71 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 72 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 73 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 74 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 75 {Double.NEGATIVE_INFINITY, NaNd}, 76 {-8.0, NaNd}, 77 {-1.0, -infinityD}, 78 {-0.0, -0.0}, 79 {+0.0, +0.0}, 80 {infinityD, infinityD}, 81 }; 82 83 // Test special cases 84 for(int i = 0; i < testCases.length; i++) { 85 failures += testLog1pCaseWithUlpDiff(testCases[i][0], 86 testCases[i][1], 0); 87 } 88 89 // For |x| < 2^-54 log1p(x) ~= x 90 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) { 91 double d = FpUtils.scalb(2, i); 92 failures += testLog1pCase(d, d); 93 failures += testLog1pCase(-d, -d); 94 } 95 96 // For x > 2^53 log1p(x) ~= log(x) 97 for(int i = 53; i <= DoubleConsts.MAX_EXPONENT; i++) { 98 double d = FpUtils.scalb(2, i); 99 failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001); 100 } 101 102 // Construct random values with exponents ranging from -53 to 103 // 52 and compare against HP-15C formula. 104 java.util.Random rand = new java.util.Random(); 105 for(int i = 0; i < 1000; i++) { 106 double d = rand.nextDouble(); 107 108 d = FpUtils.scalb(d, -53 - FpUtils.ilogb(d)); 109 110 for(int j = -53; j <= 52; j++) { 111 failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5); 112 113 d *= 2.0; // increase exponent by 1 114 } 115 } 116 117 // Test for monotonicity failures near values y-1 where y ~= 118 // e^x. Test two numbers before and two numbers after each 119 // chosen value; i.e. 120 // 121 // pcNeighbors[] = 122 // {nextDown(nextDown(pc)), 123 // nextDown(pc), 124 // pc, 125 // nextUp(pc), 126 // nextUp(nextUp(pc))} 127 // 128 // and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1]) 129 { 130 double pcNeighbors[] = new double[5]; 131 double pcNeighborsLog1p[] = new double[5]; 132 double pcNeighborsStrictLog1p[] = new double[5]; 133 134 for(int i = -36; i <= 36; i++) { 135 double pc = StrictMath.pow(Math.E, i) - 1; 136 137 pcNeighbors[2] = pc; 138 pcNeighbors[1] = FpUtils.nextDown(pc); 139 pcNeighbors[0] = FpUtils.nextDown(pcNeighbors[1]); 140 pcNeighbors[3] = FpUtils.nextUp(pc); 141 pcNeighbors[4] = FpUtils.nextUp(pcNeighbors[3]); 142 143 for(int j = 0; j < pcNeighbors.length; j++) { 144 pcNeighborsLog1p[j] = Math.log1p(pcNeighbors[j]); 145 pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]); 146 } 147 148 for(int j = 0; j < pcNeighborsLog1p.length-1; j++) { 149 if(pcNeighborsLog1p[j] > pcNeighborsLog1p[j+1] ) { 150 failures++; 151 System.err.println("Monotonicity failure for Math.log1p on " + 152 pcNeighbors[j] + " and " + 153 pcNeighbors[j+1] + "\n\treturned " + 154 pcNeighborsLog1p[j] + " and " + 155 pcNeighborsLog1p[j+1] ); 156 } 157 158 if(pcNeighborsStrictLog1p[j] > pcNeighborsStrictLog1p[j+1] ) { 159 failures++; 160 System.err.println("Monotonicity failure for StrictMath.log1p on " + 161 pcNeighbors[j] + " and " + | 71 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 72 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 73 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 74 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 75 {Double.NEGATIVE_INFINITY, NaNd}, 76 {-8.0, NaNd}, 77 {-1.0, -infinityD}, 78 {-0.0, -0.0}, 79 {+0.0, +0.0}, 80 {infinityD, infinityD}, 81 }; 82 83 // Test special cases 84 for(int i = 0; i < testCases.length; i++) { 85 failures += testLog1pCaseWithUlpDiff(testCases[i][0], 86 testCases[i][1], 0); 87 } 88 89 // For |x| < 2^-54 log1p(x) ~= x 90 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) { 91 double d = Math.scalb(2, i); 92 failures += testLog1pCase(d, d); 93 failures += testLog1pCase(-d, -d); 94 } 95 96 // For x > 2^53 log1p(x) ~= log(x) 97 for(int i = 53; i <= DoubleConsts.MAX_EXPONENT; i++) { 98 double d = Math.scalb(2, i); 99 failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001); 100 } 101 102 // Construct random values with exponents ranging from -53 to 103 // 52 and compare against HP-15C formula. 104 java.util.Random rand = new java.util.Random(); 105 for(int i = 0; i < 1000; i++) { 106 double d = rand.nextDouble(); 107 108 d = Math.scalb(d, -53 - FpUtils.ilogb(d)); 109 110 for(int j = -53; j <= 52; j++) { 111 failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5); 112 113 d *= 2.0; // increase exponent by 1 114 } 115 } 116 117 // Test for monotonicity failures near values y-1 where y ~= 118 // e^x. Test two numbers before and two numbers after each 119 // chosen value; i.e. 120 // 121 // pcNeighbors[] = 122 // {nextDown(nextDown(pc)), 123 // nextDown(pc), 124 // pc, 125 // nextUp(pc), 126 // nextUp(nextUp(pc))} 127 // 128 // and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1]) 129 { 130 double pcNeighbors[] = new double[5]; 131 double pcNeighborsLog1p[] = new double[5]; 132 double pcNeighborsStrictLog1p[] = new double[5]; 133 134 for(int i = -36; i <= 36; i++) { 135 double pc = StrictMath.pow(Math.E, i) - 1; 136 137 pcNeighbors[2] = pc; 138 pcNeighbors[1] = FpUtils.nextDown(pc); 139 pcNeighbors[0] = FpUtils.nextDown(pcNeighbors[1]); 140 pcNeighbors[3] = Math.nextUp(pc); 141 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); 142 143 for(int j = 0; j < pcNeighbors.length; j++) { 144 pcNeighborsLog1p[j] = Math.log1p(pcNeighbors[j]); 145 pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]); 146 } 147 148 for(int j = 0; j < pcNeighborsLog1p.length-1; j++) { 149 if(pcNeighborsLog1p[j] > pcNeighborsLog1p[j+1] ) { 150 failures++; 151 System.err.println("Monotonicity failure for Math.log1p on " + 152 pcNeighbors[j] + " and " + 153 pcNeighbors[j+1] + "\n\treturned " + 154 pcNeighborsLog1p[j] + " and " + 155 pcNeighborsLog1p[j+1] ); 156 } 157 158 if(pcNeighborsStrictLog1p[j] > pcNeighborsStrictLog1p[j+1] ) { 159 failures++; 160 System.err.println("Monotonicity failure for StrictMath.log1p on " + 161 pcNeighbors[j] + " and " + |