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| 1 /* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_logl.c */ | 1 /* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_logl.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 37 matching lines...) Expand 10 before | Expand all | Expand 10 after Loading... |
| 48 * IEEE exp(+-10000) 100000 5.39e-20 2.34e-20 | 48 * IEEE exp(+-10000) 100000 5.39e-20 2.34e-20 |
| 49 * | 49 * |
| 50 * In the tests over the interval exp(+-10000), the logarithms | 50 * In the tests over the interval exp(+-10000), the logarithms |
| 51 * of the random arguments were uniformly distributed over | 51 * of the random arguments were uniformly distributed over |
| 52 * [-10000, +10000]. | 52 * [-10000, +10000]. |
| 53 */ | 53 */ |
| 54 | 54 |
| 55 #include "libm.h" | 55 #include "libm.h" |
| 56 | 56 |
| 57 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 | 57 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 |
| 58 long double logl(long double x) | 58 long double logl(long double x) { |
| 59 { | 59 return log(x); |
| 60 » return log(x); | |
| 61 } | 60 } |
| 62 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 | 61 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 |
| 63 /* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x) | 62 /* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x) |
| 64 * 1/sqrt(2) <= x < sqrt(2) | 63 * 1/sqrt(2) <= x < sqrt(2) |
| 65 * Theoretical peak relative error = 2.32e-20 | 64 * Theoretical peak relative error = 2.32e-20 |
| 66 */ | 65 */ |
| 67 static const long double P[] = { | 66 static const long double P[] = { |
| 68 4.5270000862445199635215E-5L, | 67 4.5270000862445199635215E-5L, 4.9854102823193375972212E-1L, |
| 69 4.9854102823193375972212E-1L, | 68 6.5787325942061044846969E0L, 2.9911919328553073277375E1L, |
| 70 6.5787325942061044846969E0L, | 69 6.0949667980987787057556E1L, 5.7112963590585538103336E1L, |
| 71 2.9911919328553073277375E1L, | 70 2.0039553499201281259648E1L, |
| 72 6.0949667980987787057556E1L, | |
| 73 5.7112963590585538103336E1L, | |
| 74 2.0039553499201281259648E1L, | |
| 75 }; | 71 }; |
| 76 static const long double Q[] = { | 72 static const long double Q[] = { |
| 77 /* 1.0000000000000000000000E0,*/ | 73 /* 1.0000000000000000000000E0,*/ |
| 78 1.5062909083469192043167E1L, | 74 1.5062909083469192043167E1L, 8.3047565967967209469434E1L, |
| 79 8.3047565967967209469434E1L, | 75 2.2176239823732856465394E2L, 3.0909872225312059774938E2L, |
| 80 2.2176239823732856465394E2L, | 76 2.1642788614495947685003E2L, 6.0118660497603843919306E1L, |
| 81 3.0909872225312059774938E2L, | |
| 82 2.1642788614495947685003E2L, | |
| 83 6.0118660497603843919306E1L, | |
| 84 }; | 77 }; |
| 85 | 78 |
| 86 /* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), | 79 /* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), |
| 87 * where z = 2(x-1)/(x+1) | 80 * where z = 2(x-1)/(x+1) |
| 88 * 1/sqrt(2) <= x < sqrt(2) | 81 * 1/sqrt(2) <= x < sqrt(2) |
| 89 * Theoretical peak relative error = 6.16e-22 | 82 * Theoretical peak relative error = 6.16e-22 |
| 90 */ | 83 */ |
| 91 static const long double R[4] = { | 84 static const long double R[4] = { |
| 92 1.9757429581415468984296E-3L, | 85 1.9757429581415468984296E-3L, -7.1990767473014147232598E-1L, |
| 93 -7.1990767473014147232598E-1L, | 86 1.0777257190312272158094E1L, -3.5717684488096787370998E1L, |
| 94 1.0777257190312272158094E1L, | |
| 95 -3.5717684488096787370998E1L, | |
| 96 }; | 87 }; |
| 97 static const long double S[4] = { | 88 static const long double S[4] = { |
| 98 /* 1.00000000000000000000E0L,*/ | 89 /* 1.00000000000000000000E0L,*/ |
| 99 -2.6201045551331104417768E1L, | 90 -2.6201045551331104417768E1L, 1.9361891836232102174846E2L, |
| 100 1.9361891836232102174846E2L, | 91 -4.2861221385716144629696E2L, |
| 101 -4.2861221385716144629696E2L, | |
| 102 }; | 92 }; |
| 103 static const long double C1 = 6.9314575195312500000000E-1L; | 93 static const long double C1 = 6.9314575195312500000000E-1L; |
