // [A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))]
1559:
1560: x = packFloatx80(xSign, xExp, xSig);
1561: fp0 = floatx80_mul(fp0, x, status); // R'*S
1562: fp0 = floatx80_mul(fp0, fp1, status); // SIN(R')-R'
1563:
1564: RESET_PREC;
1565:
1566: a = floatx80_add(fp0, x, status);
1567:
1568: float_raise(float_flag_inexact, status);
1569:
1570: return a;
1571: }
1572: }
1573: }
1574:
1575: /*----------------------------------------------------------------------------
1576: | Hyperbolic sine
1577: *----------------------------------------------------------------------------*/
1578:
1579: floatx80 floatx80_sinh(floatx80 a, float_status *status)
1580: {
1581: flag aSign;
1582: int32_t aExp;
1583: uint64_t aSig;
1584:
1585: int32_t compact;
1586: floatx80 fp0, fp1, fp2;
1587: float32 fact;
1588:
1589: aSig = extractFloatx80Frac(a);
1590: aExp = extractFloatx80Exp(a);
1591: aSign = extractFloatx80Sign(a);
1592:
1593: if (aExp == 0x7FFF) {
1594: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
1.1.1.2 ! root 1595: return a;
1.1 root 1596: }
1597:
1598: if (aExp == 0 && aSig == 0) {
1599: return packFloatx80(aSign, 0, 0);
1600: }
1601:
1602: SET_PREC;
1603:
1604: compact = floatx80_make_compact(aExp, aSig);
1605:
1606: if (compact > 0x400CB167) {
1607: // SINHBIG
1608: if (compact > 0x400CB2B3) {
1609: RESET_PREC;
1610:
1611: return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, 0x8000, aSig, 0, status);
1612: } else {
1613: fp0 = floatx80_abs(a, status); // Y = |X|
1614: fp0 = floatx80_sub(fp0, float64_to_floatx80(LIT64(0x40C62D38D3D64634), status), status); // (|X|-16381LOG2_LEAD)
1615: fp0 = floatx80_sub(fp0, float64_to_floatx80(LIT64(0x3D6F90AEB1E75CC7), status), status); // |X| - 16381 LOG2, ACCURATE
1616: fp0 = floatx80_etox(fp0, status);
1617: fp2 = packFloatx80(aSign, 0x7FFB, one_sig);
1618:
1619: RESET_PREC;
1620:
1621: a = floatx80_mul(fp0, fp2, status);
1622:
1623: float_raise(float_flag_inexact, status);
1624:
1625: return a;
1626: }
1627: } else { // |X| < 16380 LOG2
1628: fp0 = floatx80_abs(a, status); // Y = |X|
1629: fp0 = floatx80_etoxm1(fp0, status); // FP0 IS Z = EXPM1(Y)
1630: fp1 = floatx80_add(fp0, float32_to_floatx80(0x3F800000, status), status); // 1+Z
1631: fp2 = fp0;
1632: fp0 = floatx80_div(fp0, fp1, status); // Z/(1+Z)
1633: fp0 = floatx80_add(fp0, fp2, status);
1634:
1635: fact = 0x3F000000;
1636: fact |= aSign ? 0x80000000 : 0x00000000;
1637:
1638: RESET_PREC;
1639:
1640: a = floatx80_mul(fp0, float32_to_floatx80(fact, status), status);
1641:
1642: float_raise(float_flag_inexact, status);
1643:
1644: return a;
1645: }
1646: }
1647:
1648: /*----------------------------------------------------------------------------
1649: | Tangent
1650: *----------------------------------------------------------------------------*/
1651:
1652: floatx80 floatx80_tan(floatx80 a, float_status *status)
1653: {
1654: flag aSign, xSign;
1655: int32_t aExp, xExp;
1656: uint64_t aSig, xSig;
1657:
1658: int32_t compact, l, n, j;
1659: floatx80 fp0, fp1, fp2, fp3, fp4, fp5, invtwopi, twopi1, twopi2;
