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| 1 /* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_log1pl.c */ | 1 /* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_log1pl.c */ |
| 2 /* | 2 /* |
| 3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> | 3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> |
| 4 * | 4 * |
| 5 * Permission to use, copy, modify, and distribute this software for any | 5 * Permission to use, copy, modify, and distribute this software for any |
| 6 * purpose with or without fee is hereby granted, provided that the above | 6 * purpose with or without fee is hereby granted, provided that the above |
| 7 * copyright notice and this permission notice appear in all copies. | 7 * copyright notice and this permission notice appear in all copies. |
| 8 * | 8 * |
| 9 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES | 9 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| 10 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF | 10 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| (...skipping 33 matching lines...) Expand 10 before | Expand all | Expand 10 after Loading... |
| 44 * ACCURACY: | 44 * ACCURACY: |
| 45 * | 45 * |
| 46 * Relative error: | 46 * Relative error: |
| 47 * arithmetic domain # trials peak rms | 47 * arithmetic domain # trials peak rms |
| 48 * IEEE -1.0, 9.0 100000 8.2e-20 2.5e-20 | 48 * IEEE -1.0, 9.0 100000 8.2e-20 2.5e-20 |
| 49 */ | 49 */ |
| 50 | 50 |
| 51 #include "libm.h" | 51 #include "libm.h" |
| 52 | 52 |
| 53 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 | 53 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 |
| 54 long double log1pl(long double x) | 54 long double log1pl(long double x) { |
| 55 { | 55 return log1p(x); |
| 56 » return log1p(x); | |
| 57 } | 56 } |
| 58 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 | 57 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 |
| 59 /* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) | 58 /* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) |
| 60 * 1/sqrt(2) <= x < sqrt(2) | 59 * 1/sqrt(2) <= x < sqrt(2) |
| 61 * Theoretical peak relative error = 2.32e-20 | 60 * Theoretical peak relative error = 2.32e-20 |
| 62 */ | 61 */ |
| 63 static const long double P[] = { | 62 static const long double P[] = { |
| 64 4.5270000862445199635215E-5L, | 63 4.5270000862445199635215E-5L, 4.9854102823193375972212E-1L, |
| 65 4.9854102823193375972212E-1L, | 64 6.5787325942061044846969E0L, 2.9911919328553073277375E1L, |
| 66 6.5787325942061044846969E0L, | 65 6.0949667980987787057556E1L, 5.7112963590585538103336E1L, |
| 67 2.9911919328553073277375E1L, | 66 2.0039553499201281259648E1L, |
| 68 6.0949667980987787057556E1L, | |
| 69 5.7112963590585538103336E1L, | |
| 70 2.0039553499201281259648E1L, | |
| 71 }; | 67 }; |
| 72 static const long double Q[] = { | 68 static const long double Q[] = { |
| 73 /* 1.0000000000000000000000E0,*/ | 69 /* 1.0000000000000000000000E0,*/ |
| 74 1.5062909083469192043167E1L, | 70 1.5062909083469192043167E1L, 8.3047565967967209469434E1L, |
| 75 8.3047565967967209469434E1L, | 71 2.2176239823732856465394E2L, 3.0909872225312059774938E2L, |
| 76 2.2176239823732856465394E2L, | 72 2.1642788614495947685003E2L, 6.0118660497603843919306E1L, |
| 77 3.0909872225312059774938E2L, | |
| 78 2.1642788614495947685003E2L, | |
| 79 6.0118660497603843919306E1L, | |
| 80 }; | 73 }; |
| 81 | 74 |
| 82 /* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), | 75 /* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), |
| 83 * where z = 2(x-1)/(x+1) | 76 * where z = 2(x-1)/(x+1) |
| 84 * 1/sqrt(2) <= x < sqrt(2) | 77 * 1/sqrt(2) <= x < sqrt(2) |
| 85 * Theoretical peak relative error = 6.16e-22 | 78 * Theoretical peak relative error = 6.16e-22 |
| 86 */ | 79 */ |
| 87 static const long double R[4] = { | 80 static const long double R[4] = { |
| 88 1.9757429581415468984296E-3L, | 81 1.9757429581415468984296E-3L, -7.1990767473014147232598E-1L, |
| 89 -7.1990767473014147232598E-1L, | 82 1.0777257190312272158094E1L, -3.5717684488096787370998E1L, |
| 90 1.0777257190312272158094E1L, | |
| 91 -3.5717684488096787370998E1L, | |
| 92 }; | 83 }; |
| 93 static const long double S[4] = { | 84 static const long double S[4] = { |
| 94 /* 1.00000000000000000000E0L,*/ | 85 /* 1.00000000000000000000E0L,*/ |
| 95 -2.6201045551331104417768E1L, | 86 -2.6201045551331104417768E1L, 1.9361891836232102174846E2L, |
