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 " +
|