1660: float32 twoto63;
1661: flag endflag;
1662:
1663: aSig = extractFloatx80Frac(a);
1664: aExp = extractFloatx80Exp(a);
1665: aSign = extractFloatx80Sign(a);
1666:
1667: if (aExp == 0x7FFF) {
1668: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
1669: float_raise(float_flag_invalid, status);
1.1.1.2 ! root 1670: return floatx80_default_nan(status);
1.1 root 1671: }
1672:
1673: if (aExp == 0 && aSig == 0) {
1674: return packFloatx80(aSign, 0, 0);
1675: }
1676:
1677: SET_PREC;
1678:
1679: compact = floatx80_make_compact(aExp, aSig);
1680:
1681: fp0 = a;
1682:
1683: if (compact < 0x3FD78000 || compact > 0x4004BC7E) { // 2^(-40) > |X| > 15 PI
1684: if (compact > 0x3FFF8000) { // |X| >= 15 PI
1685: // REDUCEX
1686: fp1 = packFloatx80(0, 0, 0);
1687: if (compact == 0x7FFEFFFF) {
1688: twopi1 = packFloatx80(aSign ^ 1, 0x7FFE, LIT64(0xC90FDAA200000000));
1689: twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, LIT64(0x85A308D300000000));
1690: fp0 = floatx80_add(fp0, twopi1, status);
1691: fp1 = fp0;
1692: fp0 = floatx80_add(fp0, twopi2, status);
1693: fp1 = floatx80_sub(fp1, fp0, status);
1694: fp1 = floatx80_add(fp1, twopi2, status);
1695: }
1696: loop:
1697: xSign = extractFloatx80Sign(fp0);
1698: xExp = extractFloatx80Exp(fp0);
1699: xExp -= 0x3FFF;
1700: if (xExp <= 28) {
1701: l = 0;
1702: endflag = 1;
1703: } else {
1704: l = xExp - 27;
1705: endflag = 0;
1706: }
1707: invtwopi = packFloatx80(0, 0x3FFE - l, LIT64(0xA2F9836E4E44152A)); // INVTWOPI
1708: twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000));
1709: twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(0x85A308D300000000));
1710:
1711: twoto63 = 0x5F000000;
1712: twoto63 |= xSign ? 0x80000000 : 0x00000000; // SIGN(INARG)*2^63 IN SGL
1713:
1714: fp2 = floatx80_mul(fp0, invtwopi, status);
1715: fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), status); // THE FRACTIONAL PART OF FP2 IS ROUNDED
1716: fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status), status); // FP2 is N
1717: fp4 = floatx80_mul(twopi1, fp2, status); // W = N*P1
1718: fp5 = floatx80_mul(twopi2, fp2, status); // w = N*P2
1719: fp3 = floatx80_add(fp4, fp5, status); // FP3 is P
1720: fp4 = floatx80_sub(fp4, fp3, status); // W-P
1721: fp0 = floatx80_sub(fp0, fp3, status); // FP0 is A := R - P
1722: fp4 = floatx80_add(fp4, fp5, status); // FP4 is p = (W-P)+w
1723: fp3 = fp0; // FP3 is A
1724: fp1 = floatx80_sub(fp1, fp4, status); // FP1 is a := r - p
1725: fp0 = floatx80_add(fp0, fp1, status); // FP0 is R := A+a
1726:
1727: if (endflag > 0) {
1728: n = floatx80_to_int32(fp2, status);
1729: goto tancont;
1730: }
1731: fp3 = floatx80_sub(fp3, fp0, status); // A-R
1732: fp1 = floatx80_add(fp1, fp3, status); // FP1 is r := (A-R)+a
1733: goto loop;
1734: } else {
1735: RESET_PREC;
1736:
1737: a = floatx80_move(a, status);
1738:
1739: float_raise(float_flag_inexact, status);
1740:
1741: return a;
1742: }
1743: } else {
1744: fp1 = floatx80_mul(fp0, float64_to_floatx80(LIT64(0x3FE45F306DC9C883), status), status); // X*2/PI
