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| 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */ | 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */ |
| 2 /* | 2 /* |
| 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. | 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| 4 * Debugged and optimized by Bruce D. Evans. | 4 * Debugged and optimized by Bruce D. Evans. |
| 5 */ | 5 */ |
| 6 /* | 6 /* |
| 7 * ==================================================== | 7 * ==================================================== |
| 8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | 8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 9 * | 9 * |
| 10 * Developed at SunPro, a Sun Microsystems, Inc. business. | 10 * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 11 * Permission to use, copy, modify, and distribute this | 11 * Permission to use, copy, modify, and distribute this |
| 12 * software is freely granted, provided that this notice | 12 * software is freely granted, provided that this notice |
| 13 * is preserved. | 13 * is preserved. |
| 14 * ==================================================== | 14 * ==================================================== |
| 15 */ | 15 */ |
| 16 /* cbrtf(x) | 16 /* cbrtf(x) |
| 17 * Return cube root of x | 17 * Return cube root of x |
| 18 */ | 18 */ |
| 19 | 19 |
| 20 #include <math.h> | 20 #include <math.h> |
| 21 #include <stdint.h> | 21 #include <stdint.h> |
| 22 | 22 |
| 23 static const unsigned | 23 static const unsigned |
| 24 B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */ | 24 B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */ |
| 25 B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */ | 25 B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */ |
| 26 | 26 |
| 27 float cbrtf(float x) | 27 float cbrtf(float x) { |
| 28 { | 28 double_t r, T; |
| 29 » double_t r,T; | 29 union { |
| 30 » union {float f; uint32_t i;} u = {x}; | 30 float f; |
| 31 » uint32_t hx = u.i & 0x7fffffff; | 31 uint32_t i; |
| 32 } u = {x}; |
| 33 uint32_t hx = u.i & 0x7fffffff; |
| 32 | 34 |
| 33 » if (hx >= 0x7f800000) /* cbrt(NaN,INF) is itself */ | 35 if (hx >= 0x7f800000) /* cbrt(NaN,INF) is itself */ |
| 34 » » return x + x; | 36 return x + x; |
| 35 | 37 |
| 36 » /* rough cbrt to 5 bits */ | 38 /* rough cbrt to 5 bits */ |
| 37 » if (hx < 0x00800000) { /* zero or subnormal? */ | 39 if (hx < 0x00800000) { /* zero or subnormal? */ |
| 38 » » if (hx == 0) | 40 if (hx == 0) |
| 39 » » » return x; /* cbrt(+-0) is itself */ | 41 return x; /* cbrt(+-0) is itself */ |
| 40 » » u.f = x*0x1p24f; | 42 u.f = x * 0x1p24f; |
| 41 » » hx = u.i & 0x7fffffff; | 43 hx = u.i & 0x7fffffff; |
| 42 » » hx = hx/3 + B2; | 44 hx = hx / 3 + B2; |
| 43 » } else | 45 } else |
| 44 » » hx = hx/3 + B1; | 46 hx = hx / 3 + B1; |
| 45 » u.i &= 0x80000000; | 47 u.i &= 0x80000000; |
| 46 » u.i |= hx; | 48 u.i |= hx; |
| 47 | 49 |
| 48 » /* | 50 /* |
| 49 » * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In | 51 * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In |
| 50 » * double precision so that its terms can be arranged for efficiency | 52 * double precision so that its terms can be arranged for efficiency |
| 51 » * without causing overflow or underflow. | 53 * without causing overflow or underflow. |
| 52 » */ | 54 */ |
| 53 » T = u.f; | 55 T = u.f; |
| 54 » r = T*T*T; | 56 r = T * T * T; |
| 55 » T = T*((double_t)x+x+r)/(x+r+r); | 57 T = T * ((double_t)x + x + r) / (x + r + r); |
| 56 | 58 |
| 57 » /* | 59 /* |
| 58 » * Second step Newton iteration to 47 bits. In double precision for | 60 * Second step Newton iteration to 47 bits. In double precision for |
| 59 » * efficiency and accuracy. | 61 * efficiency and accuracy. |
| 60 » */ | 62 */ |
| 61 » r = T*T*T; | 63 r = T * T * T; |
| 62 » T = T*((double_t)x+x+r)/(x+r+r); | 64 T = T * ((double_t)x + x + r) / (x + r + r); |
| 63 | 65 |
| 64 » /* rounding to 24 bits is perfect in round-to-nearest mode */ | 66 /* rounding to 24 bits is perfect in round-to-nearest mode */ |
| 65 » return T; | 67 return T; |
| 66 } | 68 } |
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