65 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 66 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 67 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 68 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 69 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 70 {infinityD, infinityD}, 71 {-infinityD, -1.0}, 72 {-0.0, -0.0}, 73 {+0.0, +0.0}, 74 }; 75 76 // Test special cases 77 for(int i = 0; i < testCases.length; i++) { 78 failures += testExpm1CaseWithUlpDiff(testCases[i][0], 79 testCases[i][1], 0, null); 80 } 81 82 83 // For |x| < 2^-54 expm1(x) ~= x 84 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) { 85 double d = FpUtils.scalb(2, i); 86 failures += testExpm1Case(d, d); 87 failures += testExpm1Case(-d, -d); 88 } 89 90 91 // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x). 92 // The least such y is ln(2^54) ~= 37.42994775023705; exp(x) 93 // overflows for x > ~= 709.8 94 95 // Use a 2-ulp error threshold to account for errors in the 96 // exp implementation; the increments of d in the loop will be 97 // exact. 98 for(double d = 37.5; d <= 709.5; d += 1.0) { 99 failures += testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null); 100 } 101 102 // For x > 710, expm1(x) should be infinity 103 for(int i = 10; i <= DoubleConsts.MAX_EXPONENT; i++) { 104 double d = FpUtils.scalb(2, i); 105 failures += testExpm1Case(d, infinityD); 106 } 107 108 // By monotonicity, once the limit is reached, the 109 // implemenation should return the limit for all smaller 110 // values. 111 boolean reachedLimit [] = {false, false}; 112 113 // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0; 114 // The greatest such y is ln(2^-53) ~= -36.7368005696771. 115 for(double d = -36.75; d >= -127.75; d -= 1.0) { 116 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, 117 reachedLimit); 118 } 119 120 for(int i = 7; i <= DoubleConsts.MAX_EXPONENT; i++) { 121 double d = -FpUtils.scalb(2, i); 122 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit); 123 } 124 125 // Test for monotonicity failures near multiples of log(2). 126 // Test two numbers before and two numbers after each chosen 127 // value; i.e. 128 // 129 // pcNeighbors[] = 130 // {nextDown(nextDown(pc)), 131 // nextDown(pc), 132 // pc, 133 // nextUp(pc), 134 // nextUp(nextUp(pc))} 135 // 136 // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1]) 137 { 138 double pcNeighbors[] = new double[5]; 139 double pcNeighborsExpm1[] = new double[5]; 140 double pcNeighborsStrictExpm1[] = new double[5]; 141 142 for(int i = -50; i <= 50; i++) { 143 double pc = StrictMath.log(2)*i; 144 145 pcNeighbors[2] = pc; 146 pcNeighbors[1] = FpUtils.nextDown(pc); 147 pcNeighbors[0] = FpUtils.nextDown(pcNeighbors[1]); 148 pcNeighbors[3] = FpUtils.nextUp(pc); 149 pcNeighbors[4] = FpUtils.nextUp(pcNeighbors[3]); 150 151 for(int j = 0; j < pcNeighbors.length; j++) { 152 pcNeighborsExpm1[j] = Math.expm1(pcNeighbors[j]); 153 pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]); 154 } 155 156 for(int j = 0; j < pcNeighborsExpm1.length-1; j++) { 157 if(pcNeighborsExpm1[j] > pcNeighborsExpm1[j+1] ) { 158 failures++; 159 System.err.println("Monotonicity failure for Math.expm1 on " + 160 pcNeighbors[j] + " and " + 161 pcNeighbors[j+1] + "\n\treturned " + 162 pcNeighborsExpm1[j] + " and " + 163 pcNeighborsExpm1[j+1] ); 164 } 165 166 if(pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j+1] ) { 167 failures++; 168 System.err.println("Monotonicity failure for StrictMath.expm1 on " + 169 pcNeighbors[j] + " and " + | 65 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 66 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 67 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 68 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 69 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 70 {infinityD, infinityD}, 71 {-infinityD, -1.0}, 72 {-0.0, -0.0}, 73 {+0.0, +0.0}, 74 }; 75 76 // Test special cases 77 for(int i = 0; i < testCases.length; i++) { 78 failures += testExpm1CaseWithUlpDiff(testCases[i][0], 79 testCases[i][1], 0, null); 80 } 81 82 83 // For |x| < 2^-54 expm1(x) ~= x 84 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) { 85 double d = Math.scalb(2, i); 86 failures += testExpm1Case(d, d); 87 failures += testExpm1Case(-d, -d); 88 } 89 90 91 // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x). 92 // The least such y is ln(2^54) ~= 37.42994775023705; exp(x) 93 // overflows for x > ~= 709.8 94 95 // Use a 2-ulp error threshold to account for errors in the 96 // exp implementation; the increments of d in the loop will be 97 // exact. 98 for(double d = 37.5; d <= 709.5; d += 1.0) { 99 failures += testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null); 100 } 101 102 // For x > 710, expm1(x) should be infinity 103 for(int i = 10; i <= DoubleConsts.MAX_EXPONENT; i++) { 104 double d = Math.scalb(2, i); 105 failures += testExpm1Case(d, infinityD); 106 } 107 108 // By monotonicity, once the limit is reached, the 109 // implemenation should return the limit for all smaller 110 // values. 111 boolean reachedLimit [] = {false, false}; 112 113 // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0; 114 // The greatest such y is ln(2^-53) ~= -36.7368005696771. 115 for(double d = -36.75; d >= -127.75; d -= 1.0) { 116 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, 117 reachedLimit); 118 } 119 120 for(int i = 7; i <= DoubleConsts.MAX_EXPONENT; i++) { 121 double d = -Math.scalb(2, i); 122 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit); 123 } 124 125 // Test for monotonicity failures near multiples of log(2). 126 // Test two numbers before and two numbers after each chosen 127 // value; i.e. 128 // 129 // pcNeighbors[] = 130 // {nextDown(nextDown(pc)), 131 // nextDown(pc), 132 // pc, 133 // nextUp(pc), 134 // nextUp(nextUp(pc))} 135 // 136 // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1]) 137 { 138 double pcNeighbors[] = new double[5]; 139 double pcNeighborsExpm1[] = new double[5]; 140 double pcNeighborsStrictExpm1[] = new double[5]; 141 142 for(int i = -50; i <= 50; i++) { 143 double pc = StrictMath.log(2)*i; 144 145 pcNeighbors[2] = pc; 146 pcNeighbors[1] = FpUtils.nextDown(pc); 147 pcNeighbors[0] = FpUtils.nextDown(pcNeighbors[1]); 148 pcNeighbors[3] = Math.nextUp(pc); 149 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); 150 151 for(int j = 0; j < pcNeighbors.length; j++) { 152 pcNeighborsExpm1[j] = Math.expm1(pcNeighbors[j]); 153 pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]); 154 } 155 156 for(int j = 0; j < pcNeighborsExpm1.length-1; j++) { 157 if(pcNeighborsExpm1[j] > pcNeighborsExpm1[j+1] ) { 158 failures++; 159 System.err.println("Monotonicity failure for Math.expm1 on " + 160 pcNeighbors[j] + " and " + 161 pcNeighbors[j+1] + "\n\treturned " + 162 pcNeighborsExpm1[j] + " and " + 163 pcNeighborsExpm1[j+1] ); 164 } 165 166 if(pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j+1] ) { 167 failures++; 168 System.err.println("Monotonicity failure for StrictMath.expm1 on " + 169 pcNeighbors[j] + " and " + |