1745:
1746: n = floatx80_to_int32(fp1, status);
1747: j = 32 + n;
1748:
1749: fp0 = floatx80_sub(fp0, pi_tbl[j], status); // X-Y1
1750: fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status), status); // FP0 IS R = (X-Y1)-Y2
1751:
1752: tancont:
1753: if (n & 1) {
1754: // NODD
1755: fp1 = fp0; // R
1756: fp0 = floatx80_mul(fp0, fp0, status); // S = R*R
1757: fp3 = float64_to_floatx80(LIT64(0x3EA0B759F50F8688), status); // Q4
1758: fp2 = float64_to_floatx80(LIT64(0xBEF2BAA5A8924F04), status); // P3
1759: fp3 = floatx80_mul(fp3, fp0, status); // SQ4
1760: fp2 = floatx80_mul(fp2, fp0, status); // SP3
1761: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0xBF346F59B39BA65F), status), status); // Q3+SQ4
1762: fp4 = packFloatx80(0, 0x3FF6, LIT64(0xE073D3FC199C4A00));
1763: fp2 = floatx80_add(fp2, fp4, status); // P2+SP3
1764: fp3 = floatx80_mul(fp3, fp0, status); // S(Q3+SQ4)
1765: fp2 = floatx80_mul(fp2, fp0, status); // S(P2+SP3)
1766: fp4 = packFloatx80(0, 0x3FF9, LIT64(0xD23CD68415D95FA1));
1767: fp3 = floatx80_add(fp3, fp4, status); // Q2+S(Q3+SQ4)
1768: fp4 = packFloatx80(1, 0x3FFC, LIT64(0x8895A6C5FB423BCA));
1769: fp2 = floatx80_add(fp2, fp4, status); // P1+S(P2+SP3)
1770: fp3 = floatx80_mul(fp3, fp0, status); // S(Q2+S(Q3+SQ4))
1771: fp2 = floatx80_mul(fp2, fp0, status); // S(P1+S(P2+SP3))
1772: fp4 = packFloatx80(1, 0x3FFD, LIT64(0xEEF57E0DA84BC8CE));
1773: fp3 = floatx80_add(fp3, fp4, status); // Q1+S(Q2+S(Q3+SQ4))
1774: fp2 = floatx80_mul(fp2, fp1, status); // RS(P1+S(P2+SP3))
1775: fp0 = floatx80_mul(fp0, fp3, status); // S(Q1+S(Q2+S(Q3+SQ4)))
1776: fp1 = floatx80_add(fp1, fp2, status); // R+RS(P1+S(P2+SP3))
1777: fp0 = floatx80_add(fp0, float32_to_floatx80(0x3F800000, status), status); // 1+S(Q1+S(Q2+S(Q3+SQ4)))
1778:
1779: xSign = extractFloatx80Sign(fp1);
1780: xExp = extractFloatx80Exp(fp1);
1781: xSig = extractFloatx80Frac(fp1);
1782: xSign ^= 1;
1783: fp1 = packFloatx80(xSign, xExp, xSig);
1784:
1785: RESET_PREC;
1786:
1787: a = floatx80_div(fp0, fp1, status);
1788:
1789: float_raise(float_flag_inexact, status);
1790:
1791: return a;
1792: } else {
1793: fp1 = floatx80_mul(fp0, fp0, status); // S = R*R
1794: fp3 = float64_to_floatx80(LIT64(0x3EA0B759F50F8688), status); // Q4
1795: fp2 = float64_to_floatx80(LIT64(0xBEF2BAA5A8924F04), status); // P3
1796: fp3 = floatx80_mul(fp3, fp1, status); // SQ4
1797: fp2 = floatx80_mul(fp2, fp1, status); // SP3
1798: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0xBF346F59B39BA65F), status), status); // Q3+SQ4
1799: fp4 = packFloatx80(0, 0x3FF6, LIT64(0xE073D3FC199C4A00));
1800: fp2 = floatx80_add(fp2, fp4, status); // P2+SP3
1801: fp3 = floatx80_mul(fp3, fp1, status); // S(Q3+SQ4)
1802: fp2 = floatx80_mul(fp2, fp1, status); // S(P2+SP3)
1803: fp4 = packFloatx80(0, 0x3FF9, LIT64(0xD23CD68415D95FA1));
1804: fp3 = floatx80_add(fp3, fp4, status); // Q2+S(Q3+SQ4)
1805: fp4 = packFloatx80(1, 0x3FFC, LIT64(0x8895A6C5FB423BCA));
1806: fp2 = floatx80_add(fp2, fp4, status); // P1+S(P2+SP3)