| 104 static const long double C2 = 1.4286068203094172321215E-6L; | 94 static const long double C2 = 1.4286068203094172321215E-6L; |
| 105 | 95 |
| 106 #define SQRTH 0.70710678118654752440L | 96 #define SQRTH 0.70710678118654752440L |
| 107 | 97 |
| 108 long double logl(long double x) | 98 long double logl(long double x) { |
| 109 { | 99 long double y, z; |
| 110 » long double y, z; | 100 int e; |
| 111 » int e; | |
| 112 | 101 |
| 113 » if (isnan(x)) | 102 if (isnan(x)) |
| 114 » » return x; | 103 return x; |
| 115 » if (x == INFINITY) | 104 if (x == INFINITY) |
| 116 » » return x; | 105 return x; |
| 117 » if (x <= 0.0) { | 106 if (x <= 0.0) { |
| 118 » » if (x == 0.0) | 107 if (x == 0.0) |
| 119 » » » return -1/(x*x); /* -inf with divbyzero */ | 108 return -1 / (x * x); /* -inf with divbyzero */ |
| 120 » » return 0/0.0f; /* nan with invalid */ | 109 return 0 / 0.0f; /* nan with invalid */ |
| 121 » } | 110 } |
| 122 | 111 |
| 123 » /* separate mantissa from exponent */ | 112 /* separate mantissa from exponent */ |
| 124 » /* Note, frexp is used so that denormal numbers | 113 /* Note, frexp is used so that denormal numbers |
| 125 » * will be handled properly. | 114 * will be handled properly. |
| 126 » */ | 115 */ |
| 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 » */ | 120 */ |
| 132 » if (e > 2 || e < -2) { | 121 if (e > 2 || e < -2) { |
| 133 » » if (x < SQRTH) { /* 2(2x-1)/(2x+1) */ | 122 if (x < SQRTH) { /* 2(2x-1)/(2x+1) */ |
| 134 » » » e -= 1; | 123 e -= 1; |
| 135 » » » z = x - 0.5; | 124 z = x - 0.5; |
| 136 » » » y = 0.5 * z + 0.5; | 125 y = 0.5 * z + 0.5; |
| 137 » » } else { /* 2 (x-1)/(x+1) */ | 126 } else { /* 2 (x-1)/(x+1) */ |
| 138 » » » z = x - 0.5; | 127 z = x - 0.5; |
| 139 » » » z -= 0.5; | 128 z -= 0.5; |
| 140 » » » y = 0.5 * x + 0.5; | 129 y = 0.5 * x + 0.5; |
| 141 » » } | 130 } |
| 142 » » x = z / y; | 131 x = z / y; |
| 143 » » z = x*x; | 132 z = x * x; |
| 144 » » z = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3)); | 133 z = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3)); |
| 145 » » z = z + e * C2; | 134 z = z + e * C2; |
| 146 » » z = z + x; | 135 z = z + x; |
| 147 » » z = z + e * C1; | 136 z = z + e * C1; |
| 148 » » return z; | 137 return z; |
| 149 » } | 138 } |
| 150 | 139 |
| 151 » /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ | 140 /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ |
| 152 » if (x < SQRTH) { | 141 if (x < SQRTH) { |
| 153 » » e -= 1; | 142 e -= 1; |
| 154 » » x = 2.0*x - 1.0; | 143 x = 2.0 * x - 1.0; |
| 155 » } else { | 144 } else { |
| 156 » » x = x - 1.0; | 145 x = x - 1.0; |
| 157 » } | 146 } |
| 158 » z = x*x; | 147 z = x * x; |
| 159 » y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6)); | 148 y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6)); |
| 160 » y = y + e * C2; | 149 y = y + e * C2; |
| 161 » z = y - 0.5*z; | 150 z = y - 0.5 * z; |
| 162 » /* Note, the sum of above terms does not exceed x/4, | 151 /* Note, the sum of above terms does not exceed x/4, |
| 163 » * so it contributes at most about 1/4 lsb to the error. | 152 * so it contributes at most about 1/4 lsb to the error. |
| 164 » */ | 153 */ |
| 165 » z = z + x; | 154 z = z + x; |
| 166 » z = z + e * C1; /* This sum has an error of 1/2 lsb. */ | 155 z = z + e * C1; /* This sum has an error of 1/2 lsb. */ |
| 167 » return z; | 156 return z; |
| 168 } | 157 } |
| 169 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 | 158 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 |
| 170 // TODO: broken implementation to make things compile | 159 // TODO: broken implementation to make things compile |
| 171 long double logl(long double x) | 160 long double logl(long double x) { |
| 172 { | 161 return log(x); |
| 173 » return log(x); | |
| 174 } | 162 } |
| 175 #endif | 163 #endif |
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