| s_cosl.c (176360) | s_cosl.c (221234) |
|---|---|
| 1/*- 2 * Copyright (c) 2007 Steven G. Kargl 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright --- 11 unchanged lines hidden (view full) --- 20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 25 */ 26 27#include <sys/cdefs.h> | 1/*- 2 * Copyright (c) 2007 Steven G. Kargl 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright --- 11 unchanged lines hidden (view full) --- 20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 25 */ 26 27#include <sys/cdefs.h> |
| 28__FBSDID("$FreeBSD: head/lib/msun/src/s_cosl.c 176360 2008-02-17 07:33:12Z das $"); | 28__FBSDID("$FreeBSD: head/lib/msun/src/s_cosl.c 221234 2011-04-29 23:13:43Z kargl $"); |
| 29 30/* | 29 30/* |
| 31 * Compute cos(x) for x where x is reduced to y = x - k * pi / 2. | |
| 32 * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows 33 * an accuracy of <= 0.7412 ULP. 34 */ 35 36#include <float.h> 37 38#include "math.h" | 31 * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows 32 * an accuracy of <= 0.7412 ULP. 33 */ 34 35#include <float.h> 36 37#include "math.h" |
| 38#define INLINE_REM_PIO2L |
|
| 39#include "math_private.h" | 39#include "math_private.h" |
| 40#include "fpmath.h" 41 | |
| 42#if LDBL_MANT_DIG == 64 | 40#if LDBL_MANT_DIG == 64 |
| 43#define NX 3 44#define PREC 2 | 41#include "../ld80/e_rem_pio2l.h" |
| 45#elif LDBL_MANT_DIG == 113 | 42#elif LDBL_MANT_DIG == 113 |
| 46#define NX 5 47#define PREC 3 | 43#include "../ld128/e_rem_pio2l.h" |
| 48#else 49#error "Unsupported long double format" 50#endif 51 | 44#else 45#error "Unsupported long double format" 46#endif 47 |
| 52static const long double two24 = 1.67772160000000000000e+07L; 53 | |
| 54long double 55cosl(long double x) 56{ 57 union IEEEl2bits z; | 48long double 49cosl(long double x) 50{ 51 union IEEEl2bits z; |
| 58 int i, e0; 59 double xd[NX], yd[PREC]; | 52 int e0; 53 long double y[2]; |
| 60 long double hi, lo; 61 62 z.e = x; 63 z.bits.sign = 0; 64 65 /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */ 66 if (z.bits.exp == 0) 67 return (1.0); 68 69 /* If x = NaN or Inf, then cos(x) = NaN. */ 70 if (z.bits.exp == 32767) 71 return ((x - x) / (x - x)); 72 73 /* Optimize the case where x is already within range. */ 74 if (z.e < M_PI_4) 75 return (__kernel_cosl(z.e, 0)); 76 | 54 long double hi, lo; 55 56 z.e = x; 57 z.bits.sign = 0; 58 59 /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */ 60 if (z.bits.exp == 0) 61 return (1.0); 62 63 /* If x = NaN or Inf, then cos(x) = NaN. */ 64 if (z.bits.exp == 32767) 65 return ((x - x) / (x - x)); 66 67 /* Optimize the case where x is already within range. */ 68 if (z.e < M_PI_4) 69 return (__kernel_cosl(z.e, 0)); 70 |
| 77 /* Split z.e into a 24-bit representation. */ 78 e0 = ilogbl(z.e) - 23; 79 z.e = scalbnl(z.e, -e0); 80 for (i = 0; i < NX; i++) { 81 xd[i] = (double)((int32_t)z.e); 82 z.e = (z.e - xd[i]) * two24; 83 } 84 85 /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */ 86 e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC); | 71 e0 = __ieee754_rem_pio2l(x, y); 72 hi = y[0]; 73 lo = y[1]; |
| 87 | 74 |
| 88#if PREC == 2 89 hi = (long double)yd[0] + yd[1]; 90 lo = yd[1] - (hi - yd[0]); 91#else /* PREC == 3 */ 92 long double t; 93 t = (long double)yd[2] + yd[1]; 94 hi = t + yd[0]; 95 lo = yd[0] - (hi - t); 96#endif 97 | |
| 98 switch (e0 & 3) { 99 case 0: 100 hi = __kernel_cosl(hi, lo); 101 break; 102 case 1: 103 hi = - __kernel_sinl(hi, lo, 1); 104 break; 105 case 2: 106 hi = - __kernel_cosl(hi, lo); 107 break; 108 case 3: 109 hi = __kernel_sinl(hi, lo, 1); 110 break; 111 } 112 113 return (hi); 114} | 75 switch (e0 & 3) { 76 case 0: 77 hi = __kernel_cosl(hi, lo); 78 break; 79 case 1: 80 hi = - __kernel_sinl(hi, lo, 1); 81 break; 82 case 2: 83 hi = - __kernel_cosl(hi, lo); 84 break; 85 case 3: 86 hi = __kernel_sinl(hi, lo, 1); 87 break; 88 } 89 90 return (hi); 91} |