1807: fp3 = floatx80_mul(fp3, fp1, status); // S(Q2+S(Q3+SQ4))
1808: fp2 = floatx80_mul(fp2, fp1, status); // S(P1+S(P2+SP3))
1809: fp4 = packFloatx80(1, 0x3FFD, LIT64(0xEEF57E0DA84BC8CE));
1810: fp3 = floatx80_add(fp3, fp4, status); // Q1+S(Q2+S(Q3+SQ4))
1811: fp2 = floatx80_mul(fp2, fp0, status); // RS(P1+S(P2+SP3))
1812: fp1 = floatx80_mul(fp1, fp3, status); // S(Q1+S(Q2+S(Q3+SQ4)))
1813: fp0 = floatx80_add(fp0, fp2, status); // R+RS(P1+S(P2+SP3))
1814: fp1 = floatx80_add(fp1, float32_to_floatx80(0x3F800000, status), status); // 1+S(Q1+S(Q2+S(Q3+SQ4)))
1815:
1816: RESET_PREC;
1817:
1818: a = floatx80_div(fp0, fp1, status);
1819:
1820: float_raise(float_flag_inexact, status);
1821:
1822: return a;
1823: }
1824: }
1825: }
1826:
1827: /*----------------------------------------------------------------------------
1828: | Hyperbolic tangent
1829: *----------------------------------------------------------------------------*/
1830:
1831: floatx80 floatx80_tanh(floatx80 a, float_status *status)
1832: {
1833: flag aSign, vSign;
1834: int32_t aExp, vExp;
1835: uint64_t aSig, vSig;
1836:
1837: int32_t compact;
1838: floatx80 fp0, fp1;
1839: float32 sign;
1840:
1841: aSig = extractFloatx80Frac(a);
1842: aExp = extractFloatx80Exp(a);
1843: aSign = extractFloatx80Sign(a);
1844:
1845: if (aExp == 0x7FFF) {
1846: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
1847: return packFloatx80(aSign, one_exp, one_sig);
1848: }
1849:
1850: if (aExp == 0 && aSig == 0) {
1851: return packFloatx80(aSign, 0, 0);
1852: }
1853:
1854: SET_PREC;
1855:
1856: compact = floatx80_make_compact(aExp, aSig);
1857:
1858: if (compact < 0x3FD78000 || compact > 0x3FFFDDCE) {
1859: // TANHBORS
1860: if (compact < 0x3FFF8000) {
1861: // TANHSM
1862: RESET_PREC;
1863:
1864: a = floatx80_move(a, status);
1865:
1866: float_raise(float_flag_inexact, status);
1867:
1868: return a;
1869: } else {
1870: if (compact > 0x40048AA1) {
1871: // TANHHUGE
1872: sign = 0x3F800000;
1873: sign |= aSign ? 0x80000000 : 0x00000000;
1874: fp0 = float32_to_floatx80(sign, status);
1875: sign &= 0x80000000;
1876: sign ^= 0x80800000; // -SIGN(X)*EPS
1877:
1878: RESET_PREC;
1879:
1880: a = floatx80_add(fp0, float32_to_floatx80(sign, status), status);
1881:
1882: float_raise(float_flag_inexact, status);
1883:
1884: return a;
1885: } else {
1886: fp0 = packFloatx80(0, aExp+1, aSig); // Y = 2|X|
1887: fp0 = floatx80_etox(fp0, status); // FP0 IS EXP(Y)
1888: fp0 = floatx80_add(fp0, float32_to_floatx80(0x3F800000, status), status); // EXP(Y)+1
1889: sign = aSign ? 0x80000000 : 0x00000000;
1890: fp1 = floatx80_div(float32_to_floatx80(sign^0xC0000000, status), fp0, status); // -SIGN(X)*2 / [EXP(Y)+1]
1891: fp0 = float32_to_floatx80(sign | 0x3F800000, status); // SIGN
1892:
1893: RESET_PREC;
1894:
1895: a = floatx80_add(fp1, fp0, status);
1896:
1897: float_raise(float_flag_inexact, status);
1898:
1899: return a;
1900: }
1901: }
1902: } else { // 2**(-40) < |X| < (5/2)LOG2
1903: fp0 = packFloatx80(0, aExp+1, aSig); // Y = 2|X|
1904: fp0 = floatx80_etoxm1(fp0, status); // FP0 IS Z = EXPM1(Y)