| 96 1.9361891836232102174846E2L, | 87 -4.2861221385716144629696E2L, |
| 97 -4.2861221385716144629696E2L, | |
| 98 }; | 88 }; |
| 99 static const long double C1 = 6.9314575195312500000000E-1L; | 89 static const long double C1 = 6.9314575195312500000000E-1L; |
| 100 static const long double C2 = 1.4286068203094172321215E-6L; | 90 static const long double C2 = 1.4286068203094172321215E-6L; |
| 101 | 91 |
| 102 #define SQRTH 0.70710678118654752440L | 92 #define SQRTH 0.70710678118654752440L |
| 103 | 93 |
| 104 long double log1pl(long double xm1) | 94 long double log1pl(long double xm1) { |
| 105 { | 95 long double x, y, z; |
| 106 » long double x, y, z; | 96 int e; |
| 107 » int e; | |
| 108 | 97 |
| 109 » if (isnan(xm1)) | 98 if (isnan(xm1)) |
| 110 » » return xm1; | 99 return xm1; |
| 111 » if (xm1 == INFINITY) | 100 if (xm1 == INFINITY) |
| 112 » » return xm1; | 101 return xm1; |
| 113 » if (xm1 == 0.0) | 102 if (xm1 == 0.0) |
| 114 » » return xm1; | 103 return xm1; |
| 115 | 104 |
| 116 » x = xm1 + 1.0; | 105 x = xm1 + 1.0; |
| 117 | 106 |
| 118 » /* Test for domain errors. */ | 107 /* Test for domain errors. */ |
| 119 » if (x <= 0.0) { | 108 if (x <= 0.0) { |
| 120 » » if (x == 0.0) | 109 if (x == 0.0) |
| 121 » » » return -1/(x*x); /* -inf with divbyzero */ | 110 return -1 / (x * x); /* -inf with divbyzero */ |
| 122 » » return 0/0.0f; /* nan with invalid */ | 111 return 0 / 0.0f; /* nan with invalid */ |
| 123 » } | 112 } |
| 124 | 113 |
| 125 » /* Separate mantissa from exponent. | 114 /* Separate mantissa from exponent. |
| 126 » Use frexp so that denormal numbers will be handled properly. */ | 115 Use frexp so that denormal numbers will be handled properly. */ |
| 127 » x = frexpl(x, &e); | 116 x = frexpl(x, &e); |
| 128 | 117 |
| 129 » /* logarithm using log(x) = z + z^3 P(z)/Q(z), | 118 /* logarithm using log(x) = z + z^3 P(z)/Q(z), |
| 130 » where z = 2(x-1)/x+1) */ | 119 where z = 2(x-1)/x+1) */ |
| 131 » if (e > 2 || e < -2) { | 120 if (e > 2 || e < -2) { |
| 132 » » if (x < SQRTH) { /* 2(2x-1)/(2x+1) */ | 121 if (x < SQRTH) { /* 2(2x-1)/(2x+1) */ |
| 133 » » » e -= 1; | 122 e -= 1; |
| 134 » » » z = x - 0.5; | 123 z = x - 0.5; |
| 135 » » » y = 0.5 * z + 0.5; | 124 y = 0.5 * z + 0.5; |
| 136 » » } else { /* 2 (x-1)/(x+1) */ | 125 } else { /* 2 (x-1)/(x+1) */ |
| 137 » » » z = x - 0.5; | 126 z = x - 0.5; |
| 138 » » » z -= 0.5; | 127 z -= 0.5; |
| 139 » » » y = 0.5 * x + 0.5; | 128 y = 0.5 * x + 0.5; |
| 140 » » } | 129 } |
| 141 » » x = z / y; | 130 x = z / y; |
| 142 » » z = x*x; | 131 z = x * x; |
| 143 » » z = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3)); | 132 z = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3)); |
| 144 » » z = z + e * C2; | 133 z = z + e * C2; |
| 145 » » z = z + x; | 134 z = z + x; |
| 146 » » z = z + e * C1; | 135 z = z + e * C1; |
| 147 » » return z; | 136 return z; |
| 148 » } | 137 } |
| 149 | 138 |
| 150 » /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ | 139 /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ |
| 151 » if (x < SQRTH) { | 140 if (x < SQRTH) { |
| 152 » » e -= 1; | 141 e -= 1; |
| 153 » » if (e != 0) | 142 if (e != 0) |
| 154 » » » x = 2.0 * x - 1.0; | 143 x = 2.0 * x - 1.0; |
| 155 » » else | 144 else |
| 156 » » » x = xm1; | 145 x = xm1; |
| 157 » } else { | 146 } else { |
| 158 » » if (e != 0) | 147 if (e != 0) |
| 159 » » » x = x - 1.0; | 148 x = x - 1.0; |
| 160 » » else | 149 else |
| 161 » » » x = xm1; | 150 x = xm1; |
| 162 » } | 151 } |
| 163 » z = x*x; | 152 z = x * x; |
| 164 » y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6)); | 153 y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6)); |
| 165 » y = y + e * C2; | 154 y = y + e * C2; |
| 166 » z = y - 0.5 * z; | 155 z = y - 0.5 * z; |
| 167 » z = z + x; | 156 z = z + x; |
| 168 » z = z + e * C1; | 157 z = z + e * C1; |
| 169 » return z; | 158 return z; |
| 170 } | 159 } |
| 171 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 | 160 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 |
| 172 // TODO: broken implementation to make things compile | 161 // TODO: broken implementation to make things compile |
| 173 long double log1pl(long double x) | 162 long double log1pl(long double x) { |
| 174 { | 163 return log1p(x); |
| 175 » return log1p(x); | |
| 176 } | 164 } |
| 177 #endif | 165 #endif |
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