1905: fp1 = floatx80_add(fp0, float32_to_floatx80(0x40000000, status), status); // Z+2
1906:
1907: vSign = extractFloatx80Sign(fp1);
1908: vExp = extractFloatx80Exp(fp1);
1909: vSig = extractFloatx80Frac(fp1);
1910:
1911: fp1 = packFloatx80(vSign ^ aSign, vExp, vSig);
1912:
1913: RESET_PREC;
1914:
1915: a = floatx80_div(fp0, fp1, status);
1916:
1917: float_raise(float_flag_inexact, status);
1918:
1919: return a;
1920: }
1921: }
1922:
1923: /*----------------------------------------------------------------------------
1924: | 10 to x
1925: *----------------------------------------------------------------------------*/
1926:
1927: floatx80 floatx80_tentox(floatx80 a, float_status *status)
1928: {
1929: flag aSign;
1930: int32_t aExp;
1931: uint64_t aSig;
1932:
1933: int32_t compact, n, j, l, m, m1;
1934: floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2;
1935:
1936: aSig = extractFloatx80Frac(a);
1937: aExp = extractFloatx80Exp(a);
1938: aSign = extractFloatx80Sign(a);
1939:
1940: if (aExp == 0x7FFF) {
1941: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
1942: if (aSign) return packFloatx80(0, 0, 0);
1.1.1.2 ! root 1943: return a;
1.1 root 1944: }
1945:
1946: if (aExp == 0 && aSig == 0) {
1947: return packFloatx80(0, one_exp, one_sig);
1948: }
1949:
1950: SET_PREC;
1951:
1952: fp0 = a;
1953:
1954: compact = floatx80_make_compact(aExp, aSig);
1955:
1956: if (compact < 0x3FB98000 || compact > 0x400B9B07) { // |X| > 16480 LOG2/LOG10 or |X| < 2^(-70)
1957: if (compact > 0x3FFF8000) { // |X| > 16480
1958: RESET_PREC;
1959:
1960: if (aSign) {
1961: return roundAndPackFloatx80(status->floatx80_rounding_precision, 0, -0x1000, aSig, 0, status);
1962: } else {
1963: return roundAndPackFloatx80(status->floatx80_rounding_precision, 0, 0x8000, aSig, 0, status);
1964: }
1965: } else { // |X| < 2^(-70)
1966: RESET_PREC;
1967:
1968: a = floatx80_add(fp0, float32_to_floatx80(0x3F800000, status), status); // 1 + X
1969:
1970: float_raise(float_flag_inexact, status);
1971:
1972: return a;
1973: }
1974: } else { // 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10
1975: fp1 = fp0; // X
1976: fp1 = floatx80_mul(fp1, float64_to_floatx80(LIT64(0x406A934F0979A371), status), status); // X*64*LOG10/LOG2
1977: n = floatx80_to_int32(fp1, status); // N=INT(X*64*LOG10/LOG2)
1978: fp1 = int32_to_floatx80(n);
1979:
1980: j = n & 0x3F;
1981: l = n / 64; // NOTE: this is really arithmetic right shift by 6
1982: if (n < 0 && j) { // arithmetic right shift is division and round towards minus infinity
1983: l--;
1984: }
1985: m = l / 2; // NOTE: this is really arithmetic right shift by 1
1986: if (l < 0 && (l & 1)) { // arithmetic right shift is division and round towards minus infinity
1987: m--;
1988: }
1989: m1 = l - m;
1990: m1 += 0x3FFF; // ADJFACT IS 2^(M')
1991:
1992: adjfact = packFloatx80(0, m1, one_sig);
1993: fact1 = exp2_tbl[j];
1994: fact1.high += m;
1995: fact2.high = exp2_tbl2[j]>>16;
1996: fact2.high += m;
1997: fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF);
1998: fact2.low <<= 48;
1999:
2000: fp2 = fp1; // N
2001: fp1 = floatx80_mul(fp1, float64_to_floatx80(LIT64(0x3F734413509F8000), status), status); // N*(LOG2/64LOG10)_LEAD
2002: fp3 = packFloatx80(1, 0x3FCD, LIT64(0xC0219DC1DA994FD2));
2003: fp2 = floatx80_mul(fp2, fp3, status); // N*(LOG2/64LOG10)_TRAIL
2004: fp0 = floatx80_sub(fp0, fp1, status); // X - N L_LEAD
2005: fp0 = floatx80_sub(fp0, fp2, status); // X - N L_TRAIL
2006: fp2 = packFloatx80(0, 0x4000, LIT64(0x935D8DDDAAA8AC17)); // LOG10
2007: fp0 = floatx80_mul(fp0, fp2, status); // R
2008:
2009: // EXPR
2010: fp1 = floatx80_mul(fp0, fp0, status); // S = R*R
2011: fp2 = float64_to_floatx80(LIT64(0x3F56C16D6F7BD0B2), status); // A5
2012: fp3 = float64_to_floatx80(LIT64(0x3F811112302C712C), status); // A4
2013: fp2 = floatx80_mul(fp2, fp1, status); // S*A5
2014: fp3 = floatx80_mul(fp3, fp1, status); // S*A4
2015: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FA5555555554CC1), status), status); // A3+S*A5
2016: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0x3FC5555555554A54), status), status); // A2+S*A4
2017: fp2 = floatx80_mul(fp2, fp1, status); // S*(A3+S*A5)
2018: fp3 = floatx80_mul(fp3, fp1, status); // S*(A2+S*A4)
2019: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FE0000000000000), status), status); // A1+S*(A3+S*A5)
2020: fp3 = floatx80_mul(fp3, fp0, status); // R*S*(A2+S*A4)
2021:
2022: fp2 = floatx80_mul(fp2, fp1, status); // S*(A1+S*(A3+S*A5))
2023: fp0 = floatx80_add(fp0, fp3, status); // R+R*S*(A2+S*A4)
2024: fp0 = floatx80_add(fp0, fp2, status); // EXP(R) - 1
2025:
2026: fp0 = floatx80_mul(fp0, fact1, status);
2027: fp0 = floatx80_add(fp0, fact2, status);
2028: fp0 = floatx80_add(fp0, fact1, status);
2029:
2030: RESET_PREC;
2031:
2032: a = floatx80_mul(fp0, adjfact, status);
2033:
2034: float_raise(float_flag_inexact, status);
2035:
2036: return a;
2037: }
2038: }
2039:
2040: /*----------------------------------------------------------------------------
2041: | 2 to x
2042: *----------------------------------------------------------------------------*/
2043:
2044: floatx80 floatx80_twotox(floatx80 a, float_status *status)
2045: {
2046: flag aSign;
2047: int32_t aExp;
2048: uint64_t aSig;
2049:
2050: int32_t compact, n, j, l, m, m1;
2051: floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2;
2052:
2053: aSig = extractFloatx80Frac(a);
2054: aExp = extractFloatx80Exp(a);
2055: aSign = extractFloatx80Sign(a);
2056:
2057: if (aExp == 0x7FFF) {
2058: if ((uint64_t) (aSig<<1)) return propagateFloatx80NaNOneArg(a, status);
2059: if (aSign) return packFloatx80(0, 0, 0);
1.1.1.2 ! root 2060: return a;
1.1 root 2061: }
2062:
2063: if (aExp == 0 && aSig == 0) {
2064: return packFloatx80(0, one_exp, one_sig);
2065: }
2066:
2067: SET_PREC;
2068:
2069: fp0 = a;
2070:
2071: compact = floatx80_make_compact(aExp, aSig);
2072:
2073: if (compact < 0x3FB98000 || compact > 0x400D80C0) { // |X| > 16480 or |X| < 2^(-70)
2074: if (compact > 0x3FFF8000) { // |X| > 16480
2075: RESET_PREC;;
2076:
2077: if (aSign) {
2078: return roundAndPackFloatx80(status->floatx80_rounding_precision, 0, -0x1000, aSig, 0, status);
2079: } else {
2080: return roundAndPackFloatx80(status->floatx80_rounding_precision, 0, 0x8000, aSig, 0, status);
2081: }
2082: } else { // |X| < 2^(-70)
2083: RESET_PREC;;
2084:
2085: a = floatx80_add(fp0, float32_to_floatx80(0x3F800000, status), status); // 1 + X
2086:
2087: float_raise(float_flag_inexact, status);
2088:
2089: return a;
2090: }
2091: } else { // 2^(-70) <= |X| <= 16480
2092: fp1 = fp0; // X
2093: fp1 = floatx80_mul(fp1, float32_to_floatx80(0x42800000, status), status); // X * 64
2094: n = floatx80_to_int32(fp1, status);
2095: fp1 = int32_to_floatx80(n);
2096: j = n & 0x3F;
2097: l = n / 64; // NOTE: this is really arithmetic right shift by 6
2098: if (n < 0 && j) { // arithmetic right shift is division and round towards minus infinity
2099: l--;
2100: }
2101: m = l / 2; // NOTE: this is really arithmetic right shift by 1
2102: if (l < 0 && (l & 1)) { // arithmetic right shift is division and round towards minus infinity
2103: m--;
2104: }
2105: m1 = l - m;
2106: m1 += 0x3FFF; // ADJFACT IS 2^(M')
2107:
2108: adjfact = packFloatx80(0, m1, one_sig);
2109: fact1 = exp2_tbl[j];
2110: fact1.high += m;
2111: fact2.high = exp2_tbl2[j]>>16;
2112: fact2.high += m;
2113: fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF);
2114: fact2.low <<= 48;
2115:
2116: fp1 = floatx80_mul(fp1, float32_to_floatx80(0x3C800000, status), status); // (1/64)*N
2117: fp0 = floatx80_sub(fp0, fp1, status); // X - (1/64)*INT(64 X)
2118: fp2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); // LOG2
2119: fp0 = floatx80_mul(fp0, fp2, status); // R
2120:
2121: // EXPR
2122: fp1 = floatx80_mul(fp0, fp0, status); // S = R*R
2123: fp2 = float64_to_floatx80(LIT64(0x3F56C16D6F7BD0B2), status); // A5
2124: fp3 = float64_to_floatx80(LIT64(0x3F811112302C712C), status); // A4
2125: fp2 = floatx80_mul(fp2, fp1, status); // S*A5
2126: fp3 = floatx80_mul(fp3, fp1, status); // S*A4
2127: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FA5555555554CC1), status), status); // A3+S*A5
2128: fp3 = floatx80_add(fp3, float64_to_floatx80(LIT64(0x3FC5555555554A54), status), status); // A2+S*A4
2129: fp2 = floatx80_mul(fp2, fp1, status); // S*(A3+S*A5)
2130: fp3 = floatx80_mul(fp3, fp1, status); // S*(A2+S*A4)
2131: fp2 = floatx80_add(fp2, float64_to_floatx80(LIT64(0x3FE0000000000000), status), status); // A1+S*(A3+S*A5)
2132: fp3 = floatx80_mul(fp3, fp0, status); // R*S*(A2+S*A4)
2133:
2134: fp2 = floatx80_mul(fp2, fp1, status); // S*(A1+S*(A3+S*A5))
2135: fp0 = floatx80_add(fp0, fp3, status); // R+R*S*(A2+S*A4)
2136: fp0 = floatx80_add(fp0, fp2, status); // EXP(R) - 1
2137:
2138: fp0 = floatx80_mul(fp0, fact1, status);
2139: fp0 = floatx80_add(fp0, fact2, status);
2140: fp0 = floatx80_add(fp0, fact1, status);
2141:
2142: RESET_PREC;
2143:
2144: a = floatx80_mul(fp0, adjfact, status);
2145:
2146: float_raise(float_flag_inexact, status);
2147:
2148: return a;
2149: }
2150: }
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